{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T15:42:15Z","timestamp":1782920535058,"version":"3.54.5"},"reference-count":85,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100005412","name":"Shahid Chamran University of Ahvaz","doi-asserted-by":"publisher","award":["SCU.EG98.827, 01\/06\/2019"],"award-info":[{"award-number":["SCU.EG98.827, 01\/06\/2019"]}],"id":[{"id":"10.13039\/501100005412","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005412","name":"Shahid Chamran University of Ahvaz","doi-asserted-by":"publisher","award":["SCU.EG98.827, 01\/06\/2019"],"award-info":[{"award-number":["SCU.EG98.827, 01\/06\/2019"]}],"id":[{"id":"10.13039\/501100005412","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005412","name":"Shahid Chamran University of Ahvaz","doi-asserted-by":"publisher","award":["SCU.EG98.827, 01\/06\/2019"],"award-info":[{"award-number":["SCU.EG98.827, 01\/06\/2019"]}],"id":[{"id":"10.13039\/501100005412","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Earth Sci Inform"],"published-print":{"date-parts":[[2024,2]]},"DOI":"10.1007\/s12145-023-01178-2","type":"journal-article","created":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T10:02:47Z","timestamp":1701424967000},"page":"365-384","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Challenges of rainfall erosivity prediction: A Novel GIS-Based Optimization algorithm to reduce uncertainty in large country modeling"],"prefix":"10.1007","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6058-822X","authenticated-orcid":false,"given":"Mostafa","family":"Kabolizadeh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4576-6275","authenticated-orcid":false,"given":"Kazem","family":"Rangzan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4848-322X","authenticated-orcid":false,"given":"Shahin","family":"Mohammadi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2576-793X","authenticated-orcid":false,"given":"Hamidreza","family":"Rabiei-Dastjerdi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,12,1]]},"reference":[{"key":"1178_CR1","doi-asserted-by":"publisher","first-page":"167","DOI":"10.5194\/gmd-12-167-2019","volume":"12","author":"R Abdelaziz","year":"2019","unstructured":"Abdelaziz R, Merkel BJ, Zambrano-Bigiarini M, Nair S (2019) Particle swarm optimization for the estimation of surface complexation constants with the geochemical model PHREEQC-3.1.2. Geosci Model Dev 12:167\u2013177. https:\/\/doi.org\/10.5194\/gmd-12-167-2019","journal-title":"Geosci Model Dev"},{"key":"1178_CR2","doi-asserted-by":"publisher","unstructured":"Achite M, Katipo\u011flu OM, Javari M, Caloiero T (2023) Hybrid interpolation approach for estimating the spatial variation of annual precipitation in the Macta basin, Algeria. Theoretical and Applied Climatology, 1-28. https:\/\/doi.org\/10.1007\/s00704-023-04685-w","DOI":"10.1007\/s00704-023-04685-w"},{"key":"1178_CR3","doi-asserted-by":"publisher","first-page":"D02115","DOI":"10.1029\/2008JD011010","volume":"114","author":"E Aguilar","year":"2009","unstructured":"Aguilar E, Aziz Barry A, Brunet M et al (2009) Changes in temperature and precipitation extremes in western central Africa, Guinea Conakry, and Zimbabwe, 1955\u20132006. J Geophys Res 114:D02115. https:\/\/doi.org\/10.1029\/2008JD011010","journal-title":"J Geophys Res"},{"key":"1178_CR4","doi-asserted-by":"publisher","unstructured":"Aguilar FJ, Ag\u00fcera F, Aguilar MA, Carvajal F (2005) Effects of terrain morphology, sampling density, and interpolation methods on grid DEM accuracy. Photogrammetric Engineering and Remote Sensing 71:805\u2013816. https:\/\/doi.org\/10.14358\/PERS.71.7.805","DOI":"10.14358\/PERS.71.7.805"},{"key":"1178_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.gsd.2021.100573","volume":"13","author":"AY Ahmad","year":"2021","unstructured":"Ahmad AY, Saleh IA, Balakrishnan P, Al-Ghouti MA (2021) Comparison GIS-Based interpolation methods for mapping groundwater quality in the state of Qatar. Groundw Sustain Dev 13:100573","journal-title":"Groundw Sustain Dev"},{"key":"1178_CR6","unstructured":"Alimohammadi A, Rabiei HR, Firouzabadi PZ (2004) A new approach for modeling uncertainty in remote sensing change detection process. In: Proceedings of the 12th International Conference on Geomatics. pp 