ISSN 0352-3551 Acta hydrotechnica 17/25 (1999) CONTENTS - VSEBINA IRENA CVITANIČ ANALIZA MOŽNIH KAKOVOSTNIH SPREMEMB SAVE V AKUMULACIJI HE VRHOVO V POVPREČ NIH IN EKSTREMNIH HIDROLOŠKIH POGOJIH S POMOČ JO MATEMATIČ NEGA MODELA ANALYSIS OF POSSIBLE QUALITY CHANGES OF THE SAVA RIVER IN THE VRHOVO IMPOUNDMENT IN AVERAGE AND EXTREME HYDROLOGICAL CONDITIONS WITH MATHEMATICAL MODEL Published by the Hydraulics Division FGG Editor-in-Chief : Matjaž Mikoš Izdaja Hidrotehnič na smer FGG Glavni urednik : Matjaž Mikoš UNIVERSITY OF LJUBLJANA FACULTY OF CIVIL AND GEODETIC ENGINEERING UNIVERZA V LJUBLJANI FAKULTETA ZA GRADBENIŠTVO IN GEODEZIJO Acta hydrotechnica Letnik 17, št. 25, 71 str., Ljubljana, julij 1999 ISSN 0352-3551 UDK (05) 532;556;626/628.6 Indeksirana v: COBISS, ICONDA http://ksh.fgg.uni-lj.si/KSH/acta/index.htm Izdaja Hidrotehnič na smer na Fakulteti za gradbeništvo in geodezijo Univerze v Ljubljani ob sofinanciranju Ministrstva za znanost in tehnologijo Republike Slovenije. Objavljeni prispevki izražajo mnenje avtorjev, ne pa vedno tudi mnenja izdajatelja. Urednika : izr.prof.dr. Matjaž Mikoš - glavni in odgovorni urednik Gregor Petkovšek - tehnič ni urednik Izdajateljski odbor : prof.dr. Mitja Brilly - Katedra za splošno hidrotehniko prof.dr. Rudi Rajar - Katedra za mehaniko tekoč in z laboratorijem doc.dr. Jože Panjan - Inštitut za zdravstveno hidrotehniko Lektoriranje slovenskega teksta: STAMAT, Ljubljana - Lidija Jesenovec Prevod v angleški jezik: Romana Hudin, FGG Lektoriranje angleškega teksta: prof. Diane O'Connor Tisk : Univerzitetna tiskarna v Ljubljani Naklada : 250 izvodov Mnenje Ministrstva za znanost in tehnologijo R Slovenije (št. 415-54/91 z dne 2.12.1992) je, da sodi Acta hydrotechnica med proizvode, za katere se plač uje 8-odstotni davek na dodano vrednost. Copyright © 1999 Acta hydrotechnica, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo, Hidrotehnič na smer, Hajdrihova 28, 1 000 Ljubljana Acta hydrotechnica Vol. 17, No. 25, 71 p., Ljubljana, July 1999 ISSN 0352-3551 UDC (05) 532;556;626/628.6 Indexed in: COBISS, ICONDA http://ksh.fgg.uni-lj.si/KSH_ANG/acta/index.htm Published by the Hydraulics Division at the Faculty of Civil and Geodetic Engineering, University of Ljubljana, with financial support of the Ministry of Science and Technology of the Republic of Slovenia. Published material expresses the authors’ opinion and not necesserily that of the publisher. Editors : Assist. Prof. Matjaž Mikoš, Dr.sc.techn. - Eitor-in-Chief & in-Charge Gregor Petkovšek - Technical Editor Publishing Board : Prof. Mitja Brilly, Ph.D. - Chair of Hydrology and Hydraulic Engineering Prof. Rudi Rajar, Ph.D. - Chair of Fluid Mechanics with a Lab Assist. Prof. Jože Panjan, Ph.D. - Institute of Sanitary Engineering Proof reading of Slovenian text: STAMAT, Ljubljana - Lidija Jesenovec English translation: Romana Hudin, FGG Proof reading of English text: Prof. Diane O'Connor Printed by : University Press, Ljubljana Number of copies : 250 Opinion of the Ministry of Science and Technology of the Republic of Slovenia (letter No. 415-54/91 from December 2, 1992) is that Acta hydrotechnica is one of the products for which 8 % VAT must be paid. Copyright © 1999 Acta hydrotechnica, University of Ljubljana, Faculty of Civil and Geodetic Engineering, Hajdrihova 28, SI - 1000 Ljubljana Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 1 Acta hydrotechnica 17/25 (1999) V S E B I N A - C O N T E N T S VSEBINA - CONTENTS......................................................................................................... 1 UVODNIK - EDITORIAL ...................................................................................................... 2 Irena CVITANIČ Analiza možnih kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in Average and Extreme Hydrological Conditions with Mathematical Model............ 5 Publikacije Acta hydrotechnica - Back Volumes of Acta hydrotechnica.......................... 67 Navodila za pripravo prispevkov za Acto hydrotechnico................................................... 70 Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 2 UVODNIK Tokratna številka Acta hydrotechnica prinaša razširjeni povzetek magistrskega dela mag. Irene Cvitanič , mlade raziskovalke na Inštitutu za zdravstveno hidrotehniko, Fakultete za gradbeništvo in geodezijo Univerze v Ljubljani, zaposlene na Hidrometeorološkem zavodu Republike Slovenije. Mag. Irena Cvitanič je konč ala srednjo tehniško šolo na kemijski smeri v Celju. Študij je nadaljevala na Univerzi v Ljubljani, Fakulteti za naravoslovje in tehnologijo, na Oddelku za kemijo in kemijsko tehnologijo, kjer je leta 1 992 diplomirala na kemijski tehnologiji, ožja usmeritev polimeri. Po opravljeni diplomi se je zaposlila na Hidrometeorološkem zavodu Republike Slovenije v Ljubljani, kjer je opravljala pripravništvo v sektorju za varstvo okolja, na oddelku za onesnaženost voda in v kemijskem laboratoriju. Leta 1994 se je na Univerzi v Ljubljani vpisala na podiplomski študij gradbeništva – hidrotehnič na smer. Decembra 1 998 je zagovorjala magistrsko nalogo s področ ja zdravstvene hidrotehnike. Pri podiplomskem študiju se je ukvarjala s preuč evanjem sodobnih metod ekološke inženirike na področ ju zašč ite in rabe voda, predvsem s prognostič nim modeliranjem kakovosti voda, ki spada med aktualna vprašanja ekološke - zdravstvene hidrotehnike. V okviru programa Tempus je bila leta 1995 na krajšem usposabljanju pri prof. Günthertu na Univerzi nemške vojske v Münchnu. Magistrsko delo mag. Irene Cvitanič je usmerjeno v spoznavanje biokemijskih procesov v naravnih vodnih ekosistemih, ne samo v problematiko napovedovanja kakovostnih sprememb, temveč v določ eni meri tudi k vsebinskemu oblikovanju kakovostnega monitoringa voda na nač in, da se zagotovi kar največ ja uporabnost zbranih kakovostnih in hidroloških podatkov. Namen naloge je bil, da se spremembe v zajezeni reki Savi kvantitativno opredelijo s pomoč jo matematič nega modela v povpreč nih in v ekstremnih hidroloških pogojih. Na tej podlagi naj se poda ocena kakovostnih sprememb v zajezeni Savi in njihov pomen za njeno kakovost v ožjem biološkem in v širšem vodnogospodarskem pogledu. V okviru naloge je najprej podana razlaga samega pojma, kakor tudi mehanizma evtrofikacije vodnih teles. Podani so temelji biokemič nih in fizikalnih procesov v rekah in jezerih. Opisane so posledice zajezitve rek, podana je primerjava lastnosti reč nih akumulacijskih jezer z naravnimi jezeri. V nadaljevanju so podani program gradnje hidroelektrarn na Savi, hidrološke lastnosti akumulacijskega jezera HE Vrhovo in kratek pregled kakovosti vode reke Save na obravnavanem območ ju pred in po zajezitvi reke Save. Za izvedbo naloge je bil izbran več parametrski matematič ni model QUAL2E. Za uporabo modela so bile izvedene terenske meritve na vtoku in iztoku iz akumulacijskega jezera HE Vrhovo. Nato so bile izvedene vse faze modeliranja, od analize obč utljivosti, umerjanja in preverjanja modela, do njegove potrditve. Tako je bil model uporabljen za napovedi kakovostnih sprememb Save v akumulaciji HE Vrhovo za raztopljeni kisik in BPK 5 . V teoretič nem pogledu so izvedene meritve in rezultati modela opozorili na problematiko modeliranja klorofila, fosforja in amonija, to je na procese, pri katerih rezultati modela ne sledijo merskim rezultatom z enako natanč nostjo, kot pri kisiku in BPK 5 . Zato bo treba pri napovedih evtrofnosti v naslednjih predvidenih energetskih zajezitvah temu vprašanju posvetiti ustrezno pozornost, tako glede na formulacijo v modelu, kot glede na dopolnitve ali spremembe kemijske analitske tehnike. V praktič nem pogledu pa rezultati naloge z veliko stopnjo verjetnosti dokazujejo, da tudi v najbolj kritič nih sušnih obdobjih in pri najvišjih naravnih temperaturah vode ni prič akovati prekomernega padca koncentracije kisika v obravnavani zajezitvi HE Vrhovo, ki bi ogrozila obstoječ o biocenozo v zajezitvi. Ljubljana, julij 1999 Glavni urednik Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 3 EDITORIAL This issue of Acta hydrotechnica is publishing an extended summary of a Master's Thesis by Irena Cvitanič , a junior researcher at the Institute of Sanitary Engineering, Faculty of Civil and Geodetic Engineering, University of Ljubljana, currently employed at the Hydrometeorological Institute of Slovenia. Irena Cvitanič completed the Secondary Technical School in Celje in the field of Chemical Science. She continued her studies at the Faculty of Natural Science and Technology, Department of Chemistry and Chemical Technology where she graduated in 1992 from Chemical Technology in the field of polymers. After her graduation she obtained employment with the Hydrometeorological Institute of Slovenia where she has gained practical experience in the field of the determination of the physical, chemical and biological parameters of water quality and in the field of regulations for estimating the quality of surface waters. In 1994, she matriculated in the Master’s Program of Civil Engineering. In December, 1998 she completed her study with a Master’s Thesis in the field of Sanitary Engineering. During her postgraduate study, she dedicated her work to the research of contemporarily methods of ecological engineering in the field of water resources protection and use. She concentrated her work in particular to the prognostic modelling of water quality, which is one of the topical questions of sanitary engineering. Within the framework of the Tempus Program, she took a short postgraduate course at the University of Federal Arms in Munich in 1995. Irena Cvitanič focuses her Master's Thesis on the understanding of the biochemical processes in natural water ecosystems. River impoundments change the natural water circulation in the stream regarding discharges and water quality. The goal of the Thesis was to develop a quantitative determination of these changes in the existing Vrhovo impoundment for average and extreme hydrological conditions using a mathematical model. Based on this, the Thesis was set to estimate the water quality changes in the impounded Sava River, as well as their influence on the water quality in the narrow biological sense and in the more extensive water management sense. The Thesis starts with the explanation of the concept and mechanisms of the eutrophication processes in bodies of water. It continues with the basis of the biochemical and physical processes in rivers and lakes and the consequences of river impoundments. Further on, the properties of river impoundments and natural lakes are compared. The Thesis also presents the program of constructing a chain of HEPP’s on the Sava River, the hydrological properties of the Vrhovo impoundment and a short review of water quality in the Sava River both before and after the construction of the impoundment. The US EPA QUAL2E Water Quality model, which is a typical multiparametric mathematical model for river ecosystems, was chosen. For its application, field measurements at the inflow into and the outflow from the Vrhovo impoundment were performed, as well as a sensitivity analysis, calibration, verification and validation of the model. The model was used for quantitative water quality predictions of the Sava River in the Vrhovo impoundment for dissolved oxygen and biochemical oxygen demand. In a theoretical respect, the performed measurements and the modelled results warned of the problems of modelling chlorophyll, phosphorus and ammonium, i.e.: of the processes where the modelled results did not coincide with the measured results with the same precision as for O 2 and BOD 5 . For the prediction of eutrophication for the future planned impoundments, adequate attention will have to be paid to this question, regarding the formulations in the model, as well as regarding the completion of the chemical analytical technique. In a practical respect, the results also prove with a strong likelihood that in the most critical dry period and when water temperatures are the highest, an excessive decrease in the concentrations of dissolved oxygen, which could have a negative influence on biocenosis in the impoundment, is not to be expected. Ljubljana, July 1999 Editor-in-Charge Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 4 Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 5 IRENA CVITANIČ mag., univ.dipl.inž.kem.tehn. – M. Civil Eng., Diploma in Chemical Techn. Hidrometeorološki zavod RS – Hydrometeorological Institute of Slovenia Vojkova 1b, SI – 1000 Ljubljana ANALIZA MOŽNIH KAKOVOSTNIH SPREMEMB SAVE V AKUMULACIJI HE VRHOVO V POVPREČ NIH IN EKSTREMNIH HIDROLOŠKIH POGOJIH S POMOČ JO MATEMATIČ NEGA MODELA povzetek magistrskega dela Fakulteta za gradbeništvo in geodezijo Univerze v Ljubljani zagovor magistrskega dela je bil opravljen 28. decembra 1998 ANALYSIS OF POSSIBLE QUALITY CHANGES OF THE SAVA RIVER IN THE VRHOVO IMPOUNDMENT IN AVERAGE AND EXTREME HYDROLOGICAL CONDITIONS WITH MATHEMATICAL MODEL summary of the Master Thesis Faculty of Civil and Geodetic Engineering, University of Ljubljana the defence of the Master Thesis was on December 28, 1998 Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 6 IZVLEČ EK Izgradnja hidroelektrarne (HE) Vrhovo je povzroč ila nastanek reč nega akumulacijskega jezera na reki Savi in s tem spremembo njenega naravnega vodnega režima, ki se odraža tudi v spremenjenih pogojih nebioloških in bioloških procesov samoč išč enja vode in tako vpliva na njene kakovostne spremembe. Posledice energetske zajezitve reke na kakovost voda so lahko pozitivne ali negativne. V nalogi so obravnavani procesi evtrofikacije, biokemič ni in fizikalni procesi v rekah in jezerih, posledice zajezitev rek ter teoretič ni temelji matematič nega modeliranja in uporabljenega več parameterskega enodimenzionalnega modela QUAL2E. Model je bil uporabljen za modeliranje in napovedovanje možnih sprememb kakovosti vode v nastali zajezitvi. Opravljena je bila analiza obč utljivosti modela. Številni parametri modela so bili določ eni z umerjanjem modela tako, da je doseženo najboljše ujemanje rezultatov modela z izmerjenim stanjem. Potrditev modela je bila izvedena z rezultati meritev v letih 1996 in 1998. Na temelju dobljenih rezultatov je bil model uporabljen za kvantitativne napovedi raztopljenega kisika in biokemijske potrebe po kisiku v akumulaciji HE Vrhovo za ekstremne in povpreč ne hidrološke pogoje. Glede na rezultate modela in terenske meritve, izvedene pri nizkih pretokih in v pogojih poteka intenzivne primarne produkcije v zajezitvi, lahko zaključ imo, da v akumulacijskem jezeru HE Vrhovo ne prihaja do prekomernega znižanja koncentracije raztopljenega kisika, ki bi povzroč ala negativne vplive na kakovost zajezene vode. Ključ ne besede: evtrofikacija, matematič ni modeli, modeliranje kakovosti voda, površinske vode, hidroelektrarna Vrhovo UDK 504.4:519.87:556.55(282.243.743) ABSTRACT The river impoundment on the Sava River was formed as a consequence of the construction of the Vrhovo Hydroelectric Power Plant (HEPP). The river impoundment changed the natural water circulation of the Sava River, a disruption which is also reflected in the changed conditions of the biological and non-biological self-purification processes in the water. Thus, it influences the water quality of the Sava River. River impoundments can affect water quality positively or negatively. This Thesis deals with the eutrophication, biochemical and physical processes in rivers and lakes, the impacts of river impoundments, the theoretical base of mathematical modelling and the employed multiparametric one-dimensional model QUAL2E. The QUAL2E model was used to model and predict the possible changes in water quality in the impoundment. A sensitivity analysis provided insight into the model operation and showed how the results of the model change when changing separate parameters. Many model parameters were determined by calibrating the model in such a manner that the best agreement between the results of the model and the measured state was achieved. The model validation was performed using the results of the measurements in 1996 and 1998. Based on the results obtained, the model was used for the quantitative prediction of dissolved oxygen and biochemical oxygen demand in the Vrhovo impoundment for extreme and average hydrological conditions. With regard to the model results and field measurements performed at low discharges and under conditions of intensive primary production in the dam, it can be concluded that an excessive decrease in concentrations of dissolved oxygen which could have negative influence on the dammed water quality does not appear in the Vrhovo impoundment. Key-words: eutrophication, mathematical models, water quality modelling, surface water, hydroelectric power station Vrhovo UDC 504.4:519.87:556.55(282.243.743) Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 7 VSEBINA SEZNAM SLIK ..................................................................................................................................9 SEZNAM SIMBOLOV....................................................................................................................10 1. UVOD ............................................................................................................................................14 2. PROBLEMATIKA KAKOVOSTI VODA V AKUMULACIJSKIH JEZERIH VODNIH ELEKTRARN..............................................................................................................................15 2.1 IZGRADNJA AKUMULACIJSKIH JEZER.........................................................................15 2.2 GRADNJA HIDROELEKTRARN NA SAVI.......................................................................19 2.3 HIDROLOŠKE LASTNOSTI AKUMULACIJSKEGA JEZERA HE VRHOVO................20 2.4 KAKOVOST VODA PRED IN PO ZAJEZITVI HE VRHOVO..........................................21 3. TEORETIČ NE OSNOVE MATEMATIČ NIH MODELOV...................................................24 3.1 SPLOŠNO O MODELIRANJU .............................................................................................24 3.2 MATEMATIČ NO MODELIRANJE KAKOVOSTI VODA ................................................24 4. MODEL QUAL2E........................................................................................................................26 4.1 SPLOŠNO O MODELU ........................................................................................................26 4.2 MATEMATIČ NE ZVEZE.....................................................................................................27 4.3 UTEMELJITEV IZBIRE MODELA.....................................................................................37 4.4 TERENSKE MERITVE IN VHODNI PODATKI MODELA ..............................................38 4.4.1 Vzorč evanje .....................................................................................................................38 4.4.2 Vhodni podatki modela....................................................................................................38 4.4.3 Razdelitev modeliranega odseka Save na odseke in rač unske elemente .........................38 4.4.4 Parametri modela .............................................................................................................39 4.5 ANALIZA OBČ UTLJIVOSTI...............................................................................................39 4.6 UMERJANJE IN PREVERJANJE MODELA ......................................................................41 4.7 POTRDITEV MODELA........................................................................................................46 4.8 NAPOVED KAKOVOSTNIH SPREMEMB SAVE V AKUMULACIJI HE VRHOVO ....57 5. ZAKLJUČ KI ................................................................................................................................61 VIRI ...................................................................................................................................................64 Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 8 CONTENTS LIST OF FIGURES............................................................................................................................9 LIST OF SYMBOLS........................................................................................................................10 1. INTRODUCTION........................................................................................................................14 2. WATER QUALITY PROBLEMS IN THE RESERVOIRS OF HYDROELECTRIC POWER PLANTS .......................................................................................................................15 2.1 CONSTRUCTION OF RESERVOIRS..................................................................................15 2.2 CONSTRUCTION OF HYDROELECTRIC POWER PLANTS ON THE SAVA RIVER .19 2.3 HYDROLOGICAL PROPERTIES OF THE RIVER IMPOUNDMENT OF THE VRHOVO HEPP ....................................................................................................................20 2.4 WATER QUALITY BEFORE AND AFTER THE IMPOUNDMENT OF THE VRHOVO HEPP ......................................................................................................................................21 3. THEORETICAL BASE OF MATHEMATICAL MODELS ..................................................24 3.1 GENERALLY ON MODELLING.........................................................................................24 3.2 MATHEMATICAL MODELLING OF WATER QUALITY...............................................24 4. THE QUAL2E MODEL ..............................................................................................................26 4.1 GENERALLY ON THE MODEL .........................................................................................26 4.2 MATHEMATICAL RELATIONSHIPS................................................................................27 4.3 REASONING OF OUR CHOICE FOR THE MODEL.........................................................37 4.4. FIELD MEASUREMENTS AND INPUT DATA FOR THE MODEL................................38 4.4.1 Sampling ..........................................................................................................................38 4.4.2 Input data for the model...................................................................................................38 4.4.3 Divisions of the modelled reach of the Sava River into sub-reaches and computational elements...................................................................................................38 4.4.4 Model parameters.............................................................................................................39 4.5 SENSITIVITY ANALYSIS...................................................................................................39 4.6 MODEL CALIBRATION AND VERIFICATION ...............................................................41 4.7 MODEL VALIDATION ........................................................................................................46 4.8 PREDICTION OF WATER QUALITY CHANGES IN THE VRHOVO IMPOUNDMENT ..................................................................................................................57 5. CONCLUSIONS...........................................................................................................................61 REFERENCES .................................................................................................................................64 Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 9 SEZNAM SLIK Slika 1 Primerjava z modelom izrač unanih vrednosti BPK 5 , O 2 in klorofila a z meritvami na pregradi HE Vrhovo Slika 2 Primerjava z modelom izrač unanih vrednosti + 4 NH , − 2 NO in − 3 NO z meritvami na pregradi HE Vrhovo Slika 3 Primerjava z modelom izrač unanih vrednosti orto-PO 4 3- in org-P z meritvami na pregradi HE Vrhovo Slika 4 Primerjava z modelom izrač unanih vrednosti BPK 5 , O 2 in klorofila a z meritvami na pregradi HE Vrhovo Slika 5 Primerjava z modelom izrač unanih vrednosti + 4 NH , − 2 NO in − 3 NO z meritvami na pregradi HE Vrhovo Slika 6 Primerjava z modelom izrač unanih vrednosti orto-PO 4 3- in org-P z meritvami na