{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:05:30Z","timestamp":1740146730386,"version":"3.37.3"},"reference-count":53,"publisher":"Public Library of Science (PLoS)","issue":"11","license":[{"start":{"date-parts":[[2021,11,18]],"date-time":"2021-11-18T00:00:00Z","timestamp":1637193600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100007801","name":"fundaci\u00f3n s\u00e9neca","doi-asserted-by":"publisher","award":["20912\/PI\/18"],"award-info":[{"award-number":["20912\/PI\/18"]}],"id":[{"id":"10.13039\/100007801","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"<jats:p>In hydrological modelling, a good result for the criterion of goodness of fit does not always imply that the hypothesis of mass conservation is fulfilled, and models can lose their essential physical soundness. We propose a way for detecting this anomaly by accounting the resulting water balance during model simulation and use it to modulate the obtained goodness of fit. We call this anomaly in water balance as \u201cinner balance error of the model\u201d. To modulate the goodness of fit values, a penalty function that depends on this error is proposed. In addition, this penalty function is introduced into a multi-criteria objective function, which is also tested. This procedure was followed in modelling the Headwater of the Tagus River (Spain), applying the monthly abcd water balance model. Modulation of the goodness of fit allowed for detecting balance errors in the modelling, revealing that in the simulation of some catchments the model tends to accumulate water in, or release water from, the reservoir that simulates groundwater storage. Although the proposed multi-criteria objective function solves the inner balance error for most catchments, in some cases the error cannot be corrected, indicating that any error in the input and output data is probably related to groundwater flows.<\/jats:p>","DOI":"10.1371\/journal.pone.0260117","type":"journal-article","created":{"date-parts":[[2021,11,18]],"date-time":"2021-11-18T18:37:18Z","timestamp":1637260638000},"page":"e0260117","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":1,"title":["Modulation of the goodness of fit in hydrological modelling based on inner balance errors"],"prefix":"10.1371","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0962-6136","authenticated-orcid":true,"given":"Francisco","family":"Pellicer-Mart\u00ednez","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4306-6643","authenticated-orcid":true,"given":"Francisco","family":"Gomariz-Castillo","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5221-1139","authenticated-orcid":true,"given":"Mar\u00eda Manuela","family":"Portela","sequence":"additional","affiliation":[]},{"given":"Isabel Mar\u00eda","family":"Mart\u00ednez-Alcal\u00e1","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8412-7647","authenticated-orcid":true,"given":"Jos\u00e9 Miguel","family":"Mart\u00ednez-Paz","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2021,11,18]]},"reference":[{"key":"pone.0260117.ref001","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.scitotenv.2014.07.042","article-title":"Key issues for determining the exploitable water resources in a Mediterranean river basin","volume":"503\u2013504","author":"M Pedro-Monzon\u00eds","year":"2015","journal-title":"Sci Total Environ"},{"key":"pone.0260117.ref002","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.jhydrol.2004.06.003","article-title":"Modeling river\/reservoir system management, water allocation, and supply reliability","volume":"300","author":"RA Wurbs","year":"2005","journal-title":"J Hydrol"},{"key":"pone.0260117.ref003","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/02626667.2015.1029482","article-title":"Advances in water resources assessment with SWAT\u2014an overview","volume":"60","author":"V Krysanova","year":"2015","journal-title":"Hydrol Sci J"},{"key":"pone.0260117.ref004","doi-asserted-by":"crossref","first-page":"5039","DOI":"10.1002\/hyp.10966","article-title":"Impacts of changing climate on the hydrology and hydropower production of the Tagus River basin","volume":"30","author":"A Lobanova","year":"2016","journal-title":"Hydrol Process"},{"key":"pone.0260117.ref005","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1080\/02626667.2017.1330542","article-title":"Improvement and comparative assessment of a hydrological modelling approach on 20 catchments of various sizes under different climate conditions","volume":"62","author":"C Gaba","year":"2017","journal-title":"Hydrol Sci J"},{"key":"pone.0260117.ref006","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1023\/A:1007916816469","article-title":"A