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).
The paper deals with the forecast of changes in erosion soil losses during the spring snowmelt due to climate change in the regions of Ukraine in the middle of the 21st century (during 2031–2050) and at its end (during 2081–2100) compared with the values of the baseline period (1961–1990). The forecast is based on the use of the so-called “hydrometeorological factor of spring soil loss”. This factor is a part of the physical-statistical mathematical model of soil erosion lossduring spring snowmelt, developed at the Department of Physical Geography of Odesa I. I. Mechnikov State (since 2000 — National) University during the 1980s – 1990s. The long-term average value of the hydrometeorological factor is linearly related to the long-term average value of spring erosion soil loss. Therefore, the relative change in the hydrometeorological factor corresponds to the relative change in soil erosion losses. The developed methodology for assessing climate-induced changes in soil erosion losses in five regions of Ukraine (North, West, Center, East and South) takes into account the change in water equivalent of snow cover at the beginning of snow melting, the change in surface runoff and its turbidity, and changes in soil erodibility. The forecast of changes in erosion soil loss was carried out using projections of annual and monthly average air temperatures and precipitation for 2031–2050 and 2081–2100 in accordance with scenario A1B from AR4 of the IPCC. As a result of the research, it was found that both in the middle and at the end of the 21st century a decrease in the rate of soil erosion during the period of spring snowmelt is expected. During 2031–2050, the expected soil losses will be less than corresponding baseline period values within the West region by 79%, within the North and East regions by 81%, and within the Center region by 85%. In the South region, the spring soil losses will be zero due to the lack of snow cover. During 2081–2100 snow cover will be absent not only in the South region, but also in the Center and East regions. In the regions North and West snow cover will remain, but the spring soil erosion losses will decrease by dozens of times and will be so small that they can also be ignored.
Formulation of the problem. Water erosion of soils is the most widespread and dangerous soil degradation process in Ukraine. The development of an effective system of soil protection measures requires the use of spatially distributed mathematical models of soil erosion losses. This, in turn, highlights the problem of spatially distributed source data, which adequately reflect the spatial differentiation of factors of the erosion process, among which the main one is the relief. The purpose of the article. Assessing the adequacy of available spatially distributed source data, including cartographic and freely distributed global digital elevation models (DEMs), for spatially distributed quantitative assessment of soil erosion losses at the local level of territorial coverage is the aim of the article. Assessing from this point of view the scale of the original cartographic data, different global DEMs and their spatial resolution, as well as the degree of spatial generalization of the original data. Materials and methods. The solution of the set tasks was performed by the method of simulation modeling with the use of physical-statistical GIS-realized mathematical model of soil erosion-accumulation, developed at Odessa I. I. Mechnikov National University. Source data arrays were tested with DEMs SRTM90 and SRTM30 with a spatial resolution of 3 and 1 angular seconds, respectively, and AW3D30 with a spatial resolution of 1 angular second, as well as with cartographic DEMs based on topographic maps of scale 1:10000 and 1:25000. For testing the initial data, three test plots with an area of 2.67, 0.59 and 0.21 km2 were selected. The plots are located in the Balta district of Odessa region on the southern spurs of the Podolska upland. Results. It is established that freely distributed global digital elevation models SRTM and AW3D30 in the conditions of flat terrain do not always allow to adequately display the structure of slope runoff and, accordingly, to correctly perform calculations of soil erosion losses. The maximum deviation of the average soil erosion losses calculated for the test plots using global DEMs from the soil losses calculated using the reference DEM for SRTM30 and AW3D30 was 27%, for SRTM90 – almost 70%. The distribution of soil losses over the area of test plots obtained using different global DEMs differs even more. When using DEM based on topographic maps, reducing the scale of the original maps from 1: 10000 to 1: 25000 leads to a decrease in the average value of soil erosion losses by about 20% due mainly to reducing the magnitude and area of distribution of maximum soil losses, and on slopes of complex shape also due to changes in the area of accumulation zones. The degree of spatial generalization of the initial data significantly affects the results of the assessment of soil erosion losses both in relation to the average values and their distribution over the area. For small areas, the use of raster cells larger than 50 m is impractical. Scientific novelty and practical significance. It has been shown for the first time that in the conditions of flat terrain at the local level of spatial coverage, the freely distributed global DEM SRTM and AW3D30 are not always hydrologically correct. The reasons and conditions of violation of this correctness are specified. It has been established that the global DEM AW3D30 has local instrumental errors that may make it impossible to use it. The most realistic values of soil erosion losses are provided by DEM SRTM with a spatial resolution of 1 angular second.
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