© Acta hydrotechnica 18/28 (2000), Ljubljana ISSN 1581-0267 41 UDK: 551.311.2 UDC: 551.311.2 Pregledni znanstveni prispevek Scientific paper PROCESNO UTEMELJENO MODELIRANJE EROZIJE TAL PROCESS BASED SOIL EROSION MODELLING Gregor Petkovšek Č lanek podaja pregled procesno utemeljenih metod za modeliranje erozije tal. V uvodu so podani zgodovina in razlogi za modeliranje erozije tal na področ jih kmetijstva in gradbeništva. Nato sledi pregled procesov erozije, konceptov modeliranja in enač b. Opisani so procesi žlebič ne in medžlebič ne erozije, pljuskovna erozija, sprošč anje in premešč anje površinskega toka in toka v žlebič ih ter nastanek kanalskega toka. Razloženi so medsebojni vplivi med posameznimi procesi in matematič na formulacija teh vplivov. V nadaljevanju so predstavljene in komentirane tradicionalne metode napovedovanja sprošč anja zemljin, kot sta USLE in Gavrilović eva enač ba. V poglavju o modernih metodah pa so predstavljeni trije novejši procesno utemeljeni modeli: ameriški WEPP, nizozemski LISEM in avstralski model TOPOG. Pri vsakem je poudrajena struktura modela ter procesi, vključ eni v model. Opisan je tudi namen in možnosti uporabe. Ključne besede: erozija tal, odplavljanje, procesno utemeljeno modeliranje, modeli s porazdeljenimi spremenljivkami. The paper presents an overview of process based methods for soil erosion modelling. In the introduction, the history and the reasons for soil erosion modelling in the fields of agriculture and civil engineering are given. Then an overview of erosion processes, modelling concepts and equations follow. The processes of rill and interrill erosion, splash erosion, detachment and transport capacity of overland and rill flow, and channel initiation are described. The interrelations between the processes and the corresponding mathematical formulations are explained. Further, the paper presents and comments on the traditional methods used for soil erosion prediction, such as USLE and the Gavrilović equation. Also, three recently developed process based models are presented: the American WEPP, the Hollandese LISEM and the Australian TOPOG model. The structure of the models is emphasized, as well as the processes incorporated. The aims and possible applications are described. Key words: soil erosion, sediment yield, process based modelling, distributed models 1. UVOD Zemeljsko površje je med drugim rezultat spiranja in odlaganja zemljin. V več ini primerov je ta proces rezultat naravnih dejavnikov. V nekaterih primerih pa erozijo tal povzroč a tudi č lovekova dejavnost. Najbolj znač ilni primeri so kmetijstvo, rudarstvo in gradbeništvo. Preuč evanje erozije tal in razvoj zašč itnih ukrepov ima na področ ju kmetijstva že kar dolgo zgodovino. Prve empirič ne modele so že pred več kot 50 leti predlagali Cook (1936), Zingg (1940) in Smith (1941). Po drugi strani pa se je na področ jih gradbeništva in rudarstva zanimanje za to problematiko pokazalo razmeroma pozno. 1. INTRODUCTION The earth’s surface is greatly influenced by soil erosion and deposition. In most cases, this process is caused by natural forces. However, some human activities also contribute notably to soil erosion, namely agriculture, mining and construction. In agriculture, erosion has been studied for a relatively long time, different prediction methods have been developed and control measures proposed. The first empirical soil erosion models were proposed more than 50 years ago by Cook (1936), Zingg (1940) and Smith (1941). On the other hand, in the fields of mining and construction, this topic emerged much later. Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 42 Razlogi za to so gospodarske narave. Za lastnika kmetijskega zemljišča izguba tal pomeni izgubo hranil in produktivne zmožnosti tal, kar ga spodbuja k prepreč evanju oziroma omejevanju erozijskih pojavov. V rudarstvu in pri gradbenih delih pa ni takih gospodarskih spodbud, zato je bilo treba uvesti ustrezno regulativo za prepreč itev nezaželenih vplivov na okolje (Hahn et al., 1994). Pri omenjenih dejavnostih je torej pomembno sprošč anje zemljin. Za urejanje vodotokov in načrtovanje vodogradbenih ukrepov pa je pomembno odplavljanje. Iz prakse so znani zlasti primeri zaplavljanja akumulacij in posledičnega nač rtovanja prodnih usedalnikov, pa tudi problem transporta polutantov, ki se premešč ajo, vezani na plavine. V tem članku s pojmom erozija tal označ ujem površinsko spiranje in odplavljanje tal (prsti) zaradi delovanja tekoč e vode. To je običaj tudi v strokovnih (iz področ ja hidrologije) virih iz angleškega govornega področ ja, medtem ko je v slovenski literaturi ta izraz obič ajno rabljen širše, tako da označ uje vse oblike erozije površja, kot so poleg vodne še plazna idr. 2. PROCESI SPROŠČ ANJA, PREMEŠČ ANJA IN ODPLA VLJANJA PLA VIN 2.1 DINAMIKA PROCESOV IN DEFINICIJA POJMOV Dinamiko erodiranja zemljin na poboč jih povodja sestavljajo procesi sprošč anja, premeščanja in odlaganja (Meyer & Wischmeier, 1 969). Sprošč anje je proces, pri katerem se delci (zrna ali agregati) loč ijo od matič nih tal. Sprošč anje je predvsem posledica erozijske moč i dežnih kapelj in vodnega toka. Vodni tok je tudi glavni vir premešč anja zemljin po poboč ju, č eprav je premešč anje deloma mogoč e tudi zaradi vpliva pljuska dežnih kapelj. Zato se premešč anje pojavi šele z nastopom površinskega odtoka in se torej prej pojavi na manj prepustni podlagi z manjšo infiltracijo. Premestitvena zmogljivost vodnega toka narašč a s hitrostjo. Ko se hitrost The reasons for that are economical. In an agricultural land, soil loss represents a loss in nutrients and productive capability, which stimulates the landowner to undertake certain measures to prevent or reduce soil erosion. In mining and construction, no such economic incentive is present, and to eliminate undesirable environmental impacts, regulations had to be imposed (Hahn et al., 1994). For the mentioned activities, soil erosion is important. For the design of hydraulic structures and river training, it is sediment delivery that matters. Reservoir sedimentation and the design of sediment retention basins are known practical problems where sediment yield, as well as the transport of pollutants attached to sediments, must be taken into account. In this paper, the term soil erosion refers to the superficial soil detachment and transport caused by running water. This kind of terminology is also used in English-speaking references, while in Slovene literature, it is usually used as a generic term that also covers processes such as landslides, etc. 2. PROCESSES OF EROSION, TRANSPORT AND SEDIMENT YIELD 2.1 PROCESS DYNAMICS AND RELATED TERMINOLOGY The soil erosion process consists of soil detachment, transport and deposition (Meyer & Wischmeier, 1969). Detachment is a process of separating the soil particles (grains or aggregates) from the ground. Detachment is caused by raindrop impact force and the shearing force of flowing water. Flowing water is also responsible for transporting soil down slope, although down slope transport can also be partially due to raindrop splash. Therefore, the transport only begins when surface runoff occurs. Consequently, transport capacity and soil erosion decrease with the infiltration rate. The transport