Articles | Volume 29, issue 15
https://doi.org/10.5194/hess-29-3745-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-29-3745-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Two-dimensional differential form of distributed Xinanjiang model
Jianfei Zhao
College of Hydrology and Water Resources, Hohai University, Nanjing, 210024, China
Zhongmin Liang
CORRESPONDING AUTHOR
College of Hydrology and Water Resources, Hohai University, Nanjing, 210024, China
Vijay P. Singh
Department of Biological & Agricultural Engineering, Texas A & M University, College Station, TX 77843-2117, USA
Zachry Department of Civil & Environmental Engineering, Texas A & M University, College Station, TX 77843-3127, USA
National Water and Energy Center, UAE University, Al Ain, P.O. Box 15551, UAE
Taiyi Wen
College of Hydrology and Water Resources, Hohai University, Nanjing, 210024, China
Yiming Hu
College of Hydrology and Water Resources, Hohai University, Nanjing, 210024, China
Binquan Li
College of Hydrology and Water Resources, Hohai University, Nanjing, 210024, China
Jun Wang
College of Hydrology and Water Resources, Hohai University, Nanjing, 210024, China
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Cited articles
Anhui Provincial Department of Water Resources (APDWR): Anhui Water Information, http://yc.wswj.net/ahsxx/LOL/, last access: 9 August 2025.
Bates, P. D., Horritt, M. S., and Fewtrell, T. J.: A simple inertial formulation of the shallow water equations for efficient two-dimensional flood inundation modelling, J. Hydrol., 387, 33–45, https://doi.org/10.1016/j.jhydrol.2010.03.027, 2010.
Beven, K.: Towards an alternative blueprint for a physically based digitally simulated hydrologic response modelling system, Hydrol. Process., 16, 189–206, https://doi.org/10.1002/hyp.343, 2002.
Beven, K. J., Kirkby, M. J., Freer, J. E., and Lamb, R.: A history of TOPMODEL, Hydrol. Earth Syst. Sci., 25, 527–549, https://doi.org/10.5194/hess-25-527-2021, 2021.
Bisht, G. and Riley, W. J.: Development and verification of a numerical library for solving global terrestrial multiphysics problems, J. Adv. Model. Earth Sy., 11, 1516–1542, https://doi.org/10.1029/2018MS001560, 2019.
Chen, L., Deng, J., Yang, W., and Chen, H.: Hydrological modelling of large-scale karst-dominated basin using a grid-based distributed karst hydrological model, J. Hydrol., 628, 130459, https://doi.org/10.1016/j.jhydrol.2023.130459, 2024.
Chen, X., Zhang, K., Luo, Y., Zhang, Q., Zhou, J., Fan, Y., Huang, P., Yao, C., Chao, L., and Bao, H.: A distributed hydrological model for semi-humid watersheds with a thick unsaturated zone under strong anthropogenic impacts: a case study in Haihe river basin, J. Hydrol., 623, 129765, https://doi.org/10.1016/j.jhydrol.2023.129765, 2023.
Clark, M. P. and Kavetski, D.: Ancient numerical daemons of conceptual hydrological modeling: 1. Fidelity and efficiency of time stepping schemes, Water Resour. Res., 46, W10510, https://doi.org/10.1029/2009WR008894, 2010.
Clark, M. P., Fan, Y., Lawrence, D. M., Adam, J. C., Bolster, D., Gochis, D. J., Hooper, R. P., Kumar, M., Leung, L. R., Mackay, D. S., Maxwell, R. M., Shen, C., Swenson, S. C., and Zeng, X.: Improving the representation of hydrologic processes in earth system models, Water Resour. Res., 51, 5929–5956, https://doi.org/10.1002/2015WR017096, 2015.
Clark, M. P., Schaefli, B., Schymanski, S. J., Samaniego, L., Luce, C. H., Jackson, B. M., Freer, J. E., Arnold, J. R., Moore, R. D., Istanbulluoglu, E., and Ceola, S.: Improving the theoretical underpinnings of process-based hydrologic models, Water Resour. Res., 52, 2350–2365, https://doi.org/10.1002/2015WR017910, 2016.
