Developing a functional linkage between hydrological variables and easily accessible terrain and soil information is a novel concept for distributed hydrological models. This approach aims to address limitations imposed by data scarcity and high computational demands. The model hypothesizes that the relationship between the evaporation flux and the absolute value of the matric potential follows a power exponential pattern. Analytic solutions for the groundwater depth, the evaporation capacity, and the storage capacity are derived with respect to the topographic index, considering the relationship between the groundwater depth and the topographic index and the influence of setting off. Subsequently, a distributed Xin’anjiang Model using the analytic solution of the storage capacity under unsteady-state conditions is constructed. This new model is employed to simulate soil moisture and discharge in the Tarrawarra Watershed. The simulation results for soil moisture and discharge are compared with those from the Storage Capacity Model and the DHSVM. Additionally, the computational speeds of all three models are compared. The findings indicate that the simulation accuracy of the new model for soil moisture and discharge surpasses that of the Storage Capacity Model and the DHSVM. Meanwhile, the computational speed of the new model is significantly faster than the DHSVM and slightly slower than the Storage Capacity Model. It offers a balance between computational efficiency, predictive accuracy, and physical mechanism representation. The data requirements of the new model are minimal and easy to procure, and it requires less computational effort. Moreover, it accurately captures the spatial and temporal dynamics of soil moisture and the discharge process of the watershed.
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