503\u2013508"},{"key":"1178_CR7","doi-asserted-by":"publisher","first-page":"993","DOI":"10.1007\/s40710-021-00529-9","volume":"8","author":"A Antonakos","year":"2021","unstructured":"Antonakos A, Lambrakis N (2021) Spatial Interpolation for the Distribution of Groundwater Level in an Area of Complex Geology Using Widely Available GIS Tools. Environmental Processes 8:993\u20131026","journal-title":"Environmental Processes"},{"key":"1178_CR8","doi-asserted-by":"publisher","first-page":"1819","DOI":"10.5194\/hess-23-1819-2019","volume":"23","author":"K Auerswald","year":"2019","unstructured":"Auerswald K, Fischer FK, Winterrath T, Brandhuber R (2019) Rain erosivity map for Germany derived from contiguous radar rain data. Hydrol Earth Syst Sci 23:1819\u20131832. https:\/\/doi.org\/10.5194\/hess-23-1819-2019","journal-title":"Hydrol Earth Syst Sci"},{"key":"1178_CR9","doi-asserted-by":"publisher","first-page":"1298","DOI":"10.1016\/j.scitotenv.2016.11.123","volume":"579","author":"C Ballabio","year":"2017","unstructured":"Ballabio C, Borrelli P, Spinoni J et al (2017) Mapping monthly rainfall erosivity in Europe. Sci Total Environ 579:1298\u20131315. https:\/\/doi.org\/10.1016\/j.scitotenv.2016.11.123","journal-title":"Sci Total Environ"},{"key":"1178_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/J.ASOC.2021.107296","volume":"106","author":"B Bayat","year":"2021","unstructured":"Bayat B, Nasseri M, Delmelle E (2021) Uncertainty-based rainfall network design using a fuzzy spatial interpolation method. Appl Soft Comput 106:107296. https:\/\/doi.org\/10.1016\/J.ASOC.2021.107296","journal-title":"Appl Soft Comput"},{"key":"1178_CR11","doi-asserted-by":"publisher","unstructured":"Behera M, Sena DR, Mandal U et al (2020) Integrated GIS-based RUSLE approach for quantification of potential soil erosion under future climate change scenarios. Environmental Monitoring and Assessment 192: 1-18.. https:\/\/doi.org\/10.1007\/S10661-020-08688-2","DOI":"10.1007\/S10661-020-08688-2"},{"key":"1178_CR12","doi-asserted-by":"crossref","unstructured":"Bhattacharjee S, Ghosh SK, Chen J (2019) Spatial interpolation. In: Semantic Kriging for Spatio-temporal Prediction. Springer 839:19\u201341","DOI":"10.1007\/978-981-13-8664-0_2"},{"key":"1178_CR13","doi-asserted-by":"publisher","unstructured":"Boumpoulis V, Michalopoulou M, Depountis N (2023) Comparison between different spatial interpolation methods for the development of sediment distribution maps in coastal areas. Earth Sci Inf 1\u20139. https:\/\/doi.org\/10.1007\/s12145-023-01017-4","DOI":"10.1007\/s12145-023-01017-4"},{"key":"1178_CR14","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1007\/s41742-019-00208-6","volume":"13","author":"U Bronowicka-Mielniczuk","year":"2019","unstructured":"Bronowicka-Mielniczuk U, Mielniczuk J, Obro\u015blak R, Przystupa W (2019) A comparison of some interpolation techniques for determining spatial distribution of nitrogen compounds in groundwater. International Journal of Environmental Research 13:679\u2013687","journal-title":"International Journal of Environmental Research"},{"key":"1178_CR15","doi-asserted-by":"publisher","unstructured":"Brown LC, Foster GR (1987) STORM EROSIVITY USING IDEALIZED INTENSITY DISTRIBUTIONS. Transactions of the American Society of Agricultural Engineers 30:379\u2013386. https:\/\/doi.org\/10.13031\/2013.31957","DOI":"10.13031\/2013.31957"},{"key":"1178_CR16","doi-asserted-by":"publisher","first-page":"3453","DOI":"10.5194\/hessd-7-3453-2010","volume":"7","author":"G Catari","year":"2010","unstructured":"Catari G, Latron J, Gallart F (2010) Assessing the sources of uncertainty associated with the calculation of rainfall kinetic energy and the erosivity R factor. Application to the Upper Llobregat Basin, NE Spain. Hydrology and Earth System Sciences Discussions 7:3453\u20133479. https:\/\/doi.org\/10.5194\/hessd-7-3453-2010","journal-title":"Hydrology and Earth System Sciences Discussions"},{"key":"1178_CR17","doi-asserted-by":"publisher","first-page":"3347","DOI":"10.3390\/rs70303347","volume":"7","author":"C Chen","year":"2015","unstructured":"Chen C, Li Y, Yan C et al (2015) A robust algorithm of multiquadric method based on an improved huber loss function for interpolating remote-sensing-derived elevation data sets. Remote Sensing 7:3347\u20133371. https:\/\/doi.org\/10.3390\/rs70303347","journal-title":"Remote