An Improved Model for Wheat Volumetric Water Content Estimation Using GNSS Refractometry

Global navigation satellite system (GNSS) refractometry is a new technique that utilizes two pairs of GNSS receivers and antennas to collect the refracted signal in the medium and the direct signal in the air, respectively. In the previous study, a linear model that uses wheat height, air temperature, and the amplitude ratio (AR) as inputs was utilized to estimate the volumetric water content (VWC) of wheat. In this study, a second-order nonlinear function is utilized to describe the relationship among GNSS AR, wheat VWC, wheat height, and air temperature, leading to an improved model for estimating wheat VWC. The function coefficients are determined by exploiting the least-squares method to the field measurements collected from April 5, 2023, to June 5, 2023. Once the function coefficients and inputs are obtained, the model can be easily used to calculate the wheat VWC. The model was validated using an independent dataset of field measurements collected from April 5, 2024, to June 5, 2024. The results show that the improved model performs significantly better than the previous linear model, and the root-mean-square (rms) error of the improved model-based GNSS wheat VWC estimation is 0.224 kg/m3 when the in situ wheat VWC ranges from 1.404 to 6.521 kg/m3. This model can help precisely control the timing and water usage of agricultural irrigation, thereby optimizing water management for crops.