capacity increases with the flow velocity. Moving down slope, the slope tends to decrease, flow Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 43 zmanjša, obič ajno zaradi zmanjšanja naklona poboč ja, nastopi odlaganje (Hahn et al., 1 994). Glede na to, ali se erozija pojavlja v žlebič ih, ki jih izdolbe vodni tok, ali na površinah med njimi, delimo erozijski proces na žlebično in medžlebično erozijo. Znač ilnosti in nač ini posameznih procesov so opisani v naslednjih toč kah. 2.2 MEDŽLEBIČ NA EROZIJA Več ina erozije v medžlebič nem prostoru je pljuskovna erozija, ki se pojavlja ob pljuskih dežnih kapelj ob tla in je posledica erozijske moč i dežnih kapelj. Odvisna je od intenzitete dežja i, kinetič ne energije dežnih kapelj k e in deleža glin p c . Nekateri avtorji upoštevajo tudi vpliv naklona poboč ja S (npr. Hirschi & Barfield, 1988a;b). Hahn et al. (1994) navaja študije, ki kažejo odvisnost pljuskovne erozije od globine površinskega toka. Te so pokazale, da se erozija poveč uje do globine vode, ki je enaka 1 /6 do 1 premera dežne kaplje, nato pa se zmanjšuje. Voda na površini namreč deluje kot razprševalec kinetič ne energije dežnih kapelj. Enač be za izrač un stopnje sprošč anja D i zaradi pljuskovne erozije so obič ajno oblike: velocity also decreases and deposition takes place (Hahn et al., 1994). Erosion in the catchment can be rill erosion, which occurs in the small channels, or rills, incised by the water, or interrill erosion, which occurs in the zone between the rills. The description of the different soil erosion processes is given in the next sections. 2.2 INTERRIL EROSION In interrill areas, most of the erosion is caused by splash erosion, which is the result of raindrop impact upon the soil. The quantity of detached soil depends on the rainfall intensity i, the kinetic energy of the raindrops k e and the soil clay percentage p c . Sometimes, slope S is also taken into account (e.g. Hirschi & Barfield, 1988a;b). Hahn et al. (1994) gives examples of studies showing the dependence of splash erosion on ponded depth. These studies showed that splash increased up to a ponded depth of 1/6 to 1 raindrop diameter, and decreased with deeper depths. The reason for this is that the water on the surface dissipates the kinetic energy of the raindrops. The splash erosion detachment rate D i is usually expressed as: p r i i k D ⋅ = (1) Koeficeint k r predstavlja erodibilnost tal in je odvisen od lastnosti zemljine, pokrovnosti oziroma rabe tal in topografskih lastnosti. i je intenziteta dežja, p pa empirič ni koeficient, katerega vrednost je obič ajno približno 1 (Jayawardena & Bhuiyan, 1 999). Č e pa želimo s to enač bo oceniti celotno medžlebič no erozijo, torej tudi del zaradi površinskega odtoka in vpliv premestitvene zmogljivosti, je vrednost p približno 2; primere različ nih modelov navaja Hahn et al. (1 994). Kinetič na energija dežnih kapelj k e v teh enač bah ne nastopa, ker jo je moč empirič no izraziti iz intenzitete dežja (npr Brown & Foster, 1 987). Pljuski dežnih kapelj deloma prispevajo tudi k premešč anju delcev zemljin, kar pa seveda velja le na nagnjenem terenu. Več ina premeščanja pa poteka pod vplivom Coefficient k r is the soil erodibility factor, which depends on the soil and cover properties, respectively, land use and topography. The symbol i is rainfall intensity, and p, the empirical coefficient whose value is usually close to 1 (Jayawardena & Bhuiyan, 1999). If this equation is used for estimating the net interrill erosion, meaning that overland flow detachment and transport capacity are also taken into account, the value of p is around 2; examples of different models are given by Hahn et al. (1994). The kinetic energy of raindrops does not occur in these equations, since it can be empirically expressed from rainfall intensity (e.g. Brown & Foster, 1987). Raindrop splash also contributes to the transport of soil, which is obviously true for a sloping surface only. However, the majority of Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 44 površinskega toka. Sloj površinsko odtekajoč e vode je obič ajno tanek in rezultirajoč e strižne sile ne zadošč ajo za dodatno spiranje zemljin. Vendar pa je zlasti zaradi dežnih kapelj, ki povzroč ajo dodatno turbulenco, ta tok zmožen premešč anja. O premestitveni zmogljivosti površinskega toka danes še ne vemo prav mnogo. Kot poudarjata Jayawardena & Bhuiyan (1999), premešč anje ni veljalo za omejitveni dejavnik medžlebič ne erozije, vendar navajata tudi nekatera opazovanja, ki kažejo nasprotno. Modeli za rač un premestitvene zmogljivosti površinskega toka T c so bili več inoma prevzeti iz področ ja premešč anja plavin v strugah. Pri teh modelih je premestitvena zmogljivost odvisna ali od pretoka vode Q, ali od strižne napetosti τ oziroma od efektivne moč i toka Ω . Pomanjkljivost takega prevzemanja modelov iz drugega področ ja je, da so količ ine vode pri površinskem toku mnogo manjše kot pri toku v strugi. Poleg tega ti modeli ne upoštevajo vpliva dežja, katerega energija ima pri plitvem površinskem toku mnogo več ji vpliv kot pri globljem toku v strugi. Jayawardena & Bhuiyan (1999) sta izvedla vrsto poskusov, pri katerih sta merila tako sproščanje kot premestitveno zmogljivost. Sprošč anje sta merila v skodelicah, ki sta jih vgradila v eksperimantalno poboč je, premestitveno zmogljivost pa sta prerač unala z modelom iz količ in erodirane zemljine, zbrane ob dnu eksperimentalnega poboč ja. Ugotovila sta, da so vsi trije omenjeni nač ini modeliranja premestitvene zmogljivosti T c zadovoljivi. To pomeni, da je mogoč e najti zvezo T c s katerimkoli parametrom Q, τ ali Ω ob zadovoljivem koeficientu korelacije (R 2 > 0.90). Vendar je pogoj za to loč itev primerov z dežjem in brez dežja; razlika v premestitveni zmogljivosti med tema dvema primeroma je reda velikosti (1 0x), se pa zmanjšuje s količ ino odtekajoč e vode in s tem z globino. transport is a result of overland flow. The film of runoff water is usually thin, and the corresponding shear stresses do not suffice for additional soil detachment. But the raindrop impact increases the turbulence in this film, which makes the overland flow capacity high enough for transport. At present, not much is known about the transport capacity of overland flow. As stated by Jayawardena & Bhuiyan (1999), the transport was generally not considered a limiting factor for interrill erosion. They, on the other hand, cite observations showing this is not always the case. Models for the transport capacity of the overland flow T c were usually from the field of stream flow sediment transport. These models relate the transport capacity to either water discharge Q, shear stress τ or effective unit stream power Ω . The disadvantage of simply using models developed for stream flow conditions is that discharges of flowing water can be much lower in the case of overland flow. Further, the impact of rainfall energy is much higher in a shallow overland flow than it is in a deeper stream flow. Jayawardena & Bhuiyan (1999) carried out a set of experiments where both detachment and transport were measured. The detachment was measured by the splash cup technique. The cups were placed in the experimental tray. The transport capacity was calculated using a model from the collected samples at the lower end of experimental tray. They found that all the mentioned transport capacity T c relationships performed well; i.e., it was possible to find a relationship between T c and any of the three parameters Q, τ or Ω with a correlation coefficient R 2 > 0.90. However, the data for the case with rain and without rain was split, and the difference in the transport capacity of the two sets was in order of magnitude (10x). The difference was reduced with larger quantities of water (and, hence, depth). Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 45 2.3 ŽLEBIČ NA EROZIJA Žlebič i so pomemben element v procesu odtoka vode in plavin iz povodja. Njihova gostota, to je število žlebič ev na enoto širine, je odvisna od strmine in dolžine poboč ja, površinskega odtoka, teksture in erodibilnosti tal in prisotnosti oziroma odsotnosti deževij (Meyer & Monke, 1965). Na zelo erodibilnih tleh erozijo omejuje premestitvena zmogljivost, žlebič i so enake velikosti vzdolž poboč ja in njihova gostota je velika (Ellison & Ellison, 1947). Na manj erodibilnih tleh pa je omejitev sprošč anje, širina žlebičev se spreminja in njihova gostota je manjša. Hahn et al. (1994) povzema, da sta Hirschi & Barfeld (1988b) izvedla analizo obč utljivosti erozije glede na gostoto žlebič ev z uporabo modela KYERMO. Pri njunem specifič nem testnem primeru sta ugotovila, da je sprošč anje največ je pri približno 6 žlebič ih na širini 4.5 metrov. Zmanjšanje pri več ji gostoti sta pripisala manjši količ ini vode v posameznem žlebič u. Hkrati sta poudarila, da so rezultati odvisni tudi od izbire uporabljenih enač b za sprošč anje in strižno silo. Razvoj žlebič ev je odvisen od potencialnega sprošč anja, premestitvene zmogljivosti, dejanskega premešč anja in medsebojnega ravnotežja teh procesov (Hahn et al., 1994). Podrobnosti so podane v naslednjih poglavjih. 2.4 MOŽNO SPROŠČ ANJE Sprošč anje zemljin v žlebič ih povzroč a turbulenca. Obstajata dve skupini enač b za modeliranje možne stopnje sprošč anja e. V prvo skupino sodijo enač be, ki temeljijo na povpreč nih parametrih toka, kot sta strižna napetost τ 0 ali specifič na moč toka ω. Primer enač be s strižno napetostjo je (Foster, 1 982): 2.3 RILL EROSION Rills are an important element of surface runoff and the sediment delivery processes. Their density, i.e. the number of rills per unit width, depends on slope steepness and length, runoff rate, soil texture and erodibility, and the presence, or absence, of rainfall (Meyer & Monke, 1965). On highly erodible soil, the limiting factor for erosion is transport capacity; the rills have the same size along the slope and their density is high (Elison & Elison, 1947). On less erodible soil, erosion is detachment-limited, the width of rills varies along the slope, and their density is lower. Hahn et al. (1994) cites an example of sensitivity analysis on the rill density. It was performed by Hirschi & Barfeld (1988b) using the KYERMO model. For their specific test condition, they found the maximum sediment yield at about 6 rills in 4.5 meters. They proposed that the decline in sediment yield at the higher rill density was due to a lower flow rate per rill. They also demonstrated that the results varied, depending on the rill detachment and the boundary shear stress equations used. The development and growth of rills is governed by the rill detachment potential, transport capacity, sediment load and their interactions (Hahn et al., 1994). Details are given in the following sections. 2.4 DETACHMENT POTENTIAL Soil detachment in rills is caused by turbulence. There are two groups of equations used for modelling the potential detachment rate e. In the first group are equations based on average flow parameters such as shear stress τ 0 or unit stream power ω. An example of such an equation is given by Foster (1982): b cr a e ) ( 0 τ τ − ⋅ = (2) kjer sta a in b empirič na koeficienta. Podobne so tudi enač be, ki upoštevajo specifič no moč toka ω. Ta je definirana kot (q je specifič ni pretok, S je padec, ρ gostota tekoč ine, g pa težnostni pospešek): where a and b are empirical coefficients. Equations that contain unit stream power are of similar form. Unit stream power ω is defined as (q is unit discharge, S is slope, ρ fluid density and g gravitational acceleration): S q g ⋅ ⋅ ⋅ = ρ ω (3) Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 46 Drug pristop temelji na parametrih, ki opisujejo turbulentna nihanja napetosti. Primer take enač be je (Nearing, 1 991 ): The second approach is based on the characteristics of intermittent turbulent flow. A relationship by Nearing (1991) is: M P F e ⋅ ⋅ = (4) kjer je F prostorska in č asovna frekvenca turbulentnih motenj, P je verjetnost, da bo izbruh motnje povzroč il sprostitev delcev dna, M pa je povpreč na masa zemljine, ki se ob izbruhu motnje sprosti. Enačbo lahko preoblikujemo (Nearing, 1991): where F is the spatial and temporal frequency of turbulent bursts, P is the probability that the burst will cause a failure event and thus detachment and M is the average mass detached, per event. This equation can also be written in the following form (Nearing, 1991): 2 / 3 2 / 1 S h P C K e ⋅ ⋅ ⋅ ⋅ = (5) kjer je K empirič ni koeficient in C Chezyjev koeficient hrapavosti. Na sliki 1 je prikazana verjetnost sprošč anja P kot presek porazdelitvenih funkcij za strižno napetost τ o in odpornost tal τ cr . where K is the empirical coefficient and C is the Chezy roughness coefficient. Figure 1 shows the probability of detachment P as the overlapped area of soil tensile strength τ cr and shear stress τ o distribution functions. 0 50 100 150 200 0.00 0.01 0.02 0.03 0.04 p [Pa] 0 cr Slika 1 . Gostota verjetnostne porazdelitve za strižno napetost τ 0 in odpornost tal τ cr (po Lei et al., 1998). Figure 1. Probability density function for shear stress τ 0 and soil tensile strength τ cr (after Lei et al., 1998). Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 47 2.5 PREMESTITVENA ZMOGLJIVOST Modeliranje premestitvene zmogljivosti tudi temelji na različ nih parametrih vodnega toka, kot so strižna napetost, efektivna strižna napetost, specifič na moč vodnega toka in efektivna moč vodnega toka. Efektivna strižna napetost je tisti del strižne napetosti, ki je posledica hrapavosti dna (npr. Einstein & Barbarossa, 1 951 ). Efektivna moč vodnega toka pa je definirana kot (Govers, 1990): 2.5 TRANSPORT CAPACITY Transport capacity modelling can also be based on different flow parameters, e.g. shear stress, effective shear stress, unit stream power and effective stream power. Effective shear stress is obtained by dividing the total shear stress into an "effective" (bed roughness) and form roughness component (Einstein & Barbarossa, 1951). Effective stream power is defined as (Govers, 1990): 3 / 2 5 . 