Sensing"},{"key":"1178_CR18","doi-asserted-by":"publisher","unstructured":"Chen Y, Song L, Liu Y, et al (2020) A Review of the Artificial Neural Network Models for Water Quality Prediction. Applied Sciences 2020, Vol 10, Page 5776 10:5776. https:\/\/doi.org\/10.3390\/APP10175776","DOI":"10.3390\/APP10175776"},{"key":"1178_CR19","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1029\/RG013i003p00243","volume":"13","author":"BH Chovitz","year":"1975","unstructured":"Chovitz BH (1975) Geodetic theory. Rev Geophys 13:243\u2013245","journal-title":"Rev Geophys"},{"key":"1178_CR20","doi-asserted-by":"publisher","first-page":"273","DOI":"10.3390\/TOXICS9110273","volume":"9","author":"KLM De Jesus","year":"2021","unstructured":"De Jesus KLM, Senoro DB, Dela Cruz JC (2021) Chan EB (2021) A Hybrid Neural Network-Particle Swarm Optimization Informed Spatial Interpolation Technique for Groundwater Quality Mapping in a Small Island Province of the Philippines. Toxics 9:273. https:\/\/doi.org\/10.3390\/TOXICS9110273","journal-title":"Toxics"},{"key":"1178_CR21","doi-asserted-by":"publisher","first-page":"1218","DOI":"10.1109\/LAWP.2022.3162160","volume":"21","author":"M Diago-Mosquera","year":"2022","unstructured":"Diago-Mosquera M, Arag\u00f3n-Zavala A, Azpilicueta L et al (2022) A 3-D indoor analysis of path loss modeling using Kriging techniques. IEEE Antennas Wirel Propag Lett 21:1218\u20131222","journal-title":"IEEE Antennas Wirel Propag Lett"},{"key":"1178_CR22","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jhydrol.2016.11.023","volume":"544","author":"N Diodato","year":"2017","unstructured":"Diodato N, Borrelli P, Fiener P et al (2017) Discovering historical rainfall erosivity with a parsimonious approach: A case study in Western Germany. J Hydrol 544:1\u20139. https:\/\/doi.org\/10.1016\/j.jhydrol.2016.11.023","journal-title":"J Hydrol"},{"key":"1178_CR23","doi-asserted-by":"crossref","unstructured":"Eberhart R, Kennedy J (1995) New optimizer using particle swarm theory. In: Proceedings of the International Symposium on Micro Machine and Human Science. IEEE, pp 39\u201343","DOI":"10.1109\/MHS.1995.494215"},{"key":"1178_CR24","unstructured":"Eberhart R, Kennedy J (1996) A new optimizer using particle swarm theory. In: MHS\u201995. Proceedings of the Sixth International Symposium on Micro Machine and Human Science. IEEE, pp 39\u201343"},{"key":"1178_CR25","doi-asserted-by":"publisher","unstructured":"Ebrahimzadeh S, Motagh M, Mahboub V, Mirdar Harijani F (2018) An improved RUSLE\/SDR model for the evaluation of soil erosion. Environ Earth Sci 2018 77:12 77:1\u201317. https:\/\/doi.org\/10.1007\/S12665-018-7635-8","DOI":"10.1007\/S12665-018-7635-8"},{"key":"1178_CR26","doi-asserted-by":"publisher","first-page":"13451","DOI":"10.1007\/s00500-021-06095-4","volume":"25","author":"S Emamgholizadeh","year":"2021","unstructured":"Emamgholizadeh S, Mohammadi B (2021) New hybrid nature-based algorithm to integration support vector machine for prediction of soil cation exchange capacity. Soft Comput 25:13451\u201313464","journal-title":"Soft Comput"},{"key":"1178_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.asej.2022.101876","volume":"14","author":"S Emamgholizadeh","year":"2023","unstructured":"Emamgholizadeh S, Bazoobandi A, Mohammadi B et al (2023) Prediction of soil cation exchange capacity using enhanced machine learning approaches in the southern region of the Caspian Sea. Ain Shams Engineering Journal 14:101876","journal-title":"Ain Shams Engineering Journal"},{"key":"1178_CR28","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.agrformet.2016.03.024","volume":"223","author":"F Fischer","year":"2016","unstructured":"Fischer F, Hauck J, Brandhuber R et al (2016) Spatio-temporal variability of erosivity estimated from highly resolved and adjusted radar rain data (RADOLAN). Agric for Meteorol 223:72\u201380. https:\/\/doi.org\/10.1016\/j.agrformet.2016.03.024","journal-title":"Agric for Meteorol"},{"key":"1178_CR29","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1016\/S0924-2716(00)00018-6","volume":"55","author":"M Gahegan","year":"2000","unstructured":"Gahegan M, Ehlers M (2000) A framework for the modelling of uncertainty between remote sensing and geographic information systems. ISPRS J Photogramm Remote Sens 55:176\u2013188","journal-title":"ISPRS J Photogramm Remote