Coupled hydrogeophysical inversion of an artificial infiltration experiment monitored with ground-penetrating radar: synthetic demonstration
Authors: Moua Rohianuu , Lesparre Nolwenn , Girard Jean-François , Belfort Benjamin , Lehmann François , Younes Anis 
Published: December 2023

Abstract. In this study, we investigate the use of ground-penetrating radar (GPR) time-lapse monitoring of artificial soil infiltration experiments. The aim is to evaluate this protocol in the context of estimating the hydrodynamic unsaturated soil parameter values and their associated uncertainties. The originality of this work is to suggest a statistical parameter estimation approach using Markov chain Monte Carlo (MCMC) methods to have direct estimates of the parameter uncertainties. Using the GPR time data from the moving wetting front only does not provide reliable results. Thus, we propose to use additional information from other types of reflectors to optimize the quality of the parameter estimation. Water movement and electromagnetic wave propagation in the unsaturated zone are modeled using a one-dimensional hydrogeophysical model. The GPR travel time data are analyzed for different reflectors: a moving reflector (the infiltration wetting front) and three fixed reflectors located at different depths in the soil. Global sensitivity analysis (GSA) is employed to assess the influence of the saturated hydraulic conductivity Ks, the saturated and residual water contents θs and θr, and the Mualem–van Genuchten shape parameters α and n of the soil on the GPR travel time data of the reflectors. Statistical calibration of the soil parameters is then performed using the MCMC method. The impact of the type of reflector (moving or fixed) is then evaluated by analyzing the calibrated model parameters and their confidence intervals for different scenarios. GSA results show that the sensitivities of the GPR data to the hydrodynamic soil parameters are different between moving and fixed reflectors, whereas fixed reflectors at various depths have similar sensitivities. Ks has a similar and strong influence on the data of both types of reflectors. Concerning the other parameters, for the wetting front, only θs and α have an influence, and only at long time steps since the total variance is zero at the very beginning of the experiment. On the other hand, for the fixed reflectors, the total variance is not zero at the very start and the parameters θs, θr, α and n can have an influence from the very beginning of the infiltration. Results of parameter estimation show that the use of calibration data from the moving or fixed reflectors alone does not enable a good identification of all soil parameters. With the moving reflector, the error between the estimated mean value and the exact target value for θr and α is 9 % and 45 %, respectively, and less than 3 % for the other parameters. The best reduction of the size of the parameter distribution is obtained for n, with a posterior distribution 9 times smaller than the prior one. For the others, this reduction ratio varies between 1 and 5. For the fixed reflectors, the estimated mean values are far from the target values for α, θr and n, representing for a reflector located at 120 cm 15 %, 27 %, and 121 %, respectively. On the other hand, when both data are combined, all soil parameters can be well estimated with narrow confidence intervals. For instance, when using both data from the moving wetting front and a fixed reflector located at 120 cm for calibration, the estimated mean values of the errors of all parameters are less than 5 %. Moreover, all parameter distributions are well reduced, with a maximum reduction for Ks, leading to a posterior distribution being 46 times smaller than the prior one, and the worst but still satisfactory being for θr for which the posterior distribution is 8 times smaller than the prior one. The methodology was applied to fine, medium, and coarse sands with very good results, particularly for the finest soil. The thickness of the unsaturated zone was also tested (0.5, 1, and 2 m) and a better estimation of the hydrodynamic parameters is obtained when the water table is deeper. In addition, the height of water applied in the infiltrometry test influences the speed of the test without affecting the performance of the proposed method.