pregradi HE Vrhovo Slika 7 Primerjava z modelom izrač unanih vrednosti BPK 5 , O 2 in klorofila a z meritvami na pregradi HE Vrhovo Slika 8 Primerjava z modelom izrač unanih vrednosti + 4 NH , − 2 NO in − 3 NO z meritvami na pregradi HE Vrhovo Slika 9 Primerjava z modelom izrač unanih vrednosti orto-PO 4 3- in org-P z meritvami na pregradi HE Vrhovo Slika 10 Z modelom izrač unano spreminjanje koncentracije kisika in BPK 5 vzdolž toka v akumulaciji HE Vrhovo za pretok 39,7 m 3 /s LIST OF FIGURES Figure 1 Modelled BOD 5 , O 2 and chlorophyll-a in comparison to measured values at the Vrhovo HEPP Dam Figure 2 Modelled + 4 NH , − 2 NO and − 3 NO as compared to the measured values at the Vrhovo HEPP Dam Figure 3 Modelled ortho-PO 4 3- and org-P as compared to measured values at the Vrhovo HEPP Dam Figure 4 Modelled BOD 5 , O 2 and chlorophyll-a as compared to the measured values at the Vrhovo HEPP Dam Figure 5 Modelled + 4 NH , − 2 NO and − 3 NO as compared to the measured values at the Vrhovo HEPP Dam Figure 6 Modelled ortho-PO 4 3- and org-P as compared to the measured values at the Vrhovo HEPP Dam Figure 7 Modelled BOD 5 , O 2 and chlorophyll-a as compared to the measured values at the Vrhovo HEPP Dam Figure 8 Modelled + 4 NH , − 2 NO and − 3 NO as compared to the measured values at the Vrhovo HEPP Dam Figure 9 Modelled ortho-PO 4 3- and org-P as compared to the measured values at the Vrhovo HEPP Dam Figure 10 Changing of DO and BOD 5 along the flow in the impoundment calculated with the model for the discharge of 39.7 m 3 /s Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 10 SEZNAM SIMBOLOV - LIST OF SYMBOLS oznaka symbol dimenzija dimension opis pomen description meaning A mg(A)/l koncentracija biomase alg algal biomass concentration AFACT faktor povpreč enja svetlobe a light averaging factor A X m 2 preč ni prerez cross-sectional area BPK - BOD mg(O 2 )/l biokemijska potreba po kisiku biochemical oxygen demand BPK 5 - - BOD 5 mg(O 2 )/l biokemijska potreba po kisiku v 5 dneh 5-day biochemical oxygen demand BPK C - - BOD C mg(O 2 )/l konč na biokemijska potreba po kisiku za razgradnjo ogljikovih spojin the concentration of ultimate carbonaceous biochemical oxygen demand BPK 5 C - - BOD 5 C mg(O 2 )/l 5-dnevna biokemijska potreba po kisiku za razgradnjo ogljikovih spojin 5-day concentration of ultimate carbonaceous biochemical oxygen demand C g/m 3 koncentracija concentration chl a µ g/l koncentracija klorofila a chlorophyll a concentration CORDO korekcijski faktor hitrosti nitrifikacije nitrification rate correction factor D L m 2 /s disperzijski koeficient dispersion coefficient f delež dnevne svetlobe fraction of daylight hours F 1 delež amonija kot vir anorganskega dušika za alge fraction of algal nitrogen uptake from ammonium pool FL omejitveni faktor svetlobe algal growth limitation factor for light FL 1 omejitveni faktor svetlobe, ki temelji na srednji dnevni intenziteti svetlobe growth attenuation factor for light, based on daylight average light intensity FL sr omejitveni faktor svetlobe, prilagojen trajanju dneva in metodi povpreč enja algae growth attenuation factor for light, adjusted for daylight hours and averaging method FN omejitveni faktor za dušik algal growth limitation factor for nitrogen FP omejitveni faktor za fosfor algal growth limitation factor for phosphorus h m srednja globina toka average depth lg a I ly/day srednja dnevna intenziteta fotosintetsko aktivne svetlobe daylight average, photosynthetically active, light intensity I(h) ly/day intenziteta svetlobe na globini h light intensity at a given depth h Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 11 I 0 ly/day intenziteta svetlobe na površini surface light intensity I tot ly celotno dnevno fotosintetsko aktivno sonč no obsevanje total daily photosynthetically active solar radiation K 1 day -1 koeficient hitrosti razgradnje ogljikovih spojin carbonaceous deoxygenation rate constant K 2 day -1 koeficient hitrosti reaeracije reaeration rate constant K 3 day -1 hitrost izgubljanja BPK C zaradi usedanja rate of loss of BOD due to settling K 4 g (O 2 )/m 2 day hitrost ploskovne porabe kisika dna benthic oxygen uptake K L ly/day konstanta Monodove enač be za svetlobo Monod equation constant for light K N mg(N)/l konstanta Monodove enač be za dušik Monod equation constant for nitrogen K P mg(P)/l konstanta Monodove enač be za fosfor Monod equation constant for phosphorus KBPK day -1 koeficient hitrosti pretvorbe BPK v BPK 5 BPK conversion rate coefficient KNITRF mg/l koeficient inhibicije nitrifikacije prvega reda first order nitrification inhibition coefficient KPK mg(O 2 )/l kemijska potreba po kisiku chemical oxygen demand M g masa mass n s/m 1/3 Manningov koeficient trenja Manning roughness factor N dušik nitrogen N 1 ≅ + 4 NH mg(N)/l koncentracija amonija concentration of ammonium nitrogen N 2 ≅ − 2 NO mg(N)/l koncentracija nitrita concentration of nitrite nitrogen N 3 ≅ − 3 NO mg(N)/l koncentracija nitrata concentration of nitrate nitrogen N 4 ≅ org.-N mg(N)/l koncentracija organskega dušika concentration of organic nitrogen N d h število ur dnevne svetlobe number of daylight hours per day N e ≅ N an mg(N)/l efektivna lokalna koncentracija razpoložljivega anorganskega dušika the effective local concentration of available inorganic nitrogen N tot mg(N)/l koncentracija totalnega (celokupnega) dušika concentration of total nitrogen O ≅ O 2 mg(O 2 )/l koncentracija raztopljenega kisika dissolved oxygen concentration Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 12 O p mg(O 2 )/l nasič ena koncentracija raztopljenega kisika pri nestandardnem zrač nem tlaku the saturation concentration of dissolved oxygen at non- standard pressure O s mg(O 2 )/l nasič ena koncentracija raztopljenega kisika pri lokalni temperaturi in tlaku the saturation concentration of dissolved oxygen at the local temperature and pressure P - fosfor phosphorus P 1 ≅ org.-P mg(P)/l koncentracija organskega fosforja the concentration of organic phosphorus P 2 ≅ ortho-PO 4 3- mg(P)/l lokalna koncentracija raztopljenega anorganskega fosforja (ortofosfata) concentration of inorganic or dissolved phosphorus P N - prednostni faktor alg za + 4 NH preference factor for + 4 NH P tot ≅ tot.-PO 4 3- mg(P)/l koncentracija totalnega (celokupnega) fosforja concentration of total phosphorus P w atm parcialen tlak vodnih par partial pressure of water vapor Q m 3 /s pretok discharge Redox mV redoks potencial redox R x m srednji efektivni hidravlič ni radij mean effective hydraulic radius S g/s zunanji in notranji izvori ali ponori external and internal source or sinks S e - naklon energijske č rte slope of the energy grade line t č as time T K temperatura vode temperature of water TN mg(N)/l totalni dušik total nitrogen u m/s povpreč na hitrost mean velocity x m razdalja distance X 20 - vrednost koeficienta pri standardni temperaturi (20°C) the value of the coefficient at the standard temperature (20°C) X T - vrednost koeficienta pri lokalni temperaturi T the value of the coefficient at the local temperature α 0 µ g(chl a)/mg(A) delež klorofila a v biomasi alg ratio of chlorophyll-a to algal biomass α 1 mg(N)/mg(A) delež dušika v biomasi alg fraction of algal biomass that is nitrogen α 2 mg(P)/mg(A) delež fosforja v biomasi alg fraction of algal biomass that is phosphorus α 3 mg(O 2 )/mg(A) hitrost produkcije kisika pri fotosintezi na enoto biomase alg O 2 production per unit of algal growth Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 13 α 4 mg(O 2 )/mg(A) hitrost porabe kisika pri respi- raciji na enoto biomase alg O 2 uptake per unit of algae respired α 5 mg(O 2 )/mg(N) hitrost porabe kisika na enoto oksidiranega amonija O 2 uptake per unit of NH 3 oxidation α 6 mg(O 2 )/mg(N) hitrost porabe kisika na enoto oksidiranega − 2 NO O 2 uptake per unit of − 2 NO oxidation β 1 day -1 koeficient hitrosti biološke oksidacije + 4 NH v − 2 NO rate constant for the biological oxidation of + 4 NH to − 2 NO β 2 day -1 koeficient hitrosti biološke oksidacije − 2 NO v − 3 NO rate constant for the biological oxidation of − 2 NO to − 3 NO β 3 day -1 koeficient hitrosti hidrolize organskega dušika v amonij rate constant for the hydrolysis of organic N to ammonia β 4 day -1 koeficient hitrosti razgradnje organskega fosforja v raztopljeni anorganski fosfor rate constant for the decay of organic-P to dissolved-P θ - empirič na konstanta za posamezen reakcijski koeficient an empirical constant for each reaction coefficient κ µ S/cm električ na prevodnost conductivity λ m -1 koeficient upadanja svetlobe light extinction coefficient λ 0 m -1 koeficient upadanja svetlobe za vodo, za vse komponente razen fitoplanktona non-algal light extinction coefficient λ 1 m -1 (µ g(chl a)/l) -1 linearni koeficient samoosenč enja alg linear algal self-shading coefficient λ 2 m -1 (µ g (chl a)/l) -2/3 nelinearni koeficient samoosenč enja alg nonlinear algal self shading coefficient µ day -1 specifič na hitrost rasti alg algal growth rate µ max day -1 maksimalna hitrost rasti alg maximum algal growth rate ρ day -1 hitrost respiracije alg algal respiration rate σ 1 m/day hitrost usedanja alg algal settling rate σ 2 mg(P)/m 2 day hitrost sprošč anja raztopljenega anorganskega fosforja z dna benthos source rate for dissolved phosphorus σ 3 mg(N)/m 2 day hitrost sprošč anja + 4 NH z dna benthos source rate for ammonia nitrogen σ 4 day -1 hitrost usedanja organskega dušika organic nitrogen settling rate σ 5 day -1 hitrost usedanja organskega fosforja organic phosphorus settling rate Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 14 1. UVOD Vodna energija je med vsemi znanimi vrstami energije še vedno najcenejša in verjetno najmanj ekološko oporeč na. Vendar tudi izgradnja akumulacijskih jezer ni brez določ enih ekoloških posledic. Pogosto ni več vprašanje, ali jez zgraditi ali ne, ker je ta odloč itev predvsem socialno-ekonomskega ali politič nega znač aja. Ostaja pa vprašanje, kako jez zgraditi in s planiranjem zagotoviti največjo koristnost na eni in najmanj škodljivih oziroma nezaželenih posledic na drugi strani. Nač rtovane energetske zajezitve reke Save bodo povzročile spremembe naravnega vodnega režima reke in spremembe v prostoru ob reki. Spremembe naravnega vodnega režima se bodo odrazile v spremenjeni dinamiki pretokov, spremenjenih transportnih in erozijskih zmogljivostih reke, možnih spremembah režima podtalnice v ožjem in širšem območ ju zajezitve, spremembi biotopa in posledič no v spremembi vodne biocenoze in obrežnega habitata. Glede na vse navedene spremembe je povsem jasno, da se bodo z zajezitvijo reke spremenili tudi pogoji, ki vplivajo na kakovost vode reke Save. Posledice energetske zajezitve reke na kakovost voda so lahko negativne ali pozitivne. Med negativne posledice zajezitve spadajo znižanje koncentracije raztopljenega kisika, povišanje temperature vode in posledično zmanjšanje sposobnosti za sprejemanje toplotnega onesnaženja ter poveč ana rast alg z vsemi posledicami. Na drugi strani pa zajezitev lahko pozitivno prispeva h kakovosti vode z zmanjšanjem množine suspendiranih snovi ter z zmanjšanjem organske in bakteriološke onesnaženosti. Namen naloge je bila kvantitativna opredelitev kakovostnih sprememb reke Save v obstoječ i akumulaciji HE (hidroelektrarne) Vrhovo v povprečnih in ekstremnih hidroloških pogojih, z uporabo večparametrskega matematičnega modela. Uporabili smo model QUAL2E (Brown & Barnwell, 1 987), ki je značilen primer več parameterskega modela reč nih ekosistemov 1. INTRODUCTION Among all known types of energy, water energy is still the cheapest and probably the least ecologically opposable. However, the construction of reservoirs is not without ecological consequences, too. It is often no longer the question of whether to build a dam or not, as this is a socio-economic and political decision. But there is still the question of how to build a reservoir and how its planning can assure maximal usefulness on the one side and minimal harmful and undesired consequences on the other. The planned impoundments for the hydroelectric power plants (HEPP) on the Sava River will change the existing natural runoff regime of the river and its riparian land. Changes in the natural river regime will be reflected in the changed dynamics of the flow, the changed transport and erosion capacities of the river, possible changes in the groundwater regime in narrow and extended impounded region, the changes of biotop and, consecutively, in the changes of water biocenosis and riverine habitats. Consequently, the conditions which influence the water quality of the Sava River will also be changed. The impacts of river impoundments on water quality can be negative or positive. The decrease in the concentrations of dissolved oxygen, the increase in water temperature and, in some special conditions, enlarged algae production are the main negative effects. On the other hand, because of the decreased quantity of suspended substances and the organic and bacteriological load in the river downstream, the impoundments can be considered as a positive influence on water quality. These positive contributions directly contribute to the self-purification capacity of natural water. The goal of the work was a quantitative determination of water quality changes in the Sava River in the existing Vrhovo Impoundment in average and extreme hydrological conditions using a multiparametric mathematical model. The US EPA QUAL2E Water Quality Model (Brown & Barnwell, 1987) was used, which is a Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 15 ter je mnogostransko uporaben za modeliranje kakovosti površinskih voda. Simulacije so bile izvedene s stacionarno opcijo modela. Izvedena je bila analiza obč utljivosti modela, s katero se pridobi vpogled v obnašanje modela in možnosti za njegovo umerjanje. Umerjanje, preverjanje in potrditev modela so bili izvedeni z eksperimentalnimi meritvami v akumulaciji HE Vrhovo v letih 1996 in 1998. Nato je bila z modelom izvedena kvantitativna napoved raztopljenega kisika in biokemijske potrebe po kisiku v akumulaciji HE Vrhovo za ekstremne in povpreč ne hidrološke pogoje. Mehanizem evtrofikacije v vodnih ekosistemih in ukrepi za kontrolo evtrofikacije so podrobneje opisani v magistrski nalogi (Cvitanič , 1 998), kjer so opisani tudi temelji biokemič nih in fizikalnih procesov v rekah in jezerih ter teoretič ni temelji matematič nih modelov. 2. PROBLEMATIKA KAKOVOSTI VODA V AKUMULACIJSKIH JEZERIH VODNIH ELEKTRARN V oceni umetnega vodnega telesa nastopata dva vidika: gospodarski in ekološki. Gospodarski vidik utemelji koristnost za družbo, ekološki vidik oceni posledice za okolje in naravna vodna telesa (Rejic, 1988). Mnoge vodne akumulacije so glede na dogajanja in procese bolj podobne rekam kot jezerom. To zlasti velja za vodne akumulacije, v katerih je vodni tok tako hiter in zadrževalni č as tako kratek, da termič na stratifikacija ne nastopi (Taub, 1984). 2.1 IZGRADNJA AKUMULACIJSKIH JEZER Akumulacijska jezera vodnih elektrarn nastanejo s pregraditvijo struge vodotoka ter dela doline ob vodotoku. Prištevamo jih k umetnim vodnim telesom, ki se od naravnih jezer razlikujejo po morfologiji, hidrologiji, nastanku, razvoju, gospodarski rabi in vplivih na okolje. Posledice njihove izgradnje so typical multiparametric model for river ecosystems and is a comprehensive and useful stream water quality model. Simulations were carried out using the stationary model option. We performed a sensitivity analysis which gave us insight into the model operation and the possibilities of its calibration. Calibration, verification and validation of the model were done using experimental measurements in the impoundment in 1996 and 1998. After that, the model was used for the quantitative prediction of dissolved oxygen and biochemical oxygen demand in the impoundment for average and extreme hydrological conditions. The Master's Thesis (Cvitanič , 1 998) gives a detailed description of eutrophication processes in water ecosystems and the measures for controlling them, as well as the basis of biochemical and physical processes in rivers and lakes, and the theoretical basis of mathematical models. 2. WATER QUALITY PROBLEMS IN THE RESERVOIRS OF HYDROELECTRIC POWER PLANTS In the evaluation of an artificial body of water, one has to consider two standpoints: economical and ecological. The economical standpoint substantiates the usefulness for society. The ecological standpoint evaluates the consequences for the environment and for natural bodies of water (Rejic, 1988). Considering the processes in water reservoirs, many reservoirs are more similar to rivers than lakes. This is particularly true for those where the current is so fast and the retention times so short that thermal stratification does not appear (Taub, 1984). 2.1 CONSTRUCTION OF RESERVOIRS HEPP reservoirs originate from impounding a river channel and part of the valley along the river. They belong to artificial bodies of water which differ from natural lakes according to their morphology, hydrology, origin, development, economic use and impacts on environment. The consequences of their Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 16 številne, kompleksne in dolgoroč ne. S stališča vodnega gospodarstva so bistvenega pomena vplivi izgradnje akumulacijskih jezer na hidrološki sistem in vodni biološki sistem (Polzer & Traer, 1990): − sprememba morfologije vodotoka, povečanje globine vode ter površine gladine, − zmanjšanje hitrosti vode in intenzitete turbulence, − zmanjšanje prodonosnosti, − pospešena sedimentacija lebdeč ih delcev, − dolvodna erozija, − sprememba svetlobnih razmer v vodnem telesu, − podaljšanje zadrževalnih č asov, − poveč ana samoč istilna sposobnost, − sprememba vsebnosti kisika in dušika, − vplivi na razvoj fitoplanktona, zooplanktona, fitobentosa, zoobentosa ter makrofitov, − znižanje števila in diverzitete rib, − vpliv na kakovost vode, posebno pri moč no obremenjenih rekah z odpadnimi vodami, − vpliv na bakteriološko obremenitev. Zajezitev rek in s tem nastanek akumulacijskih jezer pomeni poseg v vodno bilanco reke. Namesto naravnega odtoka nastane kontroliran odtok, ki ga definira režim delovanja elektrarne ali verige elektrarn. Zadrževalni č asi v akumulacijskih jezerih se gibljejo od nekaj ur do nekaj mesecev. Kinetič na energija vode v rekah povzroč a erozijo in transport plavin. Ker se hitrost vode v akumulacijskem jezeru bistveno zmanjša, se transport plavin prekine, prod in lebdeč e plavine se odlagajo v jezeru, s tem pa se manjša koristni volumen jezera. Visoke vode običajno odplavijo del sedimentov iz akumulacijskih jezer. Pod jezom pa ima reka spet veliko transportno zmogljivost, in ker je odložila plavine nad jezom, to povzroč a dolvodno erozijo, ki najmoč neje spodjeda strugo tik pod jezom (Krajnc, 1989). Problematiko je treba obravnavati s stališč a masne bilance transportiranega materiala in s construction are numerous, complex and lasting. From the standpoint of water management, the impacts of reservoirs on the hydrological and water biological systems are of prime importance (Polzer & Traer, 1990): − changes in stream morphology, greater water depth and surface area, − decreased water velocity and turbulence intensity, − decreased bed load transport rate, − accelerated sedimentation of suspended particles, − downstream erosion, − modification of light conditions in the water body, − longer retention times, − increased self-purification capacity, − changes in oxygen and nitrogen concentrations, − impacts on the growth of phytoplankton, zooplankton, phytobenthos, zoobenthos and macrophytes, − reduction in the number and diversity of fish species, − impacts on water quality, especially for the rivers extremely loaded with sewage, − impacts on bacteriological loads. River impoundment and the resulting reservoir are an intervention into the water balance of the river. Instead of natural outflow, there emerges controlled outflow, which is defined by the working regime of the power plant or a series of power plants. Retention times in the reservoirs range from several hours to several months. The kinetic energy of water in rivers causes erosion and sediment transport. Because water velocities in reservoirs are essentially reduced, sediment transport ceases, gravel or sand and suspended substances are deposited in reservoirs and this reduces their useful volume. High flows usually wash a portion of deposited sediments out of the reservoir. Downstream of the dam the river has large transport capacity, and because sediment is deposited upstream of the dam, the river erodes its bed primarily at a point closest to the dam outflow, a process called downstream Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 17 stališča akumulacije toksičnih snovi v sedimentih (Rismal, 1997a). Reč na voda lahko napaja podtalnico v prodnih naplavinah ob rekah, ali pa podtalnica odteka v reko. To je odvisno od vodostajev obeh. Ob izgradnji akumulacijskih jezer poskušajo graditelji čim bolj zmanjšati iztekanje vode iz jezer s posebnimi tehnič nimi ukrepi (tesnenje bokov akumulacij). Obstaja tudi bojazen za onesnaženje podtalnice z vodo iz akumulacij, po drugi strani pa akumulirana voda omogoč a dvig nivoja podtalnice, č e za to obstaja potreba (Krajnc, 1989). Pod pojmom samoč istilna sposobnost vode razumemo sistem fizikalnih, kemijskih in bioloških procesov, ki vodijo do razgradnje razgradljivih snovi v vodi in vrač anja produktov razgradnje v kroženje (Kolar, 1983). Snovne spremembe v procesu samoč iščenja delimo na nebiološko ter biološko samoč išč enje. V procesih nebiološkega (abiotskega) samoč iščenja (usedanje, izkosmič enje, obarjanje, absorpcija, adsorpcija, izhlapevanje, hidroliza, fotoliza, kompleksacija) poteka odstranjevanje nerazgradljivih snovi. Zmanjšanje hitrosti vode v akumulacijskih jezerih bistveno vpliva na intenzivnost fizikalno kemijskih procesov nebiološkega samoč iščenja. Vse spremembe fizikalne limnologije vplivajo na kakovost vode (fizikalno-kemijske parametre) in vodni biološki sistem. Pomembnejši pa je proces biološkega (biotskega) samoč iščenja, ki je najpomembnejši nosilec kroženja snovi in energije v vodnem okolju. Razgradnjo organskih snovi izvedejo v vodi prisotni mikroorganizmi, ki s svojim metabolizmom presnavljajo organsko onesnaženje voda - organske snovi ob prisotnosti kisika oksidirajo. Z izgradnjo akumulacijskih jezer se spremenijo tudi pogoji biološkega samoč išč enja. Vodni tok se upoč asni, torej se bistveno poveč ajo zadrževalni č asi. Samoč išč enje, ki je bilo pred zajezitvijo porazdeljeno na veliko erosion (Krajnc, 1989). These problems should be addressed from the standpoint of the mass balance of the transported material and the accumulation of toxic substances in the sediments (Rismal, 1997a). The river water can feed the groundwater in the alluvia along the river or the groundwater can flow off in the river, depending on the water levels of both. When constructing reservoirs, we attempt to reduce the outflow from reservoirs with special technical measures (the tightening of the sides of the reservoir). Further on, there exists some concern that the groundwater could get polluted by the water from reservoirs. On the other hand, the accumulated water can rise groundwater levels, if there is a need for that (Krajnc, 1989). Self-purification processes include all physical, chemical and biological processes which lead to the degradation of decomposable substances in water and the return of decomposed products into circulation. Self- purification processes are divided into abiotic and biotic processes. Non-biological self-purification processes (settling, flocculation, precipitation, absorption, adsorption, evaporation, hydrolysis, and photolysis) consist of the elimination of non-decomposable substances. The decreased water velocity in reservoirs has an important impact on the intensity of the physio-chemical processes of non-biological self-purification. All modifications in the physical limnology influence water quality (physio-chemical parameters) and the water biological system. More important is the process of biological (biotic) self-purification, which is most important in the circulation of substances and energy in water environment. The decomposition of organic substances is