Evapotranspiration is arguably the least quantified component of the hydrologic cycle. We propose two complementary strategies for estimation of evapotranspiration rates and root water uptake profiles from soil-moisture sensor-array data. One is our implementation of ensemble Kalman filter (EnKF); it treats the evapotranspiration sink term in the Richards equation, rather than soil moisture, as the observable to update. The other is a maximum likelihood estimator (MLE) applied to the same observable; it is supplemented with the Fisher information matrix to quantify uncertainty in its predictions. We use numerical experiments to demonstrate the accuracy and computational efficiency of these techniques. We found our EnKF implementation to be two orders of magnitude faster than either the standard EnKF or MLE, and our MLE procedure to require an order of magnitude fewer iterations to converge than its counterpart applied to soil moisture. These findings render our methodologies a viable and practical tool for estimation of the root water uptake profiles and evaporation rates, with the MLE technique to be used when the prior knowledge about evapotranspiration at the site is elusive.

中文翻译：

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从土壤水分传感器阵列数据估算蒸散率和根系吸水量

蒸散可以说是水文循环中量化最少的组成部分。我们提出了两种互补的策略，用于从土壤湿度传感器阵列数据估算蒸散率和根系吸水量。一个是我们对集成卡尔曼滤波器（EnKF）的实现；它将理查兹方程中的蒸散汇项而不是土壤湿度视为要更新的可观测值。另一个是应用于同一个可观察量的最大似然估计器 (MLE)；它补充有 Fisher 信息矩阵，以量化其预测中的不确定性。我们使用数值实验来证明这些技术的准确性和计算效率。我们发现我们的 EnKF 实现比标准 EnKF 或 MLE 快两个数量级，并且我们的 MLE 程序需要比应用于土壤水分的对应程序少一个数量级的迭代才能收敛。这些发现使我们的方法成为估计根系吸水剖面和蒸发率的可行且实用的工具，当有关现场蒸发蒸腾的先验知识难以捉摸时，将使用 MLE 技术。