Computer Network Information Center of the Chinese Academy of Sciences (CNIC-CAS): SRTMDEMUTM 90 m resolution digital elevation product, Geospatial Data Cloud [data set], https://www.gscloud.cn/sources/details/306?pid=302, last access: 9 August 2025.
Di Giammarco, P., Todini, E., and Lamberti, P.: A conservative finite elements approach to overland flow: the control volume finite element formulation, J. Hydrol., 175, 267–291, https://doi.org/10.1016/S0022-1694(96)80014-X, 1996.
Dongarra, J. and Keyes, D.: The co-evolution of computational physics and high-performance computing, Nat. Rev. Phys., 6, 621–627, https://doi.org/10.1038/s42254-024-00750-z, 2024.
Fang, Y.-H., Zhang, X., Corbari, C., Mancini, M., Niu, G.-Y., and Zeng, W.: Improving the Xin'anjiang hydrological model based on mass–energy balance, Hydrol. Earth Syst. Sci., 21, 3359–3375, https://doi.org/10.5194/hess-21-3359-2017, 2017.
Fatichi, S., Vivoni, E. R., Ogden, F. L., Ivanov, V. Y., Mirus, B., Gochis, D., Downer, C. W., Camporese, M., Davison, J. H., Ebel, B., Jones, N., Kim, J., Mascaro, G., Niswonger, R., Restrepo, P., Rigon, R., Shen, C., Sulis, M., and Tarboton, D.: An overview of current applications, challenges, and future trends in distributed process-based models in hydrology, J. Hydrol., 537, 45–60, https://doi.org/10.1016/j.jhydrol.2016.03.026, 2016.
Freeze, R. A. and Harlan, R. L.: Blueprint for a physically-based, digitally-simulated hydrologic response model, J. Hydrol., 9, 237–258, https://doi.org/10.1016/0022-1694(69)90020-1, 1969.
Gong, W., Duan, Q., Li, J., Wang, C., Di, Z., Ye, A., Miao, C., and Dai, Y.: An intercomparison of sampling methods for uncertainty quantification of environmental dynamic models, J. Environ. Inform., 28, 11–24, https://doi.org/10.3808/jei.201500310, 2015.
Gottardi, G. and Venutelli, M.: An accurate time integration method for simplified overland flow models, Adv. Water Resour., 31, 173–180, https://doi.org/10.1016/j.advwatres.2007.08.004, 2008.
Gupta, H. V., Clark, M. P., Vrugt, J. A., Abramowitz, G., and Ye, M.: Towards a comprehensive assessment of model structural adequacy, Water Resour. Res., 48, W08301, https://doi.org/10.1029/2011WR011044, 2012.
He, C., Valayamkunnath, P., Barlage, M., Chen, F., Gochis, D., Cabell, R., Schneider, T., Rasmussen, R., Niu, G.-Y., Yang, Z.-L., Niyogi, D., and Ek, M.: Modernizing the open-source community Noah with multi-parameterization options (Noah-MP) land surface model (version 5.0) with enhanced modularity, interoperability, and applicability, Geosci. Model Dev., 16, 5131–5151, https://doi.org/10.5194/gmd-16-5131-2023, 2023.
Hodson, T. O.: Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not, Geosci. Model Dev., 15, 5481–5487, https://doi.org/10.5194/gmd-15-5481-2022, 2022.
Höge, M., Scheidegger, A., Baity-Jesi, M., Albert, C., and Fenicia, F.: Improving hydrologic models for predictions and process understanding using neural ODEs, Hydrol. Earth Syst. Sci., 26, 5085–5102, https://doi.org/10.5194/hess-26-5085-2022, 2022.
Hong, S. and Mostaghimi, S.: Comparison of 1-D and 2-D modeling of overland runoff and sediment transport, J. Am. Water Resour. As., 33, 1103–1116, https://doi.org/10.1111/j.1752-1688.1997.tb04128.x, 1997.
Jackson, E. K., Roberts, W., Nelsen, B., Williams, G. P., Nelson, E. J., and Ames, D. P.: Introductory overview: error metrics for hydrologic modelling – a review of common practices and an open source library to facilitate use and adoption, Environ. Modell. Softw., 119, 32–48, https://doi.org/10.1016/j.envsoft.2019.05.001, 2019.