Sens"},{"key":"1178_CR30","doi-asserted-by":"publisher","first-page":"9295","DOI":"10.1038\/srep09295","volume":"5","author":"Y Gao","year":"2015","unstructured":"Gao Y, Du W, Yan G (2015) Selectively-Informed Particle Swarm Optimization. Sci Rep 5:9295. https:\/\/doi.org\/10.1038\/srep09295","journal-title":"Sci Rep"},{"key":"1178_CR31","doi-asserted-by":"publisher","unstructured":"Ghorbani MA, Khatibi R, Ruskeep\u00e4\u00e4 H (2023) A modified Taylor diagram to improve the comparison of models. Research Square. https:\/\/doi.org\/10.21203\/rs.3.rs-2776245\/v1","DOI":"10.21203\/rs.3.rs-2776245\/v1"},{"key":"1178_CR32","first-page":"2816","volume":"4","author":"MN Haddad","year":"2013","unstructured":"Haddad MN (2013) Investigating the rainfall erosivity index using geostatistics. International Journal of Agronomy and Plant Production 4:2816\u20132821","journal-title":"International Journal of Agronomy and Plant Production"},{"key":"1178_CR33","doi-asserted-by":"publisher","first-page":"1905","DOI":"10.1029\/jb076i008p01905","volume":"76","author":"RL Hardy","year":"1971","unstructured":"Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophys Res 76:1905\u20131915. https:\/\/doi.org\/10.1029\/jb076i008p01905","journal-title":"J Geophys Res"},{"key":"1178_CR34","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/0898-1221(90)90272-L","volume":"19","author":"RL Hardy","year":"1990","unstructured":"Hardy RL (1990) Theory and applications of the multiquadric-biharmonic method 20 years of discovery 1968\u20131988. Comput Math Appl 19:163\u2013208. https:\/\/doi.org\/10.1016\/0898-1221(90)90272-L","journal-title":"Comput Math Appl"},{"key":"1178_CR35","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.apacoust.2016.05.024","volume":"112","author":"BI Harman","year":"2016","unstructured":"Harman BI, Koseoglu H, Yigit CO (2016) Performance evaluation of IDW, Kriging and multiquadric interpolation methods in producing noise mapping: A case study at the city of Isparta, Turkey. Appl Acoust 112:147\u2013157. https:\/\/doi.org\/10.1016\/j.apacoust.2016.05.024","journal-title":"Appl Acoust"},{"key":"1178_CR36","doi-asserted-by":"publisher","first-page":"7273","DOI":"10.1038\/s41598-021-86618-z","volume":"11","author":"F Hateffard","year":"2021","unstructured":"Hateffard F, Mohammed S, Alsafadi K et al (2021) CMIP5 climate projections and RUSLE-based soil erosion assessment in the central part of Iran. Sci Rep 11:7273. https:\/\/doi.org\/10.1038\/s41598-021-86618-z","journal-title":"Sci Rep"},{"key":"1178_CR37","doi-asserted-by":"publisher","unstructured":"Huang J, Jing C, Fu J, Huang Z (2019) Uncertainty analysis of rainfall spatial interpolation in urban small area. In: Testbeds and research infrastructures for the development of networks and communities: 13th EAI international conference, TridentCom 2018, Shanghai, China, December 1-3, 2018, Proceedings 13. Springer International Publishing, pp 79\u201395. https:\/\/doi.org\/10.1007\/978-3-030-12971-2_5","DOI":"10.1007\/978-3-030-12971-2_5"},{"key":"1178_CR38","first-page":"354","volume":"9","author":"MN Ikechukwu","year":"2017","unstructured":"Ikechukwu MN, Ebinne E, Idorenyin U, Raphael NI (2017) Accuracy assessment and comparative analysis of IDW, spline and kriging in spatial interpolation of landform (topography): an experimental study. J Geogr Inf Syst 9:354\u2013371","journal-title":"J Geogr Inf Syst"},{"key":"1178_CR39","unstructured":"Johnston K, Ver Hoef JM, Krivoruchko K, Lucas N (2001) Using ArcGIS geostatistical analyst, vol 380. Esri,\u00a0Redlands"},{"key":"1178_CR40","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1007\/S12145-021-00741-Z\/METRICS","volume":"15","author":"M Kabolizadeh","year":"2022","unstructured":"Kabolizadeh M, Rangzan K, Zareie S et al (2022) Evaluating quality of surface water resources by ANN and ANFIS networks using Sentinel-2 satellite data. Earth Sci Inf 15:523\u2013540. https:\/\/doi.org\/10.1007\/S12145-021-00741-Z\/METRICS","journal-title":"Earth Sci Inf"},{"key":"1178_CR41","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1007\/s11600-022-00756-0","volume":"70","author":"OM Katipo\u011flu","year":"2022","unstructured":"Katipo\u011flu OM (2022) Spatial analysis of seasonal precipitation using various interpolation methods in the Euphrates basin, Turkey. Acta Geophys 