1 / ) ( R cr ω ω − = Ω (6) kjer je ω cr kritič na moč vodnega toka za zač etek premešč anja, R pa hidravlič ni polmer. Nearing et al. (1997) so izvedli šest serij poskusov toka v žlebič ih na dveh kmetijskih zemljišč ih. Poskusi so bili izvedeni tako v laboratoriju kot na terenu, pri različ nih pretokih in padcih. Merjen je bil pretok plavin q S , a je bilo ugotovljeno, da je ta v danih razmerah blizu premestitveni zmogljivosti. Kot najustreznejši parameter za oceno premestitvene zmogljivosti T C se je pokazala specifič na moč vodnega toka ω. Koeficient korelacije med izrač unanimi in merjenimi vrednostmi je bil r 2 = 0.93. Drugi parametri so dali slabše rezultate. Konč na enač ba, kjer so A, B, C in D konstante, je naslednja: where ω cr is the critical stream power (for the beginning of the transport) and R is the hydraulic radius. Nearing et al. (1997) conducted six series of rill experiments on two agricultural soils. Experiments were carried out both in laboratory and field, with quite a range of discharges and slopes. The sediment load q S was measured, but for the given conditions it was close to the transport capacity. It was found that the best parameter for transport capacity T C evaluation was stream power. The coefficient of determination between the predicted and measured values was r 2 = 0.93. Other parameters gave lower coefficients of determination. Their equation, where A, B, C and D are constants, is as follows: ) 1 /( ) log( ) log( ) log( ω ω ⋅ + ⋅ + + ⋅ + = D C D C C e e B A T (7) Govers (1990) pa kot najustreznejšo zvezo med premestitveno zmogljivostjo in hidravlič nimi parametri predlaga: On the other hand, Govers (1990) suggests the following relationship between transport capacity and hydraulic parameters as the best: c b C S q a T ⋅ ⋅ = (8) kjer so a, b in c empirič ne konstante. Tudi ta enač ba daje precej dobro korelacijo za T C . Vendar Nearing et al. (1997) opozarjajo, da se vrednosti konstant v tej enačbi precej razlikujejo za posamezne tipe zemljine in vrsto poskusa, medtem ko je njihova enač ba (7) bolj splošna. where a, b and c represent empirical constants. This equation also gives good predictions for T C . However, Nearing et al. (1997) showed that the values of the constants varied significantly among different soil materials and experiments, while their equation (7) was more universal. Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 48 2.6 DEJANSKA STOPNJA SPROŠČ ANJA IN ODLAGANJA Dejansko sprošč anje D r v žlebičih je odvisno od dejanskega pretoka plavin q S . Več ji kot je pretok plavin, manj energije je na voljo za dodatno sprošč anje. Poleg tega prisotnost plavin v toku zmanjšuje turbulenta nihanja hitrosti, plavine v premešč anju pa tudi šč itijo dno pred nadaljnjo erozijo. Lei et al. (1998) v svojem modelu uporablja naslednjo zvezo med možno in dejansko stopnjo sprošč anja v žlebič ih: 2.6 DETACHMENT AND DEPOSITION RATE The detachment rate D r in rills depends on the sediment load q S . The higher the sediment load, the less energy is available for additional detachment. Furthermore, the presence of sediments in the flow reduces the turbulent velocity fluctuations. Also, the bed is protected by the sediments already being transported. Lei et al. (1998) used the following relationship between the potential detachment rate and the detachment rate in the rills:         − ⋅ = C S r T q e D 1 (9) Kadar je pretok plavin večji od premestitvene zmogljivosti, nastopi odlaganje. Odlaganje se modelira, podobno kot erozija, na podlagi razlike pretoka plavin in premestitvene zmogljivosti: When the sediment load is higher than the transport capacity, deposition occurs. Similarly to erosion, deposition is calculated on the basis of the difference between sediment load and transport capacity: () C S r T q A − ⋅ − = α (10) kjer je α empirični linearni koeficient odlaganja [m -1 ]. 2.7 NASTANEK KANALSKEGA TOKA Prosser & Dietrich (1995) obravnavata dve procesno utemeljeni teoriji o prehodu površinskega v kanalski tok. Po prvi nastane prehod iz površinskega v kanalski tok zaradi nestabilnosti preč nih perturbacij površine pod vplivom površinskega toka. Ta teorija je primerna za napovedovanje gostote žlebič ev na slabo vezljivih tleh. Po drugi teoriji pa je nastanek kanalskega toka posledica prekorač itve erozijske odpornosti tal, ki je rezultat kohezijskih sil in vegetacijske pokrovnosti tal. Tipič en primer je nastanek novega žlebič a s splazitvijo tal. Prehod iz površinskega v kanalski tok lahko povzročijo naslednje vrste erozije (Dietrich & Dunne, 1993): − erozija Hortonovega površinskega toka where α is an empirical first-order deposition coefficient [m -1 ]. 2.7 CHANNEL INITIATION To predict the location of the channel head, two process based theories have been proposed (Prosser & Dietrich, 1995). The first suggests that the transition from overland to channel sediment transport occurs because of the lateral instability of perturbation on the surface in the presence of overland flow. This theory may be appropriate to predict rill density on poorly cohesive surfaces. The second theory relates channel initiation to the resistance to erosion, which results form soil cohesion and vegetation cover. An example of a process threshold is channel initiation by land slide. The transition from overland to channelised flow occurs by one of the following processes (Dietrich & Dunne, 1993): − erosion by Horton overland flow Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 49 − erozija zasič enega površinskega toka − erozija zaradi pronicanja − zdrs zemljine − notranja erozija. V primeru stalnega zasič enega površinskega toka lahko razvijemo enač bo za kritič ne razmere za nastanek kanalskega toka na naslednji nač in (Prosser & Dietrich, 1 995). Površinski odtok Q je enak − erosion by saturation overland flow − seepage erosion − mass failure − tunnel scour In the case of steady state saturation overland flow, the equation for critical conditions for the channel initiation can be derived the following way (Prosser & Dietrich, 1995). Discharge of overland flow Q equals b S T A i Q ⋅ ⋅ − ⋅ = (11) kjer je i intenziteta padavin, A prispevna površina, b pripadajoč a širina konture, T hidravlič na prevodnost tal in S lokalni padec. Strižno napetost na dno τ 0 izrač unamo kot where i is rainfall intensity, A is source area, b is the corresponding contour width, T is the soil transmissivity and S is the local gradient. Boundary shear stress τ 0 can be calculated as S R g ⋅ ⋅ ⋅ = ρ τ 0 (12) kjer je R hidravlič ni polmer oziroma globina toka. Pretok Q in strižno napetost τ o povežemo preko srednje hitrosti U: where R is the hydraulic radius or flow depth. The discharge Q and the shear stress τ o can be related via the mean velocity U: b R U Q ⋅ ⋅ = (13) S R g f U ⋅ ⋅ ⋅ = 8 2 (14) f je Darcy-Weissbachov koeficient trenja, ki ga v ozkem območ ju lahko izrazimo z Reynoldsovim številom Re in empirič nima koeficientoma K in c, ν je kinematič na viskoznost tekoč ine: f is the Darcy-Weissbach friction coefficient, which can be, in a certain interval, calculated from the Reynolds number Re, and the empirical coefficients K and c, ν is kinematic viscosity, such that: c K f Re ⋅ = (15) ν / Re UR = (16) Iz zvez (11) - (16) lahko ob nadomestitvi τ 0 s kritič no vrednostjo τ cr dobimo pogoj za nastanek kanalskega toka: Replacing τ 0 by the critical value τ cr and combining (11) - (16) yields the condition for channelised flow: S i T S i K g b A c c cr c + ⋅ ⋅         ⋅ ⋅ ⋅ ⋅ ≥ + + ) 2 /( 2 ) 2 /( 1 3 2 3 1 8 ρ τ ν (17) Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 50 S pomoč jo enačbe (1 7) in empirič no določ enih vrednosti K, c, T/i in τ cr , ta zadnja je