Jain, M. K. and Singh, V. P.: DEM-based modelling of surface runoff using diffusion wave equation, J. Hydrol., 302, 107–126, https://doi.org/10.1016/j.jhydrol.2004.06.042, 2005.
Kampf, S. K. and Burges, S. J.: A framework for classifying and comparing distributed hillslope and catchment hydrologic models, Water Resour. Res., 43, W05423, https://doi.org/10.1029/2006WR005370, 2007.
Kavetski, D. and Clark, M. P.: Ancient numerical daemons of conceptual hydrological modeling: 2. Impact of time stepping schemes on model analysis and prediction, Water Resour. Res., 46, W10511, https://doi.org/10.1029/2009WR008896, 2010.
Kazezyılmaz-Alhan, C. M. and Medina, M. A.: Kinematic and diffusion waves: analytical and numerical solutions to overland and channel flow, J. Hydraul. Eng., 133, 217–228, https://doi.org/10.1061/(ASCE)0733-9429(2007)133:2(217), 2007.
Knoben, W. J. M., Freer, J. E., Peel, M. C., Fowler, K. J. A., and Woods, R. A.: A brief analysis of conceptual model structure uncertainty using 36 models and 559 catchments, Water Resour. Res., 56, e2019WR025975, https://doi.org/10.1029/2019WR025975, 2020.
Kollet, S., Sulis, M., Maxwell, R. M., Paniconi, C., Putti, M., Bertoldi, G., Coon, E. T., Cordano, E., Endrizzi, S., Kikinzon, E., Mouche, E., Mügler, C., Park, Y., Refsgaard, J. C., Stisen, S., and Sudicky, E.: The integrated hydrologic model intercomparison project, IH-MIP2: a second set of benchmark results to diagnose integrated hydrology and feedbacks, Water Resour. Res., 53, 867–890, https://doi.org/10.1002/2016WR019191, 2017.
La Follette, P. T., Teuling, A. J., Addor, N., Clark, M., Jansen, K., and Melsen, L. A.: Numerical daemons of hydrological models are summoned by extreme precipitation, Hydrol. Earth Syst. Sci., 25, 5425–5446, https://doi.org/10.5194/hess-25-5425-2021, 2021.
Lam, S. K., Pitrou, A., and Seibert, S.: Numba: a LLVM-based Python JIT compiler, in: Proceedings of the Second Workshop on the LLVM Compiler Infrastructure in HPC, Austin, Texas, 15 November 2015, 7, https://doi.org/10.1145/2833157.2833162, 2015.
Li, B., Sun, T., Tian, F., Tudaji, M., Qin, L., and Ni, G.: Hybrid hydrological modeling for large alpine basins: a semi-distributed approach, Hydrol. Earth Syst. Sci., 28, 4521–4538, https://doi.org/10.5194/hess-28-4521-2024, 2024.
Liu, J., Chen, X., Zhang, J., and Flury, M.: Coupling the Xinanjiang model to a kinematic flow model based on digital drainage networks for flood forecasting, Hydrol. Process., 23, 1337–1348, https://doi.org/10.1002/hyp.7255, 2009.
Liu, Q. Q., Chen, L., Li, J. C., and Singh, V. P.: Two-dimensional kinematic wave model of overland-flow, J. Hydrol., 291, 28–41, https://doi.org/10.1016/j.jhydrol.2003.12.023, 2004.
Loritz, R., Hrachowitz, M., Neuper, M., and Zehe, E.: The role and value of distributed precipitation data in hydrological models, Hydrol. Earth Syst. Sci., 25, 147–167, https://doi.org/10.5194/hess-25-147-2021, 2021.
Lu, M., Kioke, T., and Hayakawa, N.: Distributed XinAnJiang model using radar measured rainfall data, in: Proceedings of International Conference on Water Resources & Environmental Research: Towards the 21st Century, Kyoto, Japan, 29–31 October 1996, 29–36, https://cir.nii.ac.jp/crid/1571417125513518464 (last access: 11 August 2025), 1996.
MacCormack, R. W.: A numerical method for solving the equations of compressible viscous flow, AIAA J., 20, 1275–1281, https://doi.org/10.2514/3.51188, 1982.
