Spatially distributed GIS-realized mathematical model of rainstorm erosion losses of soil

Keywords: water soil erosion, mathematical model, GIS-implementation, model verification


In connection with the wide and ever increasing spread of erosion degradation of agricultural lands in Ukraine, the task of developing mathematical models and methods for calculating water erosion of soils corresponding to the current level of erosion study and the demands of soil protection practices is becoming increasingly important. The article is devoted to the development of a spatially distributed GIS-implemented mathematical model of rainstorm soil erosion, which accounts for most of the annual soil losses (in the Steppe zone, for example, about 90 %). The development of the model is based on the most theoretically and informationally grounded model for the Steppe and Forest-Steppe of Ukraine , “the logical-mathematical model of rainstorm soil outwash” developed by H. I. Shvebs (1974, 1981), as well as the results of theoretical and field studies and mathematical modeling of the slope runoff and water erosion of soil, carried out at the Department of Physical Geography and Environmental Management of Odessa I. I. Mechnikov National University in the 1990s - 2010s, and also the possibilities of modern geoinformation technologies. For the spatial implementation of the model, a raster model of spatial data and operators of the PCRaster GIS-package (University of Utrecht, the Netherlands) were used, integrated with the Basic programming language into a single system that provides an implementation of the computational algorithm. The developed physical-statistical model of soil erosion-sedimentation takes into account the peculiarities of the formation of slope runoff and soil outwash in conditions of excessive nonstationarity of heavy rainfall, as well as spatial heterogeneity of all major natural and economic factors of water erosion on a slope, including slope steepness, exposure, longitudinal and transverse forms of slopes, soil erodibility, structure of sown areas and anti-erosion measures. Checking the adequacy of the mathematical model was performed using observational data of four experimental catchments ; two runoff plots of the Moldavan water-balance station with total area of 0.08 ha, the Ploska catchment with area of 8.5 ha (Boguslav field experimental base of Ukrainian Hydrometeorological Institute) and the Sukha catchment with area of 63 ha (Veliko-Anadol water-balance station) with observation periods of 17-31 years. Comparison of the calculated average over the catchment area of mean annual values of rainstorm soil losses, with the corresponding values obtained from measurements on these catchments, made on the basis of Nash-Sutcliff efficiency criterion (NS), allowed us to evaluate the quality of the model as good (NS = 0.72).

Author Biographies

А. A. Svetlitchnyi
Odessa I. I. Mechnikov National University
A. V. Piatkova
Odessa I. I. Mechnikov National University