performed by the microorganisms present in water which assimilate the organic pollution of the water by a process of metabolism – organic substances oxidize in the presence of oxygen. With the construction of reservoirs the conditions of biological self-purification also change. The flow slows down so retention times are Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 18 daljši odsek reke, se sedaj v bistveno več ji meri odvija v akumulacijskem jezeru. Zaradi bistveno manjših hitrosti vode in posledič no intenzivnejših procesov usedanja, se delež biološkega onesnaženja, ki nastopa v suspendirani usedljivi obliki, veliko hitreje zmanjšuje kot v nezajezenem toku. Zaradi tega pa se bistveno poveč a poraba kisika in posledič no zmanjša vsebnost raztopljenega kisika v vodi. Problem je še več ji, ker je vnos kisika preko gladine zaradi zmanjšane hitrosti vode obč utno manjši. To povzroč a velike spremembe v ekosistemu. Zajezitev rek lahko izboljša bakteriološko kakovost vode. V primerih, ko je v rekah prvotno število bakterij nizko ali pa je zadrževalni č as znotraj zajezitve dovolj dolg, se zaradi odmiranja zmanjša število fekalnih koliformnih bakterij. Izboljšanje bakteriološke kakovosti vode glede na razredč enje pa je uspešno samo v primeru, č e je dotok v zajezitev po prostornini zadosten in č e je bakteriološko ustrezne kakovosti (Venter et al., 1997). V slovenskih rekah, ki jih uvršč amo večinoma med alpske reke, predstavljajo največji del biocenoze prirasli organizmi (prerast), tako obrast (perifiton-producent kisika) kot heterotrofni organizmi (porabniki kisika). Z zajezitvijo rek se življenjski pogoji za to biocenozo poslabšajo zaradi manjšega vnosa kisika, več jih globin vode in posledič no poslabšanih svetlobnih razmer, sprememb zrnavosti usedlin na dnu. Spremembe življenjskih pogojev se odražajo v spremenjeni sestavi prerasti, zoobentosa in v sestavi ribje favne (ciprinidi) v akumulacijskih jezerih (Rismal, 1985). Pri dosedanjem opisovanju kakovosti vode v akumulacijskih jezerih smo imeli ves č as v mislih stabilizirano akumulacijsko jezero. Zavedati pa se moramo, da je vsaka akumulacija specifič en problem, pri katerem bo marsikateri od naštetih dejavnikov nepomemben, lahko se bodo pojavili novi ali pa bo samo eden med njimi moč no prevladal (Kokol, 1988). significantly increased. Self-purification, which was, before the impoundment, distributed along a longer reach of a river, is now performed to an increased extent in the reservoir. The water velocity is smaller and settling processes are more intensive, so that the part of biological pollution in a suspended settling form decreases more rapidly than in an unimpounded flow. For this reason, the oxygen consumption is essentially increased, and the concentration of dissolved oxygen decreases. The problem is even greater when considering that the input of oxygen over the surface is much smaller, owing to the reduced water velocity. This causes substantial changes in the ecosystem. River impoundment can improve the bacteriological quality of water. The level of faecal coliforms decreases because of die-off cases, when the original number of bacteria in rivers is low or when the retention time in the impoundment is long enough. The improvement of bacteriological quality by means of dilution is successful only if the inflow into the impoundment is of sufficient volume and if it is of a suitable bacteriological quality (Venter et al., 1997). In Slovenian rivers, classified mostly among Alpine rivers, attached organisms represent the largest part of biocenosis, i.e. periphyton (oxygen producers), as well as heterotrophic organisms (oxygen consumers). With river impoundments, the living conditions for the biocenosis get worse because of the smaller input of oxygen, the greater depth of water and, consequently, the worsening light conditions and modifications in sediment size. The changed living conditions are reflected in the changed composition of the attached organisms, zoobenthos, and in the composition of fish fauna (cyprinid) in reservoirs (Rismal, 1985). The above descriptions of water quality in reservoirs all refer to stabilised reservoirs. However, it has to be kept in mind that every reservoir represents a specific problem, where many of the listed factors will be unimportant, but some new could appear, or only one of all of them will be predominant. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 19 2.2 GRADNJA HIDROELEKTRARN NA SAVI Hidroelektrarna Vrhovo, ki so jo prič eli graditi leta 1987, predstavlja prvo v verigi hidroelektrarn na odseku Zidani Most – državna meja s Hrvaško. Investitor nač rtuje še graditev HE Boštanj, HE Blanca, HE Brestanica, HE Krško, HE Brežice in HE Mokrice (Kokol, 1988). Stopnje posameznih HE so izbrane tako, da se gladina zajezitev sklenjeno nadaljuje od stopnje do stopnje. Zaradi bogatih vodonosnih stranskih pritokov (Savinja, Krka) so na tem odseku najugodnejši hidrološki pogoji. Vloga verige HE bo proizvodnja vršne energije oziroma regulacija moč i in bo torej obratovala v dnevnem pretoč no akumulacijskem režimu (SEL, 1 994). HE Vrhovo je prič ela poskusno obratovati avgusta 1994 in je še vedno v fazi poskusnega obratovanja. Elektrarna je nizkotlač na s tremi turbinami za skupen inštaliran pretok 500 m 3 /s in minimalnim odtokom 100 m 3 /s zaradi težav s termič nim onesnaženjem Save pod NE Krško (Krajnc, 1994b). Glede na spremenjen vodni režim reke Save na omenjenem odseku je povsem jasno, da se bodo spremenili tudi pogoji, ki vplivajo na kakovost vode reke Save. Te spremembe pa so lahko za bilanco kakovosti vode usodne, ker Sava služi kot odvodnik več inoma nepreč išč enih odpadnih voda iz naselij in industrije gospodarsko najbolj razvitega dela Slovenije. Zato je bil sprejet »Program ukrepov za sanacijo kakovosti vode reke Save v obdobju 1986-1990«, ki temelji na zahtevi, da se izboljša kakovost reke Save nad profilom HE Vrhovo iz 3. do 4. kakovostnega razreda v 2. do 3. kakovostni razred. V program je bila uvrščena izgradnja komunalnih č istilnih naprav za vsa več ja naselja ob Savi in Savinji ter modernizacija tehnoloških postopkov in izgradnja objektov za č išč enje odplak v industrijskih delovnih organizacijah. 2.2 CONSTRUCTION OF HYDROELECTRIC POWER PLANTS ON THE SAVA RIVER The Vrhovo HEPP, whose construction began in 1987, represents the first HEPP in the series of HEPP's on the Sava River section between Zidani Most and the border with Croatia. In the future, the construction of HEPP Boštanj, HEPP Blanca, HEPP Brestanica, HEPP Krško, HEPP Brežice and HEPP Mokrice is also planned (Kokol, 1988). The stage of each HEPP is chosen in such a manner that impoundment levels continue without interruption from one stage to another. In this segment of the Sava River, the hydrological conditions are the best because of water-rich lateral tributaries (Savinja, Krka). The role of this series of HEPP’s will be the production of peak energy, thus, they will operate in a daily accumulation regime (SEL, 1994). The Vrhovo HEPP began operating in August, 1994, and it is still in the test phase of operation. The HEPP is a low-pressure plant with three turbines for the total installed discharge of 500 m 3 /s and with a minimal outflow of 100 m 3 /s due to the problems of thermal pollution of the Sava River below the NPP (nuclear power plant) Krško (Krajnc, 1994b). Considering the changed water regime in the mentioned section of the Sava River, it is quite clear that the conditions which influence the Sava River water quality will also be changed. These changes can be fatal for the water quality balance because the Sava River serves as a drain for mostly untreated domestic and industrial waste waters of the economically best developed region in Slovenia. Because of this, the Programme of Interventions for the Improvement of the Water Quality in the Sava River for the period from 1986 to 1990 was adopted. It was based on the requirement to improve water quality in the Sava River above the HEPP profile from a quality class 3 to 4 into a quality class 2 to 3. The program included the construction of waste water treatment plants for all the larger towns along the Sava River and the Savinja River, as well as the modernization of technological processes and the construction of waste water treatment plants in industrial organizations. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 20 2.3 HIDROLOŠKE LASTNOSTI AKUMULACIJSKEGA JEZERA HE VRHOVO Povodje HE Vrhovo ima površino 7198 km 2 , srednji pretok znaša 235 m 3 /s, stoletna visoka voda 3102 m 3 /s. Kota zajezitve je 191 m n.m., kota spodnje vode 182,88 m n.m., bruto padec znaša 8,12 m. Površina akumulacijskega jezera je 1,43 km 2 in prostornina 8,65·10 6 m 3 (SEL, 1994). Teoretični zadrževalni časi v akumulacijskem jezeru HE Vrhovo se bodo poveč ali od 3,8 krat pri pretoku 330 m 3 /s do 10,6 krat pri pretoku 56 m 3 /s (preglednica 1). Ti zadrževalni č asi so izrač unani za odsek v dolžini 1 2 600 m gorvodno od pregrade HE Vrhovo (Krajnc, 1 989). Kljub temu poveč anju je maksimalni zadrževalni čas v akumulacijskem jezeru 1 ,94 dni, kar uvršč a akumulacijsko jezero Vrhovo v skupino pretoč nih jezer. 2.3 HYDROLOGICAL PROPERTIES OF THE RIVER IMPOUNDMENT OF THE VRHOVO HEPP The river basin of the Vrhovo HEPP is comprised of 7189 km 2 , the average discharge is 235 m 3 /s. The impoundment lies at 191 m above sea level, the lowest water level is 182.88 m a.s.l., and the gross fall is 8.12 m. The surface of the impoundment is 1.43 km 2 and its volume is 8.65·10 6 m 3 (SEL, 1994). Theoretical retention times in the impoundment of Vrhovo HEPP will increase from 3.8 times at a discharge of 330 m 3 /s to 10.6 times at a discharge of 56 m 3 /s (Table 1). These retention times were calculated for the reach in the length of 12 600 m upstream from the dam of the HEPP (Krajnc, 1989). In spite of this increase, the maximal retention time in the impoundment is 1.94 day, which classifies it among flowing lakes. Preglednica 1 . Teoretič ni zadrževalni č asi Save pred zajezitvijo in v akumulacijskem jezeru HE Vrhovo (Krajnc, 1989). Table 1. Theoretical retention times of the Sava River before the impoundment and in the impoundment of the Vrhovo HEPP (Krajnc, 1989). Pretok Discharge Zadrževalni č as - pred zajezitvijo Retention time – before impoundment Zadrževalni č as - po zajezitvi Retention time – after impoundment [m 3 /s] [h] [h] 56 4,4 46,6 65 3,7 39,8 102 3,3 25,6 178 2,5 14,8 237 2,3 12,8 330 2,1 8,1 Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 21 2.4 KAKOVOST VODA PRED IN PO ZAJEZITVI HE VRHOVO Oceno kakovosti voda reke Save na odseku Hrastnik-Vrhovo lahko podamo na podlagi podatkov monitoringa kakovosti površinskih vodotokov v Sloveniji, ki ga izvaja Hidrometeorološki zavod Republike Slovenije. Na tem odseku se spremlja kakovost na zajemnih mestih v Hrastniku in Radeč ah za Savo in v Velikem Širju za Savinjo. V preglednici 2 je prikazano spreminjanje kakovosti voda na posameznih zajemnih mestih za obdobje 1987-1995 (HMZ, 1994; 1997a). 2.4 WATER QUALITY BEFORE AND AFTER THE IMPOUNDMENT OF THE VRHOVO HEPP The estimation of water quality in the Sava River along the Hrastnik-Vrhovo reach can be based on the data of surface water quality monitoring in Slovenia performed by the Hydrometeorological Institute of Slovenia. In this reach, water quality is monitored at the Hrastnik and Radeč e sampling points for the Sava River and at the Veliko Širje sampling point for the Savinja River. Table 2 shows the changes in water quality in the selected sampling points for the period between 1987 and 1995 (HMZ, 1994; 1997a). Preglednica 2. Primerjava kakovosti voda za obdobje 1987-1995. Table 2. Comparison of water quality for the period 1987-1995. Vodotok River Zajemno mesto Sampling point Skupna ocena Final evaluation 1987 1988 1989 1990 1991 1992 1993 1994 1995 Sava Hrastnik - - 3-4 3-4 3-(4) 3 3 3 3 Sava Radeč e 3-(4) 3-4 3-4 3-4 3-4 3 3 3 3 Savinja V. Širje 3-2 3 2-3 (2)-3 3 (2)-3 (2)-3 2-3 2-3 Kakovost Save na odseku Hrastnik - Vrhovo se je v letu 1992 izboljšala iz 3. do 4. kakovostnega razreda v 3.kakovostni razred. Še vedno pa je bilo prisotno onesnaženje iz zasavskega industrijskega bazena. Za Savo na teh zajemnih mestih je bila znač ilna visoka vsebnost kisika. V reki Savi v Radeč ah je bila visoka kemijska potreba po kisiku (KPK) s K 2 Cr 2 O 7 , povišana vsebnost dušikovih spojin (predvsem amonija in nitrita) in ortofosfata. V sedimentu so stalno prisotne težke kovine cink, svinec, nikelj in živo srebro, njihove koncentracije so odvisne tako od onesnaženja kot od hidroloških razmer. Po rezultatih saprobioloških analiz se je Sava v Hrastniku in Radeč ah uvršč ala med zmerno obremenjene ali med kritič no obremenjene vodotoke. Tudi bakteriološka slika na teh zajemnih mestih je bila zelo slaba. Vzorci vode so praviloma vsebovali veliko število bakterij fekalnega The quality of the Sava River in the Hrastnik – Vrhovo reach improved in 1992 from a quality class 3 to 4 to a quality class 3. However, the pollution from the Zasavje Industrial Basin was still present. A high concentration of dissolved oxygen was significant for the Sava River at these sampling points. In Radeč e we observed a particularly high chemical oxygen demand (COD) with K 2 Cr 2 O 7 , and the concentration of nitrogen compounds (above all ammonium and nitrite) and orthophosphate. Heavy metals such as zinc, lead, nickel, and mercury were constantly present in the river sediment. The concentrations of heavy metals depended on pollution as well as on hydrological conditions. The results of the saprobiological analyses classified the Sava River in Hrastnik and in Radeč e between a moderately to a critically charged river. The bacteriological situation was also very bad. Water samples generally contained a lot of faecal bacteria Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 22 izvora (HMZ, 1994; 1997a). Po zajezitvi leta 1994 so se kakovostne spremembe Save v zajezitvi HE Vrhovo spremljale z izvajanjem fizikalno-kemijskih in bioloških analiz. Fizikalno-kemijsko kontrolo kakovosti zajezene Save je v obdobju od leta 1995 do leta 1997 izvajal Inštitut za zdravstveno hidrotehniko (Rismal, 1997b). Rezultati meritev v letu 1995 in 1996 so pokazali le manjše, komaj zaznavne posledice v zajezeni vodi. Vendar v tem opazovanem obdobju, zaradi nedokonč anih gradbenih del v zajezenem območ ju, HE Vrhovo še ni trajno obratovala pri polni zajezitvi. Obratovalne razmere so se stabilizirale šele v drugi polovici leta 1996. Na podlagi hitrega pregleda meritev temperatur na zajemnih mestih za obdobje od leta 1 995 do leta 1 997 je mogoč e zaključ iti, da je temperaturno stanje v posameznih profilih akumulacije Vrhovo homogeno, kar pomeni, da v akumulacijskem jezeru ne nastopa termič na stratifikacija, znač ilna za naravna jezera. V letih 1995 in 1997 je Inštitut za hidravlič ne raziskave iz Ljubljane opravil 6 dodatnih celodnevnih meritev temperature vode v petih prečnih profilih v akumulacijskem bazenu HE Vrhovo. Meritve so opravili zaradi določ itve stanja po zajezitvi. V dveh meritvah v poletnih mesecih sta bili za razliko od rezultatov rednega monitoringa opaženi tako vertikalna kot horizontalna temperaturna slojevitost. Vertikalni temperaturni gradienti so posledica procesov toplotne izmenjave na površini zajezitve. Horizontalni gradienti pa so lahko posledica nepopolnega premešanja hladilne vode TET 2 Trbovlje ali dotoka Savinje v Zidanem Mostu. V zajezitvi so meritve temperature vode pokazale na opazno toplejši tok ob levem bregu, kar se kvalitativno ujema z ocenjenim vplivom dotoka Savinje, ki v poletnih mesecih segreva Savo (Rajar et al., 1998). Vertikalne temperaturne gradiente smo zabeležili tudi v meritvah v avgustu 1 998 na mostu Vrhovo, 680 m pred pregrado. (HMZ, 1994; 1997a). After the impoundment in 1994 the quality changes of the Sava River in the Vrhovo Impoundment were monitored by physio- chemical and biological analyses. The physio- chemical control of the quality of the impounded Sava River between 1995 and 1997 was performed by the Institute of Sanitary Engineering (Rismal, 1997b). The results of the measurements in 1995 and 1996 indicated only small, hardly noticeable consequences in the impounded water. Owing to unfinished construction works in the impounded area, the Vrhovo HEPP was not in permanent operation during this time. The operation was stabilised during the second part of 1996. A quick review of temperature measurements at the sampling points in the period between 1995 and 1997 shows that the temperature conditions in single profiles of the Vrhovo Impoundment were homogeneous. This indicates that thermal stratification, characteristic of natural lakes, does not appear in the Vrhovo Impoundment. In 1995 and 1997 the Institute for Hydraulic Research in Ljubljana performed six 24-hour measurements of water temperature in five cross-sections in the Vrhovo Impoundment. The measurements were performed for the purpose of determining the situation after the impoundment. In two summer measurements, vertical and horizontal temperature stratifications were found. The vertical temperature gradients were the result of heat exchange on the surface of the impoundment. Horizontal gradients resulted from the incomplete mixing of the cooling water from the Trbovlje TET 2 or the inflow of the Savinja in Zidani Most. The measurements of the water temperature in the impoundment showed a significantly warmer water current on the left bank, which was in quantitative agreement with the estimated influence of the Savinja tributary which warms up the Sava River during the summer months (Rajar et al., 1998). Vertical temperature gradients were also noted in the measurements performed on the Vrhovo Bridge in August, 1998, 680 m before Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 23 Vsekakor gre za meritve v obdobju vroč ega, stabilnega poletnega vremena. Meritve temperature vode, pH, električ ne prevodnosti, raztopljenega kisika, nasič enosti s kisikom in redoks potenciala so bile izvedene s sondo Hydrolab po vertikali v sredini profila. the river dam. The measurements were made in stable hot summer weather. Water temperature, pH, conductivity, dissolved oxygen, oxygen saturation and the redox potential were measured by Hydrolab multiprobe along the vertical in the middle of the profile. Preglednica 3. Rezultati meritev po vertikali na mostu Vrhovo, dne 13.8.1998. Table 3. Rezultati meritev po vertikali na mostu Vrhovo, dne 13.8.1998. Globina Depth Č as Time Temp. Temp. pH pH Elektroprevodnost Conductivity O 2 O 2 O 2 O 2 Redoks Redox [m] [hh:mm:ss] [°C] [-] [µ S/cm] [% nasič enosti] [% saturation] [mg/l] [mV] 0 10:25:59 22,64 8,1 417 89 7,7 393 0,5 10:16:06 22,38 8,1 418 89 7,7 372 1 10:17:11 21,89 8,1 416 88 7,7 380 2 10:18:11 21,63 8,1 417 88 7,8 384 3 10:18:53 21,41 8,1 416 88 7,8 387 4 10:19:28 21,15 8,1 413 85 7,5 391 5 10:20:03 21,10 8,0 412 83 7,4 393 6 10:20:31 21,00 8,0 413 79 7,1 396 7 10:21:17 20,98 7,9 413 74 6,6 398 8 10:22:01 20,91 7,9 415 69 6,2 402 9 10:22:34 20,87 7,9 414 68 6,1 403 10 10:23:49 20,81 7,8 416 60 5,3 406 Meritve v preglednici 3 kažejo, da nastopajo po vertikali temperaturni gradienti. Vendar pa ne gre za izrazito temperaturno slojevitost, znač ilno za jezera, kjer je za vmesni zaporni sloj znač ilen hiter padec temperature v sorazmerno ozkem vmesnem pasu. Temperaturni gradienti so višji v zgornjem 4-metrskem sloju vode, v spodnjem 6-metrskem sloju vode pa so neznatni. Koncentracija raztopljenega kisika je tako rekoč konstantna v zgornjem 3-meterskem sloju. Z nadaljnjim več anjem globine pa se koncentracija kisika manjša, pri dnu akumulacije je izmerjena koncentracija raztopljenega kisika 5,3 mg(O 2 )/l. Združba rastlinskega planktona kaže, da so življenjske razmere v akumulaciji ugodne za razvoj vrst, ki hitro izkoristijo ugodne razmere (hranila, svetlobo, manjši pretok). The measurements in Table 3 show that there appear to be vertical temperature gradients. However, it is not a matter of the explicit temperature stratification typical of lakes where a rapid decrease in temperature appears in a rather narrow intermediate layer. Temperature gradients are higher in the upper 4-meters of the water; in the lower 6-meters they are insignificant. The concentration of dissolved oxygen was practically constant in the upper 3 meters and it fell with increasing depth. At the bottom, the measured concentration of dissolved oxygen was 5.3 mg(O 2 )/l. The appearance of phytoplankton showed that vital conditions in the impoundment are favourable for the growth of species, which rapidly take advantage of good conditions (nutrients, light, smaller discharge). Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 24 3. TEORETIČ NE OSNOVE MATEMATIČ NIH MODELOV 3.1 SPLOŠNO O MODELIRANJU Dogajanja v naravi so prezapletena, da bi jih lahko opisali brez določ enih več jih ali manjših poenostavitev. Ena od možnosti je, da si pri tem pomagamo z matematič nimi modeli, v katere vnesemo večje ali manjše poenostavitve realnega dogajanja v naravi. Matematični modeli temeljijo na kvantifikaciji razmerij med specifič nimi parametri in spremenljivkami pri ponazarjanju (simulaciji) naravnih procesov. Zaradi tega so ti modeli abstraktni in ne pokažejo veliko v smislu povezave z realnimi razmerami, vendar pa pokažejo vpogled v funkcionalne odvisnosti med vzroki in posledicami v realnih razmerah. Tako lahko zelo hitro generiramo veliko podatkov in različ ne situacije za določ en problem. Model lahko uporabljamo za napovedovanje procesov šele potem, ko je umerjen in verificiran. Kombinacija meritev na terenu in matematič nega modeliranja je zelo uč inkovita metoda za preuč evanje kakovosti voda (Rajar, 1997). 3.2 MATEMATIČ NO MODELIRANJE KAKOVOSTI VODA Gospodarjenje z vodnim bogastvom posameznih povodij in v celoti je neloč ljivo povezano tako z razpoložljivimi količ inami kot s kakovostjo vodnih zalog. Zato mora izkoriščanje voda sloneti na poznavanju obstoječih hidroloških in kakovostnih lastnostih voda ter na napovedovanju sprememb, ki jih bodo nač rtovani posegi povzroč ili v količ inskem in kakovostnem pogledu (Rismal, 1985). Hidrološki in hidravlični matematič ni modeli, s katerimi je mogoč e predvideti količ inske spremembe vodnega režima zaradi nač rtovanih hidrotehnič nih in drugih posegov, so v naši hidrotehnič ni praksi že vrsto let nepogrešljivo sredstvo za načrtovanje in 3. THEORETICAL BASE OF MATHEMATICAL MODELS 3.1 GENERALLY ON MODELLING The activities in nature are too complicated to be described without defining some sort of simplification. One of the possibilities is to make use of mathematical models, implemented by some larger or smaller simplification of real activities in nature. Mathematical models are based on the quantification of the relationships between specific parameters and variables with the illustration of natural processes. For this reason, models are abstract and do not show much in the sense of their relationship to actual conditions; however, they give an insight into the functional dependencies between cause and effect in actual conditions. In this way we can very quickly generate a large number of data and different situations for a specific problem. The model can be used for the prediction of processes only after it has been calibrated and verified. The combination of field measurements and mathematical modelling is a very effective method to study water quality (Rajar, 1997). 3.2 MATHEMATICAL MODELLING OF WATER QUALITY Water resources management is inseparably connected with the available quantity, as well as the quality of water resources. For this reason, the exploitation of water must be based on the knowledge of the existing hydrological and quality characteristics of water and on the prediction of changes which will arise by the planned interventions in the quantitative and qualitative respects (Rismal, 1985). Hydrological and hydraulic models make it possible to forecast quantitative changes in the water regime due to planned hydrotechnical and other interventions. In our hydrotecnical practise, they have been an indispensable tool for many years in the planning and management of the available water resources. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 25 gospodarjenje z razpoložljivimi vodnimi zalogami. Bistveno manj pa se uporabljajo matematični modeli kakovosti voda, ki omogoč ajo prognozo sprememb kakovosti obravnavanih voda zaradi nač rtovanih posegov. Vzrok za to je predvsem v dveh dejstvih: − Problemi kakovosti voda so dobili svojo težo v vodnogospodarski problematiki šele v zadnjih desetletjih. − Matematični modeli obravnavajo spremembe kakovosti voda s formulacijami, ki bolj ali manj toč no ponazarjajo potek kakovostnih sprememb, ki so posledica fizikalnih, kemič nih in biokemič nih procesov v vodi. Razumljivo je, da z matematič nim zapisom poteka in vsebine zapletenih procesov, ki potekajo v vodi, ni mogoč e docela ponazoriti. Zato matematičnih modelov kakovostnih procesov v vodnih telesih ne smemo razumeti kot docela natanč nih posnetkov dejanskih procesov, temveč le kot poenostavitve, ki odkrivajo smernice ključ nih kakovostnih sprememb, ki so odloč ilne za presojo kakovosti voda. Tak pristop pogosto povzroča neupravič eno nezaupanje v tovrstne modele, kar dokazujejo tudi svetovne izkušnje, ki potrjujejo upravič enost nadaljnjega razvoja tovrstnih modelov. Bolj kompleksni več parametrski modeli kakovosti voda napovedujejo fizikalne, kemične in biološke medsebojne vplive mnogih komponent in organizmov, prisotnih v naravnih vodnih telesih. Ti modeli obič ajno zahtevajo več podatkov in rač unalniškega č asa, ponujajo pa podrobnejše in bolj izč rpne informacije o koloč ini in kakovosti voda. Pogosto za to vrsto modelov uporabljamo izraz ekološki modeli. Mathematical models of water quality which make it possible to predict water quality changes after the planned interventions are, on the other hand, used much less frequently. The main reasons for this are: − Water quality problems have become important water management problems only in recent decades. − Mathematical models treat the changes in water quality with the expressions which illustrate, more or less accurately, the course of quality changes, which are the consequence of physical, chemical and biochemical processes in the water. It is understandable that the course and the content of the complicated processes in the water cannot be illustrated in detail with mathematical expressions. Therefore, mathematical models of water quality processes can not be understood as perfectly accurate imitations of real processes, but only as simplifications which uncover the guidelines for the main quality changes critical for water quality evaluation. Such an approach often causes unjustified distrust in these models. This has also been proved by world experience, which confirms the necessity for further development of these models. The more complex multiparametric models of water quality predict physical, chemical and biological interactions of many components and organisms present in natural bodies of water. These models usually demand more data and computer time but they offer better, more exhaustive and detailed information on water quantity and quality. For these sorts of models, we frequently use the term ecological models. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 26 4. MODEL QUAL2E 4.1 SPLOŠNO O MODELU Model QUAL2E je značilen primer več parametrskega modela reč nih ekosistemov, ki je več stransko uporaben za modeliranje kakovosti površinskih voda. Lahko deluje kot stacionaren ali dinamič en model. Stacionaren model se lahko uporablja za preuč evanje vpliva odpadnih voda (količ ina, kakovost in lokacija) na kakovost odvodnika ali za identifikacijo količinskih in kakovostnih lastnosti razpršene obremenitve z odpadnimi vodami, kot sestavni del programa terenskih meritev. Z uporabo dinamič nega modela pa se lahko modelirajo tudi vplivi dnevnih sprememb meteoroloških podatkov na kakovost voda (primarno raztopljeni kisik in temperatura) ali raziskujejo dnevna variiranja v koncentraciji raztopljenega kisika, kot posledica rasti alg in respiracije (Brown & Barnwell, 1987). Model lahko simulira do 15 parametrov kakovosti tekoč ih voda: raztopljeni kisik, biokemijsko potrebo po kisiku, temperaturo, biomaso alg kot klorofil a, organski dušik kot N, amonij kot N, nitrite kot N, nitrate kot N, organski fosfor kot P, raztopljeni fosfor kot P, koliformne bakterije, poljubno neobstojno komponento v vodi, obstojne komponente v vodi. Model je uporaben za vodotoke, ki so dobro premešani. Zahteva se, da so glavni transportni mehanizmi, advekcija in disperzija, znač ilni vzdolž glavne smeri toka. Prvi korak v postopku modeliranja sistema je razdelitev reč nega sistema na odseke, ki predstavljajo neprekinjene odseke reke s konstantnimi hidravlič nimi lastnostmi. Vsak odsek je nato nadalje razdeljen na rač unske elemente enake dolžine. Hidravlič ni podatki, reakcijski hitrostni koeficienti, zač etni pogoji in podatki o porastu pretoka so konstantni za vse rač unske elemente znotraj odseka. 4. THE QUAL2E MODEL 4.1 GENERALLY ON THE MODEL The QUAL2E Model is a typical multiparametric model for river ecosystems, which is universally useful for modelling surface water quality. It can operate as a steady state or as a dynamic model. The steady state model can be used to study the impact of waste loads (magnitude, quality and location) on instream water quality. It can also be used in conjunction with a field sampling program to identify the magnitude and quality characteristics of non point source waste loads. By operating the model dynamically, the user can study the effects of diurnal variations in meteorological data on water quality (primarily dissolved oxygen and temperature), and also the diurnal dissolved oxygen variations due to algae growth and respiration (Brown & Barnwell, 1987). The model is capable of modelling up to 15 water quality constituents: dissolved oxygen, carbonaceous biochemical oxygen demand, temperature, algae as chlorophyll a, components of the nitrogen cycle as nitrogen (organic nitrogen, ammonium, nitrite, and nitrate), components of the phosphorus cycle as phosphorus (organic phosphorus and dissolved inorganic phosphorus), coliforms, an arbitrary nonconservative constituent, and three arbitrary conservative constituents. The model is applicable to well-mixed streams. It assumes that the major transport mechanisms, advection and dispersion, are significant only along the main direction of the flow. The first step in the process of modelling is to divide a river system into reaches that represent a continual river reach with constant hydraulic properties. Each reach is then divided into computational elements, each of the same length. The hydraulic data, reaction coefficients, initial conditions and data on flow augmentation are constant for all computational elements inside the reach. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 27 4.2 MATEMATIČ NE ZVEZE Temeljna enač ba, ki jo rešuje QUAL2E, je enodimenzijska enačba advekcijsko- disperzijskega masnega transporta, ki je numerič no integrirana v prostoru in č asu za vsako komponento kakovosti voda. Enač ba vključuje efekte advekcije, disperzije, razredč itve, reakcije in medsebojne vplive med komponentami ter zunanje in notranje izvore ali ponore. Zapis enač be za katero koli komponento C: 4.2 MATHEMATICAL RELATIONSHIPS The basic equation solved by QUAL2E is the one-dimensional advection-dispersion mass transport equation, which is numerically integrated over space and time for each water quality constituent. This equation includes the effects of advection, dispersion, dilution, constituent reactions and interactions, and sources and sinks. For any constituent C, this equation can be written as: () () S dt dC dx x A dx x C u x A dx x x C L D x A t M + ⋅ + ∂ ⋅ ⋅ ∂ − ∂       ∂ ∂ ⋅ ⋅ ∂ = ∂ ∂ (1) M masa [g]. x razdalja [m]. t č as [s]. C koncentracija komponente C [g/m 3 ]. A x preč ni prerez [m 2 ]. D L disperzijski koeficient [m 2 /s]. u povpreč na hitrost [m/s]. S zunanji in notranji izvori ali ponori [g/s]. Ker je M = V∙ C in č e predpostavimo, da je pretok stalen, torej velja t Q ∂ ∂ = 0 in nadalje t V ∂ ∂ = 0, enač bo (1 ) preuredimo v enač bo (2): M mass [g]. x distance [m]. t time [s]. C concentration of constituent C [g/m 3 ]. A x cross-sectional area [m 2 ]. D L dispersion coefficient [m 2 /s]. u mean velocity [m/s]. S external and internal sources or sinks [g/s]. Because M = V∙ C, and if we assume steady flow, i.e.: t Q ∂ ∂ = 0, and the term t V ∂ ∂ = 0, Equation (1) is rearranged in Equation (2): () V S dt dC x A C u A x A x C D A t C x x x L x + + ∂ ⋅ ⋅ ⋅ ∂ − ∂ ⋅       ∂ ∂ ⋅ ⋅ ∂ = ∂ ∂ (2) Model QUAL2E predpostavi, da je hidravlič ni režim stalen, kar pomeni, da je 0 = ∂ ∂ t Q , zato lahko hidrološko bilanco za rač unski element zapišemo: The model QUAL2E assumes that the stream hydraulic regime is steady, i.e.: 0 = ∂ ∂ t Q ; therefore, the hydrologic balance for a computational element can be written as: () i x Q t Q =       ∂ ∂ (3) kjer je () i x Q vsota zunanjih vtokov in/ali odtokov v ta element. Ko je enač ba (3) rešena za Q, druge hidravlične lastnosti reč nih where () i x Q is the sum of the external inflows into and/or withdrawals out of that element. Once Equation (3) has been solved for Q, the Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 28 odsekov določ imo funkcionalno, kjer model rač una hitrost po enač bi b Q a u ⋅ = in globino po enač bi β α Q h ⋅ = , kjer so a, b, α in β empirič ne konstante, ki so obič ajno določ ene iz pretoč nih krivulj. V nadaljevanju podajamo matematič ne zveze, ki opisujejo individualne reakcije in medsebojne zveze med komponentami. Č lenov, ki predstavljajo advekcijo in disperzijo, v naslednjih enačbah ne prikazujemo, č eprav so vključ eni v model. Model predpostavlja proporcionalnost koncentracije klorofila s koncentracijo fitoplanktonske biomase alg, kar je opisano s preprosto zvezo: other hydraulic characteristics of the stream segments can be determined by equations where the mean velocity is calculated according to equation b Q a u ⋅ = and the stream depth is calculated according to equation β α Q h ⋅ = , where a, b, α and β are empirical constants, usually determined from stage-discharge rating curves. The mathematical relationships that describe individual reactions and interactions are presented in the following paragraphs. The terms that represent advection and dispersion are not shown in the following equation, although they are incorporated in the model. Chlorophyll a is considered to be directly proportional to the concentration of the phytoplanktonic algal biomass, which is described by the following simple relationship: A a chl ⋅ = 0 α (4) chl a koncentracija klorofila a [µ g/l]. A koncentracija biomase alg [mg(A)/l]. α 0 delež klorofila a v biomasi alg (podatek, preglednica 4) [µ g(chl a)/mg(A)]. Produkcija biomase alg, ki variira po č asu, je odvisna od hitrosti rasti alg, hitrosti respiracije alg (ali specifič ne izgube), hitrosti usedanja alg in srednje globine toka, vse na določ eni lokaciji x v reč nem profilu. chl a chlorophyll a concentration [µ g/l]. A algal biomass concentration [mg(A)/l]. α 0 ratio of chlorophyll a to algal biomass (data, Table 4) [µ g(chl a)/mg(A)]. The production of algal biomass that varies in time is dependent on the growth, respiration, and settling rates of algae, and the average depth of the flow, all on a specific location x in the river profile. A h A A dt dA ⋅ − ⋅ − ⋅ = 1 σ ρ µ (5) t č as [dan]. µ specifična hitrost rasti alg, ki je temperaturno odvisna (podatek, preglednica 4) [dan -1 ]. ρ hitrost respiracije alg, temperaturno odvisna (podatek, preglednica 4) [dan -1 ]. 1 σ hitrost usedanja alg, temperaturno odvisna (podatek, preglednica 4) [m/dan]. h srednja globina toka [m]. t time [day]. µ the specific growth rate of algae, which is temperature dependent (data, Table 4) [day -1 ].. ρ the respiration rate of algae, which is temperature dependent (data, Table 4) [day -1 ]. 1 σ the settling rate for algae, which is temperature dependent (data, Table 4) [m/day]. h average depth [m]. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 29 Specifična hitrost rasti alg, hitrost respiracije alg ter hitrost usedanja alg so odvisne od temperature in bodo korigirane znotraj modela, kot vse druge spremenljivke sistema. Postopek bo prikazan kasneje. Hitrost rasti alg je odvisna od temperature, količ ine hranil (C, N, P) in svetlobe. Model ponuja tri možnosti za opis medsebojnih vplivov omejitvenih faktorjev na kinetiko rasti alg. Za simulacije z modelom smo uporabili opcijo omejitvenega hranila, ki predpostavlja, da je hitrost rasti alg omejena s svetlobo in s hranilom z manjšim omejitvenim faktorjem. Ta formulacija posnema Liebigov zakon minimuma ob predpostavki, da je ogljik v izobilju, in ima obliko: The specific growth, respiration and settling rates of algae, are known to be dependent on the temperature and are then corrected in the model, as are all other variables of the system. The procedure will be shown later. The specific growth rate of algae is known to be dependent on the temperature, the availability of required nutrients (C, N, P) and light. The model is capable of modelling the interaction among these limiting factors in three different ways. For modelling simulations, the option of limiting the nutrients was used, which represents the growth rate of algae as limited by light and by nutrients with a smaller algal growth limitation factor. The following formulation mimics Liebig's Law of the minimum at presumption that carbon is in abundance: ) , min( ) ( max FP FN FL ⋅ ⋅ = µ µ (6) max µ maksimalna hitrost rasti alg (podatek, preglednica 4) [dan -1 ]. FL omejitveni faktor svetlobe. FN omejitveni faktor za dušik. FP omejitveni faktor za fosfor. Poskusi pri konstantni temperaturi in spreminjanju razpoložljive svetlobe so pokazali, da fotosinteza narašča do maksimalnega nivoja pri narašč ajoč em sevanju. Nadaljnje narašč anje sevanja pa vodi k fotoinhibiciji in posledič no k upadanju fotosinteze. Za odvisnost rasti alg od svetlobe model ponuja tri možnosti izrač una omejitvenega faktorja svetlobe FL. V simulacijah z modelom smo uporabili Monodovo funkcijo: max µ maximum specific algal growth rate (data, Table 4) [day -1 ]. FL algal growth limitation factor for light. FN algal growth limitation factor for nitrogen. FP algal growth limitation factor for phosphorus. Experiments at constant temperature and changing available light showed an increasing rate of photosynthesis with increasing light intensity u p to the maximum value. Further increase in light intensity leads to photo- inhibition, and, consequently, to a decreasing rate of photosynthesis. The model recognises three options for computing the algal growth limitation factor for light FL. In the simulations with the model, the Monod function was used: ) ( ) ( h I K h I FL L + = (7) I(h) intenziteta svetlobe na globini h [ly/dan]. K L konstanta Monodove enač be za svetlobo; intenziteta svetlobe, kjer je hitrost rasti 50 odstotkov maksimalne hitrosti rasti, temperaturno odvisna (podatek, preglednica 4) [ly/dan]. h globina toka [m]. I(h) light intensity at a given depth h [ly/day]. K L constant of Monod equation for light; light intensity at the velocity of growth 50% of the maximal velocity of growth, temperature dependent (data, Table 4) [ly/day]. h depth [m]. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 30 Prodiranje (ali inverzno njeno upadanje) vstopajoč e sonč ne energije opisuje model z Beer-Lambertovim zakonom, po katerem se intenziteta svetlobe eksponentno spreminja z globino: Penetration of the incoming solar energy is described by the Beer-Lambert Law, according to which the light intensity changes exponentially with the depth: h e I h I ⋅ − ⋅ = λ 0 ) ( (8) I 0 intenziteta svetlobe na površini [ly/dan]. λ koeficient upadanja svetlobe [m -1 ]. Intenziteta sončne energije, ki doseže zemeljsko površino, znaša okoli 0,56 kW/m 2 . Dejanska intenziteta, ki prispe na vodno gladino, je odvisna od letnega č asa, pokritosti z oblaki in reflektivnih lastnosti vode. Velikost koeficienta upadanja svetlobe v vodnih telesih (λ) je odvisna od nač ina, kako koeficient definiramo. Simulacije daljših obdobij zahtevajo dinamič en izrač un λ z upoštevanjem sezonskih sprememb motnosti vode, ki jih povzroč ajo vodne rastline in suspendirani delci v vodi. λ je odvisen od vsebnosti anorganskih trdnih delcev, delcev detritusa in nivoja fitoplanktona (Krajnc, 1994a). Enač bo (8) vstavimo v enač bo (7) in jo integriramo po globini vode h. Rezultat integriranja je globinsko povpreč ena vrednost FL: I 0 surface light intensity [ly/day]. λ light extinction coefficient [m -1 ]. The intensity of solar radiation that reaches the surface of the earth is approximately 0.56 kW/m 2 . The real light intensity at the surface is a function of location, time of year, meteorological conditions and the reflective properties of water. The value of light extinction coefficient (λ) depends on the way it is formulated. In long term simulations, λ should be computed dynamically to account for seasonal variations in turbidity due to the shading of algae or variations in suspended solid load. λ depends on the amount of inorganic particles, particles of detritus and the phytoplankton level (Krajnc, 1994a). Equation (8) is substituted into Equation (7) and integrated over depth h. The depth- averaged light attenuation factor FL is obtained:         ⋅ + + ⋅ = ⋅ − h L L e I K I K h FL λ λ 0 0 ln 1 (9) Za simulacijo stacionarne rasti alg potrebujemo v računih srednje vrednosti omejitvenega faktorja za svetlobo FL sr za dnevni cikel, ki jo izrač unamo po enač bi (1 0). Vrednosti za I tot in N d priskrbi uporabnik modela. Steady state algal simulations require a computation of the average value of FL sr , the algal growth attenuation factor for light, over the diurnal cycle, which is computed according to Equation (10). Values I tot and N d are supplied by the user. 1 FL f AFACT FL sr ⋅ ⋅ = (10)         ⋅ + + ⋅ ⋅ = ⋅ − h a L a L e I K I K h FL λ λ lg lg 1 ln 1 (11) d tot a N I I = lg (12) Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 31 FL sr omejitveni faktor svetlobe, prilagojen s trajanjem dneva in metodo povpreč enja AFACTfaktor povprečenja svetlobe, da zagotovimo podobnost med izračunom, ki uporablja srednjo dnevno vrednost sonč nega obsevanja in izrač unom, ki uporablja srednje urne vrednosti FL (obseg vrednosti od 0,85 do 1,00) f delež ur dnevne svetlobe v 24 urah FL 1 omejitveni faktor svetlobe, ki temelji na srednji dnevni intenziteti svetlobe lg a I srednja dnevna intenziteta fotosintetsko aktivne svetlobe (podatek) [ly/dan]. I tot celotno dnevno fotosintetsko aktivno sonč no obsevanje [ly]. N d število ur dnevne svetlobe [h]. Odvisnost rasti alg od vsebnosti hranil računa model QUAL2E s pomoč jo omejitvenega faktorja rasti alg za dušik FN in omejitvenega faktorja rasti alg za fosfor FP, ki sta definirana z Monodovim izrazom: FL sr algae growth attenuation factor for light, adjusted for daylight hours and averaging method AFACT light averaging factor, used to provide similarity between calculations using a single average daily value of solar radiation and computations using the average of hourly values of FL (range of values is between 0.85 and 1.00). f fraction of daylight hours. FL 1 growth attenuation factor for light, based on daylight average light intensity. lg a I daylight average, photosynthetically active, light intensity (data) [ly/day]. I tot total daily photosynthetically active solar radiation [ly]. N d number of daylight hours per day [h]. The dependence of algal growth on the availability of nutrients is calculated by the help of the algal growth limitation factors for nitrogen (FN) and for phosphorus (FP), which are defined by the Monod expressions: N e e K N N FN + = (13) P K P P FP + = 2 2 (14) N e efektivna lokalna koncentracija razpolo- žljivega anorganskega dušika [mg(N)/l]. K N konstanta Monodove enač be za dušik (podatek, preglednica 4) [mg (N)/l]. K P konstanta Monodove enač be za fosfor (podatek, preglednica 4) [mg(P)/l]. P 2 lokalna koncentracija raztopljenega anorganskega fosforja (ortofosfata) [mg(P)/l]. Model predpostavlja, da alge uporabljajo kot vir anorganskega dušika amonij in/ali nitrat. Efektivna koncentracija razpoložljivega dušika je podana z izrazom: N e effective local concentration of available inorganic nitrogen [mg(N)/l]. K N Monod equation constant for nitrogen (data, Table 4) [mg(N)/l]. K P Monod equation constant for phosphorus (data, Table 4) [mg(P)/l]. P 2 local concentration of inorganic dissolved phosphorus (orthophosphate) [mg(P)/l]. Algae are assumed to use ammonium and/or nitrate as a source of inorganic nitrogen. The effective concentration of the available nitrogen is given by: 3 1 N N N e + = (15) Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 32 N 1 koncentracija amonija ( + 4 NH ) [mg(N)/l]. N 3 koncentracija nitrata [mg(N)/l]. Empirič ni konstanti K N in K P imata funkcijo reguliranja hitrosti rasti alg, pri č emer upoštevata pomembnost faktorjev, ki omejujejo rast alg. Transformacije dušika iz ene oblike v drugo so v modelu opisane z diferencialnimi enač bami od 1 6 do 20. Bilanco organskega dušika določ a enač ba: N 1 concentration of ammonium nitrogen ( + 4 NH ) [mg(N)/l]. N 3 concentration of nitrate nitrogen [mg(N)/l]. The empirical constants K N and K P are used to adjust the algal growth rate to account for those factors that can potentially limit algal growth. The model describes the transformations of nitrogen from one form to another by differential Equations 16 to 20. Organic nitrogen balance is defined by equation: 4 4 4 3 1 4 N N A dt dN ⋅ − ⋅ − ⋅ ⋅ = σ β ρ α (16) N 4 koncentracija organskega dušika [mg(N)/l]. 3 β koeficient hitrosti hidrolize organskega dušika v amonij, temperaturno odvisen (podatek, preglednica 4) [dan -1 ]. 1 α delež dušika v biomasi alg (podatek, preglednica 4) [mg(N)/mg(A)]. 4 σ hitrost usedanja organskega dušika, temperaturno odvisna (podatek, preglednica 4) [dan -1 ]. Za transformiranje amonija velja enač ba: N 4 concentration of organic nitrogen [mg(N)/l]. 3 β rate constant for the hydrolysis of organic N to ammonium, temperature dependent (data, Table 4) [day -1 ]. 1 α fraction of algal biomass that is nitrogen (data, Table 4) [mg(N)/mg(A)]. 4 σ rate coefficient for organic nitrogen settling, temperature dependent (data, Table 4) [day -1 ]. The transformation of ammonium is determined by equation: A F h N N dt N ⋅ ⋅ ⋅ − + ⋅ − ⋅ = µ α σ β β 1 1 3 1 1 4 3 1 (17) () 3 1 1 1 1 N P N P N P F N N N ⋅ − + ⋅ ⋅ = (18) 1 β koeficient hitrosti biološke oksidacije amonija, temperaturno odvisen (podatek, preglednica 4) [dan -1 ]. 3 σ hitrost sproščanja amonija z dna, temperaturno odvisna (podatek, preglednica 4) [mg(N)/m 2 dan]. F 1 delež amonija kot vir anorganskega dušika za alge. P N preferenč ni faktor za amonij (podatek, preglednica 4). 1 β rate constant for the biological oxidation of ammonium, temperature dependent (data, Table 4) [day -1 ]. 3 σ benthos source rate for ammonium, temperature dependent (data, Table 4) [mg(N)/m 2 day]. F 1 share of algal nitrogen uptake from ammonium pool. P N preference factor for ammonium nitrogen (data, Table 4). Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 33 Za koncentracijo nitritnega dušika velja: The concentration of nitrite nitrogen is given by: 2 2 1 1 2 N N dt dN ⋅ − ⋅ = β β (19) N 2 koncentracija nitrita[mg(N)/l]. 2 β koeficient hitrosti biološke oksidacije − 2 NO v − 3 NO (podatek, preglednica 4) [dan -1 ]. Koncentracijo nitrata model izrač una po enač bi (20): N 2 concentration of nitrite nitrogen [mg(N)/l]. 