Maxwell, R. M., Putti, M., Meyerhoff, S., Delfs, J. O., Ferguson, I. M., Ivanov, V., Kim, J., Kolditz, O., Kollet, S. J., Kumar, M., Lopez, S., Niu, J., Paniconi, C., Park, Y. J., Phanikumar, M. S., Shen, C., Sudicky, E. A., and Sulis, M.: Surface-subsurface model intercomparison: a first set of benchmark results to diagnose integrated hydrology and feedbacks, Water Resour. Res., 50, 1531–1549, https://doi.org/10.1002/2013WR013725, 2014.
McGuire, K. J., Klaus, J., and Jackson, C. R.: Interflow, subsurface stormflow and throughflow: a synthesis of field work and modelling, Hydrol. Process., 38, e15263, https://doi.org/10.1002/hyp.15263, 2024.
Murphy, B., Yurchak, R., and Müller, S.: GeoStat-Framework/PyKrige (1.7.2), Zenodo [code], https://doi.org/10.5281/zenodo.11360184, 2024.
Nan, Y., Chen, C., Zhao, Y., Tian, F., and Mcdonnell, J.: A historical overview of experimental hydrology in China, Hydrol. Process., 38, e15233, https://doi.org/10.1002/hyp.15233, 2024.
Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual models part I – a discussion of principles, J. Hydrol., 10, 282–290, https://doi.org/10.1016/0022-1694(70)90255-6, 1970.
National Geomatics Center of China (NGCC): GlobeLand30–30 m resolution global land cover dataset, National Catalogue Service For Geographic Information [data set], https://www.webmap.cn/commres.do?method=globeIndex (last access: 9 August 2025), 2020.
National Meteorological Information Centre (NMIC): Daily surface climatological data for China (V3.0), China Meteorological Data Service Centre [data set], http://data.cma.cn/data/cdcdetail/dataCode/SURF_CLI_CHN_MUL_DAY_V3.0.html (last access: 13 February 2022), 2012.
Nippgen, F., Mcglynn, B. L., and Emanuel, R. E.: The spatial and temporal evolution of contributing areas, Water Resour. Res., 51, 4550–4573, https://doi.org/10.1002/2014WR016719, 2015.
O'Callaghan, J. F. and Mark, D. M.: The extraction of drainage networks from digital elevation data, Comput Vision Graph., 28, 323–344, https://doi.org/10.1016/S0734-189X(84)80011-0, 1984.
Ouyang, W., Ye, L., Chai, Y., Ma, H., Chu, J., Peng, Y., and Zhang, C.: A differentiable, physics-based hydrological model and its evaluation for data-limited basins, J. Hydrol., 649, 132471, https://doi.org/10.1016/j.jhydrol.2024.132471, 2025.
Overton, D. E. and Brakensiek, D. L.: A kinematic model of surface runoff response, in: Proceedings of the Wellington Symposium, Wellington, New Zealand, 1–8 December 1970, 100–112, https://unesdoc.unesco.org/ark:/48223/pf0000012503 (last access: 11 August 2025), 1970.
Panday, S. and Huyakorn, P. S.: A fully coupled physically-based spatially-distributed model for evaluating surface/subsurface flow, Adv. Water Resour., 27, 361–382, https://doi.org/10.1016/j.advwatres.2004.02.016, 2004.
Paniconi, C. and Putti, M.: Physically based modeling in catchment hydrology at 50: survey and outlook, Water Resour. Res., 51, 7090–7129, https://doi.org/10.1002/2015WR017780, 2015.
Perrini, P., Cea, L., Chiaravalloti, F., Gabriele, S., Manfreda, S., Fiorentino, M., Gioia, A., and Iacobellis, V.: A runoff-on-grid approach to embed hydrological processes in shallow water models, Water Resour. Res., 60, e2023WR036421, https://doi.org/10.1029/2023WR036421, 2024.
Qu, Y. and Duffy, C. J.: A semidiscrete finite volume formulation for multiprocess watershed simulation, Water Resour. Res., 43, W08419, https://doi.org/10.1029/2006WR005752, 2007.
Reggiani, P., Sivapalan, M., and Majid Hassanizadeh, S.: A unifying framework for watershed thermodynamics: balance equations for mass, momentum, energy and entropy, and the second law of thermodynamics, Adv. Water Resour., 22, 367–398, https://doi.org/10.1016/S0309-1708(98)00012-8, 1998.
