{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T12:51:47Z","timestamp":1792155107080,"version":"4.4.0"},"reference-count":21,"publisher":"Wiley","license":[{"start":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T00:00:00Z","timestamp":1792108800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T00:00:00Z","timestamp":1792108800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/100000203","name":"United States Geological Survey","doi-asserted-by":"publisher","award":["G22AC00385\u201000"],"award-info":[{"award-number":["G22AC00385\u201000"]}],"id":[{"id":"10.13039\/100000203","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["ngwa.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Groundwater"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>This paper presents the development and benchmarking of a fully three\u2010dimensional (3D) Richards' equation solver integrated into MODFLOW 6. The popular unsaturated zone package (the UZF package) currently in MODFLOW relies on simplified approaches that neglect capillary effects and assumes one\u2010dimensional (1D) vertical flow. In contrast, the Richards' equation implementation presented here is based on a 3D head\u2010based mixed formulation using the van Genuchten moisture retention and relative permeability functions to capture the more detailed physics of variably saturated flow. The numerical implementation within the MODFLOW 6 framework leverages the advanced, robust numerical techniques already built into the software including upstream weighting, Newton\u2013Raphson and Picard linearization approaches, advanced linear solvers and a flexible finite\u2010volume framework. Three benchmark tests were used to evaluate the performance of this Richards' equation implementation in MODFLOW 6 against established codes such as HYDRUS, MODFLOW VSF, SUTRA, and USG\u2010T. Results indicate that this package accurately reproduces moisture dynamics and capillary pressure distributions with computational efficiency and robustness. This advancement not only improves the physical realism of saturated\/unsaturated subsurface flow simulations but also provides a practical tool for further research in variably saturated flow modeling within the MODFLOW framework.<\/jats:p>","DOI":"10.1111\/gwat.70112","type":"journal-article","created":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T12:18:41Z","timestamp":1792153121000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Implementation and Evaluation of Fully 3D Richards' Equation in\n                    <scp>MODFLOW<\/scp>\n                    6"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-9497-1504","authenticated-orcid":false,"given":"Sebasti\u00e1n","family":"V\u00e1zquez\u2010Gasty","sequence":"first","affiliation":[{"name":"GSI Environmental Inc.  Irvine CA 92618"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sorab","family":"Panday","sequence":"additional","affiliation":[{"name":"GSI Environmental Inc.  Irvine CA 92618"},{"name":"University of Nebraska\u2010Lincoln  Lincoln NE"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5610-9759","authenticated-orcid":false,"given":"Christian","family":"Langevin","sequence":"additional","affiliation":[{"name":"S.S. Papadopulos and Associates Inc.  Saint Paul MN 55127\u20102587"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6279-8447","authenticated-orcid":false,"given":"Tirthankar","family":"Roy","sequence":"additional","affiliation":[{"name":"University of Nebraska\u2010Lincoln  Lincoln NE"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,16]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1139\/T09\u2010050"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.2136\/vzj2011.0145"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1080\/19648189.2014.926294"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1061\/JRCEA4.0000425"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2014.07.006"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1029\/WR024i005p00755"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1029\/WR026i007p01483"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022\u20101694(92)90032\u2010Q"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1029\/WR025i006p01259"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1111\/gwmr.12662"},{"key":"e_1_2_9_12_1","unstructured":"Langevin C.D. J.D.Hughes A.Provost M.J.Russcher E.Morway M.J.Reno W.P.Bonelli R.G.Niswonger S.Panday S.S.Titus D.Merrick andE.R.Banta.2026.MODFLOW version 6.7.0.https:\/\/doi.org\/10.5066\/P1IJAXDZ"},{"key":"e_1_2_9_13_1","doi-asserted-by":"crossref","unstructured":"Niswonger R.G. D.E.Prudic andR.S.Regan.2006.Documentation of the unsaturated\u2010zone flow (UZF1) package for modeling unsaturated flow between the land surface and the water table with MODFLOW\u20102005. U.S. Geological Survey Techniques and Methods No. 6\u2010A19.https:\/\/doi.org\/10.3133\/tm6A19","DOI":"10.3133\/tm6A19"},{"key":"e_1_2_9_14_1","unstructured":"Panday S.2025.USG\u2010transport version 2.6.0: Transport and other enhancements to MODFLOW\u2010USG. GSI Environmental.http:\/\/www.gsi\u2010net.com\/en\/software\/freesoftware\/USG\u2010Transport.html"},{"key":"e_1_2_9_15_1","doi-asserted-by":"crossref","unstructured":"Panday S. C.D.Langevin R.G.Niswonger M.Ibaraki andJ.D.Hughes.2013.MODFLOW\u2013USG version 1: An unstructured grid version of MODFLOW for simulating groundwater flow and tightly coupled processes using a control volume finite\u2010difference formulation (p. book 6 chap. A45 66 p). US Geological Survey.","DOI":"10.3133\/tm6A45"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.advwatres.2004.02.016"},{"key":"e_1_2_9_17_1","unstructured":"Simunek J. M.Van Genuchteh andM.Sejna.2005.The HYDRUS\u20101D software package for simulating the one\u2010dimensional movement of water heat and multiple solutes in variably\u2010saturated media. University of California\u2010Riverside Research Reports."},{"key":"e_1_2_9_18_1","volume-title":"User's Guide to the Variably Saturated Flow (VSF) Process to MODFLOW","author":"Thoms R.B.","year":"2006"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0309\u20101708(96)00008\u20105"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.2136\/sssaj1980.03615995004400050002x"},{"key":"e_1_2_9_21_1","doi-asserted-by":"crossref","unstructured":"Voss C.I. A.M.Provost J.M.McKenzie andB.L.Kurylyk.2024.SUTRA: A code for simulation of saturated\u2010unsaturated variable\u2010density groundwater flow with solute or energy transport\u2014documentation of the version 4.0 enhancements\u2014freeze\u2010thaw capability saturation and relative\u2010permeability relations spatially varying properties and enhanced budget and velocity outputs. U.S. Geological Survey Techniques and Methods No. 6\u2010A63.https:\/\/doi.org\/10.3133\/tm6A63","DOI":"10.3133\/tm6A63"},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jhydrol.2011.07.002"}],"container-title":["Groundwater"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/ngwa.onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/gwat.70112","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ngwa.onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/gwat.70112","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ngwa.onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/gwat.70112","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T12:18:42Z","timestamp":1792153122000},"score":1,"resource":{"primary":{"URL":"https:\/\/ngwa.onlinelibrary.wiley.com\/doi\/10.1111\/gwat.70112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,16]]},"references-count":21,"alternative-id":["10.1111\/gwat.70112"],"URL":"https:\/\/doi.org\/10.1111\/gwat.70112","archive":["Portico"],"relation":{},"ISSN":["0017-467X","1745-6584"],"issn-type":[{"value":"0017-467X","type":"print"},{"value":"1745-6584","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,16]]},"assertion":[{"value":"2026-02-04","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-09-08","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-10-16","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"gwat.70112"}}