Depth extrapolation of field-scale soil moisture time series derived with cosmic-ray neutron sensing (CRNS) using the soil moisture analytical relationship (SMAR) model

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.