A comparison between ES-MDA and restart EnKF for the purpose of the simultaneous identification of a contaminant source and hydraulic conductivity

Understanding a contaminant source may help in a better management and risk assessment of a polluted aquifer. However, contaminant source information may not be available when a pollutant is detected in a drinking well. The restart ensemble Kalman filter (restart EnKF, also named r-EnKF) has been demonstrated in synthetic and laboratory experiments as an efficient solution for the identification of a contaminant source. Recently, the ensemble smoother with multiple data assimilation (ES-MDA) has been proposed as an alternative to the r-EnKF as a more efficient solution given that the r-EnKF needs to restart the simulation of the state equation from time zero after each data assimilation step. An analysis, in a synthetic aquifer, of the accuracy of the ES-MDA for the simultaneous identification of a contaminant source and the spatial distribution of hydraulic conductivity by assimilating both piezometric head and concentration observations is carried out using the r-EnKF as a benchmark. The conclusion is that the ES-MDA can outperform the r-EnKF, but the expected speed advantage, associated with the possibility of assimilating all data at once, does not exist. For the ES-MDA to reach the same level of accuracy as the r-EnKF, the number of multiple data assimilations must be large, and final computing time is similar for both approaches. However, the ES-MDA can do much better than the r-EnKF if the number of iterations increases even further, with the consequent increase of computational cost.