znašala 16 Pa, so Dietrich et al. (1992; 1993) na podlagi digitalnega modela terena (DTM) pravilno napovedali elemente s kanalskim tokom v 92 odstotkih in elemente s samo površinskim tokom v 77 odstotkih primerov. Prosser & Dietrich (1995) pa sta ugotavljala vpliv zatravljenosti na erozijsko odpornost tal. Terenske poskuse sta izvedla v povodju reke Tennessee. Poskusno območ je sta ogradila in vanj dovajala takšno količ ino vode, da so pretoki ustrezali že izmerjenim dogodkom. Pri gosti travi se spiranje in premešč anje ni pojavilo pri strižnih napetostih, manjših od 104 do 108 Pa. Ko so travo porezali, so ugotovili 3- do 9-kratno zmanjšanje tega praga (20 do 40 Pa). Tudi upor toku vode se je zmanjšal za najmanj red velikosti. Kljub temu pa se še vedno ni pojavil kanalski tok. Avtorja tudi opozarjata, da je kritič na strižna napetost precej obč utljiv parameter, saj njeno dvojno poveč anje pomeni 4- do 8-kratno poveč anje prispevne površine, potrebne za nastanek kanalskega toka. Kljub temu pa so njuni poskusi potrdili uporabnost hipoteze o pragu erozijske odpornosti tal za zatravljene površine. 3. TRADICIONALNO NAPOVEDOV ANJE EROZIJE TAL 3.1 ENAČ BA USLE Tradicionalne metode za napovedovanje erozije tal izhajajo s področ ja kmetijstva. To so empirični modeli, namenjeni napovedovanju sproščanja, to je količ ini zemljine, ki jo voda izloč i iz matič nih tal. Znač ilen primer takega modela je Univerzalna enač ba izgub zemljine (USLE, "Universal Soil Loss Equation"). Model je sestavljen iz glavne enač be in pomožnih enač b oziroma preglednic in grafikonov za določanje posameznih vrednosti glavne enač be. Enač ba je bila uporabljena pri nač rtovanju za napovedovanje vpliva rabe tal na erozijo (Hahn et al., 1994). Prvotno je bila razvita za napovedovanje srednje letne izgube tal, kasneje pa Dietrich et al. (1992; 1993) applied this equation to a digital terrain model (DTM). The values of the parameters K, c, T/i and τ cr , the former's value being 16 Pa, were empirically determined. Thus, 92% of channeled elements and 77% of the unchanneled elements were correctly attributed. Prosser & Dietrich (1995) demonstrated the effect of vegetation cover on erosion resistance. Their experiments were conducted in a field site in the Tennessee Valley catchment. Flume walls were constructed and water was supplied to the flume such that discharges were comparable to previously measured events. Under dense grass cover, sediment transport didn't occur at shear stresses lower than 104÷108 Pa. When the grass was clipped, the threshold was reduced by 3÷9 times (20-40 Pa). Also, flow resistance was reduced by at least an order of magnitude. But still, no channelised flow occurred. Furthermore, the authors found that critical shear stress is quite a delicate parameter, since its 2-fold variation results in 4÷8-fold variation in the source area required to support a channel. But, in spite of that, the experiments provided support for the assumption that channel initiation in grassland is threshold dependent. 3. TRADITIONAL SOIL EROSION PREDICTION 3.1 THE USLE EQUATION Traditional methods for soil erosion prediction were developed for agricultural land. These are empirical models. Their purpose is to predict soil loss, i.e. the amount of soil lost from the surface by water impact. The most known example of such a model is the Universal Soil Loss Equation (USLE). The model consists of one main relationship and a set of equations, tables and figures for the determination of the parameters of the main relationship. This equation has been widely used for planning purposes to predict the impact of land use on soil erosion (Hahn et al., 1994). Originally, it was developed for the prediction of the average annual soil loss, but Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 51 spremenjena tako, da je bilo z njo mogoč e napovedovati erozijo tudi meseč no in celo ob posameznem dogodku, t.j. nalivu. V novejšem č asu je bil model izboljšan z novimi spoznanji in je zdaj znan pod imenom RUSLE ("Revised USLE", t.j. popravljena USLE). Glavna enač ba RUSLE/USLE je v obliki zmnožka: later it was modified to estimate monthly and even single event (i.e. single storm) erosion. In recent times, the model has been improved with the new data available. The modification is named RUSLE (Revised USLE). The main relationship of RUSLE/USLE is a multiplicative one: RKLSCP A = (18) A [kg/ha∙leto] je povpreč na izguba tal na enoto površine, ki je odvisna od aktivnih hidroloških in topografskih dejavnikov (R, L, S) in reaktivnih dejavnikov (K, C, P), ki opisujejo erodibilnost, pokrovnost in rabo tal. Posamezni dejavniki so (Hahn et al., 1994): R dejavnik padavin in odtoka, to je število enot dežja za energijo padavin in odtok, in vode iz taljenja snega za odtok [MJ·mm/ha·h·leto], K dejavnik erodibilnost zemljine glede na standardne razmere (raba tal, padec, in dolžina poboč ja), L dejavnik dolžine poboč ja, to je razmerje med izgubo tal pri podani dolžini in standardni dolžini 22.1 m, S dejavnik naklona poboč ja, to je razmerje med izgubo tal pri podanem padcu in standardnem padcu 9 odstotkov, C dejavnik pokrovnosti in obdelave tal, to je razmerje med izgubo tal pri podani pokrovnosti in izgubo tal z neobdelanega polja, P dejavnik kmetijskih zašč itnih ukrepov, to je razmerje med izgubo tal s polja, ki se obdeluje s podanimi ukrepi in izgubo tal s polja, ki se obdeluje z oranjem navzgor in navzdol. Enač ba se največ uporablja v ZDA. Tam so za določevanje vsakega od omenjenih dejavnikov izdelane enač be, grafikoni oziroma karte. Primer uporabe v Evropi za Bavarsko podaja Lang (1 997), za Južni Limburg na Nizozemskem pa De Roo (1998). Kasneje je bila na temelju USLE razvita spremenjena USLE oziroma MUSLE (Modified USLE). Razlika je v nadomestitvi dejavnika R z dejavnikom energije odtoka. A [kg/ha·year] is the average soil loss per unit area, which depends on active hydrological and topographic factors (R, L, S) and reactive factors (K, C, P), such as soil erodibility, cover and land use. The factors are (Hahn et al., 1994): R rainfall-runoff factor, i.e. the number of rainfall units for rainfall energy and runoff, and runoff from snowmelt [MJ·mm/ha·h·year], K erodibility factor in comparison to standard conditions (land use, slope, slope length), L slope length factor, which is the ratio of soil loss from a given slope to that of the standard slope length of 22.1 m, S slope steepness factor, which is a ratio of the soil loss from a given slope relative to that of the standard slope of 9%, C cover and management factor, which is a ratio of the soil loss from a field of a given cover, and management relative to that in continuous fallow, P is the supporting conservation practise, which is a ratio of the soil loss from a field, of a given conservation support practise relative to that with straight row farming up and downhill. The method is mostly used in the USA, where equations, charts and maps were defined for the determination of these factors. In Europe, it has been used in Bavaria (Lang 1997) and in South Limburg, in the Netherlands (De Roo, 1998). Later, on the basis of the USLE equation, the modified USLE, or MUSLE, was developed. The difference is in replacing the R factor with the runoff energy factor. Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 52 3.2 GAVRILOVIĆ EVA ENAČ BA Za območ je Sredozemlja je Gavrilović (1 970) predlagal naslednjo enač bo za izrač un srednjega letnega sproščanja zemljin W [m 3 /leto] zaradi vodne erozije: 3.2 THE GAVRILOVIĆ EQUATION For the Mediterranean region, Gavrilović (1970) proposed the following equation to predict average annual sediment production W [m 3 /year] due to water erosion: W Z T Y F K K H W ⋅ ⋅ ⋅ ⋅ = 5 . 1 1 4 . 3 (19) kjer je F W površina povodja [km 2 ], H Y so srednje letne padavine [mm], K T je temperaturni koeficient območ ja, ki je funkcija srednje letne temperature, K Z pa je erozijski koeficient območ ja, ki se oceni na podlagi ustreznih preglednic ali pa izrač una kot: where F W is the catchment area [km 2 ], H Y is the average annual rainfall [mm], K T is the coefficient of temperature, which is a function of mean annual temperature, and K Z is the coefficient of erosion, which can be estimated using corresponding tables or calculated from: ) ( 0 S K K K K Y X Z + ⋅ ⋅ = (20) V tej enač bi je K Y koeficient erodibilnosti tal, K X je koeficient zašč itenosti tal zaradi rastlin ipd., K 0 je koeficient razvitosti erozijskih procesov, S pa srednji nagib v povodju. Kadar je povodje oziroma izbrana površina heterogena glede na erozijski koeficient K Z , Gavrilović (1 970) predlaga, da se skupni K Z izrač una kot povpreč je, uteženo s pripadajočimi površinami. To sicer z matematič nega vidika ni povsem jasno, saj sprošč anje W ni linearna funkcija K Z , torej: In this equation, K Y is the soil erodibility coefficient, K X is the soil protection coefficient due to vegetation etc., K 0 is the coefficient of the development of the erosional process and S is the average slope. When the catchment or the concerned area is not uniform with respect to the coefficient of erosion K Z , Gavrilović (1970) suggested calculating the mean K Z as the sub-area weighted average. From a mathematical point of view, this is not very clear, since W is not a linear function of K Z , therefore: 5 . 1 , , 5 . 1 , ,         ⋅ ⋅ ≠ ⋅ ∑ ∑ i i Z W i W W i i Z i W K F F F K F (21) Vendar ta razlika v primerjavi s toč nostjo metode ni bistvena. Vzemimo sprošč anje zemljin z dveh enako velikih površin in razmerjem v erozijskem koeficientu 1 :5. Č e ju obravnavamo kot enotno površino po enač bi (21 ), dobimo za 1 5 odstotkov nižjo vrednost za sprošč anje, kot č e ju obravnavamo kot dve loč eni površini. Kljub temu se matematič no pravilen račun povprečnega erozijskega koeficienta K Z glasi: However, this difference is not significant compared to the accuracy of the method. Let us calculate the sediment production form two equally large areas with an erosion coefficient ratio of 1:5. If calculated as one area using equation (21), the obtained sediment production is 15 percent lower than if calculated as two separate units. Nevertheless, the mathematically correct expression for average erosion coefficient K Z is: 67 . 0 5 . 1 , .         ⋅ = ∑ i i Z W i w Z K F F K (22) Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 53 Za posamezne koeficiente iz enač b (1 9) in (20) obstajajo preglednice vrednosti za vsako opisano stanje. Enač ba je bila preverjena na podatkih z območ ja nekdanje Jugoslavije in Severne Afrike (Gavrilović , 1 970). Pintar et al. (1986) so ugotovili, da so za vrednotenje erozije v Sloveniji največ je dnevne padavine H D,max ustreznejši parameter od srednjih letnih padavin H Y . Nadalje poroč ajo, da srednja letna temperatura ni pomemben parameter. Tako so za napovedovanje sprošč anja plavin predlagali spremenjeno enač bo: Tables giving a description for the different values exist for each of the coefficients of the equations (19) and (20). The equation was validated on the data from former Yugoslavia and North Africa (Gavrilović , 1 970). Pintar et al. (1986) found that, for erosion prediction in Slovenia, the maximum daily precipitation H D,max is more appropriate than the average annual precipitation H Y . Furthermore, they report that the mean annual temperature is not significant. To predict sediment production, they proposed a modified equation: W Z D F K H W ⋅ ⋅ ⋅ = 5 . 1 max , 20 (22) 4. MODERNE METODE 4.1 TEMELJI IN RAZVOJ MODELOV Rezultat v prejšnji toč ki opisanih modelov je količ ina sprošč anja zemljin. Ta pa pogosto ni enaka odplavljanju, t.j. količ ini zemljine, ki je bila dejansko odstranjena s poboč ja. Prej ko slej se na poboč ju namreč pojavijo razmere, ko voda ni več sposobna odnašati vsega erodiranega materiala in zato nastopi odlaganje. Sodobne metode za napovedovanje odplavljanja zemljin zato temeljijo na modelih, ki upoštevajo celoten cikel erozijskega procesa: sprošč anje, premešč anje in odlaganje, kakor tudi njihove medsebojne vplive. Diagram poteka rač una je razviden iz slike 2. Hahn et al. (1994) podaja zgodovinski pregled razvoja erozijskih modelov. Prvi fizikalno utemeljen model se je pojavil konec šestdesetih let (Meyer & Wischmeier, 1969). Polteoretič na FMO enač ba (Foster et al., 1 977) je bila kasneje uporabljena v rač unalniškem modelu CREAMS ("Chemicals-Runoff- Erosion in Agricultural Management Systems", Kemikalije-odtok-erozija za upravljalske sisteme v kmetijstvu). Ta model je namenjen napovedovanju erozije na enoto kmetijske površine pri stalnih razmerah. Hirschi & Barfield (1988a;b) sta za raziskave erozije razvila procesno utemeljen model KYERMO. Ta model je namenjen simulaciji 4. MODERN METHODS 4.1 THE BASIS AND DEVELOPMENT OF THE MODELS The models described in the previous section can be used to predict soil erosion. This is, however, often different from sediment yield, which is the amount of sediment that is actually removed from the slope. The reason for that is that sooner or later, the sediment load exceeds the transport capacity, and deposition of the eroded material occurs. Modern methods for sediment yield prediction are, therefore, based on the models, which take into account the entire erosion process: detachment and transport and deposition, as well as their interactions. These interrelationships are shown in Figure 2. Hahn et al. (1994) gives the historical overview of erosion modelling. The first physically based model was developed in the late sixties (Meyer & Wischmeier, 1969). The semitheoretical FMO equation (Foster et al., 1977) was later used in a computer model called CREAMS (Chemicals-Runoff-Erosion in Agricultural Management Systems). This model was intended for use on a field-sized area under steady-state conditions. Hirschi & Barfield (1988a;b) developed a research- oriented process-based model KYERMO. This Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 54 posameznega dogodka in napoveduje sprošč anje in erozijo v posameznih žlebič ih na podlagi pretoka vode v njem. Med vrsto procesno utemeljenih modelov, razvitih v zadnjih letih (npr. EUROSEM, 2D in 3D EROSION ...), so v nadaljnjem besedilu opisani trije: WEPP, LISEM in TOPOG. model is intended for the simulation of single events. It predicts sediment detachment and transport in individual rills as a function of flow rates. Among many process based models developed in recent years (e.g. EUROSEM, 2D & 3D EROSION ...), three are described in the next section: WEPP, LISEM and TOPOG. D < T C q S,D q S,U D ri D ro D T Cri T Cro T C + + + D > T C Slika 2. Procesno utemeljeno modeliranje erozije (po Meyer & Wischmeier, 1969) Simboli: q S,U - dotok plavin od zgoraj, q S,D - odtok plavin navzdol, D ri - sprošč anje zaradi dežja, D ro - sprošč anje zaradi odtoka, D - skupno sprošč anje, T Cri - premestitvena zmogljivost dežja, T Cro - premestitvena zmogljivost odtoka, T C - skupna premestitvena zmogljivost. Figure 2. Process based erosion modelling (after Meyer & Wischmeier, 1969). Symbols: q S,U - soil from upslope, q S,D - soil carried downslope, D ri - detachment by rainfall, D ro - detachment by runoff, D - total detached, T Cri - rainfall transport capacity, T Cro - runoff transport capacity, T C - total transport capacity. 