Comparison of Two Ensemble Kalman-Based Methods for Estimating Aquifer Parameters from Virtual 2-D Hydraulic and Tracer Tomographic Tests

Abstract

We compare two ensemble Kalman-based methods to estimate the hydraulic conductivity field of an aquifer from data of hydraulic and tracer tomographic experiments: (i) the Ensemble Kalman Filter (EnKF) and (ii) the Kalman Ensemble Generator (KEG). We generated synthetic drawdown and tracer data by simulating two pumping tests, each followed by a tracer test. Parameter updating with the EnKF is performed using the full transient signal. For hydraulic data, we use the standard update scheme of the EnKF with damping, whereas for concentration data, we apply a restart scheme, in which solute transport is resimulated from time zero to the next measurement time after each parameter update. In the KEG, we iteratively assimilate all observations simultaneously, here inverting steady-state heads and mean tracer arrival times. The inversion with the dampened EnKF worked well for the transient pumping-tests, but less for the tracer tests. The KEG produced similar estimates of hydraulic conductivity but at significantly lower costs. We conclude that parameter estimation in well-defined hydraulic tests can be done very efficiently by iterative ensemble Kalman methods, and ambiguity between state and parameter updates can be completely avoided by assimilating temporal moments of concentration data rather than the time series themselves.

Comparison of Two Ensemble-Kalman Filter Based Methods for Estimating Aquifer Parameters from Real 3-D Hydraulic and Tracer Tomographic Tests

“…We applied the same ensemble-Kalman filter based methods for parameter estimation as those used in the synthetic study of the companion paper [58]: the Ensemble Kalman Filter (EnKF) and the Kalman Ensemble Generator (KEG). Ensemble-Kalman filter based methods are recursive processes with a forecast-update cycle defined by Equation (13) (forecast) and Equation (14) (update) [71].…”

“…This work is the follow up to a synthetic study [58] on the application of two data assimilation methods to the estimation of spatially distributed hydraulic conductivity: (1) the Ensemble Kalman Filter (EnKF) and (2) the Kalman Ensemble Generator (KEG). In the preceding synthetic study [58], we showed that the EnKF and KEG are well-fitted for the estimation of spatially distributed hydraulic conductivity fields from hydraulic-and tracer-tomographic data. In this paper, we applied these techniques to field experiments and to the estimation of aquifer parameters with the data collected in real tomographic aquifer tests.…”

“…We used the same numerical models to simulate groundwater flow and solute transport but extended the problem to three spatial dimensions. To minimize repetition, we refer the reader to the previous paper [58] and the references therein for a more in-depth description of the theory behind groundwater flow, solute transport, and the application of ensemble-Kalman filter based methods to groundwater problems. The experimental work presented here was applied at the hydrogeological research site Lauswiesen in Germany.…”

“…Like in the synthetic study [58], we applied the standard update scheme of the EnKF to assimilate transient drawdown data. In this scheme the parameters (and/or model states) are updated by evaluating the model performance from the current state to one step forward in time.…”

“…For the assimilation of tracer concentrations, we applied a restart scheme of the EnKF, in which parameters are updated in the analysis of a time step and solute transport is resimulated from the initial time until the next available measurement time step [59][60][61][62]. Although computationally more demanding, the restart scheme is necessary to honor mass conservation and consistency between hydraulic parameters and model states during transport simulations [58]. In contrast, parameter updating with the KEG was performed by assimilating all available information simultaneously, with an iterative approach in which the same data are reused to update all ensemble members.…”