2 β rate constant for the biological oxidation of − 2 NO to − 3 NO (data, Table 4) [day -1 ]. The concentration of nitrate nitrogen is computed according to Equation (20): () A F N dt dN ⋅ ⋅ ⋅ − − ⋅ = µ α β 1 2 2 3 1 (20) Model ima zmožnost upoštevati inhibicijo nitrifikacije pri nizkih vsebnostih raztopljenega kisika z izrač unom korekcijskega faktorja hitrosti nitrifikacije z enač bo prvega reda: The model has the capability of inhibiting the rate of nitrification at low values of dissolved oxygen by computing an inhibition correction factor: () O KNITRF e CORDO ⋅ − − = 1 (21) CORDO korekcijski faktor hitrosti nitrifikacije. KNITRF koeficient inhibicije nitrifikacije prvega reda [mg/l]. O koncentracija raztopljenega kisika [mg/l]. Korekcijski faktor, ki ima vrednost od 0 do 1 , se nato uporabi za izrač un zmanjšanih konstant hitrosti oksidacije amonija (β 1,inhib ) in hitrosti oksidacije nitrita (β 2,inhib ), kot sledi: CORDO nitrification rate correction factor. KNITRF first order nitrification inhibition coefficient [mg/l]. O dissolved oxygen concentration [mg/l]. The correction factor with its value between 0 and 1 is then applied for computing the reduced rate constants of ammonium oxidation ( inhib , 1 β ) and nitrite oxidation ( inhib , 2 β ) by: 1 , 1 β β ⋅ = CORDO inhib (22) 2 , 2 β β ⋅ = CORDO inhib (23) Fosforjev cikel je v mnogih pogledih podoben dušikovemu. Z odmiranjem alg se generira organski fosfor. Ta se nato spremeni v raztopljeno anorgansko obliko, ki jo lahko alge uporabijo za primarno produkcijo. Transformacije fosforja iz ene oblike v drugo ponazarjata diferencialni enač bi 24 in 25: In many respects the phosphorus cycle operates like the nitrogen cycle. Organic forms of phosphorus are generated by the death of algae, then it converts to the dissolved inorganic state, where it is available to algae for primary production. The transformations of phosphorus from one form to another are described by differential Equations 24 and 25: Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 34 1 5 1 4 2 1 P P A dt dP ⋅ − ⋅ − ⋅ ⋅ = σ β ρ α (24) P 1 koncentracija organskega fosforja [mg(P)/l]. 2 α delež fosforja v biomasi alg (podatek, preglednica 4) [mg(P)/mg(A)]. 4 β koeficient hitrosti razgradnje organskega fosforja, temperaturno odvisen (podatek, preglednica 4) [dan -1 ]. 5 σ hitrost usedanja organskega fosforja, temperaturno odvisna (podatek, preglednica 4) [dan -1 ]. P 1 concentration of organic phosphorus [mg(P)/l]. 2 α fraction of algal biomass that is phosphorus (data, Table 4) [mg(P)/mg(A)]. 4 β organic phosphorus decay rate, temperature dependent (data, Table 4) [day -1 ]. 5 σ organic phosphorus settling rate, temperature dependent (data, Table 4) [day -1 ]. A h P dt dP ⋅ ⋅ − + ⋅ = µ α σ β 2 2 1 4 2 (25) P 2 koncentracija raztopljenega anorganskega fosforja (ortofosfat) [mg(P)/l]. 2 σ hitrost sproščanja raztopljenega anorganskega fosforja z dna, temperaturno odvisna (podatek, preglednica 4) [mg(P)/m 2 dan]. Za opis konč ne ogljikove biokemijske potrebe po kisiku model predpostavlja reakcijo prvega reda. Uporabljena funkcija biokemijske potrebe po kisiku (BPK C ) upošteva tudi dodatno odstranitev BPK zaradi sedimentacije, izpiranja (odplavljanja) in flokulacije, ki ne kažejo potrebe po kisiku: P 2 concentration of inorganic or dissolved phosphorus (orthophosphate) [mg(P)/l]. 2 σ benthos source rate for the dissolved phosphorus, temperature dependent (data, Table 4) [mg(P)/m 2 day]. The model assumes a first order reaction to describe the deoxygenation of the ultimate carbon in the stream. The BOD function as expressed in the model (BOD C ) also takes into account the additional BOD removal due to sedimentation, erosion and flocculation, which do not exert an oxygen demand: C C C BPK K BPK K dt dBPK ⋅ − ⋅ − = 3 1 (26) BPK C konč na biokemijska potreba po kisiku za razgradnjo ogljikovih spojin [mg/l]. K 1 koeficient hitrosti razgradnje ogljikovih spojin, temperaturno odvisen (podatek, preglednica 4) [dan -1 ]. K 3 hitrost izgubljanja BPK C zaradi usedanja, temperaturno odvisna (podatek, preglednica 4) [dan -1 ]. BOD C concentration of ultimate carbonaceous biochemical oxygen demand [mg/l]. K 1 carbonaceous deoxygenation rate constant, temperature dependent (data, Table 4) [day -1 ]. K 3 rate of loss of BOD due to settling, temperature dependent (data, Table 4) [day -1 ]. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 35 Model praviloma simulira konč no (celotno) biokemijsko potrebo po kisiku, uporabniku pa je na voljo tudi simulacija 5-dnevne biokemijske potrebe po kisiku. Enač ba povezave se glasi: Generally the model simulates the ultimate BOD. However, the user may choose to use 5- day input and output BOD values. The conversion equation is: ( ) KBPK C C e BPK BPK ⋅ − ⋅ = 5 5 1 (27) KBPK koeficient pretvorbe BPK C v BPK 5 C (podatek; 0,23 dan -1 ) [dan -1 ]. Bilanca kisika v vodotoku je odvisna od sposobnosti vodotoka za reaeracijo. Ta sposobnost je funkcija advekcijskih in difuzijskih procesov v sistemu ter notranjih virov in odtokov kisika. Poleg atmosferske reaeracije sta glavna vira kisika produkcija kisika s fotosintezo in raztopljeni kisik v dotokih v sistem. Odtoke raztopljenega kisika pa predstavljajo biokemijska oksidacija ogljikovih in dušikovih organskih snovi, poraba kisika dna (bentič ne plasti) in kisik, potreben za respiracijo (dihanje) alg. Poraba raztopljenega kisika za dihanje ostalih organizmov je zanemarljiva. Hitrost spreminjanja vsebnosti raztopljenega kisika opisuje diferencialna enač ba: KBPK conversion rate coefficient for BOD C into BOD 5 C (data; 0,23 day -1 ) [day -1 ]. The oxygen balance in a stream system depends on the capacity of the stream to reaerate itself. This capacity is a function of the advection and diffusion processes occurring within the system and the internal sources and sinks of oxygen. The major sources of oxygen, in addition to atmospheric reaeration, are the oxygen produced by photosynthesis and the oxygen contained in the incoming flow. The sinks of dissolved oxygen include the biochemical oxidation of carbonaceous and nitrogenous organic matter, the benthic oxygen demand and the oxygen utilised by algae respiration. The oxygen utilised by the respiration of other organisms is negligible. The rate of change of dissolved oxygen is described by the differential equation: () ( ) 2 2 6 1 1 5 4 1 4 3 2 N N h K BPK K A O O K dt dO C s ⋅ ⋅ − ⋅ ⋅ − − ⋅ − ⋅ ⋅ − ⋅ + − ⋅ = β α β α ρ α µ α (28) O koncentracija raztopljenega kisika[mg/l]. O s nasičena koncentracija raztopljenega kisika pri lokalni temperaturi in tlaku (izrač un po enač bi 29) [mg/l]. 3 α hitrost produkcije kisika pri fotosintezi na enoto biomase alg (podatek, preglednica 4) [mg(O)/mg(A)]. 4 α hitrost porabe kisika pri respiraciji na enoto biomase alg (podatek, preglednica 4) [mg(O)/mg(A)]. 5 α hitrost porabe kisika na enoto oksidiranega amonija (podatek, preglednica 4) [mg(O)/mg(N)]. 6 α hitrost porabe kisika na enoto oksidiranega nitrita (podatek, preglednica 4) [mg(O)/mg(N)]. O dissolved oxygen concentration [mg/l]. O s saturation concentration of dissolved oxygen at the local temperature and pressure (calculation according to Equation 29) [mg/l]. 3 α rate of oxygen production per unit of algal photosynthesis (data, Table 4) [mg(O)/mg(A)]. 4 α rate of oxygen uptake per unit of algae respired (data, Table 4) [mg(O)/mg(A)]. 5 α rate of oxygen uptake per unit of ammonium nitrogen (data, Table 4) [mg(O)/mg(N)]. 6 α rate of oxygen uptake per unit of nitrite nitrogen oxidation (data, Table 4) [mg(O)/mg(N)]. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 36 K 2 hitrost reaeracije, temperaturno odvisna (podatek, preglednica 4) [dan -1 ]. K 4 hitrost ploskovne porabe kisika dna (podatek, preglednica 4) [g/m 2 dan]. Hitrost reaeracije se najbolj pogosto izraža kot funkcija globine vodotoka in hitrosti. Qual2E ponuja 8 možnosti za ocenjevanje ali vnos vrednosti hitrosti reaeracije. Za globoke, poč asne predele rek se lahko reaeracija rač una z uporabo formul za reke ali z uporabo formul za jezera. Najbolj primerna iz skupine za reke za takšne odseke reke je metoda O'Connor- Dobbins, č eprav je za zelo poč asne odseke rek napovedana hitrost reaeracije od 0,01 do 0,05 dan -1 (Bowie et al., 1985). Topnost kisika v vodi upada z narašč anjem temperature in koncentracije raztopljenih soli v vodi ter z upadanjem zrač nega tlaka. Model uporablja naslednjo enačbo za izrač un nasič ene koncentracije kisika: K 2 reaeration rate constant, temperature dependent (data, Table 4) [day -1 ]. K 4 benthic oxygen uptake (data, Table 4) [g/m 2 day]. The reaeration rate constant is most often expressed as the function of stream depth and velocity. Qual2E provides eight options for estimation or reading of the reaeration rate constant values. In deep, slowly moving regions of river, reaeration can be calculated by using a river formula or lake formula. The O'Connor Dobbins method is probably the most appropriate stream formula to use, although for very slowly moving river regions, the predicted reaeration coefficient can be between 0.01 and 0.05 day -1 (Bowie et al., 1985). The solubility of dissolved oxygen in water decreases with the increase of temperature and a dissolved solids concentration, and a decrease in atmospheric pressure. The model uses a predictive equation for the saturation concentration of dissolved oxygen:         ⋅ −         ⋅ +         ⋅ −         ⋅ + − = 4 11 3 10 2 7 5 10 621949 , 8 10 243800 , 1 10 642308 , 6 10 575701 , 1 34410 , 139 ln T T T T O s (29) O s nasič ena koncentracija kisika pri tlaku 1 atm [mg/l]. T temperatura vode [K]. Za nestandardni zrač ni tlak se koncentracija raztopljenega kisika pri nasič enosti korigira, č e se rač una toplotna bilanca, z enač bo: O s equilibrium oxygen concentration at 1 atm [mg/l]. T water temperature [K]. For non-standard conditions of pressure, the equilibrium concentration of dissolved oxygen is corrected only when the temperature is modelled by the equation: () () () ()       − ⋅ − ⋅ − ⋅ − ⋅ ⋅ = φ φ 1 1 1 1 wv a a wv a s p P P P P P O O (30) O p nasičena koncentracija raztopljenega kisika pri nestandardnem zrač nem tlaku [mg/l]. P a zrač ni tlak [atm]. P wv parcialen tlak vodnih par [atm], ki se izrač una po enač bi: O p equilibrium oxygen concentration at non-standard atmospheric pressure [mg/l]. P a atmospheric pressure [atm]. P wv partial pressure of water steam [atm], calculated by the following equation: () ( ) 2 216961 70 , 3840 8571 , 11 ln T T P wv − − = (31) Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 37 ( ) ( ) 2 8 5 10 436 , 6 10 426 , 1 000975 , 0 t t ⋅ ⋅ + ⋅ ⋅ − = − − φ (32) t temperatura [ºC]. Več ina koeficientov v enač bah je odvisna od temperature. Vstopni podatki so vrednosti koeficientov pri 20 ºC, njihove vrednosti pri temperaturi, ki nastopa v sistemu, pa se izrač unajo po enač bi: t temperature [ºC]. The majority of rate coefficients are temperature dependent. These coefficients are input at 20 ºC and are then corrected to the local temperature of the system by the equation: () ° − ⋅ = 20 20 T T X X θ (33) X T vrednost koeficienta pri lokalni temperaturi T. X 20 vrednost koeficienta pri standardni temperaturi (20 ºC). θ empirična konstanta za posamezen reakcijski koeficient. Vrednosti θ lahko poda uporabnik modela, č e tega ne stori, pa model uporabi svoje vrednosti. 4.3 UTEMELJITEV IZBIRE MODELA Uporabo modela QUAL2E utemeljujemo z naslednjimi argumenti: − Zadrževalni č asi v akumulacijskem jezeru so sorazmerno kratki. Za najmanjši nizki obdobni pretok Save v Radeč ah (39,7 m 3 /s) znaša izrač unan zadrževalni č as 54,6 ur, za pretoke v velikosti 100 m 3 /s, ki jo mora HE Vrhovo spušč ati za zagotovitev potrebne količ ine hladilne vode za jedrsko elektrarno Krško, pa 23,4 ur. − Enodimenzionalni model smo uporabili ob predpostavki, da dolge, ozke zajezitve lahko obravnavamo na enak nač in kot nezajezene vodotoke, to je s popolno vertikalno in horizontalno premešanostjo polutantov v preč nih profilih. − Model se je že uporabljal v slovenskem prostoru za napoved sprememb kakovosti voda v prihodnjih zajezitvah hidroelektrarn, ni pa se še izvedla njegova potrditev na že obstoječ i zajezitvi. X T value of coefficient at local temperature T. X 20 value of coefficient at the standard temperature (20 ºC). θ an empirical constant for each reaction coefficient. The values of θ may be specified by the user. In the absence of the user specified values, the default values are employed. 4.3 REASONING OF OUR CHOICE FOR THE MODEL The use of the QUAL2E Model is based on the following arguments: − Retention times in the impoundment are comparatively short. For the minimal low discharge within a period in the Radeč e cross section (39.7 m 3 /s) of the Sava River, the calculated retention time amounts to 54.6 h. For the discharge of 100 m 3 /s, which must be released from the Vrhovo HEPP to assure the necessary quantity of cooling water for the Krško NE, the retention time amounts to 23.4 hours. − A one dimensional model was used on the presumption that long narrow impoundments can be treated in the same way as unimpounded streams, i.e. with a complete vertical and horizontal mixing of the pollution in the cross-sectional profiles. − The model has already been used in Slovenia to predict water quality changes in the planned impoundments for the HEPP, but its validation on an existing impoundment has not yet been performed. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 38 4.4 TERENSKE MERITVE IN VHODNI PODATKI MODELA 4.4.1 Vzorč evanje Za umerjanje matematič nega modela in kvantitativno opredelitev sprememb kakovosti Save v akumulaciji HE Vrhovo z matematič nim modelom QUAL2E je bilo treba opraviti meritve na vtoku in iztoku iz akumulacije. Za določ itev kakovosti vode na vtoku v akumulacijo smo izvajali vzorč evanja triurnih povpreč nih vzorcev in meritve za Savo v Suhadolu in za Savinjo v Velikem Širju. Za določitev kakovosti vode na iztoku iz akumulacije pa smo izvajali vzorč evanja in meritve na pregradi HE Vrhovo. Prvo vzorč evanje je potekalo od 1 6.9.1 996 do 20.9.1 996. Vnovič no vzorč evanje, katerega namen je bil pridobiti dodatne podatke za validacijo modela, je bilo izvedeno avgusta 1998. 4.4.2 Vhodni podatki modela Vhodne podatke modela predstavljajo pretoki na VP Hrastnik za Savo in pretoki na VP Veliko Širje za Savinjo, rezultati fizikalno kemijskih analiz (temperatura vode, koncentracija raztopljenega kisika, biokemijska potreba po kisiku, koncentracije klorofila a, organskega dušika, amonija, nitrita, nitrata, raztopljenega ortofosfata in koncentracija organskega fosforja) na zajemnem mestu Suhadol na Savi ter na zajemnem mestu Veliko Širje na Savinji, podatki o srednjih dnevnih vrednostih energije globalnega sonč nega obsevanja in povpreč ne vrednosti trajanja svetlega dneva v Sloveniji. 4.4.3 Razdelitev modeliranega odseka Save na odseke in rač unske elemente Razdelitev modeliranega odseka Save od Suhadola do pregrade HE Vrhovo na odseke in rač unske elemente predstavlja prvi korak v postopku modeliranja z modelom QUAL2E. Modelirali smo odsek reke Save v dolžini 9,88 km gorvodno od pregrade HE Vrhovo. 4.4. FIELD MEASUREMENTS AND INPUT DATA FOR THE MODEL 4.4.1 Sampling For the model calibration and for the quantitative determination of water quality changes in the Vrhovo Impoundment using the QUAL2E mathematical model, measurements at the inflow into the impoundment and at the outflow from the impoundment had to be done. We designed the sampling of three hour average samples at the inflow into the impoundment (for the Sava River in Suhadol and for the Savinja River in Veliko Širje) and at the outflow from the impoundment (on the Vrhovo HEPP dam). The first sampling campaign was carried out from 16 September, 1996 to 20 September, 1996. With the intention of acquiring additional data for the model validation, another sampling campaign was carried out in August, 1998. 4.4.2 Input data for the model The input data for the model were: the discharges at the Hrastnik Water Gauge Station on the Sava River and the discharges at the Veliko Širje Water Gauge Station on the Savinja River; the results of the physical- chemical analyses (water temperature, the concentration of dissolved oxygen, biochemical oxygen demand, chlorophyll a, concentrations of organic nitrogen, ammonium, nitrite, nitrate, dissolved orthophosphate and organic phosphorus) at the Suhadol sampling site on the Sava River and at the Veliko Širje sampling site on the Savinja River; the data on average daylight solar radiation and the number of daylight hours per day in Slovenia. 4.4.3 Divisions of the modelled reach of the Sava River into sub-reaches and computational elements The first step in the process of modelling with the QUAL2E model was the division of the modelled reach of the Sava River from Suhadol to the Vrhovo River Dam, a total length of 9.88 km, into a number of sub- reaches and computational elements. It was Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 39 Razdelili smo ga na 26 odsekov različ nih dolžin, ti pa so razdeljeni na rač unske elemente dolžine 1 30 m. Hidravlič ne lastnosti reč nih odsekov smo določ ili funkcionalno. Za različ ne pretoke od 65 m 3 /s do 150 m 3 /s poznamo hitrosti in globine v preč nih profilih. Na podlagi tega smo z matematič nim programom NONLIN (Sherrod, 1 992) izrač unali empirič ne konstante a, b, α, β v enač bah b Q a u ⋅ = in β α Q h ⋅ = za posamezne odseke. Vtok Savinje v Savo v Zidanem Mostu smo modelirali kot toč kovni vnos. 4.4.4 Parametri modela V modelu QUAL2E nastopajo v preglednici 4 opisani parametri. Parametri nimajo fiksne vrednosti, ampak se gibljejo znotraj določ enega intervala vrednosti, ki so navedeni po Brownu in Barnwelu (1987). 4.5 ANALIZA OBČ UTLJIVOSTI Z analizo obč utljivosti smo ugotavljali reakcijo modela na spremembe vrednosti parametrov v modelu. Analizo smo izvedli s sistematič nim spreminjanjem vrednosti enega od parametrov, ki smo jo poveč ali oziroma zmanjšali za 50 odstotkov, pri konstantnih vrednostih ostalih parametrov in pri konstantnih vhodnih spremenljivkah. Opazovali smo vpliv spreminjanja tega parametra na rezultate modela. Vrednosti parametrov, navedene v preglednici 4 v zadnjem stolpcu so bile uporabljene kot osnovne vrednosti, ki smo jih pri izvedbi analize obč utljivosti modela poveč ali oziroma zmanjšali za 50 odstotkov. Analizo občutljivosti smo izvedli za parametre modela, katerih interval vrednosti je velik. Ti parametri so α 0 , β 1 , β 2 , β 3 , β 4 , µ max , ρ, K 1 , K 3 , K 4 , K L , K N , K P , σ 1 , σ 4 , σ 5 , λ 0 , λ 1 , P N . divided into 26 sub-reaches of varying lengths and into computational elements, each being 130 meters long. The hydraulic characteristics of the stream sub-reaches were determined in a functional form. For different discharges (Q) from 65 m 3 /s to 150 m 3 /s, the average velocity ( u ) and depth (h) of the corresponding cross-sections were known. Based on this, empirical constants a, b, α, β in equations b Q a u ⋅ = and β α Q h ⋅ = for each reach, were calculated using the NONLIN Mathematical Programme (Sherrod, 1992). Savinja is a tributary of the Sava River. It was modelled as a point source to the main stream of the Sava. 4.4.4 Model parameters The QUAL2E Model contains many system parameters; they are shown in Table 4. The parameters do not have fixed values, but they range within the defined interval of values listed according to Brown & Barnwel (1987). 4.5 SENSITIVITY ANALYSIS With the sensitivity analysis we established the relative sensitivity of the model predictions to changes in the values of the model parameters. The analysis was performed with the systematic changing of the values of a single parameter, enlarged or reduced by 50 percent, while all other parameters and input variables remained constant. We observed the impact of the changes in this parameter on the model results. The parameter values, listed in the last column in Table 4, were used as the basic values for the sensitivity analysis enlarged or reduced by 50 percent. The sensitivity analysis was performed for the model parameters for which the range of values is large. These parameters are α 0 , β 1 , β 2 , β 3 , β 4 , µ max , ρ, K 1 , K 3 , K 4 , K L , K N , K P , σ 1 , σ 4 , σ 5 , λ 0 , λ 1 , P N . Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 40 Preglednica 4: Opis parametrov modela Qual2E Table 4. Qual2E Model parameter specification. Oznaka v tekstu Description Enota Unit Interval vrednosti Interval of values Izbrana vrednost za analizo obč utljivosti Selected value for sensitivity analysis α 0 µ g(chl a)/mg(A) 10-100 50 α 1 mg(N)/mg(A) 0,07-0,09 0,085 α 2 mg(P)/mg(A) 0,01-0,02 0,0135 α 3 mg(O 2 )/mg(A) 1,4-1,8 1,6 α 4 mg(O 2 )/mg(A) 1,6-2,3 1,95 α 5 mg(O 2 )/mg(N) 3,0-3,5 3,5 α 6 mg(O 2 )/mg(N) 1,0-1,14 1,07 β 1 day -1 0,1-1,0 0,5 β 2 day -1 0,2-2,0 1,0 β 3 day -1 0,02-0,4 0,2 β 4 day -1 0,01-0,7 0,36 µ max day -1 1,0-3,0 2 ρ day -1 0,05-0,5 0,2 K 1 day -1 0,02-3,4 0,23 K 2 day -1 0,0-100,0 opcija 3 option 3 K 3 day -1 -0,36-0,36 0,1 K 4 g(O 2 )/m 2 day spremenljivka variable 0,5 K L ly/day 7,85-39,24 34,56 K N mg(N)/l 0,01-0,3 0,15 K P mg(P)/l 0,001-0,05 0,02 σ 1 m/day 0,15-1,8 0,5 σ 2 mg(P)/m 2 day spremenljivka variable 0,0012 σ 3 mg(N)/m 2 day spremenljivka variable 0,0005 σ 4 day -1 0,001-0,1 0,05 σ 5 day -1 0,001-0,1 0,05 λ 0 m -1 spremenljivka variable 1,7 λ 1 m -1 (µ g(chl a)/l) -1 0,0066-0,0656 0,005 λ 2 m -1 (µ g(chl a)/l) -2/3 0,0541 0 P N - 0,0-1,0 0,2 Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 41 Ugotovili smo smiselno odzivanje rezultatov modela na spreminjanje posameznih parametrov. Model na nobenega od obravnavanih parametrov ni preobč utljiv, ne odziva pa se na spreminjanje naslednjih parametrov: konstante Monodove enač be za dušik (K N ), prednostnega faktorja za amonij (P N ), linearnega koeficienta samoosenč enja alg (λ 1 ). Podrobnejši opis in grafič na predstavitev rezultatov analize obč utljivosti modela sta podana v magistrski nalogi (Cvitanič , 1 998). 4.6 UMERJANJE IN PREVERJANJE MODELA Umerjanje modela izvajamo s prilagajanjem parametrov modela tako, da rezultati modela č im bolj ustrezajo izmerjenemu stanju. Zaradi pomanjkanja analitič nih rešitev istoč asno z umerjanjem izvajamo preverjanje modela. V letu 1996 so bili na voljo rezultati fizikalno-kemijskih analiz za 22 vzorcev na vsakem mestu vzorč evanja, ki predstavljajo triurne povprečne vzorce za 5-dnevno vzorč evanje. Zadnjih 1 5 rezultatov meritev smo uporabili za umerjanje in preverjanje modela, preostalih 7 pa za potrditev modela. Rezultate vzorč evanja v letu 1 998 pa smo uporabili kot nov, neodvisen dogodek, ki smo ga uporabili za dodatno validacijo modela. V posamezni simulaciji predstavljajo vhodne podatke triurne povpreč ne vrednosti. Z modelnim izrač unom torej zasledujemo triurno povpreč no stanje vzdolž toka in spremembe kakovosti vode na modeliranem odseku Save od Suhadola do pregrade HE Vrhovo. Za BPK 5 , O 2 in klorofil a smo dosegli zadovoljivo ujemanje med meritvami in rezultati modela, kar dokazuje izrač unan integral ploščine pod krivuljami, ki so prikazane na sliki 1. Za amonij z umerjanjem modela nismo dosegli boljšega ujemanja med izrač unanimi in izmerjenimi vrednostmi. Rezultati so prikazani We established the logical response of the model results to the changes in the values of single parameters. The model is not too sensitive to any of the treated parameters, but it does not respond to changes in the values of the following parameters: constant of Monod equation for nitrogen (K N ), algae preference factor for ammonium (P N ), linear algae self- shading coefficient (λ 1 ). A detailed description and graphic presentation of the sensitivity analysis results are given in the Master's Thesis (Cvitanič , 1998). 