70:859\u2013878. https:\/\/doi.org\/10.1007\/s11600-022-00756-0","journal-title":"Acta Geophys"},{"key":"1178_CR42","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1002\/HYP.13323","volume":"33","author":"A Kavian","year":"2019","unstructured":"Kavian A, Alipour A, Soleimani K et al (2019) The increase of rainfall erosivity and initial soil erosion processes due to rainfall acidification. Hydrol Process 33:261\u2013270. https:\/\/doi.org\/10.1002\/HYP.13323","journal-title":"Hydrol Process"},{"key":"1178_CR43","doi-asserted-by":"publisher","first-page":"e22729","DOI":"10.1002\/mmce.22729","volume":"31","author":"D Klink","year":"2021","unstructured":"Klink D, Meyer P (2021) A comparison of techniques for finding coefficients of polynomial chaos models for antenna problems. Int J RF Microwave Comput Aided Eng 31:e22729","journal-title":"Int J RF Microwave Comput Aided Eng"},{"key":"1178_CR44","unstructured":"Leberl F (1973) Interpolation in square grid DTM. ITC Journal"},{"key":"1178_CR45","doi-asserted-by":"publisher","first-page":"105957","DOI":"10.1016\/j.catena.2021.105957","volume":"211","author":"S Lee","year":"2022","unstructured":"Lee S, Bae JH, Hong J et al (2022) Estimation of rainfall erosivity factor in Italy and Switzerland using Bayesian optimization based machine learning models. CATENA 211:105957. https:\/\/doi.org\/10.1016\/j.catena.2021.105957","journal-title":"CATENA"},{"key":"1178_CR46","doi-asserted-by":"publisher","unstructured":"Li X, Ye X (2018) Variability of rainfall erosivity and erosivity density in the Ganjiang River Catchment, China: Characteristics and influences of climate change. Atmosphere 9(2):48. https:\/\/doi.org\/10.3390\/atmos9020048","DOI":"10.3390\/atmos9020048"},{"key":"1178_CR47","doi-asserted-by":"publisher","first-page":"891","DOI":"10.1007\/S12145-022-00773-Z\/METRICS","volume":"15","author":"T Melville","year":"2022","unstructured":"Melville T, Wuddivira M, Sutherland M (2022) Geospatial modelling of rainfall erosivity in the humid tropics using remotely sensed data. Earth Sci Inf 15:891\u2013904. https:\/\/doi.org\/10.1007\/S12145-022-00773-Z\/METRICS","journal-title":"Earth Sci Inf"},{"key":"1178_CR48","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1080\/17538947.2021.1919230","volume":"14","author":"S Mohammadi","year":"2021","unstructured":"Mohammadi S, Balouei F, Haji K et al (2021) Country-scale spatio-temporal monitoring of soil erosion in Iran using the G2 model. Int J Digital Earth 14:1019\u20131039. https:\/\/doi.org\/10.1080\/17538947.2021.1919230","journal-title":"Int J Digital Earth"},{"key":"1178_CR49","doi-asserted-by":"publisher","unstructured":"Mostafazadeh R, Talebi Khiavi H, Esmali Ouri A et al (2023) Plot-size runoff and sediment yield affected by the type of geological formations and implications for water erosion in a semi-arid region. Model Earth Syst Environ 1\u201314.\u00a0https:\/\/doi.org\/10.1007\/s40808-023-01813-3","DOI":"10.1007\/s40808-023-01813-3"},{"key":"1178_CR50","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1016\/j.jhydrol.2016.01.022","volume":"534","author":"K Nanko","year":"2016","unstructured":"Nanko K, Moskalski SM, Torres R (2016) Rainfall erosivity-intensity relationships for normal rainfall events and a tropical cyclone on the US southeast coast. J Hydrol 534:440\u2013450. https:\/\/doi.org\/10.1016\/j.jhydrol.2016.01.022","journal-title":"J Hydrol"},{"key":"1178_CR51","first-page":"364","volume":"6","author":"D Nikkami","year":"2015","unstructured":"Nikkami D, Mahdian MH (2015) Rainfall erosivity mapping in Iran. J Watershed Eng Manag 6:364\u2013376","journal-title":"J Watershed Eng Manag"},{"key":"1178_CR52","doi-asserted-by":"publisher","first-page":"128956","DOI":"10.1016\/j.jhydrol.2022.128956","volume":"617","author":"A Oliaye","year":"2023","unstructured":"Oliaye A, Kim S-H, Bae D-H (2023) A new approach to weather radar adjustment for heavy rainfall events using ANFIS-PSO. J Hydrol 617:128956","journal-title":"J Hydrol"},{"key":"1178_CR53","doi-asserted-by":"publisher","first-page":"4014024","DOI":"10.1061\/(ASCE)HE.1943-5584.0000964","volume":"19","author":"H Otieno","year":"2014","unstructured":"Otieno H, Yang J, Liu W, Han D (2014) Influence of Rain Gauge Density on Interpolation Method Selection. J Hydrol Eng 19:4014024. https:\/\/doi.org\/10.1061\/(ASCE)HE.1943-5584.0000964","journal-title":"J