Soil and Water Loss Estimation Mathematical Models: A Review
Resumo
The erosion process is natural but has intensified in recent years due to anthropogenic activities, becoming a socio-environmental issue resulting from soil degradation. This process impacts various areas, and its measurement is a critical tool for adopting management strategies and conservation practices. Mathematical models can estimate soil losses under different environmental conditions. When integrated with GIS environments, these models significantly reduce execution and study costs, while generating valuable information, creating maps, and characterizing the environment. This study aimed to perform a systematic literature review on mathematical models for soil and water loss and to highlight some of their applications through the analysis of articles published in journals and indexed in electronic databases. Over the years, various models have been developed, and their use has proven essential for implementing conservation practices and restoring degraded areas. Due to the complexity of the process, it is crucial to consider the parameters available in each situation to select the most appropriate model.
Referências
Agricultural Research Service, 2012. Erosion productivity - impact calculator. Available at: Agricultural Research Service. <http://www.ars.usda.gov/Research/docs.htm?docid=9791> [Accessed 12 May 2024].
Alewell, C., Borrelli, P., Meusburger, K. and Panagos, P., 2019. Using the USLE: Chances, challenges and limitations of soil erosion modelling. International Soil and Water Conservation Research, 7(3), pp.203-225. https://doi.org/10.1016/j.iswcr.2019.05.004
Anache, J.A.A., Wendland, E.C., Oliveira, P.T.S., Flanagan, D.C. and Nearing, M.A., 2017. Runoff and soil erosion plot-scale studies under natural rainfall: A meta-analysis of the Brazilian experience. Catena, 152, pp. 29-39. https://doi.org/10.1016/j.catena.2017.01.003
Aouichaty, N. and Koulali, Y., 2024. Impact of spatial resolution on soil loss estimation: a case study of abandoned quarries in Morocco. Mediterranean Geoscience Reviews, 6, pp. 249–268. https://doi.org/10.1007/s42990-024-00138-2
Aragão, R., 2000. Estimativa dos parâmetros do modelo distribuído WESP com dados da bacia experimental de Sumé-PB. Masters. Universidade Federal da Paraíba – Campus II.
Bellinaso, T.B., 2015. Regionalização do fator escoamento superficial da Musle. In: Associação Brasileira de Recursos Hídricos, XXI Simpósio Brasileiro de Recursos Hídricos. Brasília – DF, 22-27 November 2015. Porto Alegre: ABRHidro.
Bertoni, J. and Lombardi Neto, F., 2014. Conservação do solo. São Paulo: Ícone.
Beskow, S., Mello, C.R., Norton, L.D., Curi, N., Viola, M.R. and Avanzi, J.C., 2009. Soil erosion prediction in the Grande River Basin, Brazil using distributed modeling. Catena, 79(1), pp. 49-59. https://doi.org/10.1016/j.catena.2009.05.010
Browning, G.M, Parish, C.L. and Glass, J., 1947. A method for determining the use and limitations of rotation and conservation practices in the control of soil erosion in Iowa. Agronomy Journal, 39(1), pp. 65-73. https://doi.org/10.2134/agronj1947.00021962003900010008x
Cardoso, D.P., dos Santos, W.P., Silva, S.H.G., Merlo, M.N., Acuña-Guzman, S.F., Acerbi Júnior, F.W., Viola, M.R., Silva, M.L.N., Curi, N., and Avanzi, J.C., 2024. Estimation and assessment of water erosion in the Peixe Angical basin, Brazil. Journal of South American Earth Sciences, 149, 105235. https://doi.org/10.1016/j.jsames.2024.105235
Cassol, E.A., Silva, T.S., Eltz, F.L.F and Levien, R., 2018. Soil Erodibility under Natural Rainfall Conditions as the K Factor of the Universal Soil Loss Equation and Application of the Nomograph for a Subtropical Ultisol. Revista Brasileira de Ciência do Solo, 42. https://doi.org/10.1590/18069657rbcs20170262
Castro, A.M., Alves, W.S., Marcionilio, S.M.L.O., Moura, D.M.B., and Oliveira, D.M.S., 2022. Soil losses related to land use and rainfall seasonality in a watershed in the Brazilian Cerrado. Journal of South American Earth Sciences, 119, p.104020. https://doi.org/10.1016/j.jsames.2022.104020
Checchia, T., 2005. Avaliação de perda de solo por erosão hídrica e estudo de energia na bacia do Rio Caeté, Alfredo Wagner - Santa Catarina. Masters. Universidade Federal de Santa Catarina.