Review on Monthly Water Balance Models for Water Resources Investigations","volume":"12","author":"C-Y Xu","year":"1998","journal-title":"Water Resour Manag"},{"key":"pone.0260117.ref007","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.jhydrol.2008.07.021","article-title":"Water balance modeling over variable time scales based on the Budyko framework\u2013Model development and testing","volume":"360","author":"L Zhang","year":"2008","journal-title":"J Hydrol"},{"key":"pone.0260117.ref008","doi-asserted-by":"crossref","first-page":"1961","DOI":"10.1007\/978-3-319-73645-7_119","volume-title":"Handbook of Environmental Materials Management","author":"K Abdollahi","year":"2019"},{"key":"pone.0260117.ref009","doi-asserted-by":"crossref","first-page":"1210","DOI":"10.1080\/02626667.2011.610323","article-title":"Modelling catchment inflows into Lake Victoria: uncertainties in rainfall\u2013runoff modelling for the Nzoia River","volume":"56","author":"M Kizza","year":"2011","journal-title":"Hydrol Sci J"},{"key":"pone.0260117.ref010","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1007\/s00477-014-1000-6","article-title":"Application of the generalized likelihood uncertainty estimation (GLUE) approach for assessing uncertainty in hydrological models: a review","volume":"29","author":"M Mirzaei","year":"2015","journal-title":"Stoch Environ Res Risk Assess"},{"key":"pone.0260117.ref011","doi-asserted-by":"crossref","first-page":"04017024","DOI":"10.1061\/(ASCE)HE.1943-5584.0001542","article-title":"Multicore parallel genetic algorithm with Tabu strategy for rainfall-runoff model calibration","volume":"22","author":"S Liao","year":"2017","journal-title":"J Hydrol Eng"},{"key":"pone.0260117.ref012","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.advwatres.2017.04.011","article-title":"Calibrating a hydrological model in stage space to account for rating curve uncertainties: general framework and key challenges","volume":"105","author":"AE Sikorska","year":"2017","journal-title":"Adv Water Resour"},{"key":"pone.0260117.ref013","doi-asserted-by":"crossref","first-page":"2723","DOI":"10.1002\/hyp.7072","article-title":"Do Nash values have value? Discussion and alternate proposals","volume":"22","author":"RE Criss","year":"2008","journal-title":"Hydrol Process"},{"key":"pone.0260117.ref014","doi-asserted-by":"crossref","first-page":"3392","DOI":"10.1029\/2017WR022466","article-title":"Improved rainfall\u2010runoff calibration for drying climate: Choice of objective function","volume":"54","author":"K Fowler","year":"2018","journal-title":"Water Resour Res"},{"key":"pone.0260117.ref015","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.envsoft.2019.05.001","article-title":"Introductory overview: Error metrics for hydrologic modelling\u2013A review of common practices and an open source library to facilitate use and adoption","volume":"119","author":"EK Jackson","year":"2019","journal-title":"Environ Model Softw"},{"key":"pone.0260117.ref016","doi-asserted-by":"crossref","first-page":"W10601","DOI":"10.1029\/2011WR010962","article-title":"On typical range, sensitivity, and normalization of Mean Squared Error and Nash-Sutcliffe Efficiency type metrics","volume":"47","author":"HV Gupta","year":"2011","journal-title":"Water Resour Res"},{"key":"pone.0260117.ref017","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/0022-1694(70)90255-6","article-title":"River flow forecasting through conceptual models part I\u2014A discussion of principles","volume":"10","author":"JE Nash","year":"1970","journal-title":"J Hydrol"},{"key":"pone.0260117.ref018","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.jhydrol.2009.08.003","article-title":"Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling","volume":"377","author":"H V Gupta","year":"2009","journal-title":"J Hydrol"},{"key":"pone.0260117.ref019","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.jhydrol.2012.01.011","article-title":"Runoff conditions in the upper Danube basin under an ensemble of climate change scenarios","volume":"424\u2013425","author":"H Kling","year":"2012","journal-title":"J Hydrol"},{"key":"pone.0260117.ref020","doi-asserted-by":"crossref","first-page":"125488","DOI":"10.1016\/j.jhydrol.2020.125488","article-title":"A rational performance criterion for hydrological model","volume":"590","author":"D Liu","year":"2020","journal-title":"J Hydrol"},{"key":"pone.0260117.ref021","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1016\/S0022-1694(00)00279-1","article-title":"Automatic calibration of a conceptual rainfall\u2013runoff model using multiple objectives","volume":"235","author":"H Madsen","year":"2000","journal-title":"J