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Joint estimation of soil moisture profile and hydraulic parameters by ground‐penetrating radar data assimilation with maximum likelihood ensemble filter

Ground‐Penetrating Radar (GPR) has recently become a powerful geophysical technique to characterize soil moisture at the field scale. We developed a data assimilation scheme to simultaneously estimate the vertical soil moisture profile and hydraulic parameters from time‐lapse GPR measurements. The assimilation scheme includes a soil hydrodynamic model to simulate the soil moisture dynamics, a full‐wave electromagnetic wave propagation model, and petrophysical relationship to link the state variable with the GPR data and a maximum likelihood ensemble assimilation algorithm. The hydraulic parameters are estimated jointly with the soil moisture using a state augmentation technique. The approach allows for the direct assimilation of GPR data, thus maximizing the use of the information. The proposed approach was validated by numerical experiments assuming wrong initial conditions and hydraulic parameters. The synthetic soil moisture profiles were generated by the Hydrus‐1D model, which then were used by the electromagnetic model and petrophysical relationship to create “observed” GPR data. The results show that the data assimilation significantly improves the accuracy of the hydrodynamic model prediction. Compared with the surface soil moisture assimilation, the GPR data assimilation better estimates the soil moisture profile and hydraulic parameters. The results also show that the estimated soil moisture profile in the loamy sand and silt soils converge to the “true” state more rapidly than in the clay one. Of the three unknown parameters of the Mualem‐van Genuchten model, the estimation of n is more accurate than that of α and Ks. The approach shows a great promise to use GPR measurements for the soil moisture profile and hydraulic parameter estimation at the field scale.