{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T16:03:46Z","timestamp":1789488226369,"version":"build-2803163510"},"reference-count":7,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T00:00:00Z","timestamp":1773619200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T00:00:00Z","timestamp":1773619200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["ngwa.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Groundwater"],"published-print":{"date-parts":[[2026,5]]},"abstract":"<jats:p>This paper presents exact one\u2010dimensional (1D) analytical solutions for steady\u2010state groundwater flow in a heterogeneous leaky confined aquifer, accounting for spatial variability in both aquifer and aquitard properties. Unlike traditional models that assume uniform conditions, the proposed approach incorporates natural heterogeneity arising from variable depositional and post\u2010depositional processes. The aquifer system is divided into discrete vertical zones, each characterized by distinct hydraulic properties. The solutions describe steady\u2010state flow in a horizontally extensive confined aquifer recharged by leakage from an overlying unconfined aquifer through a thin, heterogeneous aquitard and discharging to a downgradient fixed\u2010head boundary. The upgradient boundary may represent either a no\u2010flow condition or a fixed head. The analytical solutions provide exact 1D, steady\u2010state reference results for assessing the effects of lateral heterogeneity and for evaluating the spatial discretization required in numerical groundwater flow models to resolve sharp hydraulic head transitions and flow redistribution across zones with contrasting conductivities. Validation against MODFLOW 6 simulations demonstrates excellent agreement, confirming the correctness and robustness of the analytical formulation. A Python implementation of the analytical solutions is openly available in a public GitHub repository, ensuring reproducibility and facilitating further exploration of heterogeneous leaky aquifer systems.<\/jats:p>","DOI":"10.1111\/gwat.70059","type":"journal-article","created":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T14:02:48Z","timestamp":1773669768000},"page":"295-302","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analytical Solutions for Steady\u2010State Flow in Heterogeneous Leaky Aquifers: Verification against\n                    <scp>MODFLOW<\/scp>\n                    6"],"prefix":"10.1111","volume":"64","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4431-1965","authenticated-orcid":false,"given":"Mohamed","family":"Hayek","sequence":"first","affiliation":[{"name":"INTERA Incorporated, Swiss Branch  Hardstrasse 73 CH\u20105430 Wettingen Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,3,16]]},"reference":[{"key":"e_1_2_9_2_1","volume-title":"Hydraulic of Groundwater","author":"Bear J.","year":"1979"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1745\u20106584.2007.00393.x"},{"key":"e_1_2_9_4_1","first-page":"16","volume-title":"Contaminant Transport through Aquitards: A State\u2010of\u2010the\u2010Science Review","author":"Cherry J.A.","year":"2006"},{"issue":"8","key":"e_1_2_9_5_1","first-page":"1225","article-title":"Analysis of data from pumping tests in leaky aquifers","volume":"69","author":"Hantush M.S.","year":"1964","journal-title":"Journal of Geophysical Research"},{"key":"e_1_2_9_6_1","volume-title":"Documentation for the MODFLOW 6 Groundwater Flow Model. Techniques and Methods 6\u2010A55","author":"Langevin C.D.","year":"2017"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/0613045"},{"key":"e_1_2_9_8_1","volume-title":"Groundwater Mechanics","author":"Strack O.D.L.","year":"1989"}],"container-title":["Groundwater"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/ngwa.onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/gwat.70059","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ngwa.onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/gwat.70059","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ngwa.onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/gwat.70059","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T15:17:30Z","timestamp":1789485450000},"score":1,"resource":{"primary":{"URL":"https:\/\/ngwa.onlinelibrary.wiley.com\/doi\/10.1111\/gwat.70059"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,16]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,5]]}},"alternative-id":["10.1111\/gwat.70059"],"URL":"https:\/\/doi.org\/10.1111\/gwat.70059","archive":["Portico"],"relation":{},"ISSN":["0017-467X","1745-6584"],"issn-type":[{"value":"0017-467X","type":"print"},{"value":"1745-6584","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,16]]},"assertion":[{"value":"2025-11-13","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-02-23","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-03-16","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}