Hydrol"},{"key":"pone.0260117.ref022","doi-asserted-by":"crossref","first-page":"e42","DOI":"10.1590\/2318-0331.252020190155","article-title":"Objective functions used as performance metrics for hydrological models: state-of-the-art and critical analysis","volume":"25","author":"L Ferreira PM de","year":"2020","journal-title":"RBRH"},{"key":"pone.0260117.ref023","doi-asserted-by":"crossref","first-page":"89","DOI":"10.5194\/adgeo-5-89-2005","article-title":"Comparison of different efficiency criteria for hydrological model assessment","volume":"5","author":"P Krause","year":"2005","journal-title":"Adv Geosci"},{"key":"pone.0260117.ref024","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/S0022-1694(00)00393-0","article-title":"Does a large number of parameters enhance model performance? Comparative assessment of common catchment model structures on 429 catchments","volume":"242","author":"C Perrin","year":"2001","journal-title":"J Hydrol"},{"key":"pone.0260117.ref025","doi-asserted-by":"crossref","first-page":"934","DOI":"10.1007\/s11769-019-1068-5","article-title":"Searching for an optimized single-objective function matching multiple objectives with automatic calibration of hydrological models","volume":"29","author":"F Tian","year":"2019","journal-title":"Chinese Geogr Sci"},{"key":"pone.0260117.ref026","doi-asserted-by":"crossref","first-page":"5443","DOI":"10.5194\/hess-21-5443-2017","article-title":"Streamflow characteristics from modeled runoff time series\u2013importance of calibration criteria selection","volume":"21","author":"S Pool","year":"2017","journal-title":"Hydrol Earth Syst Sci"},{"key":"pone.0260117.ref027","doi-asserted-by":"crossref","first-page":"153","DOI":"10.2166\/nh.1997.0009","article-title":"A simple automatic calibration routine for the HBV Model","volume":"28","author":"G Lindstr\u00f6m","year":"1997","journal-title":"Hydrol Res"},{"key":"pone.0260117.ref028","doi-asserted-by":"crossref","first-page":"3796","DOI":"10.1002\/2014WR016520","article-title":"Optimizing hydrological consistency by incorporating hydrological signatures into model calibration objectives","volume":"51","author":"M Shafii","year":"2015","journal-title":"Water Resour Res"},{"key":"pone.0260117.ref029","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2020\/8594727","article-title":"Evaluation method of multiobjective functions\u2019 combination and its application in hydrological model evaluation","volume":"2020","author":"J Huo","year":"2020","journal-title":"Comput Intell Neurosci"},{"key":"pone.0260117.ref030","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.jhydrol.2005.07.007","article-title":"A manifesto for the equifinality thesis","volume":"320","author":"K Beven","year":"2006","journal-title":"J Hydrol"},{"key":"pone.0260117.ref031","first-page":"15","article-title":"Evaluation of bayesian networks as a tool for participatory water resources management: application to the upper Guadiana basin in Spain","author":"P Zorrilla","year":"2010","journal-title":"Ecol Soc"},{"key":"pone.0260117.ref032","doi-asserted-by":"crossref","first-page":"1848","DOI":"10.1016\/j.jhydrol.2014.09.067","article-title":"Assessment of interbasin groundwater flows between catchments using a semi-distributed water balance model","volume":"519","author":"F Pellicer-Mart\u00ednez","year":"2014","journal-title":"J Hydrol"},{"key":"pone.0260117.ref033","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1080\/02626660903546118","article-title":"Estimating potential evapotranspiration without continuous daily data: possible errors and impact on water balance simulations","volume":"55","author":"L Oudin","year":"2010","journal-title":"Hydrol Sci J"},{"key":"pone.0260117.ref034","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.jhydrol.2012.12.004","article-title":"Performance evaluation of hydrological models: Statistical significance for reducing subjectivity in goodness-of-fit assessments","volume":"480","author":"A Ritter","year":"2013","journal-title":"J Hydrol"},{"key":"pone.0260117.ref035","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/0022-1694(92)90041-S","article-title":"Methodology and comparative study of monthly water balance models in Belgium, China and Burma","volume":"134","author":"GL Vandewiele","year":"1992","journal-title":"J Hydrol"},{"key":"pone.0260117.ref036","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.jhydrol.2010.01.001","article-title":"The impact of droughts and water management on various hydrological systems in the headwaters of the Tagus River (central Spain)","volume":"386","author":"J Lorenzo-Lacruz","year":"2010","journal-title":"J