Santos, L., Thirel, G., and Perrin, C.: Continuous state-space representation of a bucket-type rainfall-runoff model: a case study with the GR4 model using state-space GR4 (version 1.0), Geosci. Model Dev., 11, 1591–1605, https://doi.org/10.5194/gmd-11-1591-2018, 2018.
Schoups, G., Vrugt, J. A., Fenicia, F., and van de Giesen, N. C.: Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models, Water Resour. Res., 46, W10530, https://doi.org/10.1029/2009WR008648, 2010.
Seibert, J. and Bergström, S.: A retrospective on hydrological catchment modelling based on half a century with the HBV model, Hydrol. Earth Syst. Sci., 26, 1371–1388, https://doi.org/10.5194/hess-26-1371-2022, 2022.
Shaw, J., Kesserwani, G., Neal, J., Bates, P., and Sharifian, M. K.: LISFLOOD-FP 8.0: the new discontinuous Galerkin shallow-water solver for multi-core CPUs and GPUs, Geosci. Model Dev., 14, 3577–3602, https://doi.org/10.5194/gmd-14-3577-2021, 2021.
Shen, C. and Phanikumar, M. S.: A process-based, distributed hydrologic model based on a large-scale method for surface–subsurface coupling, Adv. Water Resour., 33, 1524–1541, https://doi.org/10.1016/j.advwatres.2010.09.002, 2010.
Shu, L., Ullrich, P. A., and Duffy, C. J.: Simulator for Hydrologic Unstructured Domains (SHUD v1.0): numerical modeling of watershed hydrology with the finite volume method, Geosci. Model Dev., 13, 2743–2762, https://doi.org/10.5194/gmd-13-2743-2020, 2020.
Shu, L., Ullrich, P., Meng, X., Duffy, C., Chen, H., and Li, Z.: rSHUD v2.0: advancing the Simulator for Hydrologic Unstructured Domains and unstructured hydrological modeling in the R environment, Geosci. Model Dev., 17, 497–527, https://doi.org/10.5194/gmd-17-497-2024, 2024.
Song, Y., Knoben, W. J. M., Clark, M. P., Feng, D., Lawson, K., Sawadekar, K., and Shen, C.: When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling, Hydrol. Earth Syst. Sci., 28, 3051–3077, https://doi.org/10.5194/hess-28-3051-2024, 2024.
Stacke, T. and Hagemann, S.: HydroPy (v1.0): a new global hydrology model written in Python, Geosci. Model Dev., 14, 7795–7816, https://doi.org/10.5194/gmd-14-7795-2021, 2021.
Su, B., Kazama, S., Lu, M., and Sawamoto, M.: Development of a distributed hydrological model and its application to soil erosion simulation in a forested catchment during storm period, Hydrol. Process., 17, 2811–2823, https://doi.org/10.1002/hyp.1435, 2003.
Taheri, M., Ranjram, M., and Craig, J. R.: An upscaled model of fill-and-spill hydrological response, Water Resour. Res., 59, e2022WR033494, https://doi.org/10.1029/2022WR033494, 2023.
Todini, E.: A mass conservative and water storage consistent variable parameter Muskingum-Cunge approach, Hydrol. Earth Syst. Sci., 11, 1645–1659, https://doi.org/10.5194/hess-11-1645-2007, 2007.
Tong, B.: Fine-scale rainfall-runoff processes simulation using grid Xinanjiang (grid-XAJ) modell, PhD thesis, Hohai University, LW223611, Hohai University Library, Nanjing, 153 pp., https://thesis.chaoxing.com/back/thesis/downLoadFile?thesisId=196936&fid=24578&sign=790ad94f-3e9a-4255-a4ef-0a7ec7259dd1&type=1&thesisId=196936 (last access: 11 August 2025), 2022.
Tran, Q. Q., De Niel, J., and Willems, P.: Spatially distributed conceptual hydrological model building: a generic top-down approach starting from lumped models, Water Resour. Res., 54, 8064–8085, https://doi.org/10.1029/2018WR023566, 2018.