4.6 MODEL CALIBRATION AND VERIFICATION The calibration of the model is performed by adjusting the model parameters in such a manner that the simulated performance of the model is in correspondence with the measured state as much as possible. Due to the lack of analytical solutions, the verification of the model is performed simultaneously with the model calibration. In 1996 the results of the physical-chemical analyses for 22 samples from each sampling point were available. These results represent 3- hour average samples for 5-days sampling. The set of the last 15 samples was used for the model calibration, while the set of the remaining 7 samples was used for the model validation. The sampling results from 1998 were used as a new, independent event for additional model validation. Input data for each simulation were three- hour average values. Therefore, a three-hour average state of flow and water quality on the modelled section of the Sava River was simulated with model calculations. A satisfactory agreement between the measured and the modelled results was achieved for BOD 5 , dissolved O 2 and chlorophyll a. This is proved by the calculated integral of square dimension under curves, shown in Figure 1. For ammonium such good agreement between the calculated and the measured results could not be reached. From the results Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 42 na sliki 2, iz katere je razvidno, da so rezultati modela v nekem č asovnem obdobju previsoki, v naslednjem pa znantno prenizki. Zaključ ili smo, da so v akumulacijskem jezeru neznani izvori in ponori amonija, ki niso vključ eni v model. Vendar pa je ujemanje merjenih in izrač unanih rezultatov v okviru reda velikosti. Primerjava rezultatov modela in izmerjenih vrednosti za nitrit in nitrat na pregradi HE Vrhovo, prikazana na sliki 2, kaže, da je model za ti dve spremeljivki uspešno umerjen. Rezultati modela za ortofosfat in organski fosfor so v večini izračunov, glede na izmerjene koncentracije prenizki, vendar s spreminjanjem parametrov, ki vplivajo na ti dve spremenljivki, ne moremo doseč i višjih vrednosti. Primerjava meritev in izrač unov modela za organski fosfor na sliki 3 kaže na zadovoljivo kvalitativno ujemanje, kvantitativno pa se pojavljajo precejšnje razlike, ki so v več kot polovici primerov več je od 20 odstotkov. Na podlagi primerjave rezultatov modela z rezultati meritev smo zaključili, da je umerjanje in preverjanje modela ob danih možnostih uspešno zaključ eno. Vzroke več jih razlik med izračunanimi in izmerjenimi vrednostmi, ki so se pojavile pri amoniju in organskem fosforju, bi bilo treba raziskati z nadaljnjimi kakovostnimi in nač rtnimi meritvami v akumulacijskem jezeru HE Vrhovo. Določ itve organskega fosforja bi bilo treba izvesti še v nefiltiranih vzorcih vode, ker bi s tem zajeli raztopljeni in partikularni organski fosfor v vodi, in izvesti izrač une z modelom. Tako bi ugotovili, ali je ujemanje med izrač uni modela in meritvami v tem primeru boljše (Cvitanič , 1 998). in Figure 2, it is evident that the results of the model were too high for one period and rather too low for the next. It can be concluded that there are unknown sources and sinks of ammonium in the impoundment, which were not included in the model. However, the modelled results were within an acceptable range. The comparison of the modelled and the measured results for nitrite and nitrate on the Vrhovo Dam showed that the model was successfully calibrated for these two variables (Figure 2). The concentrations of orthophosphate and organic phosphorus calculated by the model were, in most simulations, lower than the measured concentrations. Higher values could not have been obtained by varying only those parameters that influence these two variables. The comparison of the modelled and the measured results for organic phosphorus (Figure 3) showed a satisfactory qualitative agreement, but there appeared quite large quantitative differences, which were, in more than half of the cases, larger than 20 percent. Based on the comparison of the modelled and the measured results, it was concluded that the calibration of the model was successfully accomplished regarding the given input (measured) data. The causes for the greater differences between the calculated and the measured values of ammonium and organic phosphorus must be researched with additional quality and systematic measurements in the Vrhovo Impoundment. The determinations of organic phosphorus also have to be done in unfiltered water samples, because in this way dissolved and particular organic phosphorus would be determined. Then a new calibration test has to be done to obtain better agreement with the measurements (Cvitanič , 1 998). Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 43 Slika 1 . Primerjava z modelom izrač unanih vrednosti BPK 5 , O 2 in klorofila a z meritvami na pregradi HE Vrhovo. Figure 1. Modelled BOD 5 , O 2 and chlorophyll-a in comparison to measured values at the Vrhovo HEPP Dam. Primerjava modeliranih in izmerjenih vrednosti za BPK 5 , O 2 in klorofil a Modelled versus measured BOD 5 , O 2 and chlorophyll a 0.00 1.00 2.00 3.00 4.00 0 2 4 6 8 10 12 14 16 Vzorec / Sample klorofil a / chlorophyll a [mg/l] 0.0 3.0 6.0 9.0 12.0 izmerjen / measured BOD 5 modeliran / modelled BOD 5 izmerjen / measured chl a modeliran / modelled chl a izmerjen / measured O 2 modeliran / modelled O 2 BPK 5 / BOD 5 [mg(O 2 )/l] O 2 [mg(O 2 )/l] Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 44 Slika 2. Primerjava z modelom izrač unanih vrednosti + 4 NH , − 2 NO in − 3 NO z meritvami na pregradi HE Vrhovo. Figure 2. Modelled + 4 NH , − 2 NO and − 3 NO as compared to the measured values at the Vrhovo HEPP Dam. Primerjava modeliranih in izmerjenih vrednosti za NH 4 + , NO 2 - in NO 3 - Modelled versus measured NH 4 + , NO 2 - and NO 3 - 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 024681 01 21 41 6 Vzorec / Sample NH 4 + [mg(N)/l] 0.00 0.50 1.00 1.50 2.00 2.50 izmerjen / measured NH 4 + modeliran / modelled NH 4 + izmerjen / measured NO 2 - modeliran / modelled NO 2 - izmerjen / measured NO 3 - modeliran / modelled NO 3 - NO 2 - [mg(N)/l] NO 2 - [mg(N)/l] Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 45 Slika 3. Primerjava z modelom izrač unanih vrednosti orto-PO 4 3- in org-P z meritvami na pregradi HE Vrhovo. Figure 3. Modelled ortho-PO 4 3- and org-P as compared to measured values at the Vrhovo HEPP Dam. Primerjava modeliranih in izmerjenih vrednosti za orto-PO 4 3- in org. P Modelled versus measured ortho-PO 4 3- and org. P 0.00 0.10 0.20 0.30 0.40 024681 01 21 41 6 Vzorec / Sample 0.00 0.02 0.04 0.06 0.08 org. P [mg(P)/l] izmerjen orto-PO 4 3- / measured ortho-PO 4 3- modeliran orto-PO 4 3- / modelled ortho-PO 4 3- izmerjen org.-P / measured org.-P modeliran org.-P / modelled org.-P orto-PO 4 3- / ortho-PO 4 3- [mg(P)/l] Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 46 4.7 POTRDITEV MODELA V prvi fazi smo izvajali potrditev modela z rezultati 7 meritev, ki niso bili uporabljeni za umerjanje modela, so pa del iste serije terenskih meritev, katere rezultati so bili uporabljeni za umerjanje modela. Za BPK 5 , O 2 , klorofil a, amonij, nitrit in nitrat je potrjeno zadovoljivo kvantitativno ujemanje rezultatov modela z rezultati meritev, kar je razvidno iz grafič nega prikaza rezultatov na slikah 4 in 5. Č eprav so izrač unane vrednosti BPK 5 in O 2 ves č as nižje od izmerjenih vrednosti na pregradi HE Vrhovo, so razlike med izrač unanimi in izmerjenimi vrednostmi manjše od 10 odstotkov, kar je sprejemljivo za kvantitativno obravnavo problema. Za amonij lahko ugotovimo, da so razlike med izračunanimi in izmerjenimi koncentracijami manjše kot v fazi umerjanja modela ter so manjše od 20 odstotkov, razen pri zadnjem vzorcu, kjer se pojavi več ja razlika. Na sliki 5 prikazana primerjava meritev in izrač unov modela za nitrit in nitrat kaže na nekoliko previsoke izrač unane vrednosti za obe spremenljivki. Vendar so razlike med izračunanimi in izmerjenimi vrednostmi za nitrit manjše od 20 odstotkov, za nitrat pa manjše od 10 odstotkov, kar je sprejemljivo za kvantitativno obravnavo problema. Z modelom izračunane koncentracije ortofosfata in organskega fosforja so v glavnem nižje od izmerjenih koncentracij (slika 6). Glede na dobljene rezultate v tej fazi, modela ne moremo povsem zanesljivo uporabiti za kvantitativne napovedi ortofosfata in organskega fosforja v akumulaciji. 4.7 MODEL VALIDATION In the first phase the model validation was performed with a set of 7 measurements which belonged to the same measurement campaign, from which a different set of 15 measurements was used for the model calibration. A suitable quantitative agreement between the simulated and the measured results was obtained for BOD 5 , DO, chlorophyll a, ammonium, nitrite and nitrate. This is evident from the graphic presentation of the results in Figures 4 and 5. Although the calculated values for BOD and DO were lower from the measured values at the Vrhovo HEPP Dam throughout, the differences between the calculated and the measured values were smaller than 10 percent, which is acceptable for the quantitative treatment of the problem. For ammonium it can be established that the differences between the measured and the calculated results were smaller than in the model calibration phase and were smaller than 20 percent, with the exception of the last sample, where a larger difference appeared. The comparison between the measured and the modelled results for nitrite and nitrate are shown in Figure 5. It is evident that the modelled values were somewhat too high for both variables. However, the differences between the calculated and the measured results for nitrite were smaller than 20 percent, and for nitrate, smaller than 10 percent, which is acceptable for the quantitative treatment of the problem. The modelled concentrations of orthophosphate and organic phosphorus were, in most simulations, lower than the measured concentrations (Figure 6). Considering the results of this validation, the model cannot be reliably applied for the quantitative prediction of orthophosphate and organic phosphorus in the impoundment. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 47 Slika 4. Primerjava z modelom izrač unanih vrednosti BPK 5 , O 2 in klorofila a z meritvami na pregradi HE Vrhovo. Figure 4. Modelled BOD 5 , O 2 and chlorophyll-a as compared to the measured values at the Vrhovo HEPP Dam. Primerjava modeliranih in izmerjenih vrednosti za orto-PO 4 3- in org. P Modelled versus measured ortho-PO 4 3- and org. P 0.00 0.10 0.20 0.30 0.40 024681 01 21 41 6 Vzorec / Sample 0.00 0.02 0.04 0.06 0.08 org. P [mg(P)/l] izmerjen orto-PO 4 3- / measured ortho-PO 4 3- modeliran orto-PO 4 3- / modelled ortho-PO 4 3- izmerjen org.-P / measured org.-P modeliran org.-P / modelled org.-P orto-PO 4 3- / ortho-PO 4 3- [mg(P)/l] Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 48 Slika 5. Primerjava z modelom izrač unanih vrednosti + 4 NH , − 2 NO in − 3 NO z meritvami na pregradi HE Vrhovo. Figure 5. Modelled + 4 NH , − 2 NO and − 3 NO as compared to the measured values at the Vrhovo HEPP Dam. Primerjava modeliranih in izmerjenih vrednosti za NH 4 + , NO 2 - in NO 3 - Modelled versus measured NH 4 + , NO 2 - and NO 3 - 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 012345678 Vzorec / Sample NO 2 - [mg(N)/l] 0.00 0.50 1.00 1.50 2.00 2.50 izmerjen / measured NH 4 + modeliran / modelled NH 4 + izmerjen / measured NO 2 - modeliran / modelled NO 2 - izmerjen / measured NO 3 - modeliran / modelled NO 3 - NH 4 + [mg(N)/l] NO 3 - [mg(N)/l] Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 49 Slika 6. Primerjava z modelom izrač unanih vrednosti orto-PO 4 3- in org-P z meritvami na pregradi HE Vrhovo. Figure 6. Modelled ortho-PO 4 3- and org-P as compared to the measured values at the Vrhovo HEPP Dam. Primerjava modeliranih in izmerjenih vrednosti za orto-PO 4 3- in org. P Modelled versus measured ortho-PO 4 3- and org. P 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 012345678 Vzorec / Sample 0.00 0.02 0.04 0.06 0.08 org. P [mg(P)/l] izmerjen orto-PO 4 3- / measured ortho-PO 4 3- modeliran orto-PO 4 3- / modelled ortho-PO 4 3- izmerjen org.-P / measured org.-P modeliran org.-P / modelled org.-P orto-PO 4 3- / ortho-PO 4 3- [mg(P)/l] Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 50 Treba bi bilo izvesti več kakovostnih vzorč evanj na vtokih v akumulacijo in iztoku iz akumulacije ter na nekem preč nem profilu v sami akumulaciji. Komponente fosforja je treba določ iti v filtriranih in nefiltriranih vzorcih vode. Izrač uni z modelom bi morali biti izvedeni za obe rezličici določ itev fosforjevih komponent. Primerjava rezultatov za obe različici bo pokazala, ali se z določ itvijo komponent fosforja v nefiltriranih vzorcih voda dobi kvantitativno boljše ujemanje modelnih izrač unov z izmerjenim stanjem na pregradi HE Vrhovo. Prav tako moramo upoštevati, da je model poenostavitev procesov v naravi in ne vključ uje vseh komponent in procesov v naravi. Transformacije fosforjevih komponent v modelu vključ ujejo le kroženje fosforjevih komponent do primarne produkcije, ne vključ ujejo pa kroženja snovi in energije na višjih prehranjevalnih ravneh, ki vključ ujejo zooplankton, ribje populacije in druge organizme. Rezultati potrditve modela z neodvisno serijo meritev, izvedenih avgusta 1998 pri nizkih pretokih in izrazito poletnih meteoroloških razmerah kažejo, da smo dosegli zadovoljivo kvantitativno ujemanje med meritvami in rezultati modela le za raztopljeni kisik, za vse ostale rač unane spremenljivke pa ni ustrezno, kar je razvidno iz slik 7, 8 in 9. Z modelom izrač unane vrednosti BPK 5 so v povpreč ju za 49 odstotkov nižje od izmerjenih vrednosti. Izmerjene vrednosti BPK 5 na pregradi HE Vrhovo vključujejo tudi razgradljivo organsko biomaso alg, katerih rast je, kot je razvidno iz določ itev klorofila a, precej intenzivna. Model pa, kot je razvidno iz sheme interakcij med komponentami v modelu, ne upošteva novonastale biološko razgradljive biomase alg, ki nastane v primeru intenzivne rasti alg (primarne produkcije). Posledice navedenih ugotovitev pa so dobljene razlike med izmerjenimi in izrač unanimi vrednostmi BPK 5 . Poleg tega so izrač unane vrednosti klorofila a v povpreč ju za 63 Several quality samplings at the inflow into the impoundment, at the outflow from the impoundment and on some cross-sectional profiles in the impoundment could have been performed. The components of phosphorus must be determined in both filtered and unfiltered water samples. Calculations with the model must be performed for both variants of determining phosphorus components. The comparison of results for both variants will show whether the determination of phosphorus components in unfiltered samples gives better quantitative agreement between the calculated and the measured results. We also have to take into consideration that the model is a simplification of the processes in nature, and it does not strictly include all the components and processes in nature. The transformations of phosphorus components in the model include only the cycling of the phosphorus components up to primary production, but they do not include the cycling of substances and energy on higher nutrient levels, which include zooplankton, fish populations and other organisms. In the second phase, the model validation was performed with an independent set of measurements carried out in August, 1998 at low discharges and at pronounced summer meteorological conditions. Suitable quantitative agreement between the measured and the modelled results was obtained only for dissolved oxygen. For all other simulated variables the agreement was not so good. The results are shown in Figures 7, 8 and 9. The modelled values for BOD 5 were, on an average, 49 percent lower than the measured values. The measured values of BOD 5 at the Vrhovo HEPP Dam also included the decomposable organic algae biomass, for which the growth was rather intense, as it was evident from the determination of the concentration of chlorophyll a. The newly originated biologically decomposable algae biomass, originating in the case of intensive algae growth (primary production), is not considered in the model calculation of BOD. Because of this, the calculated values of BOD 5 were lower than the measured values. Besides that, the modelled values for chlorophyll a were, on an average, for 63 percent lower from the measured values. This means that in advantageous conditions for increased algae growth, the model did not respond correctly Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 51 odstotkov nižje od izmerjenih vrednosti. To pomeni, da se model v pogojih, ko nastopijo ugodne razmere za poveč ano rast alg, ki so bili izmerjeni v teh meritvah, ne odziva pravilno s parametri, določ enimi v postopku umerjanja modela. Zadovoljivo ujemanje med izmerjenimi in izrač unanimi koncentracijami klorofila a bi dosegli z izrač uni z 1 0-krat nižjim koeficientom upadanja svetlobe, kot je bil določen z umerjanjem modela. Ker množina klorofila a vpliva na koncentracijo raztopljenega kisika, bi bilo treba izvesti več nadaljnjih serij meritev klorofila a in prodiranja svetlobe v vodno telo s Secchijevim diskom za natanč nejšo določ itev koeficienta upadanja svetlobe (λ), ki ima dominanten vpliv na primarno produkcijo v obravnavani akumulaciji. Kot je razvidno iz slike 8, potrditev modela glede dušikovih spojin ni zadovoljiva. Pri tej meritvi smo imeli na voljo tudi določ itve organskega dušika v nefiltriranih vzorcih voda. Izrač unane koncentracije organskega dušika so v primerjavi z izmerjenimi koncentracijami organskega dušika znatno prenizke. Nasprotno pa so izračunane koncentracije amonija previsoke glede na izmerjene koncentracije v vzorcih voda. Č e pa primerjamo rezultate meritev in rezultate modela za totalni dušik, ki je seštevek vseh nastopajočih dušikovih komponent v dušikovem ciklu, vidimo, da so razlike zanemarljive. To pomeni, da parametri, določ eni v fazi umerjanja modela, ki so dominantni za pretvorbo ene oblike dušika v drugo v vodnem telesu, niso ustrezni za novo neodvisno serijo meritev. Iz navedenega lahko zaključimo, da je za umerjanje tako kompleksnega sistema potrebno več neodvisnih serij meritev, ali pa se celo vrednosti parametrov č asovno spreminjajo po do zdaj še neznani zakonitosti. Glede na primerjavo rezultatov meritev in rezultatov modela za ortofosfat in organski fosfor, ki so grafič no prikazani na sliki 9, ugotavljamo, da potrditev modela z neodvisno serijo meritev za ti dve spremenljivki ni kvantitativno zadovoljiva, čeprav se with the parameters determined in the procedure of the model calibration. Satisfactory agreement between the measured and the calculated chlorophyll a concentrations would be reached with calculations with 10 times lower light extinction coefficient (λ) than was determined by the model calibration. Because the quantity of chlorophyll a influences the dissolved oxygen concentration, more additional sets of measurements of chlorophyll a and the penetration of light in the body of water with a Secchi Discus for more precise determination of the light extinction coefficient (λ), which has dominant influence on primary production in the impoundment, have to be performed. As is evident from Figure 8, the model validation was not satisfactory in the case of nitrogen compounds. At this set of measurements, the determination of organic nitrogen in the water samples was also available. The calculated concentrations of organic nitrogen were considerably too low compared to the measured concentrations. On the other hand, the calculated ammonium concentrations were too high compared to the measured concentrations in the water samples. If the measured and the modelled results for total nitrogen (sum of all nitrogen components in the nitrogen cycle) are compared, the differences are negligible. This means that model parameters defined in the model calibration, which are dominant for the conversion of nitrogen from one form to another in the body of water, were not appropriate for another independent set of measurements. It can be concluded that for the calibration of such a complex system, more series of independent measurements are needed, or that even the values of the model parameters change in time. The measured concentrations of orthophosphate and organic phosphorus compared to the modelled results are shown in Figure 9. It was discovered that the model validation with an independent set of measurements for these two variables was not quantitatively satisfactory, although the qualitative response was correct. With regard to the stated results of the model validation, the following can be concluded: A.The first part of the calculations for the model validation was performed with a set Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 52 kvalitativno pravilno odziva. Glede na navedene rezultate lahko za potrditev modela podamo naslednje ugotovitve: A. Prvi del izrač unov za potrditev modela je bil izveden z meritvami, ki pripadajo seriji meritev, s katero je bil model umerjen. Potrditev modela je bila zadovoljiva za vse rač unane spremenljivke, razen za ortofosfat in organski fosfor. Domnevamo, da je razlog za odstopanja med izmerjenimi in izračunanimi koncentracijami teh dveh spremenljivk sistemska napaka. Poleg tega smo pri modelnih izrač unih za fosforjevi komponenti opazili, da z izračuni ni mogoče dobiti pravilnih rezultatov za kratkotrajno izrazito poveč ano onesnaženje s fosforjevimi spojinami na vhodu v akumulacijo. Maksimumi v onesnaženju se vzdolž toka v zajezitvi zmanjšajo zaradi vzdolžne disperzije, adsorpcije na mikroorganizme oziroma zaradi fizikalnih in biokemijskih pretvorb raztopljenega, koloidnega in adsorbiranega fosforja v partikularni fosfor. B. Drugi del izrač unov za potrditev modela je bil izveden z neodvisno serijo meritev, ki je potekala v bistveno drugač nih pogojih. Dobljeni rezultati so bili veliko slabši kot v prvem delu. Potrditev je kvantitativno ustrezna le za kisik, za vse druge rač unane spremenljivke pa ni ustrezna. Razlogov za neuspešno potrditev modela je lahko več : − Premalo podatkov za kakovostno umerjanje modela. Za natančnejše kvantitativno modeliranje parametrov kakovosti Save v zajezitvi HE Vrhovo bi bilo treba izvesti natanč nejše umerjanje modela. Za to bi bilo nedvomno potrebnih več serij kakovostnih meritev v hidroloških in meteoroloških pogojih, za katere naj bi se z umerjenim modelom napovedovale spremembe kakovosti Save v akumulacijskem jezeru HE Vrhovo. − QUAL2E je enodimenzionalni model, ki of measurements which belonged to the same measurement campaign from which a different set of measurements was used for the model calibration. The model validation was satisfactory for all the calculated variables with the exception of orthophosphate and organic phosphorus. We believe that the reason for the differences between the measured and the calculated concentrations of these two variables is a systematic error. Besides that, at the model calculations for the phosphorus constituents, it was noticed that with the calculations it was not possible to obtain correct results for short-lived, markedly enlarged pollution, with phosphorus compounds at the inflow into the impoundment. Maximums in the pollution were reduced along the flow in the impoundment because of longitudinal dispersion, adsorption on microorganisms or because of the physical and biochemical transformations of dissolved, colloidal and adsorbed phosphorus into particulate phosphorus. B. The second part of the calculations for the model validation was performed with an independent set of measurements, which were performed under essentially different conditions. The results were much worse than in the first part. The validation was quantitatively suitable for dissolved oxygen only; for all other simulated variables it was not suitable. To find the possible reasons for poor performance, we checked the data, the analytical procedures, the model assumptions and the model concepts. We ended up with this list of possible reasons for the relatively unsuccessful model validation: − Not enough data for quality model calibration. For a more accurate quantitative modelling of water quality parameters in the Vrhovo Impoundment, more accurate model calibration will have to be done. For this purpose, it would undoubtedly be necessary to perform more series of quality measurements in different hydrological and meteorological conditions, for which the calibrated model has to be used for the prediction of the change in water quality of the Sava River in the impoundment. − QUAL2E is a 1D (one-dimensional) model, Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 53 zahteva, da so glavni transportni mehanizmi značilni vzdolž glavne smeri toka. Hidrodinamika modela ima pri transportu snovi in snovnih pretvorbah velik pomen. V poletnem č asu so bili v akumulacijskem jezeru HE Vrhovo izmerjeni horizontalni in vertikalni temperaturni gradienti, kar pomeni, da bi morala biti hidrodinamika modela zajeta vsaj z dvodimenzionalnim ali celo tridimenzionalnim modelom. − Meritve v zajezitvi kažejo, da se zgornji sloji vode č ez dan moč neje segrejejo kot spodnji. Prav tako meritve parametrov kakovosti voda v poletnem obdobju kažejo na njihovo različno horizontalno in vertikalno razporeditev. Torej ne gre za popolno premešanost polutantov v preč nih profilih. Navedene ugotovitve kažejo, da bi bilo treba v modeliranje parametrov kakovosti vode v zajezitvi vključ iti vsaj