Hydrol"},{"volume-title":"Esquema Provisional de Temas Importantes de la parte espa\u00f1ola de la Demarcaci\u00f3n Hidrogr\u00e1fica del Tajo","year":"2008","author":"CHT","key":"pone.0260117.ref037"},{"volume-title":"Modelo Digital del Terreno con paso de malla de 25 m","year":"2020","author":"IGN","key":"pone.0260117.ref038"},{"volume-title":"Sistema de informaci\u00f3n del anuario de aforos","year":"2020","author":"MITECO","key":"pone.0260117.ref039"},{"volume-title":"Anuario de aforos 2016\u201317","year":"2019","author":"CEDEX","key":"pone.0260117.ref040"},{"volume-title":"Evaluaci\u00f3n de recursos h\u00eddricos en r\u00e9gimen natural en Espa\u00f1a (1940\/41-2017\/18)","year":"2019","author":"CEDEX","key":"pone.0260117.ref041"},{"volume-title":"Modelo SIMPA. Periodo de simulaci\u00f3n: 1940\/41 a 2017\/18","year":"2020","author":"MITECO","key":"pone.0260117.ref042"},{"key":"pone.0260117.ref043","doi-asserted-by":"crossref","first-page":"05015019","DOI":"10.1061\/(ASCE)HE.1943-5584.0001282","article-title":"New Multisite Cascading Calibration Approach for Hydrological Models: Case Study in the Red River Basin Using the VIC Model","volume":"21","author":"X Xue","year":"2016","journal-title":"J Hydrol Eng"},{"key":"pone.0260117.ref044","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1080\/02626668609491024","article-title":"Operational testing of hydrological simulation models","volume":"31","author":"V KLEME\u0160","year":"1986","journal-title":"Hydrol Sci J"},{"key":"pone.0260117.ref045","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1287\/inte.28.5.29","article-title":"Design and use of the microsoft excel solver","volume":"28","author":"D Fylstra","year":"1998","journal-title":"Interfaces (Providence)"},{"key":"pone.0260117.ref046","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1145\/355769.355773","article-title":"Design and testing of a Generalized Reduced Gradient code for nonlinear programming","volume":"4","author":"LS Lasdon","year":"1978","journal-title":"ACM Trans Math Softw"},{"key":"pone.0260117.ref047","doi-asserted-by":"crossref","unstructured":"Thomas Jr. HA. Improved methods for national water assessment, water resources contract: WR15249270. Cambridge, USA; 1981. doi: 10.3133\/70046351","DOI":"10.3133\/70046351"},{"key":"pone.0260117.ref048","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1029\/WR020i008p01137","article-title":"On the treatment of evapotranspiration, soil moisture accounting, and aquifer recharge in monthly water balance models","volume":"20","author":"WM Alley","year":"1984","journal-title":"Water Resour Res"},{"key":"pone.0260117.ref049","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/0022-1694(94)90233-X","article-title":"A two-parameter monthly water balance model for french watersheds","volume":"162","author":"Z Makhlouf","year":"1994","journal-title":"J Hydrol"},{"key":"pone.0260117.ref050","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.jhydrol.2011.04.027","article-title":"Monthly versus daily water balance models in simulating monthly runoff","volume":"404","author":"QJ Wang","year":"2011","journal-title":"J Hydrol"},{"key":"pone.0260117.ref051","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.jhydrol.2005.06.014","article-title":"Stepwise development of a two-parameter monthly water balance model","volume":"318","author":"S Mouelhi","year":"2006","journal-title":"J Hydrol"},{"key":"pone.0260117.ref052","doi-asserted-by":"crossref","first-page":"4361","DOI":"10.1002\/hyp.10586","article-title":"Analysis of incorporating groundwater exchanges in hydrological models","volume":"29","author":"F Pellicer-Mart\u00ednez","year":"2015","journal-title":"Hydrol Process"},{"key":"pone.0260117.ref053","article-title":"A ranking system for comparing models\u2019 performance combining multiple statistical criteria and scenarios: The case of reference evapotranspiration models","author":"VG Aschonitis","year":"2019","journal-title":"Environ Model Softw"}],"container-title":["PLOS ONE"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0260117","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,18]],"date-time":"2021-11-18T18:38:12Z","timestamp":1637260692000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0260117"}},"subtitle":[],"editor":[{"given":"Vassilis G.","family":"Aschonitis","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,11,18]]},"references-count":53,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2021,11,18]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0260117","relation":{},"ISSN":["1932-6203"],"issn-type":[{"type":"electronic","value":"1932-6203"}],"subject":[],"published":{"date-parts":[[2021,11,18]]}}}