1. Ascough II, J.C, Baffaut, C, Nearing, M.A, Liu, B.Y., 1997. The WEPP watershed model: I. Hydrology and erosion. Transactions of the ASAE, 40(4), 921– 933.
2. Chorny, S. G., 1996. Skhylovi zroshuvani ahrolandshafty: eroziia, hruntoutvorennia, ratsionalne vykorystannia [Slope irrigated agro-landscapes: erosion, soil formation, rational use]. Borisphen, Kherson, (in Ukrainian)
3. De Roo, A.P.J, Wesseling, C.G, Ritsema, C.J., 1996. LISEM: a single event physically-based hydrologic and soil erosion model for drainage basins. I: Theory, input and output. Hydrological Processes, 10, 1107–1117.
4. Kanash, O., Osypchuk, S., 2003. Erosiia gruntiv Ukrainy: suchasnyi stan, aspekty raionuvannia, tendentsiia bahatorichnykh zmin [Soil Erosion in Ukraine: the present state, aspects of zoning, the tendency of many years of change]. Genesis, geography and ecology of soil. Publishing Center of Ivan Franko National University of Lviv, Lviv, 158- 163 (in Ukrainian)
5. Koval’chuk, I.P., Yevsyukov, T.O., Mkrtchian, O. S., Lobans’ka, N. I., 2009. Heoprostorove modeliuvannia potentsialu rozvytku dehradatsiinykh protsesiv na ornykh zemliakh [Geospatial modeling of the potential of degradation processes on arable land]. Land system and cadaster, 4, 72-82 (in Ukrainian)
6. Lavrovskiy, A.B., Igumentcev, A.F., Anisimov, S.V., Shchegoleva, L.G., 1987. K voprosu postroeniya modeli stoka i smyva pochvy pri livnevoi erozii [On the question of constructing a model of flow and soil losses during shower erosion]. Proc. All- Union cоnf. “The regularities of manifestation of erosion and channel processes in various natural conditions”. Publishing Mosk. Univ., Moscow, 89-90 (in Russian)
7. Morgan, R.P.C, Quinton, J.N., Smith, R.E., Govers, G., Poesen, J.W.A., Auerswald, K., Chisci, G., Torri, D., Styczen, M.E., 1998. The European soil erosion model (EUROSEM): a dynamic approach for predicting sediment transport from fields and small catchments. Earth Surface Processes and Landforms, 23, 527-544.
8. Natsionalna dopovid pro stan rodiuchosti gruntiv Ukrainy [National report on soil fertility in Ukraine], 2010. Baliuk, S.A., Medvedev, V.V., Tarariko, O.G., Grekov O.V., Balaev, A.D. (eds). VIK PRINT, Kyiv (in Ukrainian).
9. Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models part I — A discussion of principles. Journ. Hydrology, 10(3), 282–290.
10. PCRaster: Software for Environmental Modeling, 2018. Retrieved from: downloads/latest-release/.
11. Pravila po opredeleniju maksimal’nyh rashodov vody dozhdevyh pavodkov s malyh vodosborov pri proekti-rovanii protivojerozionnyh gidrotehnicheskih sooruzhenij na ravninnoj territorii USSR. VSN 10.15 USSR 1-87 [Rules for determining the maximum flow of rainwater floods from small catchments when designing anti-erosion hydrau-lic structures in the lowland territory of the USSR. VSN 10.15 USSR 1-87], 1987. Kyiv (in Russian).
12. Pyatkova, A.V., 2008. Osobennosty modelirovaniya vodnoy erosiyi s uchetom prostranstvennoy izmenchivosty eye factorov [Features of soil water erosion modeling taking into account spatial changeability of its factors], Mete-orology, Climatology and Hydrology, 50,437-442 (in Russian).
13. Piatkova, A.V., 2013. Urakhuvannia struktury skhylovoho stikannia pry prostorovomu modeliuvanni zlyvovoho zmyvu gruntu [Taking into account the surfact flowing structure on the space modeling of rainfall soil losses]. Gerald of the Odessa National University. Series:Geography & Geology, 18, 82-
87 (in Ukrainian).
14. Renard, K.G., Foster, G.R., Weesies, G.A., McCook, D.K., Yoder, D.C., 1993. Predicting soil erosion by water: a guide to conservation planning with the Revised Universal Soil Loss Equation (RUSLE), Agriculture Handbook #703, U.S. Department of Agriculture, Washington.
15. Schindewolf, M.; Schmidt, J., 2012. Parameterization of the EROSION 2D/3D soil erosion model using a small-scale rainfall simulator and upstream runoff simulation. Catena, 91, 47–55.
16. Shvebs, H.I., 1974. Formirovaniye vodnoy erozii. stoka nanosov i ikh otsenka [Formation of water erosion, sediment yield and their assessment]. Hydrometeoizdat, Leningrad (in Russian).
17. Shvebs, H.I., 1981. Teoreticheskiye osnovy eroziovedeniya [Theoretical foundations of erosion]. Vyshcha shkola, Ky-iv-Odesa (in Russian).
18. Smith, R.E, Goodrich, D.C, Quinton, J.N., 1995. Dynamic, distributed simulation of watershed erosion: The KINEROS2 and EUROSEM models. Journal of Soil and Water Conservation, 50, 517–520.
19. Spravochnik po pochvozashhitnomu zemledeliju, 1990 [Handbook of Soil Protective Agriculture]. I. N. Bezruchko, L.Ya. Milchevskaya (eds). Urozhay, Kiev (in Russian).
20. Sribnyi, I.A., 1977. Srednegodovoy stok vody i smyv pochvy so sklonov [The average annual water flow and soil out-wash from the slopes]. Water construction on small rivers. Budivelnik, Kiev, 145-147 (in Russian).
21. Sribnyi, I.A., Vergunov, V.A., 1993. Vyznachennia zmyvu hruntu zi skhyliv [Determination of the soil losses from the slopes]. Herald of agrarian science, 7, 42-46 (in Ukrainian).
22. Svetlitchnyi, A.A., 1995. Prostranstvenno-vremennaya otsenka livnevoy erozii pochv [Spatial-temporal assessment of soil erosion], Dep. SSTB of Ukraine, №1911-Uk95 (in Russian).
23. Svetlitchnyi, A.A., 1999. Printsipyi sovershenstvovaniya empiricheskih modeley smyiva pochvyi [The principals of improving empirical models of soil erosion]. Eurasian Soil Science, 32(8), 917-923.
24. Svitlychnyi O. O., Ivanova A. V., 2003. Pryncypy prostorovogo modelyuvannya gidrometeorologichnyh umov zlyvovogo zmyvu gruntu [Principles of spatial modelling of hydrometeorological conditions of soil storm wash off]. Gerald of the Odessa National University. Series:Geography & Geology, 8, 77-82 (in Ukrainian).
25. Svetlitchnyi, A.A., Shvebs, H.I., Cherny, S.G., 2004. Eroziovedenie: teoreticheskie i prikladnyie aspektyi [Soil erosion science: theoretical and applied aspects]. VTD “University Book”, Sumy (in Russian).
26. Svetlitchnyi, A.A., Plotnitskiy, S.V., Stepovaya, O.Y., 2003. Spatial distribution of soil moisture convent within catchments and its modeling on the basis of topographic data. Journal of Hydrology, 277, 50-60.
27. Vinogradov A., Nikiforovskiy A., 2015. Analiz sootvetstvija kriteriev kachestva modelirovanija processov formirovani-ja stoka malyh rek [Quality conformity analysis of runoff formation modeling criteria for small rivers]. Herald of Moscow State University. Series: Nature Sciences, 2, 33-38.