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

Abstract. 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. Many of these applications require information on soil water dynamics in deeper soil layers. Cosmic-ray neutron sensing (CRNS) allows for 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. Simple depth-extrapolation approaches often used in remote sensing applications 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 physically-based soil moisture analytical relationship SMAR is usually also calibrated to sensor data, but could be applied without calibration if all its parameters were known. However, in particular its water loss parameter 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 at a forest site with sandy soils with and without calibration. Comparing the model results against in-situ reference measurements down to depths of 450 cm shows that the SMAR models both with and without modification do not capture the observed soil moisture dynamics well. The performance of the SMAR models nevertheless meets a previously used benchmark RMSE of ≤ 0.06 cm³ cm⁻³ in both, calibrated and uncalibrated scenarios. Only with effective parameters in a non-physical range, a better model performance could be achieved. 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 with SMAR. However, a more accurate estimation of the sensitive measurement depth of the CRNS improved the soil moisture estimates in the second layer. Despite the fact that the soil moisture dynamics are not well represented at our study site using physically reasonable parameters, the 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.