{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:30:46Z","timestamp":1760146246280,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T00:00:00Z","timestamp":1729123200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (Portuguese Foundation for Science and Technology)","award":["UIDB\/04292\/2020","UIDP\/04292\/2020","LA\/P\/0069\/2020"],"award-info":[{"award-number":["UIDB\/04292\/2020","UIDP\/04292\/2020","LA\/P\/0069\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Water"],"abstract":"<jats:p>A one-dimensional numerical overland flow model based on the cascade plane theory was developed to estimate rainfall-induced runoff and soil erosion on converging and diverging plane surfaces. The model includes three components: (i) soil infiltration using Horton\u2019s infiltration equation, (ii) overland flow using the kinematic wave approximation of the one-dimensional Saint-Venant shallow water equations for a cascade of planes, and (iii) soil erosion based on the sediment transport continuity equation. The model\u2019s performance was evaluated by comparing numerical results with laboratory data from experiments using a rainfall simulator and a soil flume. Four independent experiments were conducted on converging and diverging surfaces under varying slope and rainfall conditions. Overall, the numerically simulated hydrographs and sediment graphs closely matched the laboratory results, showing the efficiency of the model for the tested controlled laboratory conditions. The model was then used to numerically explore the impact of different plane soil surface geometries on runoff and soil loss. Seven geometries were studied: one rectangular, three diverging, and three converging. A constant soil surface area, the rainfall intensity, and the slope gradient were maintained in all simulations. Results showed that increasing convergence angles led to a higher peak and total soil loss, while decreasing divergence angles reduced them.<\/jats:p>","DOI":"10.3390\/w16202955","type":"journal-article","created":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T04:42:15Z","timestamp":1729140135000},"page":"2955","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["One-Dimensional Numerical Cascade Model of Runoff and Soil Loss on Convergent and Divergent Plane Soil Surfaces: Laboratory Assessment and Numerical Simulations"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6669-8611","authenticated-orcid":false,"given":"Babar","family":"Mujtaba","sequence":"first","affiliation":[{"name":"Research Institute on Mines and Environment (RIME), Universit\u00e9 du Qu\u00e9bec en Abitibi-T\u00e9miscamingue (UQAT), 445 Blvd. De l\u2019Universit\u00e9, Rouyn-Noranda, QC J9X 5E4, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0135-2249","authenticated-orcid":false,"given":"Jo\u00e3o L. M. P.","family":"de Lima","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Faculty of Sciences and Technology, University of Coimbra, Rua Lu\u00eds Reis Santos, 3030-788 Coimbra, Portugal"},{"name":"MARE\u2014Marine and Environmental Sciences Centre\/ARNET\u2014Aquatic Research Network, University of Coimbra, 3030-790 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5134-4175","authenticated-orcid":false,"given":"M. Isabel P.","family":"de Lima","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Faculty of Sciences and Technology, University of Coimbra, Rua Lu\u00eds Reis Santos, 3030-788 Coimbra, Portugal"},{"name":"MARE\u2014Marine and Environmental Sciences Centre\/ARNET\u2014Aquatic Research Network, University of Coimbra, 3030-790 Coimbra, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1016\/S0309-1708(02)00067-2","article-title":"The influence of the pattern of moving storms on overland flow","volume":"25","author":"Singh","year":"2002","journal-title":"Adv. Water Resour."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1061\/(ASCE)HE.1943-5584.0000740","article-title":"An analytical closed form solution for 1D kinematic overland flow under moving rainstorms","volume":"18","author":"Isidoro","year":"2013","journal-title":"J. Hydrol. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1002\/hyp.5915","article-title":"A simulation model for unified interrill erosion and rill erosion on hillslopes","volume":"20","author":"Liu","year":"2006","journal-title":"Hydrol. Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.catena.2008.09.005","article-title":"Sediment transport rate-based model for rainfall-induced soil erosion","volume":"76","author":"Deng","year":"2008","journal-title":"Catena"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1061\/(ASCE)HE.1943-5584.0000032","article-title":"Two-dimensional hillslope scale soil erosion model","volume":"14","author":"An","year":"2009","journal-title":"J. Hydrol. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1007\/s40333-014-0066-9","article-title":"Evaluation of an erosion-sediment transport model for a hillslope using laboratory flume data","volume":"6","author":"Arguelles","year":"2014","journal-title":"J. Arid Land"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1463","DOI":"10.2136\/sssaj2005.0015","article-title":"Slope Shape Effects on Erosion","volume":"69","author":"Nearing","year":"2005","journal-title":"Soil Sci. Soc. Am. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"04017097","DOI":"10.1061\/(ASCE)EE.1943-7870.0001302","article-title":"Longitudinal Hillslope Shape Effects on Runoff and Sediment Loss: Laboratory Flume Experiments","volume":"144","author":"Isidoro","year":"2018","journal-title":"J. Environ. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1127\/zfg\/2019\/0578","article-title":"Importance of the hydraulics of converging and diverging flows on soil erosion override effects of rock fragment cover patterns: Experimental assessment","volume":"62","author":"Mujtaba","year":"2019","journal-title":"Z. Geomorphol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"105503","DOI":"10.1016\/j.catena.2021.105503","article-title":"Surface roughness effects on soil loss rate in complex hillslopes under laboratory conditions","volume":"206","author":"Mombini","year":"2021","journal-title":"Catena"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"106060","DOI":"10.1016\/j.catena.2022.106060","article-title":"Modeling the effects of topography and slope gradient of an artificially formed slope on runoff, sediment yield, water and soil loss of sandy soil","volume":"212","author":"Chen","year":"2022","journal-title":"Catena"},{"key":"ref_12","unstructured":"Goodman, R.E., and Shi, G. (1985). Block Theory and Its Application to Rock Engineering, Prentice Hall."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.jksus.2017.06.004","article-title":"Plane failure in rock slopes\u2014A review on stability analysis techniques","volume":"31","author":"Raghuvanshi","year":"2019","journal-title":"J. King Saud Univ."},{"key":"ref_14","unstructured":"Lopes, V.L. (1987). A Numerical Model of Watershed Erosion and Sediment Yield. [Ph.D. Thesis, University of Arizona in Tucson]."},{"key":"ref_15","unstructured":"Singh, V.P. (1995). KINEROS\u2014A kinematic runoff and erosion model. Computer Models of Watershed Hydrology, Water Resources Publications."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1029\/TR014i001p00446","article-title":"The role of infiltration in the hydrologic cycle","volume":"14","author":"Horton","year":"1933","journal-title":"Eos Trans. Am. Geophys. Union"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"401","DOI":"10.2136\/sssaj1937.03615995000100000074x","article-title":"The interpretation and application of runoff plane plot experiments with reference to soil erosion problems","volume":"1","author":"Horton","year":"1938","journal-title":"Soil Sci. Soc. Am. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"399","DOI":"10.2136\/sssaj1941.036159950005000C0075x","article-title":"An Approach Toward a Physical Interpretation of Infiltration-Capacity","volume":"5","author":"Horton","year":"1941","journal-title":"Soil Sci. Soc. Am. J."},{"key":"ref_19","unstructured":"Chow, V.T., Maidment, D.R., and Mays, L.W. (1988). Applied Hydrology, McGraw Hill."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Brutsaert, W. (2005). Hydrology: An Introduction, Cambridge University Press.","DOI":"10.1017\/CBO9780511808470"},{"key":"ref_21","unstructured":"Singh, V.P. (1996). Kinematic Wave Modelling in Water Resources: Surface-Water Hydrology, John Wiley and Sons Ltd."},{"key":"ref_22","first-page":"259","article-title":"Modeling the erosion process","volume":"Volume 5","author":"Haan","year":"1982","journal-title":"Hydrologic Modeling of Small Watersheds"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1029\/WR010i003p00485","article-title":"Concepts of mathematical modeling of sediment yield","volume":"10","author":"Bennett","year":"1974","journal-title":"Water Resour. Res."},{"key":"ref_24","unstructured":"Trimble, S.W. (1985). Erosion and sediment yield equations: Solutions for overland flow. Soil Erosion and Conservation, Proceedings of the Workshop on USLE Replacement, West Lafayette, IN, USA, 7\u20139 January 1985, USDA, National Soil Erosion Laboratory, Purdue University."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/0022-1694(82)90021-X","article-title":"Unsteady overland sedimentation","volume":"56","author":"Croley","year":"1982","journal-title":"J. Hydrol."},{"key":"ref_26","unstructured":"Mehta, A.J. (1983, January 9\u201312). Characterization tests for cohesive sediments. Proceedings of the Conference on Frontiers in Hydraulic Engineering, ASCE\/MIT, Cambridge, MA, USA."},{"key":"ref_27","first-page":"497","article-title":"Modeling sedimentation processes in small watersheds","volume":"174","author":"Lopes","year":"1988","journal-title":"IAHS Publ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/S2095-6339(15)30007-1","article-title":"Using meshes to change the characteristics of simulated rainfall produced by spray nozzles","volume":"2","author":"Carvalho","year":"2014","journal-title":"Int. Soil Water Conserv. Res."},{"key":"ref_29","unstructured":"Kibler, D.F., and Woolhiser, D.A. (1970). The Kinematic Cascade as a Hydrologic Model, Colorado State University. Hydrology Papers 39."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"279","DOI":"10.2478\/johh-2024-0017","article-title":"Empirical and physical modelling of soil erosion in agricultural hillslopes","volume":"72","author":"Seidou","year":"2024","journal-title":"J. Hydrol. Hydromech."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"108202","DOI":"10.1016\/j.catena.2024.108202","article-title":"Modeling soil erosion dynamic processes along hillslopes with vegetation impact across different land uses on the Loess Plateau of China","volume":"243","author":"Wang","year":"2024","journal-title":"Catena"}],"container-title":["Water"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4441\/16\/20\/2955\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:14:59Z","timestamp":1760112899000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4441\/16\/20\/2955"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,17]]},"references-count":31,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["w16202955"],"URL":"https:\/\/doi.org\/10.3390\/w16202955","relation":{},"ISSN":["2073-4441"],"issn-type":[{"type":"electronic","value":"2073-4441"}],"subject":[],"published":{"date-parts":[[2024,10,17]]}}}