Hydrol Eng"},{"key":"1178_CR54","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1016\/j.scitotenv.2015.01.008","volume":"511","author":"P Panagos","year":"2015","unstructured":"Panagos P, Ballabio C, Borrelli P et al (2015) Rainfall erosivity in Europe. Sci Total Environ 511:801\u2013814. https:\/\/doi.org\/10.1016\/j.scitotenv.2015.01.008","journal-title":"Sci Total Environ"},{"key":"1178_CR55","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/j.catena.2015.09.015","volume":"137","author":"P Panagos","year":"2016","unstructured":"Panagos P, Ballabio C, Borrelli P, Meusburger K (2016) Spatio-temporal analysis of rainfall erosivity and erosivity density in Greece. CATENA 137:161\u2013172","journal-title":"CATENA"},{"key":"1178_CR56","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41598-017-04282-8","volume":"7","author":"P Panagos","year":"2017","unstructured":"Panagos P, Borrelli P, Meusburger K et al (2017) Global rainfall erosivity assessment based on high-temporal resolution rainfall records. Sci Rep 7:1\u201312. https:\/\/doi.org\/10.1038\/s41598-017-04282-8","journal-title":"Sci Rep"},{"key":"1178_CR57","doi-asserted-by":"publisher","first-page":"127865","DOI":"10.1016\/j.jhydrol.2022.127865","volume":"610","author":"P Panagos","year":"2022","unstructured":"Panagos P, Borrelli P, Matthews F et al (2022) Global rainfall erosivity projections for 2050 and 2070. J Hydrol 610:127865","journal-title":"J Hydrol"},{"key":"1178_CR58","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.catena.2016.07.006","volume":"147","author":"W Qin","year":"2016","unstructured":"Qin W, Guo Q, Zuo C et al (2016) Spatial distribution and temporal trends of rainfall erosivity in mainland China for 1951\u20132010. CATENA 147:177\u2013186. https:\/\/doi.org\/10.1016\/j.catena.2016.07.006","journal-title":"CATENA"},{"key":"1178_CR59","doi-asserted-by":"publisher","first-page":"1725","DOI":"10.3390\/rs14071725","volume":"14","author":"H Rabiei-Dastjerdi","year":"2022","unstructured":"Rabiei-Dastjerdi H, Mohammadi S, Saber M et al (2022) Spatiotemporal Analysis of NO2 Production Using TROPOMI Time-Series Images and Google Earth Engine in a Middle Eastern Country. Remote Sensing 14:1725","journal-title":"Remote Sensing"},{"key":"1178_CR60","first-page":"357","volume":"74","author":"D Rado\u010daj","year":"2020","unstructured":"Rado\u010daj D, Juri\u0161i\u0107 M, \u017dupan R, Antoni\u0107 O (2020) Spatial Prediction of Heavy Metal Soil Contents in Continental Croatia Comparing Machine Learning and Spatial Interpolation Methods. Geodetski List 74:357\u2013372","journal-title":"Geodetski List"},{"key":"1178_CR61","doi-asserted-by":"publisher","first-page":"e00610","DOI":"10.1016\/J.GEODRS.2023.E00610","volume":"32","author":"TA R\u00e4s\u00e4nen","year":"2023","unstructured":"R\u00e4s\u00e4nen TA, T\u00e4htikarhu M, Uusi-K\u00e4mpp\u00e4 J et al (2023) Evaluation of RUSLE and spatial assessment of agricultural soil erosion in Finland. Geoderma Reg 32:e00610. https:\/\/doi.org\/10.1016\/J.GEODRS.2023.E00610","journal-title":"Geoderma Reg"},{"key":"1178_CR62","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/j.catena.2016.07.017","volume":"147","author":"A Risal","year":"2016","unstructured":"Risal A, Bhattarai R, Kum D et al (2016) Application of Web ERosivity Module (WERM) for estimation of annual and monthly R factor in Korea. CATENA 147:225\u2013237. https:\/\/doi.org\/10.1016\/j.catena.2016.07.017","journal-title":"CATENA"},{"key":"1178_CR63","unstructured":"Rousseva S, Lozanova L, Nekova D, et al (2010) Soil erosion risk in Bulgaria and recommendations for soil protective use of agricultural land. Part I: Northern Bulgaria (304 pp) & Part II Southern Bulgaria (320 pp)"},{"key":"1178_CR64","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1007\/s11069-015-1607-z","volume":"77","author":"SHR Sadeghi","year":"2015","unstructured":"Sadeghi SHR, Hazbavi Z (2015) Trend analysis of the rainfall erosivity index at different time scales in Iran. Nat Hazards 77:383\u2013404. https:\/\/doi.org\/10.1007\/s11069-015-1607-z","journal-title":"Nat Hazards"},{"key":"1178_CR65","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1016\/j.scitotenv.2015.09.068","volume":"541","author":"SH Sadeghi","year":"2016","unstructured":"Sadeghi SH, Hazbavi Z, Harchegani MK (2016) Controllability of