Two-dimensional differential form of distributed Xinanjiang model
<p>The distributed hydrologic models (DHMs) evolved from lumped hydrologic models, inheriting their modeling philosophy along with persistent numerical-error issues. Historically, these models tend to use established one-dimensional (1D) methods for slope concentration, which often struggle to...
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| Format: | Article |
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Copernicus Publications
2025-08-01
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| Series: | Hydrology and Earth System Sciences |
| Online Access: | https://hess.copernicus.org/articles/29/3745/2025/hess-29-3745-2025.pdf |
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| author | J. Zhao Z. Liang V. P. Singh V. P. Singh V. P. Singh T. Wen Y. Hu B. Li J. Wang |
| author_facet | J. Zhao Z. Liang V. P. Singh V. P. Singh V. P. Singh T. Wen Y. Hu B. Li J. Wang |
| author_sort | J. Zhao |
| collection | DOAJ |
| description | <p>The distributed hydrologic models (DHMs) evolved from lumped hydrologic models, inheriting their modeling philosophy along with persistent numerical-error issues. Historically, these models tend to use established one-dimensional (1D) methods for slope concentration, which often struggle to effectively represent complex terrains. In this study, we formulated a purely differential form of mathematical equations for the distributed Xinanjiang model and developed a fully coupled numerical solution framework. We also introduced two-dimensional (2D) diffusion wave equations for surface slope concentration and derived 2D linear reservoir equations for subsurface slope concentration to replace their 1D counterparts. This culminated in the development of a two-dimensional differential form of the distributed Xinanjiang (TDD-XAJ) model. Two numerical experiments and the application of the TDD-XAJ model in a humid watershed were conducted to demonstrate the model. Our results suggested that (a) numerical errors in the existing distributed Xinanjiang model are significant and may be exacerbated by a potential terrain amplification effect, which could be effectively controlled by the fully coupled numerical framework within the TDD-XAJ model; (b) the 2D slope concentration methods showed enhanced terrain capture ability and eliminated the reliance on the flow direction algorithms used in 1D methods; and (c) the TDD-XAJ model exhibited improved simulation capabilities compared to the existing model when applied in the Tunxi watershed, particularly for flood volume. This study emphasizes the need to revisit DHMs which stem from lumped hydrological models, focusing on model equations and numerical implementations, which could enhance model performance and benefit the hydrological modeling community.</p> |
| format | Article |
| id | doaj-art-e640f704120845cab9efeb7c1a51f622 |
| institution | Kabale University |
| issn | 1027-5606 1607-7938 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Hydrology and Earth System Sciences |
| spelling | doaj-art-e640f704120845cab9efeb7c1a51f6222025-08-20T03:36:41ZengCopernicus PublicationsHydrology and Earth System Sciences1027-56061607-79382025-08-01293745376910.5194/hess-29-3745-2025Two-dimensional differential form of distributed Xinanjiang modelJ. Zhao0Z. Liang1V. P. Singh2V. P. Singh3V. P. Singh4T. Wen5Y. Hu6B. Li7J. Wang8College of Hydrology and Water Resources, Hohai University, Nanjing, 210024, ChinaCollege of Hydrology and Water Resources, Hohai University, Nanjing, 210024, ChinaDepartment of Biological & Agricultural Engineering, Texas A & M University, College Station, TX 77843-2117, USAZachry Department of Civil & Environmental Engineering, Texas A & M University, College Station, TX 77843-3127, USANational Water and Energy Center, UAE University, Al Ain, P.O. Box 15551, UAECollege of Hydrology and Water Resources, Hohai University, Nanjing, 210024, ChinaCollege of Hydrology and Water Resources, Hohai University, Nanjing, 210024, ChinaCollege of Hydrology and Water Resources, Hohai University, Nanjing, 210024, ChinaCollege of Hydrology and Water Resources, Hohai University, Nanjing, 210024, China<p>The distributed hydrologic models (DHMs) evolved from lumped hydrologic models, inheriting their modeling philosophy along with persistent numerical-error issues. Historically, these models tend to use established one-dimensional (1D) methods for slope concentration, which often struggle to effectively represent complex terrains. In this study, we formulated a purely differential form of mathematical equations for the distributed Xinanjiang model and developed a fully coupled numerical solution framework. We also introduced two-dimensional (2D) diffusion wave equations for surface slope concentration and derived 2D linear reservoir equations for subsurface slope concentration to replace their 1D counterparts. This culminated in the development of a two-dimensional differential form of the distributed Xinanjiang (TDD-XAJ) model. Two numerical experiments and the application of the TDD-XAJ model in a humid watershed were conducted to demonstrate the model. Our results suggested that (a) numerical errors in the existing distributed Xinanjiang model are significant and may be exacerbated by a potential terrain amplification effect, which could be effectively controlled by the fully coupled numerical framework within the TDD-XAJ model; (b) the 2D slope concentration methods showed enhanced terrain capture ability and eliminated the reliance on the flow direction algorithms used in 1D methods; and (c) the TDD-XAJ model exhibited improved simulation capabilities compared to the existing model when applied in the Tunxi watershed, particularly for flood volume. This study emphasizes the need to revisit DHMs which stem from lumped hydrological models, focusing on model equations and numerical implementations, which could enhance model performance and benefit the hydrological modeling community.</p>https://hess.copernicus.org/articles/29/3745/2025/hess-29-3745-2025.pdf |
| spellingShingle | J. Zhao Z. Liang V. P. Singh V. P. Singh V. P. Singh T. Wen Y. Hu B. Li J. Wang Two-dimensional differential form of distributed Xinanjiang model Hydrology and Earth System Sciences |
| title | Two-dimensional differential form of distributed Xinanjiang model |
| title_full | Two-dimensional differential form of distributed Xinanjiang model |
| title_fullStr | Two-dimensional differential form of distributed Xinanjiang model |
| title_full_unstemmed | Two-dimensional differential form of distributed Xinanjiang model |
| title_short | Two-dimensional differential form of distributed Xinanjiang model |
| title_sort | two dimensional differential form of distributed xinanjiang model |
| url | https://hess.copernicus.org/articles/29/3745/2025/hess-29-3745-2025.pdf |
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