Groundwater recharge estimation (GRE), particularly at a regional scale, is an important challenge in hydrogeology. Unsaturated zone flow (UZF) modeling is now being used increasingly for GRE, though its validity relies on the accurate estimation of the soil hydraulic parameters (SHPs). In this study, a regional spatial-nonstationarity-based inverse-UZF-modeling framework is developed for GRE. The regional-scale investigation is achieved using a multiple column approach and by applying the software package HYDRUS-1D. Considering the inverse modeling, the SHPs are calibrated against observed data from the stations of a large-scale monitoring network. Moreover, a nonstationary kriging technique is implemented to provide a regional map of recharge from the calculated values. Additionally, to report probability maps of recharge, a probabilistic approach through the sequential Gaussian simulation algorithm is incorporated. The proposed methodology has been tested at 100 stations of the Oklahoma Mesonet network across Oklahoma (USA) for the period 2014–2019. The comparison between the simulated and observed pressure head data endorses the performance of the regional-scale inverse UZF modeling. The distribution of recharge in the produced map increases from northwest to southeast, following the similar pattern of rainfall. Finally, the probabilistic approach results in an e-type (mean) map yielding an expected value of 166 mm/year statewide mean recharge, and 90% confidence interval maps that provide a workable range of 139–194 mm/year for planning purposes. With the rapid expansion of large-scale monitoring networks, this study can be applied to other areas where such observed data exist.

地下水补给估算 (GRE)，特别是在区域范围内，是水文地质学的一个重要挑战。不饱和区流 (UZF) 模型现在越来越多地用于 GRE，尽管其有效性依赖于对土壤水力参数 (SHP) 的准确估计。在这项研究中，为 GRE 开发了一个基于区域空间非平稳性的逆 UZF 建模框架。使用多列方法和应用软件包 HYDRUS-1D 实现了区域规模的调查。考虑到逆向建模，SHP 是根据来自大型监测网络站点的观测数据进行校准的。此外，采用非平稳克里金技术，根据计算值提供区域补给图。此外，为了报告补给的概率图，结合了通过顺序高斯模拟算法的概率方法。所提出的方法已在 2014-2019 年期间在俄克拉荷马州（美国）的俄克拉荷马州 Mesonet 网络的 100 个站点进行了测试。模拟和观测压头数据之间的比较证实了区域尺度反 UZF 建模的性能。生成的地图中的补给分布从西北向东南增加，遵循类似的降雨模式。最后，概率方法产生的 e 型（平均）地图产生了 166 毫米/年全州平均补给的预期值，以及 90% 置信区间地图，为规划目的提供了 139-194 毫米/年的可行范围。随着大规模监控网络的快速扩张，