Ebling, E.D., Reichert, J.M., Pelaéz, J.J.Z., Rodrigues, M.F.R., Valente, M.L., Calvacante, R.B., Reggiani, P. and Srinivasan, R., 2021. Event-based hydrology and sedimentation in paired watersheds under commercial eucalyptus and grasslands in the Brazilian Pampa biome. International Soil and Water Conservation Research, 9(2), pp. 180-194. https://doi.org/10.1016/j.iswcr.2020.10.008
FAO, 2015. Status of the World’s Soil Resources (SWSR) – Main Report. Available at: Food and Agriculture Organization of the United Nations and Intergovernmental Technical Panel on Soils, Rome, Italy. <http://www.fao.org/3/a-i5199e.pdf> [Accessed 08 June 2024].
Fatima, B., Hlila, R., El Kadiri, K., Ouallali, A., Belkendil, A., Beroho, M., Aqil, T., Davis, B.J., and Soufan, W., 2024. Modelling, quantification and estimation of the soil water erosion using the Revised Universal Soil Loss Equation with Sediment Delivery Ratio and the analytic hierarchy process models. Earth Surface Processes and Landforms, 49, pp. 3158–3176. https://doi.org/10.1002/esp.5882
Flanagan, D.C. and Nearing, M.A., 1995. USDA: Water erosion prediction project. Technical Documentation, 10. Available at: <https://www.ars.usda.gov/midwest-area/west-lafayette-in/national-soil-erosion-research/docs/wepp/wepp-model-documentation/> [Accessed 17 May 2024].
Grum, B., Woldearegay, K., Hessel, R., Baartman, J.E.M., Abdulkair, M., Yazew, E., Kessler, A., Ritsema, C.J. and Geissen, V., 2017. Assessing the effect of water harvesting techniques on event-based hydrological responses and sediment yield at a catchment scale in northern Ethiopia using the Limburg Soil Erosion Model (LISEM). Catena, 159, pp. 20-34. https://doi.org/10.1016/j.catena.2017.07.018
Kinnell, P.I.A., 2010. Event soil loss, runoff and the Universal Soil Loss Equation family of models: A review. Journal of Hydrology, 385(1–4), pp. 384–397. https://doi.org/10.1016/j.jhydrol.2010.01.024
Kruk, E., 2021. Use of chosen methods for determination of the USLE soil erodibility factor on the example of loess slope. Journal of Ecological Engineering, 22(1), pp. 151-161. https://doi.org/10.12911/22998993/128861
Laws, J.O. and Parsons, D.A., 1943. The Relation of Raindrop-Size to Intensity. Transactions American Geophysical Union, 24, pp. 452-460. https://doi.org/10.1029/TR024i002p00452
Lense, G.H.E.; Cristo, T.; Moreira, R.S.; Avanzi, J.C. and Mincato, R.L., 2019. Estimates of soil losses by the erosion potential method in tropical latosols. Ciência e Agrotecnologia, 43, pp. 1-10. https://doi.org/10.1590/1413-7054201943012719
Lopes, V.L., 1987. A numerical model of watershed erosion and sediment yield. PhD. University of Arizona.
Lopes, W.T.A., 2003. Efeito de escala na modelagem hidrossedimentológica na região semi-árida da Paraíba. Masters. Universidade Federal de Campina Grande.
Mallmann, E.H., Salvador, C.G. and Michel, G.P., 2019. Aplicação da MUSLE considerando diferentes métodos de cálculo do fator topográfico LS. In: Associação Brasileira de Recursos Hídricos, XXIII Simpósio Brasileiro de Recursos Hídricos, 23. Foz do Iguaçu - PR, 24-18 November 2019. Porto Alegre: ABRHidro.
Monchareon, L., 1982. Application of soil maps and report for soil and water conservation. Bangkok: department of land development.
Musgrave, G.W., 1947. The quantitative evaluation of factors in water erosion a first approximation. Journal of Soil and Water Conservation, 2(3), pp. 133-138,170.
Nachtigall, S.D., Nunes, M.C.M., Moura-Bueno, J.M.M., Lima, C.L.R., Miguel, P., Beskow, S. and Silva, T.P., 2020. Modelagem espacial da erosão hídrica do solo associada à sazonalidade agroclimática na região sul do Rio Grande do Sul, Brasil. Engenharia Sanitária e Ambiental, 25(6). https://doi.org/10.1590/S1413-4152202020190136
Nearing, M.A., Lane, I.J. and Lopes, V.I., 1994. Modelling soil erosion. In: R. Lal, ed. 1994. Soil erosion: research methods. Ankeny: Soil and Water Conservation Society. pp. 127-156.
Paiva, F.M.L., 2008. Estudo comparativo entre três modelos de base física na modelagem hidrossedimentológica em microbacias na região semiárida paraibana. Masters. Universidade Federal de Campina Grande.