še vertikalno dimenzijo. To pomeni, da bi bilo treba kakovost vode v zajezitvi modelirati z dvodimenzionalnim modelom. − Srednja vrednost energije globalnega sonč nega obsevanja za Slovenijo za povsem jasen dan v avgustu znaša 564 ly. Model pa dovoljuje za vrednost srednje dnevne energije globalnega sonč nega obsevanja vnos maksimalne vrednosti 400 ly, kar pomeni, da smo bili prisiljeni izvesti izrač une s to vrednostjo. − Med parametri modela ima prevladujoč vpliv na primarno produkcijo, izmerjeno kot klorofil a, v obravnavani akumulaciji, koeficient upadanja svetlobe (λ). Zato bi bilo treba za natančnejšo določ itev koeficienta upadanja svetlobe v akumulaciji izvesti več nadaljnjih serij meritev prodiranja svetlobe v vodno telo s Secchijevim diskom in določ itev klorofila a. − Model v izrač unu biokemijske potrebe po kisiku ne upošteva novonastale biološko razgradljive biomase alg. Zato so z modelom izrač unane BPK 5 nižje od izmerjenih vrednosti. which assumes that the major transport mechanisms are significant only along the main direction of flow. The hydrodynamics of the model is of vital importance for pollution transport and transformation. In the summer period, horizontal and vertical temperature gradients were measured in the Vrhovo Impoundment. This means that the hydrodynamics of the model must be modelled with, at least, a two-dimensional model or even a three-dimensional model. − The measurements in the impoundment showed that during the day the upper water layers heated up more than the lower ones. In the same way, the measurements of water quality variables in the summer period also showed non-homogeneous horizontal and vertical distribution. This means that we do deal with a complete mix of pollutants in the cross sections. This finding again points out that 1D model (in the longitudinal direction) is not appropriate. Thus, at least the vertical dimension has to be included in the modelling of water quality parameters, which means that water quality in the impoundment has to be modelled with (at least) a two-dimensional model. − The average daily solar radiation for an absolutely sunny August day in Slovenia is 564 ly. The maximal input value for average daily solar radiation allowed by the model is 400 ly, which means that calculations were performed with this truncated value, instead with the true one. − Among the model parameters, there is the extinction coefficient (λ), which has the most dominant influence on the system behaviour in the Vrhovo Impoundment (e.g. observed primary production, measured as chlorophyll a). Therefore, more additional sets of measurements of chlorophyll a and the penetration of light in the body of water using a Secchi Discus have to be performed for a more precise determination of the light extinction coefficient (λ) in the impoundment. – The newly originated biologically decomposable algae biomass is not considered in the model calculation of BOD. Because of this, the calculated values of BOD 5 were lower than the measured values Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 54 Slika 7. Primerjava z modelom izrač unanih vrednosti BPK 5 , O 2 in klorofila a z meritvami na pregradi HE Vrhovo. Figure 7. Modelled BOD 5 , O 2 and chlorophyll-a as compared to the measured values at the Vrhovo HEPP Dam. Primerjava modeliranih in izmerjenih vrednosti za BPK 5 , O 2 in klorofil a Modelled versus measured BOD 5 , O 2 and chlorophyll a 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 01234567 Vzorec / Sample klorofil a / chlorophyll a [mg/l] izmerjen / measured BOD 5 modeliran / modelled BOD 5 izmerjen / measured O 2 modeliran / modelled O 2 izmerjen / measured chl a modeliran / modelled chl a O 2 [mg(O 2 )/l], BPK 5 / BOD 5 [mg(O 2 )/l] Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 55 Slika 8. Primerjava z modelom izrač unanih vrednosti + 4 NH , − 2 NO in − 3 NO z meritvami na pregradi HE Vrhovo. Figure 8. Modelled + 4 NH , − 2 NO and − 3 NO as compared to the measured values at the Vrhovo HEPP Dam. Primerjava modeliranih in izmerjenih vrednosti za NH 4 + , NO 2 - in NO 3 - Modelled versus measured NH 4 + , NO 2 - and NO 3 - 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 01234567 Vzorec / Sample NO 2 - [mg(N)/l] 0.00 0.50 1.00 1.50 2.00 2.50 izmerjen / measured NH 4 + modeliran / modelled NH 4 + izmerjen / measured NO 2 - modeliran / modelled NO 2 - izmerjen / measured NO 3 - modeliran / modelled NO 3 - NH 4 + [mg(N)/l] NO 3 - [mg(N)/l] Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 56 Slika 9. Primerjava z modelom izrač unanih vrednosti orto-PO 4 3- in org-P z meritvami na pregradi HE Vrhovo. Figure 9. Modelled ortho-PO 4 3- and org-P as compared to the measured values at the Vrhovo HEPP Dam. Primerjava modeliranih in izmerjenih vrednosti za orto-PO 4 3- in org. P Modelled versus measured ortho-PO 4 3- and org. P 0.00 0.20 0.40 0.60 0.80 1.00 01234567 Vzorec / Sample 0.00 0.02 0.04 0.06 0.08 0.10 org. P [mg(P)/l] izmerjen orto-PO 4 3- / measured ortho-PO 4 3- modeliran orto-PO 4 3- / modelled ortho-PO 4 3- izmerjen org.-P / measured org.-P modeliran org.-P / modelled org.-P orto-PO 4 3- / ortho-PO 4 3- [mg(P)/l] Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 57 4.8 NAPOVED KAKOVOSTNIH SPREMEMB SAVE V AKUMULACIJI HE VRHOVO Kvantitativno napoved kakovostnih sprememb Save v akumulaciji HE Vrhovo smo izvedli le za raztopljeni kisik in BPK 5 . Vedeti pa moramo, da z modelom izrač unane vrednosti BPK 5 ne vključ ujejo novonastale biološko razgradljive biomase alg v primeru intenzivne rasti alg v akumulaciji. S tem povzroč ena dodatna poraba po kisiku je vključ ena v modelu v določ itvi raztopljenega kisika, potrebnega za respiracijo alg. Model torej privzema le zunanji vnos BPK 5 , medtem ko so zunanji in notranji viri potrebe po raztopljenemu kisiku pravilno definirani v izrazu za raztopljeni kisik. Napoved smo izvedli za ekstremne in povpreč ne hidrološke pogoje, in sicer za najmanjši nizki pretok v obdobju (simulacija A), srednji nizki pretok v obdobju (simulacija B) in največji nizki pretok v obdobju (simulacija C). Vhodna podatka za O 2 in BPK 5 pa sta iz naših meritev v letu 1998. 4.8 PREDICTION OF WATER QUALITY CHANGES IN THE VRHOVO IMPOUNDMENT Quantitative water quality prediction of the Sava River in the Vrhovo Impoundment was performed only for DO and BOD 5 . It has to be pointed out that the BOD 5 values calculated by the model do not include newly grown decomposable algae biomass, which could be a serious systematic error (compared to the measurements) in the case of intensive algae growth (eutrophication). Instead, this additional oxygen consumption is included in the determination of the DO in the impoundment. Thus, the model assumes the BOD 5 only as the external load, while all external and internal loads are properly conceptualised in the DO term. The predictions were performed for extreme and average hydrological conditions, i.e.: for the minimal low discharge within a period (simulation A), the average low discharge within a period (simulation B) and the maximal low discharge within a period (simulation C). The input data for DO and BOD 5 are from the measurements in 1998. Preglednica 5. Primerjava izmerjenih vhodnih podatkov v Suhadolu in rezultatov modela na pregradi HE Vrhovo. Table 5. Measured input data in Suhadol as compared to the modelled results at the Vrhovo HEPP Dam. Simulacija Q [m 3 /s] Σt [h] O 2 [mg(O 2 )/l] BPK 5 [mg(O 2 )/l] BOD 5 Simulation Input Input Izrač un Computation Input Input Izrač un Computation A 39,7 54,6 8,53 7,70 2,54 1,00 B 58,8 37,4 8,53 7,82 2,54 1,30 C 84,0 27,1 8,53 7,91 2,54 1,55 Kljub temu, da z modelom ne moremo izvesti kvantitativne napovedi za vse načrtovane parametre kakovosti voda, z izrač unom spremembe koncentracije kisika v akumulaciji dobimo podatek o spremembi odloč ilnega parametra za presojo kakovostnih sprememb reke Save. Rezultati izvedenih In spite of the fact that, due to the unfavourable validation results, quantitative predictions by the model cannot have been reliably done for all the planned water quality parameters, an approximate information on the changes of the most critical variables for the estimation of the quality changes in the Sava River was obtained with the calculation of Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 58 izrač unov so podani v preglednici 5. Vsebnost raztopljenega kisika se najbolj zmanjša pri najmanjšem nizkem obdobnem pretoku, kjer znaša zmanjšanje 0,83 mg(O 2 )/l. Pri tem pretoku se tudi najbolj zniža organsko onesnaženje, izraženo kot BPK 5 , znižanje znaša 1,54 mg(O 2 )/l. Pri več jih pretokih je znižanje koncentracije kisika in BPK 5 še manjše. Manjše zmanjšanje BPK 5 je pri več jih pretokih posledica hitrejšega toka vode in s tem krajšega zadrževalnega č asa opazovanega onesnaženja med vhodnim in izhodnim profilom. Na sliki 10 je prikazano z modelom izrač unano spreminjanje koncentracij kisika in BPK 5 vzdolž toka v akumulaciji, kjer je opazen vpliv vtoka Savinje v Zidanem Mostu. dissolved oxygen concentrations in the impoundment. The results of the calculations are given in Table 5. The concentration of the dissolved oxygen was reduced most at the minimal low period discharge, where the reduction reached 0.83 mg(O 2 )/l. Organic pollution expressed as BOD 5 was also reduced, the most at this discharge. The reduction of DO and BOD 5 was smaller for the larger discharges. Of course, the smaller BOD 5 reduction at the larger discharges was a consequence of faster stream current and the resulting shorter retention time of the observed element between the input and the output profile. The changing of DO and BOD 5 along the flow in the impoundment calculated with the model is shown in Figure 10. Here the influence of the inflow of the Savinja River in Zidani Most is noticeable. Napoved A z modelom Simulation A with the model 0 0.5 1 1.5 2 2.5 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 Stacionaža / distance [km] BPK 5 / BOD 5 [mg(O 2 )/l] 7.5 7.75 8 8.25 8.5 8.75 9 O 2 [mg(O 2) /l] BPK5 (mg O2/l) O2 (mg O2/l) Slika 1 0. Z modelom izrač unano spreminjanje koncentracije kisika in BPK 5 vzdolž toka v akumulaciji HE Vrhovo za pretok 39,7 m 3 /s. Figure 10. Changing of DO and BOD 5 along the flow in the impoundment calculated with the model for the discharge of 39.7 m 3 /s. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 59 Oceno kakovostnih sprememb Save v akumulacijskem jezeru lahko poenostavljeno podamo tudi na podlagi enodnevnih meritev, izvedenih avgusta 1998 v stabilnih razmerah pri visokih temperaturah vode in nizkih pretokih. Rezultati meritev so podani v magistrski nalogi (Cvitanič , 1 998). Voda se je od Suhadola do pregrade HE Vrhovo segrela v zgornji 0,5-metrski plasti za približno 2,8°C. Č e pa upoštevamo povpreč no temperaturo vode, izmerjeno v vertikali na preč nem prerezu most Vrhovo, ki znaša 21,4 °C, pa znaša povišanje temperature vode 2,4°C. Vsebnost raztopljenega kisika se v akumulaciji zmanjša. Izmerjeno zmanjšanje koncentracije kisika vzdolž toka Save znaša od 0,38 mg(O 2 )/l do 1,6 mg(O 2 )/l. Organsko onesnaženje, izraženo kot BPK 5 , se vzdolž toka poveč a, ob upoštevanju, da meritev BPK 5 na pregradi vključuje dodatno organsko onesnaženje zaradi intenzivne rasti alg. Koncentracija amonija se vzdolž toka nekoliko zmanjša, enako velja za nitrit in nitrat. Nasprotno pa se vsebnost ortofosfata v akumulaciji poveč a. V akumulaciji izmerjena koncentracija klorofila a na globini 0,5 m znaša 15 µ g/l, kar kaže na intenzivno primarno produkcijo v akumulaciji. Zaključ imo lahko, da je na obravnavanem odseku Save prisotnih dovolj hranil za nastop evtrofikacije, ki pa se ne pojavlja v takšnem obsegu, da bi povzroč ala več je težave, ker so zadrževalni časi zaradi pretočnega tipa akumulacije prekratki. Največji izrač unan zadrževalni č as vode v zajezitvi pri pretoku 39,7 m 3 /s znaša 54,6 h (2,28 dni), rast alg pa je največja pri daljših zadrževalnih č asih, približno od 3 do 20 dni. Z ekološkega vidika je najbolj kritična posledica evtrofikacije zmanjšanje koncentracije kisika, posebno v več jih globinah akumulacije, kot posledica razgradnje odmrlih alg. Vendar je iz meritev razvidno, da je na dnu akumulacije koncentracija kisika 5,3 mg(O 2 )/l. V zajetem vzorcu vode v akumulaciji so bile zastopane vrste rastlinskega planktona, ki hitro izkoristijo The estimation of the water quality changes of the Sava River in the impoundment can be given in a simplified form on the basis of one- day measurements performed in August, 1998 in stable conditions at high water temperature and low discharges. The results of the measurements are given in the Master’s Thesis (Cvitanič , 1 998). From Suhadol to the Vrhovo HEPP Dam, the upper 0,5 meter of the water layer was heated by approximately 2.8°C. However, if we consider the average water temperature, measured in the vertical at the cross sectional profile of the Vrhovo Bridge (21.4°C), the increase of the water temperature reached 2.4°C. The dissolved oxygen concentration in the impoundment was reduced. The measured reduction of the dissolved oxygen concentration along the flow of the Sava River was between 0.38 mg(O 2 )/l and 1.6 mg(O 2 )/l. Organic pollution, expressed as BOD 5 , increased along the flow, considering that the measured BOD 5 at the Vrhovo HEPP Dam included additional organic pollution because of the intensive algae growth. The concentration of ammonium was slightly reduced along the flow; the same holds true for nitrite and nitrate. On the other hand, the concentration of orthophosphate in the impoundment was increased. The measured concentration of chlorophyll a at a depth of 0.5 m reached 15 µ g/l, which indicates intensive primary production in the impoundment. It can be concluded that there were enough nutrients present at the treated section of the Sava River for the entrophication to appear. But it did not appear to such an extent that it would cause greater problems, as the retention times in the impoundment were too short. The largest retention time in the impoundment at a discharge of 39.7 m 3 /s was 54.6 h (2.28 days), but the growth of algae was the greatest at longer retention times, between approximately 3 and 20 days. From the ecological point of view, the most critical consequence of eutrophication is the decrease in oxygen concentration, particularly in the deeper parts of the impoundment. The decrease is the consequence of algae decomposition. However, from the measurements, it is clear that at the bottom of the impoundment the dissolved oxygen concentration was 5,3 mg(O 2 )/l. The species of phytoplankton, which Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 60 ugodne razmere za svoj razvoj. V akumulaciji HE Vrhovo se glede na izvedene modelne izračune in terenske meritve, v pogojih, ugodnih za nastop intenzivne primarne produkcije, za zdaj ne pojavljajo zmanjšanja v koncentraciji raztopljenega kisika, ki bi bila skrb zbujajoč a ali problematič na. Jasno pa je, da lahko v poletnem času, ko nastopijo visoke temperature vode in nizki pretoki, prič akujemo intenzivno primarno produkcijo alg v akumulaciji. Posledica tega je sekundarna polucija, ki se odraža v upadanju koncentracije kisika v vodi in v poveč ani biokemijski potrebi po kisiku. Treba pa bi bilo prouč iti vpliv teh procesov na parametre kakovosti voda v predvidenih zajezitvah vzdolž toka Save, še posebej, ker se predvidene zajezitve sklenjeno nadaljujejo od stopnje do stopnje. To pomeni manjšo reaeracijsko sposobnost vode, usedanje odmrlih alg in makrofitov na dno akumulacij in s tem povzročanje nizkih vrednosti raztopljenega kisika v večjih globinah akumulacij. Pri višjih pretokih in s tem krajših zadrževalnih časih vode v akumulaciji izostanejo pogoji za povečano primarno produkcijo. Znižanje koncentracije kisika je neznatno, pokaže pa se vpliv akumulacije na redukcijo BPK 5 , kar pomeni pozitiven prispevek k povečanju samoč istilne sposobnosti vodotoka. Izvedeni izrač uni z modelom kažejo, da se organsko onesnaženje v akumulaciji, izraženo kot BPK 5 , pri pretoku 39,7 m 3 /s zmanjša za 1,54 mg(O 2 )/l, kar je ekvivalentno č istilni napravi za skoraj 90.000 populacijskih enot (ena populacijska enota pomeni obremenitev 60 g BPK 5 /dan). Pri pretoku 58,8 m 3 /s je zmanjšanje BPK 5 ekvivalentno čistilni napravi za 1 05.000 populacijskih enot, pri pretoku 84,0 m 3 /s pa je zmanjšanje BPK 5 ekvivalentno č istilni napravi za skoraj 120.000 populacijskih enot. rapidly take advantage of good conditions, were present in the water sample from the impoundment. With regard to the model results and field measurements achieved at low discharges and in conditions of intensive primary production in the dam, it can be concluded that an excessive decrease of dissolved oxygen concentration, which can have a negative influence on the impounded water quality, did not appear in the Vrhovo Impoundment. Nevertheless, it is clear that in the summer time, when the water temperature is high and the discharges are low, intensive primary algae production can be expected. The consequence of this is secondary pollution, which is reflected in the decreased oxygen concentration and in an increased value of BOD. The influence of these processes on the water quality parameters in the foreseen impoundments along the Sava River have to be investigated, especially because the levels of each HEPP was chosen in such manner that the levels of the impoundments continue from one stage to another. This means a smaller reaeration capacity of water, a settling of the macrophytes and algae which died off on the bottom of the impoundment, and this causes low dissolved oxygen concentrations in the deeper parts of the impoundments. At higher discharges and shorter retention times of the water in the impoundment, the conditions for increased primary production cannot fully develop. Thus, the decrease of DO is minimal, while the influence on the BOD 5 reduction can still be seen. This is a positive contribution to river's self-purification capacity. From the model calculations, it can be seen that the organic pollution, expressed as BOD 5 , at a discharge of 39.7 m 3 /s was reduced by 1.54 mg(O 2 )/l. This was equivalent to a wastewater treatment plant of almost 90.000 PE (one population equivalent, PE, is the load of one person per day, and is 60 g BOD 5 /day). At a discharge of 58.8 m 3 /s the reduction of BOD 5 was equivalent to a wastewater treatment plant of 105.000 PE, and at a discharge of 84.0 m 3 /s, the reduction of BOD 5 was equivalent to a wastewater treatment plant of nearly 120,000 PE. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 61 5. ZAKLJUČ KI Matematični modeli kakovosti voda omogoč ajo napoved sprememb kakovosti voda zaradi nač rtovanih posegov v vodni režim, prouč evanje vplivov zunanjih in notranjih virov onesnaženja na kakovost voda, simuliranje možnih strategij gospodarjenja z vodnim bogastvom, izboljšanje razumevanja sistemov in določ itev nedostopnih vhodnih podatkov iz merjenih izhodnih podatkov. Za analizo možnih kakovostnih sprememb reke Save v akumulaciji HE Vrhovo, ki je nastala z zajezitvijo Save avgusta 1994, smo uporabili večparametrski enodimenzionalni model Qual2E. Enodimenzionalni model smo uporabili ob predpostavki, da lahko dolge, ozke zajezitve obravnavamo na enak nač in kot nezajezene vodotoke, to je s popolno vertikalno in horizontalno premešanostjo polutantov v preč nih profilih. Model vsebuje veliko število parametrov, ki smo jih morali zaradi pomanjkanja izmerjenih vrednosti oceniti z umerjanjem modela. Interval vrednosti parametrov smo povzeli po literaturi. Pred umerjanjem modela smo izvedli analizo obč utljivosti modela. S tem smo dobili vpogled v naravo modela in v možnosti za umerjanje modela. Ugotovili smo smiselno odzivanje rezultatov modela na spreminjanje posameznih parametrov. Preverjanje modela, izvedeno istoč asno z umerjanjem modela, je potrdilo kvalitativno ujemanje modela z realnim stanjem. Modeli so poenostavitve procesov v naravi in ponavadi vključujejo vse pomembne procese ter komponente obravnavanega problema, toda prezrte podrobnosti imajo lahko vpliv na konč ni rezultat. Te vplive lahko do določ ene mere upoštevamo s pravilno določitvijo parametrov modela v fazi umerjanja modela. Umerjanje uporabljenega modela, ki naj bi potrdilo še kvantitativno ujemanje modela z realnim stanjem, je bilo ob danih možnostih uspešno zaključ eno. Vzroke za večje razlike med izračunanimi in izmerjenimi vrednostmi, ki so se pojavile pri amoniju in organskem fosforju, in katerih s 5. CONCLUSIONS Mathematical water quality models make it possible to predict changes in water quality due to the planned interventions in the water regime, investigate the impacts of external and internal sources of pollution on water quality, simulate the possible strategies of water resource management, improve the understanding of systems and to define unapproachable input data from the measured output data. The river impoundment on the Sava River emerged after the construction of the Vrhovo Hydroelectric Power Plant (HEPP). A multiparametric one-dimensional QUAL2E model was used to analyse and predict possible changes of the water quality in the Sava River in the formed impoundment. The one dimensional model was used on the presumption that long narrow impoundments can be treated in the same way as unimpounded streams, i.e.: with the complete vertical and horizontal mixing of pollution in the cross-sectional profiles. The model contains a large number of model parameters. Due to the lack of measured values, these model parameters had to be estimated by calibrating the model. The usual range of values was taken from literature. Before the model calibration, a sensitivity analysis was performed. In this way we obtained insight into the model operation and the possibilities for its calibration. We established a logical response of the model results to changes in the values of a single parameter. The model verification was performed simultaneously with the model calibration. Qualitative agreement of the model with the real state was confirmed. Models are a simplification of processes in nature and they usually include all the important processes and components of the treated problems. However, some overlooked details could have an impact on the final result. Such impacts could be considered, to a certain extent, with the correct determination of the model parameters in the model calibration phase. It was concluded that the calibration of the model, which has to also confirm the quantitative agreement of the model with the real state, regarding the given input (measured) data, was successfully Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 62 spreminjanjem parametrov v danem intervalu nismo uspeli zmanjšati, bi bilo treba raziskati z nadaljnjimi kakovostnimi in nač rtnimi meritvami v akumulacijskem jezeru HE Vrhovo. Druga faza izvedene potrditve modela z neodvisno serijo meritev v spremenjenih pogojih v akumulaciji pa ni dala povsem zadovoljivih rezultatov. Primerjava izrač unov modela z izmerjenimi vrednostmi je pokazala ustrezno kvantitativno ujemanje le za raztopljeni kisik. Ujemanje za druge spremenljivke je bilo slabše. Ker nobene od naštetih komponent v danem č asu ni bilo mogoč e bistveno izboljšati, smo se zadovoljili s sedanjo stopnjo toč nosti modela. Z modelom smo izvedli kvantitativno napoved sprememb Save v zajezitvi za ekstremne in povpreč ne hidrološke pogoje za raztopljeni kisik in biokemijsko potrebo po kisiku. Ugotovili smo, da je znižanje koncentracije kisika največje pri najmanjšem nizkem pretoku obdobja in znaša 0,83 mg(O 2 )/l. Glede na rezultate modela in terenske meritve, izvedene pri nizkih pretokih in pogojih poteka intenzivne primarne produkcije v zajezitvi, lahko zaključ imo, da v akumulacijskem jezeru HE Vrhovo ne prihaja do prekomernega znižanja koncentracije raztopljenega kisika, ki bi povzroč ala negativne vplive na kakovost zajezene vode. V danem primeru gre v zajezitvi predvsem za spremembe, ki vplivajo na rekreacijsko vrednost vode, na biocenozo vode ter uporabnost vode v tehnološke in druge namene. Spremembe biocenoze so predvsem posledica spremenjenih fizikalnih lastnosti vodnega toka, na katere po zajezitvi ni mogoč e vplivati. Zato lahko na biocenozo in uporabnost zajezene reč ne vode vplivamo samo z obvladovanjem parametrov kakovosti voda, ki so v celoti posledica zunanje (toč kovne, disperzne) in notranje polucije zajezene vode. Naše nadaljnje delo bi moralo biti usmerjeno v odpravo pomanjkljivosti, s katerimi smo se sreč ali pri dosedanjem delu. Pri tem se po eni strani kaže potreba po accomplished. The reasons for the greater differences between the calculated and the measured values of ammonium and organic phosphorus, which could not have been reduced by only varying the parameters, have to be researched with additional quality and systematic measurements in the Vrhovo Impoundment The second phase of the model validation was performed using an independent set of measurements, which were performed in the changed conditions in the impoundment. The results were not satisfying. The comparison of the modelled results and the measured values showed suitable quantitative agreement only for dissolved oxygen. The agreement for all other simulated variables was inadequate. Since it was not possible to essentially improve any of the listed components in the given time, we accepted the present accuracy of the model. The quantitative water quality prediction of changes of the Sava River at the Vrhovo Impoundment was performed for extreme and average hydrological conditions for dissolved oxygen and biochemical oxygen demand. We established that the concentration of the dissolved oxygen was reduced the most at a minimal low period discharge where the reduction reached 0.83 mg(O 2 )/l. With regard to the model results and the field measurements achieved at low discharges and under conditions of intensive primary production in the dam, it can be concluded that an excessive decrease in the concentration of dissolved oxygen, which could have a negative influence on the impounded water quality, does not appear in the Vrhovo Impoundment. In the given case, the changes which influenced the recreational value of the water, the water biocenosis and the applicability of water for technological and other purposes took place in the impoundment. The changes in biocenosis were, in the first place, the consequence of the changed physical properties of the stream current, which can not be influenced after the impoundment. For this reason, we can influence the biocenosis and the applicability of the impounded river water only by controlling the water quality parameters, which were, as a whole, the consequence of the external (point sources, dispersed sources) and internal pollution of the impounded water. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 63 obsežnejših terenskih meritvah in kakovostnih laboratorijskih analizah vzorcev, po drugi strani pa so potrebne tudi izboljšave matematič nega modela oziroma prehod na vsaj dvodimenzionalni model. Pri modeliranju kakovosti voda se lahko s pravilno opravljenimi in s popolnejšimi meritvami ter z laboratorijskimi analizami izognemo mnogim dilemam in potrebi, da določ ene parametre modela, ki jih je mogoč e izmeriti, računamo ali privzemamo iz literature. Predvsem pa je v prvi vrsti treba vedeti, kaj želimo z modeliranjem doseč i. Č e je namen izrač unov modela napoved kritič nih razmer v poletnih razmerah, bodo vse nadaljnje meritve usmerjene na ta č as in je smiselno, da se z izvajanjem kakovostnih meritev pridobi čim več informacij o dogajanju v akumulacijskem jezeru. Temeljni cilj nadaljnjih terenskih meritev mora biti pridobitev natančnih vhodnih podatkov oziroma pridobitev natančnejših in ustreznejših rezultatov meritev, ki bodo omogoč ile izvedbo natanč nejšega umerjanja modela. Model bi bilo treba dograditi tako, da bi bilo za primer modeliranja zajezitve mogoč e hidravlične lastnosti odsekov opisati geometrič no, vključ no z možnostjo vnosa kot gladin zajezitve, kjer je vsak odsek predstavljen kot trapezoiden kanal. Opis biokemijske potrebe po kisiku v modelu je treba dopolniti tako, da bo v njem vključ en tudi prirast biološko razgradljive biomase alg. Model je treba dopolniti tako, da bo mogoč e za vrednosti srednje dnevne energije globalnega sončnega obsevanja vnesti vrednosti, več je od 400 ly. Č e se bodo pri nadaljnjem umerjanju in potrditvi modela z neodvisnimi serijami meritev še vedno pojavljale več je razlike med izmerjenimi in izračunanimi vrednostmi spremenljivk kakovosti voda, bo treba v modelu parametre, za katere se bo izkazalo, da so problematični, definirati kot funkcijo vplivnih dejavnikov. Our further work must be focused on making up the deficiencies that we encountered in our previous work. On one side, there appeared the need for more extensive field measurements and quality laboratory analyses of the samples; on the other, improvements of the mathematical model or a transition to at least a two dimensional model are required. When modelling water quality, correctly performed and more thorough measurements together with laboratory analyses can help us to avoid many dilemmas and the need to assume from literature or calculate certain model parameters which can be measured. First of all, the goal of our modelling must be noted. If the intention of simulations is the prediction of critical states during summer conditions, all additional measurements will be directed into this time and the purpose of quality measurements will be to acquire as much information on the activities in the impoundment as possible. The main goal of the additional measurements must be the acquisition of accurate input data or the acquisition of more accurate and more appropriate measurement results, which will enable us to elaborate a more accurate model calibration. The model has to be improved in such a manner that it will make it possible to geometrically describe the hydraulic characteristics of the sub-reaches in the impoundment, including the possibility of entering the surface level in the impoundment, where each reach is represented as a trapezoidal channel. The description of BOD in the model has to be completed by also including the newly originated biologically decomposable algae biomass. The model must be completed in such a manner that it will allow the entrance of values greater than 400 ly for the average daily solar radiation. If, in the additional model calibration and validation with independent sets of measurements, there still appears some major differences between the measured and the calculated values of the water quality variables, the model parameters that prove problematical will have to be defined as a function of influential factors. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 64 VIRI REFERENCES Bowie, G.L., Mills, W.B., Donald, B.P., Campbell, C.L., Pagenkopf, J.R., Rupp, G.L., Johnson K.M., Chan, P.W.H., Gherini, S.A. (1985). 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In Metode merjenja in Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 65 obdelave z rač unskimi primeri (Measurements Methods and Analysis with Computational Cases), Bled, April 21-26, 1985, pp.1-46 (in Slovenian). Rismal, M. (1 997a). Prognostič ni modeli omogoč ajo smotrno izrabo in varstvo voda: ekološka problematika energetske zajezitve Save (Prognostic Models Make Suitable Water Usage and Conservation Possible: Ecological Problems Regarding the Energetic Impoundments of the Sava River). Delo 39, No.180, p.7 (in Slovenian). Rismal, M. (1 997b). Poroč ilo o rezultatih meritev kakovostnih sprememb zajezene Save na HE Vrhovo v letih 1995-1997 (A Report on Results of Measurements of Quality Changes in the Impounded Sava River at the Vrhovo HEPP in the Period from 1995 to 1997). University of Ljubljana, Faculty of Civil and Geodetic Engineering, Institute of Sanitary Engineering, Ljubljana (in Slovenian). SEL (1 994). Hidroelektrarne Moste, Mavč ič e, Medvode, Vrhovo (The HEPP’s Moste, Mavč ič e, Medvode, and Vrhovo). Savske elektrarne Ljubljana, Ljubljana (in Slovenian). Sherrod, P.H. (1992). NONLIN, Nonlinear Regression Analysis Program - Manual. Nashville. Streeter, H.W., Phelps, E.B. (1925). A Study of the Pollution and Natural Purification of the Ohio River. U.S. Public Health Service, Washington, DC Bulletin 146. Taub, F.B. (1984). Ecosystems of the World 23; Lakes and Reservoirs. Elsevier Science Publishers B.V., Amsterdam. Venter, S.N., Steynberg, M.C., de Wet, C.M.E., Hohls, D., du Plessis, G., Kfir, R. (1997). A Situational Analysis of the Microbial Water Quality in a Peri-Urban Catchment in South Africa. Water Science Technology 35, No.11-12, pp.119-124. Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 66 Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 67 Publikacije Acta hydrotechnica / Back Volumes of Acta hydrotechnica LETNIK 1 (1983) / VOLUME 1 (1983) št.1 (oktober 1983) / No. 1 (October 1983) Pšenič nik, M. : Razvoj Laboratorija za mehaniko tekoč in in Inštituta za zdravstveno hidrotehniko / Development of the Fluid Mechanics Laboratory and the Institute of Sanitary Hydrotechnics Brilly, M. : Hidrodinamika onesnaženja podzemnih voda, disertacija 25. 4. 1 983 / Hydrodynamics of Groundwater Pollution, Doctoral thesis LETNIK 2 (1984) / VOLUME 2 (1984) št.2 (junij 1984) / No. 2 (June 1984) Rakč ević , S. : Vzporedni izpust kot nadomestilo za zgornje vodostane pri hidroelektrarnah s francisovimi turbinami, disertacija 27.6.1983 / By-pass Valve as Substitute for Upstream Surge Tanks for Hydroelectric Power Plants with Francis Turbines, Doctoral thesis LETNIK 3 (1985) / VOLUME 3 (1985) št. 3 (junij 1985) / No. 3 (June 1985) Steinman, F. : Prispevek k analizi dinamič nih zakonitosti natege, magistrska naloga 24.11 .1 983 / A contribution to Analysis of Dynamic Processes in Air-Regulated Siphons, Master thesis Panjan, J. : Teoretič na analiza vplivov na proces sedimentacije, magistrska naloga 1 7.7.1 984 / Theoretical Analysis of the Influences on the Sedimentation Process, Master thesis 1. izr. št. (junij 1985) / Spec. No. 1 (June 1985) Referati 4. Goljevšč kovega spominskega dne 8.3.1 985 / Proceedings of the 4th Goljevšč ek Memorial Day LETNIK 4 (1986) / VOLUME 4 (1986) 2. izr. št. (junij 1986) / Spec. No. 2 (June 1986) Referati 5. Goljevšč kovega spominskega dne 11 .3.1 986 / Proceedings of the 5th Goljevšč ek Memorial day LETNIK 5 (1987) / VOLUME 5 (1987) št. 4. (december 1987) / No. 4 (December 1987) Kovač ič , I. : Postopna metoda za rač un visokovodnih valov v strugah / Step-by-step Computation Method of Flood Waves in Rivers Petrešin, E. : Analiza obstoječ ih analitič nih izrazov koeficientov hrapavosti s predlogom za izboljšavo v vodovodnem omrežju / Analysis of Existing Analytic Expressions for the Roughness Coefficients with a Proposal for their Improvement Concerning Application in Water Supply Network Pšenič nik, M. : Nova konstrukcija ostnega merila in merske cevke sistema Pitot-Prandtl / New Construction of Point Measuring Device and Pitot-Prandtl Measuring Tube LETNIK 6 (1988) / VOLUME 6 (1988) št. 5 (december 1988) / No. 5 (December 1988) Č etina, M. : Matematič no modeliranje dvodimenzionalnih turbulentnih tokov, magistrska naloga 20.6.1 988 / Mathematical Modelling of Two-Dimensional Turbulent Flows, Master thesis 3. izr.št. (marec 1988) / Spec. No. 3 (March 1988) Referati 7. Goljevšč kovega spominskega dne 11 .3.1 988 / Proceedings of the 7th Goljevšč ek Memorial Day LETNIK 7 (1989) / VOLUME 7 (1989) št. 6 (april 1989) / No. 6 (April 1989) Mikoš, M. : Urejanje hribovskih vodotokov, magistrska naloga 20.6.1988 / Control of Mountain Streams, Master thesis 4. izr. št. (april 1989) / Spec. No. 4 (April 1989) Referati 8. Goljevšč kovega spominskega dne 27.3.1 989 / Proceedings of the 8th Goljevšč ek Memorial Day Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 68 LETNIK 8 (1990) / VOLUME 8 (1990) št. 7 (marec 1990) / No. 7 (March 1990) Gorišek, M. : Simulacija infiltracije padavin v drobnih in grobih peskih s primesmi proda, magistrska naloga 19.7.1989 / Simulation of Infiltration in Coarse and Fine Sands with Gravel, Master thesis Pleško, T. : Endogena respiracija aktivnega blata v procesu č išč enja odpadnih vod v odvisnosti od temperature vode, magistrska naloga 28.9.1989 / Endogenous Respiration of the Activated Sludge in Sewage Treatment Process in Dependence of Water Temperature, Master thesis Krajnc, U. : Prognoza spremembe kvalitete Save v akumulacijskem bazenu HE Vrhovo z matematič nim modelom, magistrska naloga 7.11.1989 / Modeling Changes in the Sava River Water Quality Caused by Impounding Water at the Vrhovo Hydroelectric Power Plant, Master thesis št. 8 (december 1990) (Ob natisu pomotoma označ ena kot št. 7) / No. 8 (December 1990) Č ehovin, I. : Meritve hidrodinamič nih velič in na hidravlič nih modelih, magistrska naloga 7.6.1 990 / Measurement of Hydrodynamic Quantities in Hydraulic Models, Master thesis Marinč ek, M. : Izrač un visokovodnih valov na Savinji s pomoč jo kvazidimenzionalnega matematič nega modela, magistrska naloga 9.5.1990 / Modelling Flood Wave Propagation in the Savinja River Using a Quasi Two-Dimensional Mathematical Model, Master thesis LETNIK 9 (1991) / VOLUME 9 (1991) ni publikacij / no publications LETNIK 10 (1992) / VOLUME 10 (1992) št. 9 (oktober 1992) / No. 9 (October 1992) Smith, M.B. : Uporaba modelov z distribuiranimi parametri pri obrambi urbaniziranih površin pred poplavami, disertacija 4.5.1992 / A Distributed Parameter Hydrologic Model for Urban Stormwater Protection, Doctoral thesis Globevnik, L. : Uporaba GIS-OV pri iskanju optimalnih vodnih virov za namakanje Zgornje Vipavske doline, magistrska naloga 15.5.1992 / The GIS Based Analysis of Optimal Water Resources for Irrigation in the Upper Vipava Valley, Master thesis LETNIK 11 (1993) / VOLUME 11 (1993) št. 10 (november 1993) / No. 10 (November 1993) Mikoš, M. : Fluvialna abrazija prodnatih plavin, disertacija 21.6.1993 / Fluvial Abrasion of Gravel Sediments, Doctoral thesis LETNIK 12 (1994) / VOLUME 12 (1994) št. 11 (maj 1994) / No. 11 (May 1994) Širca, A. : Modeliranje transporta polutantov po metodi sledenja delcev, magistrska naloga 23.12.1992 / Modelling of Pollutant Transport by Particle Tracking Method, Master thesis Kobold, M. : Določ anje minimalnih pretokov vodotokov v Sloveniji po metodologiji FRIEND, magistrska naloga 7.12.1993 / The Low Flow Estimation of Slovene Streams by FRIEND Methodology, Master thesis LETNIK 13 (1995) / VOLUME 13 (1995) ni publikacij / no publications LETNIK 14 (1996) / VOLUME 14 (1996) št. 12 (maj 1996) / No. 12 (May 1996) Zbornik referatov 1 5. Goljevšč kovega spominskega dne 1 4.marec 1 996 / Proceedings of the 1 5th Goljevšč ek Memorial Day št. 13 (maj 1996) / No. 13 (May 1996) Gorišek, M. : Difuzijsko gibanje snovi raztopljenih v vodi skozi porozni prostor iz drobnozrnatih materialov, disertacija 5.6.1995 / Diffusion of Chemical Species Dissolved in Water in Porous Medium of Fine Grain Soils, Doctoral Thesis Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 69 št. 14 (avgust 1996) / No. 14 (August 1996) Širca, A. : Modeliranje hidrodinamike in transporta živosrebrovih spojin v Tržaškem zalivu, disertacija 27.5.1996 / Modelling of Hydrodynamics and of Transport of Mercury Compounds in Trieste Bay, Doctoral Thesis LETNIK 15 (1997) / VOLUME 15 (1997) št. 15 (januar 1997) / No. 15 (January 1997) Krzyk, M. : Dvodimenzijski matematič ni model konvekcijsko-difuzijskega transporta snovi in lebdeč ih plavin v površinskih vodah, magistrska naloga 8.11.1996 / Two-Dimensional Mathematical Model of Convective-Diffusion Transport of Concentration and Suspended Load in Free Surface Flows, Master Thesis št. 16 (april 1997) / No. 16 (April 1997) Panjan, J. : Procesi kosmič enja z vidika usedanja in zgošč evanja suspendiranih delcev pri č išč enju odpadne vode, disertacija 10.3.1994 / Flocculation Process in the Light of Sedimentation and Thickening of Suspended Particles in Waste Water Treatment, Doctoral Thesis št. 17 (julij 1997) / No. 17 (July 1997) Zbornik referatov 1 6. Goljevšč kovega spominskega dne 1 3.marec 1 997 / Proceedings of the 1 6th Goljevšč ek Memorial Day št. 18 (avgust 1997) / No. 18 (August 1997) LOC Proceedings of oral presentations FRIEND’97, Postojna 1 - 4 October 1997, Slovenia / Zbornik referatov Mednarodne konference FRIEND’97, Postojna 1. - 4.oktobra 1997, Slovenija št. 19 (avgust 1997) / No. 19 (August 1997) LOC Proceedings of poster presentations FRIEND’97, Postojna 1 - 4 October 1997, Slovenia / Zbornik posterjev Mednarodne konference FRIEND’97, Postojna 1. - 4.oktobra 1997, Slovenija št. 20 (november 1997) / No. 20 (November 1997) Č enč ur-Curk, B. : Terenski eksperimentalni poligoni kot osnova pri študiju prenosa snovi v nezasič eni kraško-razpoklinski kamnini, magistrska naloga 24.10.1997 / Experimental Field Sites as a Basis for the Study of Solute Transport in the Vadose Zone of Karstified Rock, Master Thesis LETNIK 16 (1998) / VOLUME 16 (1998) št. 21 (marec 1998) / No. 21 (March 1998) Šifrant poreč ja Donave / Danube river basin coding št. 22 (november 1998) / No. 22 (November 1998) Vodopivec, N. : Bilanca hranil, proizvodnje in stabilizacije blata pri različ nih postopkih biološkega č išč enja odpadnih voda, magistrska naloga 30.6.1998 / Nutrient Balances, Sludge Production and Sludge Stabilisation at Different Waste Water Treatment Technologies, Master Thesis št. 23 (december 1998) / No. 23 (December 1998) Zbornik referatov 1 7. Goljevšč kovega spominskega dne 27.marec 1 998 / Proceedings of the 1 7th Goljevšč ek Memorial Day LETNIK 17 (1999) / VOLUME 17 (1999) št. 24 (junij 1999) / No. 24 (June 1999) Umek, T. : Celostno gospodarjenje z vodami na obalnem območ ju, magistrska naloga 1 2.11 .1 998 / Comprehensive Water Management in the Coastal Region, Master Thesis št. 25 (julij 1999) / No. 25 (July 1999) Cvitanič , I. : Analiza možnih kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela, magistrska naloga 28.1 2.1 998 / Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in Average and Extreme Hydrological Conditions with Mathematical Model, Master Thesis Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 70 NAVODILA ZA PRIPRAVO PRISPEVKOV 1. Prispevki za Acta hydrotechnica 1.1 Acta hydrotechnica je znanstveno-strokovna periodič na publikacija, katere izdajatelj in založnik je Univerza v Ljubljani, Hidrotehnič na smer Fakultete za gradbeništvo in geodezijo (FGG), ki jo sestavljajo Katedra za mehaniko tekoč in z laboratorijem (LMTe), Katedra za splošno hidrotehniko (KSH) in Inštitut za zdravstveno hidrotehniko (IZH). Predstavniki omenjenih enot tudi sestavljajo izdajateljski odbor revije. 1.2 Acta hydrotechnica izhaja dvakrat na leto v obliki zaporednih številk, dodatno razvršč enih v letnik. 1.3 Acta hydrotechnica je namenjena objavam prispevkov strokovnjakov in raziskovalcev s področ ja vodarstva in hidrotehnike. Acta hydrotechnica objavlja prispevke s področ ja vodarstva in hidrotehnike v obliki izvirnih in preglednih znanstvenih č lankov, preliminarnih objav in strokovnih č lankov. 1.4 Prispevki so napisani enakovredno v slovenskem in angleškem jeziku, kar zagotavlja ohranjanje in razvijanje slovenskega strokovnega izrazoslovja na področ ju vodarstva in hidrotehnike ter obenem zagotavlja berljivost revije v tujini. Dolžina prispevka je omejena na 30 000 znakov. Dolžina prispevka, ki je povzetek magistrske naloge ali doktorskega dela, je omejena na 100 000 znakov. Prednost pri objavi imajo krajši prispevki. 1.5 Prispevke je treba oddati v elektronski in pisni obliki na uredništvo Acta hydrotechnica. 1.6 Vsi prispevki so oblikovno podvrženi uredniški recenziji v skladu s temi navodili in vsebinsko podvrženi recenziji dveh strokovnjakov s področ ja prispevka. 1.7 Pri oblikovanju prispevkov za Acta hydrotechnica je treba upoštevati slovenske standarde za dokumentacijo in informatiko. 1.8 Za vsebino prispevkov in prevod v angleški jezik odgovarjajo avtorji. 1.9 Vsi prispevki so lektorirani, tako slovensko kakor tudi angleško besedilo. 2. Oblikovanje prispevkov za Acta hydrotechnica 2.1 Vsak prispevek mora biti sestavljen iz naslednjih enot, enakovredno podanih v slovenskem in angleškem jeziku: ! naslov prispevka ! podatki o avtorju ali avtorjih ! izvleč ek (abstract) in ključ ne besede (key-words) ! glavno besedilo ! zahvala (acknowledgements) naroč niku naloge, raziskave ali študije (neobvezno) ! pregled uporabljenih izrazov (terminology) in oznak (notations) (neobvezno) ! viri (references) Njihov natanč nejši opis je podan v naslednjih odstavkih. 2.2 Naslov prispevka naj bo jasen, jedrnat in naj izraža bistvo prispevka. Dolžina naslova je največ 90 znakov, razen ko gre za povzetke magistrskih in doktorskih del, kjer je lahko naslov prispevka enak uradnemu naslovu dela. 2.3 Podatki o avtorju obsegajo ime in priimek, opis znanstvene strokovne stopnje in poln naslov delovnega mesta. 2.4 Vsak prispevek mora spremljati izvleč ek (abstract) v obsegu okoli 1 50 besed v vsakem od obeh jezikov. Izvleč ka morata strnjeno podati celoten prispevek vključ no z zaključ ki. Avtor naj navede do 8 ključ nih besed. 2.5 Glavno besedilo naj bo razdeljeno po decimalnem sistemu (1. PRVO POGLAVJE, 1.1 PRVO PODPOGLAVJE, 1.1.1 Zadnja poddelitev). Vire v besedilu navedemo z imenom avtorja in letnico objave (Manning, 1892), (Strickler & Nikuradse, 1924b), (Einstein et al., 1951), (Colebrook, 1932; 1934). Merske enote naj bodo v skladu z veljavnim sistemom SI. Datum naj bo podan po naslednjem vrstnem redu : dan-mesec-leto (23.4.1998). Cvitanič , I.: Analiza kakovostnih sprememb Save v akumulaciji HE Vrhovo v povpreč nih in ekstremnih hidroloških pogojih s pomoč jo matematič nega modela - Analysis of Possible Quality Changes of the Sava River in the Vrhovo Impoundment in average and extreme Hydrological Condition with Mathematical Model © Acta hydrotechnica 17/25 (1999), 71 p., Ljubljana 71 Kratice in opombe pod č rto naj se uporabljajo le izjemoma. Ilustracije (preglednice in slike) v besedilu naj bodo skozi vse besedilo enotno oštevilč ene z arabskimi številkami in naj se ne okrajšujejo (preglednica 1, slika 14, Table 2, Figure 4). Praviloma mora biti ilustracija dvojezič na. Č e je ilustracija privzeta iz drugega že objavljenega dela, je potrebno ob njenem opisu dodati tudi njen izvor. Enač be v besedilu naj bodo oštevilč ene z arabskimi številkami v okroglih oklepajih enotno skozi vse besedilo, pri daljših prispevkih (več kakor 1 avtorsko polo) lahko tudi enotno za vsako poglavje posebej. Navajanje enač b naj v besedilu ne bo okrajšano (enač ba (11 ), enač ba (2.1 7)). 2.6 V besedilu uporabljeni viri morajo biti navedeni v abecednem vrstnem redu in neoštevilč eno, na koncu prispevka, enotno za oba jezika. Č e je vir pisan v jeziku, ki ni angleški, naj naslovu vira v oklepaju sledi prevod naslova v anglešč ino, na koncu navedbe pa dostavek, v katerem jeziku je pisan, npr. (in Slovenian). Glede na vrsto mora avtor navesti vire takole: ! knjige : Schumm, S.A., Mosley, M.P., Weaver, W.E. (1987). Experimental fluvial geomorphology. Wiley, New York, 413 p. ! posamezne prispevke v knjigi : Large, A.R.G., Petts, G.E. (1994). “Rehabilitation of River Margins” in P. Calow, G.E. Petts, Eds., The Rivers Handbook - Volume 2. Blackwell, Oxford, 401-418. ! diplomska, magistrska in doktorska dela : Širca, A. (1996): Modeliranje hidrodinamike in transporta živosrebrovih spojin v Tržaškem zalivu (Modelling of Hydrodynamics and of Transport of Mercury Compounds in Trieste Bay). Unpublished Doctoral Thesis, Univerza v Ljubljani, FGG, 164 p. (in Slovenian). ! objave, kjer je avtor pravna oseba (skupinski avtor) : VGI (1993). Vodnogospodarski ureditveni nač rt Save Dolinke - idejna zasnova (Water Management Master Plan of the Upper Sava River). VGI, Ljubljana, Report C-161 (in Slovenian). ! č lanke iz zbornika del : Krzyk, M., Pemič , A. (1 995). Primjena vrtložnog prigušivač a u hidrotehnič kim sistemima pod tlakom (Application of Vortex Diode in Pressurised Hydrotechnical Systems). Proceedings of the 1 st Croatian Conference on Waters "Sustainable Developement and Water Management", Dubrovnik, Book 2, 369-376 (in Croatian). ! č lanke iz znanstvene in strokovne revije : Lamouroux, N., Souchon, Y., Herouin, E. (1 995). Predicting velocity frequency distributions in stream reaches, Water Resources Research 31, 2367-2375. ! dela, ki jim ni mogoč e določ iti avtorja : Zakon o varstvu okolja (1 993). Uradni list RS, št. 32, 1234. Environmental Protection Act (in Slovenian).