4.2 MODEL WEPP Model WEPP ("Water Erosion Prediction Project", Projekt napovedovanja vodne erozije) je zasnovan na podlagi obširne baze podatkov, zbranih v ta namen. Ta procesno utemeljeni model je namenjen napovedovanju erozijskih procesov na enotnem poboč ju ali pa v manjših povodjih (Flanagan et al., 1995). Različ ica za povodja povezuje poboč ja z reč nimi strugami in zajezitvami (slika 3a). S tem se je WEPP že približal dvodimenzionalnemu modeliranju erozijskih procesov. Ciljni namen modela je nač rtovanje projektov in zašč itnih ukrepov ter pregled in 4.2 THE WEPP MODEL The WEPP model (Water Erosion Prediction Model) was developed on the basis of field data. A large database was collected with this purpose in mind. This process based model can be used for the prediction of erosion processes on hillslopes or small catchments (Flanagan et al., 1995). In the catchment version, the model links hillslope profiles to channels and impoundments (Figure 3a). By this feature, WEEP approaches two dimensional erosion modelling. Anticipated applications of the model include project planning, conservation planning, inventory and Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 55 ocena stanja. Največja prednost pred tradicionalnimi modeli je možnost č asovne in prostorske simulacije procesov. Model obravnava naslednje procese: žlebič no in medžlebič no erozijo, premešč anje in odlaganje, infiltracijo, konsolidacijo zemljin, vpliv tal in pokrovnosti na sprošč anje in infiltracijo, zablatenje površine, žlebič no hidravliko, površinski odtok, rast rastlin, razgradnjo organskih ostankov, perkolacijo, izhlapevanje, transpiracijo, taljenje snega, vpliv zmrzovanja na infiltracijo in erodibilnost, podnebje, vpliv obdelovanja na lastnosti tal, naključ no hrapavost površine in vpliv kontur. Model upošteva prostorsko in časovno spreminjanje površja, hrapavosti površine, lastnosti tal in rastlinskega pokrova ter rabo tal (Flanagan et al., 1995). Model ima tudi modul za generacijo vremenskih podatkov. Model WEPP ne upošteva jarkovne erozije. Prav tako je uporaba modela omejena na površine, kjer prevladuje Hortonov površinski odtok in je infiltracija zanemarljiva. Različ ica za poboč ja je primerna za dolžine poboč ij nekaj deset metrov, za več ja območ ja pa je treba uporabiti različ ico za povodja (Flanagan et al., 1995). 4.3 MODEL LISEM Med leti 1991 in 1994 se je v pokrajini Južni Limburg na Nizozemskem izvajal projekt na temo erozije tal. Poleg terenskih meritev in laboratorijskih raziskav je bilo del projekta tudi modeliranje procesa (De Roo, 1996a). Za razvoj lastnega modela, ki temelji na okolju GIS, so se odloč ili zaradi naslednjih razlogov (De Roo, 1996b): − izboljšanje opisa procesov, na primer infiltracije in sprošč anja, − vgraditev v okolje GIS, na primer zaradi boljšega opisa površja, − razvoj modela, ki omogoča uporabo podatkov daljinskega zaznavanja; dostopnost primernih podatkov je težava pri vseh procesno utemeljenih modelih. assessment. The most important advantage over the traditional models is the capability of temporal and spatial simulation of the processes. The model considers the following processes: rill and interrill erosion; sediment transport and deposition; infiltration; soil consolidation; the residue and canopy effect on soil detachment and infiltration; surface sealing; rill hydraulics; surface runoff; plant growth; residue decomposition; percolation; evaporation; transpiration; snow melt; the frozen soil effects on infiltration and erodibility; climate; the tillage effects on soil properties and the random roughness and conture effects. The model takes into account the spatial and temporal changes in the topography, surface roughness, soil properties, crops and the conditions of land use (Flanagan et al., 1995). A component for weather generation is also included in the model. The WEPP model does not consider gully erosion. Furthermore, the model can only be used for the hydrology dominated Hortonian overland flow with negligible infiltration. The hillslope version can be used for slope lengths of tens of meters. For larger areas, the catchment representation is necessary (Flanagan et al., 1995). 4.3 THE LISEM MODEL Between 1991 and 1994, a soil erosion project was carried out in the South Limburg region in the Netherlands. In addition to field measurement and laboratory investigations, modelling was also a part of the project (De Roo, 1996a). They decided to develop a new GIS based model for the following reasons (De Roo, 1996b): − improvement of process descriptions, infiltration and detachment, for example, − implementation in GIS, e.g. to prevent the unnecessary lumping of topography, − development of a model that allows input from remotely sensed data; the data availability is a major problem in physically based modelling Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 56 Model je zapisan v jeziku dinamič nega rastrskega GIS okolja PCRaster (Wesseling et al., 1996), ki so ga razvili na univerzi v Utrechtu. Ta omogoča zelo uč inkovito kodiranje, saj je imela različ ica iz leta 1 996 manj kot 200 vrstic. S tem je zagotovljeno preprosto spreminjanje, vzdrževanje in uporaba delov kode za druge namene (De Roo, 1996b). V modelu obravnavani procesi so naslednji (De Roo, 1996b): prestrezanje padavin, površinsko zadrževanje v mikrodepresijah, infiltracija, navpični tok vode v tleh, površinski tok, tok v strugi, sprošč anje zaradi dežja neposredno ali kapljanje s površine rastlin, sproščanje in premestitvena zmogljivost površinskega toka ter žlebič na in medžlebična erozija. Vpliv traktorskih kolesnic in majhnih utrjenih poti, ki so manjše od velikosti ene celice, je tudi upoštevan v modelu. 