runoff and soil loss from small plots treated by vinasse-produced biochar. Sci Total Environ 541:483\u2013490. https:\/\/doi.org\/10.1016\/j.scitotenv.2015.09.068","journal-title":"Sci Total Environ"},{"key":"1178_CR66","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/s11069-017-2752-3","volume":"87","author":"SH Sadeghi","year":"2017","unstructured":"Sadeghi SH, Zabihi M, Vafakhah M, Hazbavi Z (2017) Spatiotemporal mapping of rainfall erosivity index for different return periods in Iran. Nat Hazards 87:35\u201356. https:\/\/doi.org\/10.1007\/s11069-017-2752-3","journal-title":"Nat Hazards"},{"key":"1178_CR67","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1002\/2015JD024243","volume":"121","author":"M Schindelegger","year":"2016","unstructured":"Schindelegger M, Dobslaw H (2016) A global ground truth view of the lunar air pressure tide L2. J Geophys Res Atmos 121:95\u2013110. https:\/\/doi.org\/10.1002\/2015JD024243","journal-title":"J Geophys Res Atmos"},{"key":"1178_CR68","doi-asserted-by":"publisher","first-page":"4359","DOI":"10.5194\/hess-20-4359-2016","volume":"20","author":"S Schmidt","year":"2016","unstructured":"Schmidt S, Alewell C, Panagos P, Meusburger K (2016a) Regionalization of monthly rainfall erosivity patterns in Switzerland. Hydrol Earth Syst Sci 20:4359\u20134373","journal-title":"Hydrol Earth Syst Sci"},{"key":"1178_CR69","doi-asserted-by":"publisher","first-page":"4359","DOI":"10.5194\/hess-20-4359-2016","volume":"20","author":"S Schmidt","year":"2016","unstructured":"Schmidt S, Alewell C, Panagos P, Meusburger K (2016b) Regionalization of monthly rainfall erosivity patternsin Switzerland. Hydrol Earth Syst Sci 20:4359\u20134373. https:\/\/doi.org\/10.5194\/hess-20-4359-2016","journal-title":"Hydrol Earth Syst Sci"},{"key":"1178_CR70","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/j.catena.2019.01.005","volume":"176","author":"JY Shin","year":"2019","unstructured":"Shin JY, Kim T, Heo JH, Lee JH (2019) Spatial and temporal variations in rainfall erosivity and erosivity density in South Korea. CATENA 176:125\u2013144. https:\/\/doi.org\/10.1016\/j.catena.2019.01.005","journal-title":"CATENA"},{"key":"1178_CR71","doi-asserted-by":"publisher","first-page":"7183","DOI":"10.1029\/2000JD900719","volume":"106","author":"KE Taylor","year":"2001","unstructured":"Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res Atmos 106:7183\u20137192","journal-title":"J Geophys Res Atmos"},{"key":"1178_CR72","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/S12145-017-0321-7\/METRICS","volume":"11","author":"H Vijith","year":"2018","unstructured":"Vijith H, Dodge-Wan D (2018) Spatio-temporal changes in rate of soil loss and erosion vulnerability of selected region in the tropical forests of Borneo during last three decades. Earth Sci Inf 11:171\u2013181. https:\/\/doi.org\/10.1007\/S12145-017-0321-7\/METRICS","journal-title":"Earth Sci Inf"},{"key":"1178_CR73","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.gloplacha.2014.01.009","volume":"115","author":"A Vrieling","year":"2014","unstructured":"Vrieling A, Hoedjes JCB, van der Velde M (2014) Towards large-scale monitoring of soil erosion in Africa: Accounting for the dynamics of rainfall erosivity. Glob Planet Change 115:33\u201343. https:\/\/doi.org\/10.1016\/j.gloplacha.2014.01.009","journal-title":"Glob Planet Change"},{"key":"1178_CR74","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1016\/j.jhydrol.2012.07.026","volume":"464\u2013465","author":"PD Wagner","year":"2012","unstructured":"Wagner PD, Fiener P, Wilken F et al (2012) Comparison and evaluation of spatial interpolation schemes for daily rainfall in data scarce regions. J Hydrol 464\u2013465:388\u2013400. https:\/\/doi.org\/10.1016\/j.jhydrol.2012.07.026","journal-title":"J Hydrol"},{"key":"1178_CR75","doi-asserted-by":"crossref","unstructured":"Wang LL, Yang E, Huang J, Jiao P (2013) Spatial and temporal characteristics of rainfall erosivity of Shanghai in recent ten years. Appl Mech Mater 295:2084\u20132089","DOI":"10.4028\/www.scientific.net\/AMM.295-298.2084"},{"key":"1178_CR76","unstructured":"Wischmeier WH, Smith DD (1978) Predicting rainfall erosion losses: a guide to conservation planning. Department of Agriculture (No. 537), Science and Education Administration"},{"key":"1178_CR77","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/s10113-010-0127-3","volume":"11","author":"Z