Abstract. Ground-based soil moisture measurements at the field scale are highly beneficial for different hydrological applications, including the validation of space-borne soil moisture products, landscape water budgeting, or multi-criteria calibration of rainfall–runoff models from field to catchment scale. Cosmic-ray neutron sensing (CRNS) allows for the non-invasive monitoring of field-scale soil moisture across several hectares around the instrument but only for the first few tens of centimeters of the soil. Many of these applications require information on soil water dynamics in deeper soil layers. Simple depth-extrapolation approaches often used in remote sensing may be used to estimate soil moisture in deeper layers based on the near-surface soil moisture information. However, most approaches require a site-specific calibration using depth profiles of in situ soil moisture data, which are often not available. The soil moisture analytical relationship (SMAR) is usually also calibrated to sensor data, but due to the physical meaning of each model parameter, it could be applied without calibration if all its parameters were known. However, its water loss parameter in particular is difficult to estimate. In this paper, we introduce and test a simple modification of the SMAR model to estimate the water loss in the second layer based on soil physical parameters and the surface soil moisture time series. We apply the model with and without calibration at a forest site with sandy soils. Comparing the model results with in situ reference measurements down to depths of 450 cm shows that the SMAR models both with and without modification as well as the calibrated exponential filter approach do not capture the observed soil moisture dynamics well. While, on average, the latter performs best over different tested scenarios, the performance of the SMAR models nevertheless meets a previously used benchmark RMSE of ≤ 0.06 cm3 cm−3 in both the calibrated original and uncalibrated modified version. Different transfer functions to derive surface soil moisture from CRNS do not translate into markedly different results of the depth-extrapolated soil moisture time series simulated by SMAR. Despite the fact that the soil moisture dynamics are not well represented at our study site using the depth-extrapolation approaches, our modified SMAR model may provide valuable first estimates of soil moisture in a deeper soil layer derived from surface measurements based on stationary and roving CRNS as well as remote sensing products where in situ data for calibration are not available.

中文翻译：

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使用土壤湿度分析关系 (SMAR) 模型，通过宇宙射线中子传感 (CRNS) 导出现场尺度土壤湿度时间序列的深度外推


摘要。现场尺度的地面土壤湿度测量对于不同的水文应用非常有益，包括验证空间土壤湿度产品、景观水预算或从现场到流域尺度的降雨径流模型的多标准校准。宇宙射线中子传感 (CRNS) 可以对仪器周围几公顷的现场土壤湿度进行非侵入性监测，但仅限于土壤的前几十厘米。许多这些应用需要有关更深土层中土壤水动态的信息。遥感中常用的简单深度外推方法可用于根据近地表土壤湿度信息估计更深层的土壤湿度。然而，大多数方法需要使用原位土壤湿度数据的深度剖面进行特定地点的校准，而这些数据通常无法获得。土壤湿度分析关系（SMAR）通常也根据传感器数据进行校准，但由于每个模型参数的物理意义，如果其所有参数已知，则无需校准即可应用。然而，其失水参数尤其难以估计。在本文中，我们介绍并测试了 SMAR 模型的简单修改，以根据土壤物理参数和表面土壤湿度时间序列来估计第二层的水损失。我们在沙质土壤的森林地点应用了经过校准和未经校准的模型。将模型结果与深度达 450 cm 的原位参考测量结果进行比较表明，经过修改和未经修改的 SMAR 模型以及校准的指数滤波器方法都不能很好地捕获观测到的土壤湿度动态。 虽然平均而言，后者在不同的测试场景中表现最佳，但 SMAR 模型的性能仍然满足先前使用的校准原始版本和未校准修改版本中 ≤ 0.06 cm3 cm−3 的基准 RMSE。从 CRNS 导出表面土壤湿度的不同传递函数不会转化为 SMAR 模拟的深度外推土壤湿度时间序列的明显不同的结果。尽管我们的研究地点使用深度外推方法并没有很好地表示土壤湿度动态，但我们修改后的 SMAR 模型可以提供对更深土层中土壤湿度的有价值的初步估计，该估计是根据基于固定和流动 CRNS 的表面测量得出的以及无法获得现场校准数据的遥感产品。