Joint Data Assimilation and Parameter Calibration in on-line groundwater modelling using Sequential Monte Carlo techniques

As computational power grows and wireless sensor networks find their way into common practice, it becomes increasingly feasible to pursue on-line numerical groundwater modelling. The reconciliation of model predictions with sensor measurements often necessitates the application of Sequential Monte Carlo (SMC) techniques, most prominently represented by the Ensemble Kalman Filter. In the pursuit of on-line predictions it seems advantageous to transcend the scope of pure data assimilation and incorporate on-line parameter calibration as well. Unfortunately, the interplay between shifting model parameters and transient states is non-trivial. Several recent publications (e.g. Chopin et al., 2013, Kantas et al., 2015) in the field of statistics discuss potential algorithms addressing this issue. However, most of these are computationally intractable for on-line application. In this study, we investigate to what extent compromises between mathematical rigour and computational restrictions can be made within the framework of on-line numerical modelling of groundwater. Preliminary studies are conducted in a synthetic setting, with the goal of transferring the conclusions drawn into application in a real-world setting. To this end, a wireless sensor network has been established in the valley aquifer around Fehraltorf, characterized by a highly dynamic groundwater system and located about 20 km to the East of Zürich, Switzerland. By providing continuous probabilistic estimates of the state and parameter distribution, a steady base for branched-off predictive scenario modelling could be established, providing water authorities with advanced tools for assessing the impact of groundwater management practices. Chopin, N., Jacob, P.E. and Papaspiliopoulos, O. (2013): SMC2: an efficient algorithm for sequential analysis of state space models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75 (3), p. 397-426. Kantas, N., Doucet, A., Singh, S.S., Maciejowski, J., and Chopin, N. (2015): On Particle Methods for Parameter Estimation in State-Space Models. Statistical Science, 30 (3), p. 328.-351.