Application of a soil moisture diagnostic equation for estimating root-zone soil moisture in arid and semi-arid regions

•The soil moisture diagnostic equation was applied to estimate root-zone (0–100cm) soil moisture.•Four USDA Soil Climate Analysis Network sites in arid and semi-arid regions were tested.•Root mean square errors of the estimated soil moistures at four testing sites were less than 3.2 (%).•The errors in the estimated soil moisture were non-cumulative and no recalibration was needed.•No numerical iteration and initial soil moisture are required in the proposed approach. Knowledge of soil moisture in the root zone is critical for crop growth estimation and irrigation scheduling. In this study, a soil moisture diagnostic equation is applied to estimate soil moisture at depths of 0–100cm (because the majority of crop roots are in the top 100cm of soil) at four USDA Soil Climate Analysis Network (SCAN) sites in arid and semi-arid regions: TX2105 in northwest Texas, NM2015 and NM2108 in east New Mexico, and AZ2026 in southeast Arizona. At each site, a dataset of 5–6years of records of daily soil moisture, daily mean air temperature, precipitation and downward solar radiation is compiled and processed. Both the sinusoidal wave function of day of year (DOY) and a linear function of the potential evapotranspiration (PET) are used to approximate the soil moisture loss coefficient. The first four years of data are used to derive the soil moisture loss function and the empirical parameters in the soil moisture diagnostic equation. The derived loss function and empirical parameters are then applied to estimate soil moisture in the last fifth or sixth year at each site. Root mean square errors (RMSEs) of the estimated volumetric soil moistures in five different soil columns (i.e., 5cm, 10cm, 20 or 30cm, 50cm, and 100cm) are less than 3.2 (%V/V), and the accuracy of the estimated soil moistures using the sinusoidal soil moisture loss function is slightly better than the PET-based loss functions. In addition to the three advantages of this soil moisture diagnostic equation, i.e., (1) non-cumulative errors in the estimated soil moisture, (2) no regular recalibration is required to correct the cumulative errors, and (3) no numerical iteration and initial moisture inputs are needed since only precipitation data are required, this study also demonstrates that the soil moisture diagnostic equation not only can be used to estimate surface soil moisture, but also the entire root-zone soil moisture.