Quantifying the spatial and temporal dynamics of soil moisture is an important subject in vadose zone hydrology. Although progress has been made to measure soil water content, soil water flow needs to be simulated for many applications. An analytical solution for soil water content, resulting from vertical flow and simplified mathematical conditions and hydraulic properties, was derived with the Cole‐Hopf transformation. The solution serves as a transfer function with the calibrated boundary condition and water content as respective input and output. This transfer function was applied to time series of soil water content, obtained from weekly observations with a neutron probe over a 1282‐day period at five depths and 16 locations. Water retention and saturated hydraulic conductivity were measured on soil samples in the laboratory. The transfer function was calibrated to observed time series of soil water content θ(t) with a median coefficient of determination R² = 0.980. It was then used to predict θ(t) using constants from the calibration location and hydraulic parameters from the prediction location. There was a fairly good correspondence between predicted and observed θ(t) using calibrations elsewhere (R² = 0.783). As an alternative, an observed time series θ(t) was scaled by multiplying it by the ratio of experimental saturated water contents for prediction and observation location. This scaling approach led to poorer predictions (R² = 0.651). The analytical solution provides a flexible approach to quantify soil moisture for a variety of scenarios regarding available data on topography, climate, soil properties, and soil hydraulic parameters.

中文翻译：

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田间土壤水分剖面的解析解

在渗流带水文学中，量化土壤水分的时空动态是重要的课题。尽管在测量土壤含水量方面已经取得了进展，但是在许多应用中都需要模拟土壤水流。通过Cole-Hopf变换得出了由垂直流，简化的数学条件和水力特性引起的土壤含水量的分析解决方案。该解决方案充当传递函数，其中校准的边界条件和水含量分别作为输入和输出。该传递函数适用于土壤水含量的时间序列，该时间序列是从中子探针在1282天的时间内在五个深度和16个位置进行的每周观测获得的。在实验室中对土壤样品进行了保水率和饱和导水率的测量。θ（t），中位确定系数R ²  = 0.980。然后，使用来自校准位置的常数和来自预测位置的液压参数来预测θ（t）。使用其他地方的校准值，预测的和观察到的θ（t）之间存在相当好的对应关系（R ²  = 0.783）。或者，将观察到的时间序列θ（t）乘以用于预测和观察位置的实验饱和水含量的比值来缩放。这种缩放方法导致较差的预测（R ² = 0.651）。该分析解决方案提供了一种灵活的方法，可以根据有关地形，气候，土壤特性和土壤水力参数的可用数据，针对各种场景量化土壤水分。