4.4 MODEL TOPOG TOPOG sta skupaj razvili CSIRO Land and Water in Cooperative Research Centre for Catchment Hydrology iz Avstralije. Ta model je determinističen hidrološki paket s porazdeljenimi parametri (CSIRO, 1999). Temelji na natanč ni analizi površja, kar pa zahteva tudi kakovostne podatke. Namenjen je predvsem za raziskovalne namene in ga lahko uporabljamo za opis topografskih atributov, prostorsko napovedovanje vodne bilance ter nevarnosti površinske erozije in plazenja, za simulacijo nestalnih hidroloških pojavov v povodju, modeliranje rasti in spreminjanja rastja in posledič ni vpliv na odtok vode iz povodja, modeliranje širjenja polutantov in dinamike plavin na površini povodja. Paket sestavlja več kot 30 programov, ki so rač unski, pomožni, kontrolni ali pa namenjeni grafični predstavitvi. Računske celice so prilagojene površju. Primer delitve povodja na celice lahko vidimo na sliki 3b. Avtorji priporočajo uporabo modela za manjša povodja, do velikosti 10 km 2 . The model is written in a dynamic modelling language of PCRaster GIS environment (Wesseling et al., 1996), developed at the University of Utrecht. It allows very efficient coding; the version of 1996 had fewer than 200 lines. This simplifies model modification, and maintenance and reusability of parts of the code for use for other purposes (De Roo, 1996b). The model incorporates the following processes (De Roo, 1996b): rainfall interception; surface storage in micro- depressions; infiltration; vertical water movement; overland flow; channel flow; the detachment by rainfall by throughfall or drainage from leaves; the overland flow detachment and transport capacity and rill and interrill erosion. The influence of tractor wheelings and small paved roads that are less than the cell size are also taken into account in the model. 4.4 THE TOPOG MODEL TOPOG has been developed jointly by the CSIRO Land and Water and the Cooperative Research Centre for Catchment Hydrology from Australia. It is a deterministic distributed-parameter hydrological model (CSIRO, 1999) based on a sophisticated terrain analysis, which also requires appropriate input data. It is intended as a research tool, and can be used to describe the topographic attributes, to predict the spatial distribution of waterlogging, erosion hazard and landslide risk, to simulate the unsteady hydrological behaviour of catchments, to model the growth of vegetation and its influence on water balance, and to model solute movement and sediment dynamics over the soil surface. The package consists of over 30 programs, which are either computational, utility, control or graphical routines. The computational cells are topography fitted. An example of catchment division into cells can be seen in Figure 3b. The model is intended for application to small catchments up to 10 km 2 . Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 57 a) b) Slika 3. a) Združevanje elementov v modelu WEPP (Flanagan et al., 1 995): H- poboč je, I- zajezitev, C- struga, WO- iztok iz povodja. b) Delitev površja na celice v modelu TOPOG (CSIRO, 1999). Temna debela č rta je vrh grebena, svetla pa dno doline. Celice so prilagojene površini. Figure 3. a) The linkage of the elements in WEPP (Flanagan et al., 1995): H- hillslope, I- impoundment, C- channel, WO- catchment outlet. b) Dividing the landscape into cells in TOPOG (CSIRO, 1999). The dark line is the top of a ridge; the bright bold lines, the bottom of a valley. Cells are topography fitted. 5. ZAKLJUČ KI V novejšem č asu so razne raziskovalne ustanove razvile več procesno utemeljenih modelov za napovedovanje erozije tal. Ti modeli omogoč ajo č asovno in prostorsko modeliranje celotnega kroga erozijskih procesov, od sproščanja, premeščanja do odlaganja. Uporabljati jih je mogoč e za posamezna pobočja ali pa na manjših povodjih. Njihova slabost je veliko število vhodnih parametrov (topografija, lastnosti tal, podatki o rastju itd.). Te parametre je pogosto težko dovolj zanesljivo oceniti oziroma izmeriti, kar lahko vodi do napač nih napovedi modela (De Roo, 1998). Tradicionalni modeli so primerni za napovedovanje srednjega letnega sprošč anja s poboč ij s preprosto geometrijo, kar je tudi njihov edini namen. V teh primerih so ravno tako uspešni kot bolj kompleksni procesno utemeljeni modeli, kar kaže primerjava med enač bami USLE/RUSLE 5. CONCLUSION In recent years, different research organisations have developed several process based models for erosion prediction. These models are capable of temporal and spatial modelling of the entire erosion process, including detachment, transport and deposition. They can be used either for individual hillslopes or smaller catchments. However, their disadvantage is the large number of input parameters needed (topography, soil properties, vegetation data, etc.). Estimating and measuring these parameters is often associated with a high degree of uncertainty, which can lead to poor model prediction (De Roo, 1998). Traditional models can be used to predict average annual soil loss from hillslopes of simple geometry, which is also their only purpose. But, in these cases, they can be just as successful as the more complex process based models, as shown by comparing the USLE/RUSLE equations Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 58 in modelom WEPP (Neraing & Nicks, 1998). Za modeliranje erozije tal v povodjih, in predvsem dotoka plavin v vodotoke, ter za č asovne in prostorske napovedi, pa je nujna uporaba modernejših metod. V Sloveniji se je do zdaj za ocenjevanje sprošč anja zemljin uporabljala Gavrilović eva metoda. Primer so ocene za povodja Soč e in primorsko-istrskih vodotokov (BF, 1970). Danes pa lahko storimo korak naprej. Geodetska uprava RS je pripravila digitalne modele reliefa v mreži 1 00x1 00 m ali manj (GURS, 2000), ki so podlaga za natanč nejšo obravnavo procesa. Tako bi bilo na primer v povodju Idrijce, kjer je znan problem spiranja živega srebra, treba uporabiti katerega od omenjenih modelov (npr. WEPP ali LISEM). Opozoriti pa je treba, da so za uporabo modernih simulacijskih orodij potrebni tudi zanesljivi podatki. with the WEPP model (Nearing & Nicks, 1998). However, to predict soil erosion in catchments, and especially sediment yield, as well as for temporal and spatial predictions, the modern methods must be used. Up to now, the Gavrilović method has been used to estimate sediment yield from catchments in Slovenia. An example is an assessment of sediment production in the Soč a basin and the coastal region (BF, 1970). But today, we can move further. The Surveying and Mapping Authority of the Republic of Slovenia has prepared the Digital Relief Model for the whole territory in a grid of 100x100 m or less (GURS, 2000). This is the basis for more accurate process modelling. A well known problem that could be handled with one of the mentioned models (e.g. WEPP, LISEM) is the erosion of the mercury-contaminated sites near Idrija. However, to use the process based models, accurate data is also needed. DODATEK: SLOVENSKO-ANGLEŠKI SLOVARČ EK POJMOV S PODROČ JA MODELIRANJA EROZIJE TAL Modeliranje model za simulacijo posameznega dogodka procesno utemeljeno modeliranje Vodni tok izbruh turbulentne motnje moč vodnega toka specifič na moč vodnega toka Erozija tal pljuskovna erozija * žlebič * sprošč anje potencialno sprošč anje premešč anje premestitvena zmogljivost odplavljanje dotok plavin pretok plavin * povzeto po Mikoš & Zupanc (2000) APPENDIX: SLOVENE-ENGLISH DICTIONARY OF SOIL EROSION MODELLING TERMINOLOGY Modelling single event based model process based modelling Water flow turbulent burst stream power unit stream power Soil erosion splash erosion rill detachment detachment potential transport transport capacity sediment yield sediment delivery sediment load * after Mikoš & Zupanc (2000) Petkovšek, G.: Procesno utemeljeno modeliranje erozije tal - Process Based Soil Erosion Modelling © Acta hydrotechnica 18/28 (2000), 41-60, Ljubljana 59 VIRI - REFERENCES BF (1 970). 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