Ul Hassan, Z., Jefferson, A. J., Avellaneda, P. M., and Bhaskar, A. S.: Assessment of hydrological parameter uncertainty versus climate projection spread on urban streamflow and floods, J. Hydrol., 638, 131546, https://doi.org/10.1016/j.jhydrol.2024.131546, 2024.
Wang, J., Lu, Z., Han, D. W., Liu, Y., and Rico Ramirez, M. A.: Hydrological model adaptability to rainfall inputs of varied quality, Water Resour. Res., 59, e2022WR032484, https://doi.org/10.1029/2022WR032484, 2023.
Woldegiorgis, B. T., Baulch, H., Wheater, H., Crossman, J., Clark, M., Stadnyk, T., and Bajracharya, A.: Impacts of uncontrolled operator splitting methods on parameter identification, prediction uncertainty, and subsurface flux representation in conceptual hydrological models, Water Resour. Res., 59, e2022WR033250, https://doi.org/10.1029/2022WR033250, 2023.
Wu, N., Zhang, K., Naghibi, A., Hashemi, H., Ning, Z., Zhang, Q., Yi, X., Wang, H., Liu, W., Gao, W., and Jarsjö, J.: Comparative Hydrological Modeling of Snow-Cover and Frozen Ground Impacts Under Topographically Complex Conditions, Hydrol. Earth Syst. Sci. Discuss. [preprint], https://doi.org/10.5194/hess-2024-324, in review, 2024.
Yao, C., Li, Z., Bao, H., and Yu, Z.: Application of a developed Grid-Xinanjiang model to Chinese watersheds for flood forecasting purpose, J. Hydrol. Eng., 14, 923–934, https://doi.org/10.1061/(ASCE)HE.1943-5584.0000067, 2009.
Yao, C., Li, Z., Yu, Z., and Zhang, K.: A priori parameter estimates for a distributed, grid-based Xinanjiang model using geographically based information, J. Hydrol., 468–469, 47–62, https://doi.org/10.1016/j.jhydrol.2012.08.025, 2012.
Zhang, Q., Zhang, K., Chao, L., Chen, X., and Wu, N.: A unified runoff generation scheme for applicability across different hydrometeorological zones, Environ. Modell. Softw., 180, 106138, https://doi.org/10.1016/j.envsoft.2024.106138, 2024.
Zhao, J.: Code for TDD-XAJ, Zenodo [code], https://doi.org/10.5281/zenodo.14227068, 2024a.
Zhao, J.: Data for TDD-XAJ, Zenodo [data set], https://doi.org/10.5281/zenodo.14226969, 2024b.
Zhao, J., Duan, Y., Hu, Y., Li, B., and Liang, Z.: The numerical error of the Xinanjiang model, J. Hydrol., 619, 129324, https://doi.org/10.1016/j.jhydrol.2023.129324, 2023.
Zhao, R.: The Xinanjiang model applied in China, J. Hydrol., 135, 371–381, https://doi.org/10.1016/0022-1694(92)90096-E, 1992.
Zhao, R. and Zhuang, Y.: Regional patterns of rainfall-runoff relationship, Journal of Hohai University (Natural Sciences), S2, 53–68, 1963.
Zhao, R., Zhuang, Y., Fang, L., Liu, X., and Zhang, Q.: The Xinanjiang model, in: Proceedings of the Oxford Symposium, Oxford, England, 15–18 April 1980, 351–356, https://unesdoc.unesco.org/ark:/48223/pf0000043527 (last access: 11 August 2025), 1980.
Zhu, D., Ren, Q., Xuan, Y., Chen, Y., and Cluckie, I. D.: An effective depression filling algorithm for DEM-based 2-D surface flow modelling, Hydrol. Earth Syst. Sci., 17, 495–505, https://doi.org/10.5194/hess-17-495-2013, 2013.
Short summary
This paper reformulates the model equations of the distributed Xinanjiang hydrological model in fully differential form and incorporates two-dimensional slope runoff routing methods, which are solved using appropriate numerical techniques. The main contribution is to provide an approach for distributed hydrological models that have evolved from lumped counterparts to reduce inherited numerical errors and to improve terrain representation, thereby enhancing their physical realism and simulation accuracy.
This paper reformulates the model equations of the distributed Xinanjiang hydrological model in...