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基于物理信息神经网络的土壤水力特性估测

Estimation of soil hydraulic properties based on physics-informed neural networks

  • 摘要: 土壤水力特性是表征土壤水分运动的重要参数,在水文模拟、水土保持和农业管理中具有重要作用,但现有估测方法仍存在操作复杂、耗时耗力和适用性受限等缺点。为此,该研究提出一种基于物理信息神经网络(physics-informed neural networks, PINN)与Richardson–Richards方程(RRE)的土壤水力特性估测方法,并结合HYDRUS反演模块,分别估测了栓皮栎林区土壤、油松林区土壤和农田壤土3种土壤的水力特性,将实测数据用作对PINN估测结果的对比验证。结果表明,PINN对3种土壤样本的土壤水分特征曲线估测值和实测值之间的全区域均方根误差(root mean square error, RMSE)分别为0.144、0.040及0.015cm3/cm3,相对均方根误差(relative root mean square error, RRMSE)分别为39.26%、9.45%和4.85%,在土壤体积含水率小于0.4 cm3/cm3区间内,2种林区土壤的RMSE分别降至0.072及0.008 cm3/cm3,RRMSE分别降至37.16%和2.37%;饱和导水率估测值和实测值之间的相对误差分别为2.56%、2.50%和7.89%;在缺少实测值的情况下,非饱和导水率估测值和基于独立观测数据构建的参考值进行对比分析,其RMSE分别为3.0×10−4、7.3×10−5及7.1×10−3cm/min,RRMSE分别为8.39%、1.19%和39.96%。总体来看,PINN能够稳定刻画不同土壤类型的水力特性变化规律。该方法无需预先设定设置初始条件与边界条件作为网络训练约束,有效降低了建模复杂度,能在观测数据有限条件下展现出良好的应用潜力。该研究可为土壤水文分析提供一种可靠的技术路径。

     

    Abstract: Soil hydraulic properties are key parameters for characterizing water infiltration, storage, and transport in soils, as well as their interactions with surface runoff and groundwater recharge. They play an essential role in hydrological simulation, soil and water conservation assessment, and agricultural water management. However, conventional methods for estimating soil hydraulic properties are often labor-intensive, time-consuming, and limited in their applicability. To address these limitations, this study proposes a method for estimating soil hydraulic properties based on physics-informed neural networks (PINN) and the Richardson–Richards equation (RRE). By incorporating the governing equation of soil water movement as the physical constraint, the proposed method is trained only with soil moisture observations and does not require initial or boundary conditions as training constraints, thereby reducing modeling complexity while maintaining physical consistency.Three representative soil types, namely cork oak forest soil, Pinus tabuliformis forest soil, and farmland soil, were selected as the study objects. Time series of volumetric water content measured at four soil depths during infiltration experiments were used as the input data for the PINN model. Meanwhile, the inverse modeling module of HYDRUS was employed to estimate soil hydraulic parameters and construct reference soil water characteristic curves (SWCC) and unsaturated hydraulic conductivity (Ku) data for validating the PINN estimation results. The root mean square error (RMSE), relative root mean square error (RRMSE), and relative error were used to evaluate the estimation accuracy of the proposed model.The results showed that the RMSEs between the volumetric water contents estimated from the PINN-derived SWCCs and the measured volumetric water contents were 0.144, 0.040, and 0.015 cm³/cm³ for the cork oak forest soil, Pinus tabuliformis forest soil, and farmland soil, respectively, with corresponding RRMSEs of 39.26%, 9.45%, and 4.85%. In the unsaturated range where the volumetric water content was lower than 0.4 cm³/cm³, the RMSEs for the two forest soils further decreased to 0.072 and 0.008 cm³/cm³, respectively, while the corresponding RRMSEs decreased to 37.16% and 2.37%, indicating that the proposed model achieved higher estimation accuracy in the unsaturated range. The relative errors between the PINN-estimated saturated hydraulic conductivity (Ks) and the measured values were 2.56%, 2.50%, and 7.89%, respectively. Owing to the lack of measured unsaturated hydraulic conductivity data, the PINN-estimated Ku values were further compared with the reference hydraulic conductivity curves constructed from independent observations. The corresponding RMSEs were 3.0×10−4, 7.3×10−5, and 7.1×10−3 cm/min, with corresponding RRMSEs of 8.39%, 1.19%, and 39.96%, respectively. Overall, the proposed PINN model effectively captured the hydraulic behavior of different soil types and provided stable estimates of soil hydraulic properties. Moreover, the method does not require the explicit specification of initial or boundary conditions, thereby reducing modeling complexity and demonstrating strong potential under limited data availability. This study provides a reliable technical approach for soil hydrological analysis and offers promising applications in soil moisture dynamics research, agricultural water management, and ecohydrological modeling.

     

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