Xin","year":"2011","unstructured":"Xin Z, Yu X, Li Q, Lu XX (2011) Spatiotemporal variation in rainfall erosivity on the Chinese Loess Plateau during the period 1956\u20132008. Reg Environ Change 11:149\u2013159. https:\/\/doi.org\/10.1007\/s10113-010-0127-3","journal-title":"Reg Environ Change"},{"key":"1178_CR78","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1007\/s00500-016-2383-8","volume":"22","author":"X Xu","year":"2018","unstructured":"Xu X, Rong H, Trovati M et al (2018) CS-PSO: chaotic particle swarm optimization algorithm for solving combinatorial optimization problems. Soft Comput 22:783\u2013795","journal-title":"Soft Comput"},{"key":"1178_CR79","doi-asserted-by":"publisher","unstructured":"Yin S, Nearing MA, Borrelli P, Xue X (2017) Rainfall erosivity: an overview of methodologies and applications. Vadose Zone J 16(12): 1\u201316. https:\/\/doi.org\/10.2136\/vzj2017.06.0131","DOI":"10.2136\/vzj2017.06.0131"},{"key":"1178_CR80","unstructured":"Zabihi M, Sadeghi SH, Vafahkhah M (2016) Spatial analysis of rainfall erosivity index patterns at different time scales in Iran. Watershed Engineering and Management 7(4):442\u2013457"},{"key":"1178_CR81","doi-asserted-by":"publisher","first-page":"842","DOI":"10.1016\/j.petrol.2017.08.002","volume":"157","author":"I Zahmatkesh","year":"2017","unstructured":"Zahmatkesh I, Soleimani B, Kadkhodaie A et al (2017) Estimation of DSI log parameters from conventional well log data using a hybrid particle swarm optimization\u2013adaptive neuro-fuzzy inference system. J Petrol Sci Eng 157:842\u2013859. https:\/\/doi.org\/10.1016\/j.petrol.2017.08.002","journal-title":"J Petrol Sci Eng"},{"key":"1178_CR82","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.geodrs.2018.01.002","volume":"12","author":"M Zerihun","year":"2018","unstructured":"Zerihun M, Mohammedyasin MS, Sewnet D et al (2018) Assessment of soil erosion using RUSLE, GIS and remote sensing in NW Ethiopia. Geoderma Reg 12:83\u201390","journal-title":"Geoderma Reg"},{"key":"1178_CR83","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/s00704-015-1694-5","volume":"128","author":"Q Zhao","year":"2017","unstructured":"Zhao Q, Liu Q, Ma L et al (2017) Spatiotemporal variations in rainfall erosivity during the period of 1960\u20132011 in Guangdong Province, southern China. Theoret Appl Climatol 128:113\u2013128. https:\/\/doi.org\/10.1007\/s00704-015-1694-5","journal-title":"Theoret Appl Climatol"},{"key":"1178_CR84","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/j.catena.2016.06.028","volume":"145","author":"G Zhijia","year":"2016","unstructured":"Zhijia G, Xingwu D, Bing L et al (2016) The spatial distribution and temporal variation of rainfall erosivity in the Yunnan Plateau, Southwest China: 1960\u20132012. CATENA 145:291\u2013300. https:\/\/doi.org\/10.1016\/j.catena.2016.06.028","journal-title":"CATENA"},{"key":"1178_CR85","doi-asserted-by":"publisher","first-page":"126714","DOI":"10.1016\/j.jhydrol.2021.126714","volume":"602","author":"P Zhu","year":"2021","unstructured":"Zhu P, Zhang G, Wang H et al (2021) Effectiveness of typical plant communities in controlling runoff and soil erosion on steep gully slopes on the Loess Plateau of China. J Hydrol 602:126714","journal-title":"J Hydrol"}],"container-title":["Earth Science Informatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12145-023-01178-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12145-023-01178-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12145-023-01178-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,27]],"date-time":"2024-01-27T11:26:35Z","timestamp":1706354795000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12145-023-01178-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,1]]},"references-count":85,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["1178"],"URL":"https:\/\/doi.org\/10.1007\/s12145-023-01178-2","relation":{},"ISSN":["1865-0473","1865-0481"],"issn-type":[{"value":"1865-0473","type":"print"},{"value":"1865-0481","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,1]]},"assertion":[{"value":"30 July 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 November 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 December 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}