Picini, A.G., Valeriano, M.M., Neto, F.L. and Júnior, J.Z., 2005. Ajuste dos simuladores de dados meteorológicos do modelo EPIC para diferentes locais do Estado de São Paulo. Revista Brasileira de Engenharia Agrícola e Ambiental, 9(2). https://doi.org/10.1590/S1415-43662005000200015
Piscoya, V.C., Souza, W.P., Cantalice, J.R.B., Filho, M.C.F., Melo, R.C.P. and Filho, R.N.A., 2020. Wepp model for rill erosion estimation in a Brazilian semiarid watershed. Revista Caatinga, 33(3), pp. 835–843. https://doi.org/10.1590/1983-21252020v33n327rc
Pruski, F.F., 2013. Conservação de solo e água: práticas mecânicas para o controle da erosão hídrica. Viçosa: Editora UFV.
Purcino, M.D., 2017. Espacialização dos parâmetros físico-hídricos do solo e associação com a vulnerabilidade à erosão hídrica em dois ambientes antropizados do Ribeirão do Cipó. Masters. Universidade Federal de Alfenas.
Renard, K.G., Foster, G.R., Weesies, G.A., McCool, D.K. and Yoder, D.C., 1997. Predicting soil erosion by water — a guide to conservation planning with the Revised Universal Soil Loss Equation (RUSLE). Available at: United States Department of Agriculture, Agricultural Research Service (USDA-ARS) Handbook No. 703. <https://www3.epa.gov/npdes/pubs/ruslech2.pdf> [Accessed 17 May 2024].
Salumbo, A.M. de O., 2020. A Review of Soil Erosion Estimation Methods. Agricultural Sciences, 11, pp. 667–691. https://doi.org/10.4236/as.2020.118043
Samarinas, N., Tsakiridis, N.L., Kalopesa, E., and Zalidis, G.C., 2024. Soil Loss Estimation by Water Erosion in Agricultural Areas Introducing Artificial Intelligence Geospatial Layers into the RUSLE Model. Land, 13(2). https://doi.org/10.3390/land13020174
Santos, I., Fill, H.D., Sugai, M.R.V.B., Buba, H., Kishi, R.T., Marone, E., Lautert, L.F.C., 2001. Hidrometria aplicada. Curitiba: LACTEC/UFPR.
Schwamback, D., Amorim Brandão, A.R., Rosalem, L.M.P., Oliveira, P.T.S., Anache, J.A.A., Wendland, E., Berndtsson, R., and Persson, M., 2024. Land use transformations in the Brazilian Savanna: A decade of soil erosion and runoff measurements. Catena, 246, p.108412. https://doi.org/10.1016/j.catena.2024.108412
Smith, D.D., 1941. Interpretation of soil conservation data for field use. Agricultural Engineering, 22(5), pp. 173-175.
Stone, R.P. and Hilborn, D., 2012. Universal soil loss equation (USLE) factsheet. Ontario: Ministry of Agriculture, Food and Rural Affairs.
Tucci, C.E.M., 2005. Modelos hidrológicos. 2.ed. Porto Alegre: ABRH/UFRGS.
Walker, S.J., 2017. An alternative method for deriving a USLE nomograph K factor equation. In: The Modelling and Simulation Society of Australia and New Zealand Inc., 22nd International Congress on Modelling and Simulation. Tasmania - Australia, 3-8 December 2017. Canberra: The Modelling and Simulation Society of Australia and New Zealand Inc.
Wischmeier, W.H., 1977. Soil erodibility by rainfall and runoff. In: T.J. Toy ed. Erosion: Research techniques, erodibility and sediment delivery. 1977 Norwich: GEO Abstracts. pp. 45–56.
Wischmeier, W.H. and Smith., D.D., 1965, Predicting rainfall erosion losses from cropland east of the Rocky Mountains, Guide for selection of practices for soil and water conservation. Agriculture Handbook No 282. Washington: U.S. Department of Agriculture.
Wischmeier, W.H. and Smith, D.D., 1978. Prediting rainfall erosion losses: a guide to conservation planning. Agriculture Handbook, 537. Washington: U.S. Department of Agriculture.
Williams, J.R., 1975. Sediment-yield prediction with universal equation using runoff energy factor. Oxford: USDA Sedimentation Laboratory, pp. 244-252.
Williams, J.R., Dyke, P.T. and Jones, C.A., 1983. EPIC: a model for assessing the effects of erosion on soil productivity. In: W.K. LAUENROTH, G.V. SKOGERBOE, M. FLUG (eds.) Developments in Environmental Modelling, pp. 553-572.
Zingg, A.W., 1940. Degree and length of land slope as it affects soil loss in runoff. Agricultural Engineering, 21 (2), pp. 59-64.
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