Calibration of subsurface batch and reactive-transport models involving complex biogeochemical processes

In this study, the calibration of subsurface batch and reactive-transport models involving complex biogeochemical processes was systematically evaluated. Two hypothetical nitrate biodegradation scenarios were developed and simulated in numerical experiments to evaluate the performance of three calibration search procedures: a multi-start non-linear regression algorithm (i.e. multi-start Levenberg–Marquardt), a global search heuristic (i.e. particle swarm optimization), and a hybrid algorithm that combines the particle swarm procedure with a regression-based “polishing” step. Graphical analysis of the selected calibration problems revealed heterogeneous regions of extreme parameter sensitivity and insensitivity along with abundant numbers of local minima. These characteristics hindered the performance of the multi-start non-linear regression technique, which was generally the least effective of the considered algorithms. In most cases, the global search and hybrid methods were capable of producing improved model fits at comparable computational expense. In other cases, the multi-start and hybrid calibration algorithms yielded comparable fitness values but markedly differing parameter estimates and associated uncertainty measures.     

Dual states estimation of a subsurface flow-transport coupled model using ensemble Kalman filtering

Modeling the spread of subsurface contaminants requires coupling a groundwater flow model with a contaminant transport model. Such coupling may provide accurate estimates of future subsurface hydrologic states if essential flow and contaminant data are assimilated in the model. Assuming perfect flow, an ensemble Kalman filter (EnKF) can be used for direct data assimilation into the transport model. This is, however, a crude assumption as flow models can be subject to many sources of uncertainty. If the flow is not accurately simulated, contaminant predictions will likely be inaccurate even after successive Kalman updates of the contaminant model with the data. The problem is better handled when both flow and contaminant states are concurrently estimated using the traditional joint state augmentation approach. In this paper, we introduce a dual estimation strategy for data assimilation into a one-way coupled system by treating the flow and the contaminant models separately while intertwining a pair of distinct EnKFs, one for each model. The presented strategy only deals with the estimation of state variables but it can also be used for state and parameter estimation problems. This EnKF-based dual state-state estimation procedure presents a number of novel features: (i) it allows for simultaneous estimation of both flow and contaminant states in parallel; (ii) it provides a time consistent sequential updating scheme between the two models (first flow, then transport); (iii) it simplifies the implementation of the filtering system; and (iv) it yields more stable and accurate solutions than does the standard joint approach. We conducted synthetic numerical experiments based on various time stepping and observation strategies to evaluate the dual EnKF approach and compare its performance with the joint state augmentation approach. Experimental results show that on average, the dual strategy could reduce the estimation error of the coupled states by 15% compared with the joint approach. Furthermore, the dual estimation is proven to be very effective computationally, recovering accurate estimates at a reasonable cost.     

Quantifying the effects of three-dimensional subsurface heterogeneity on Hortonian runoff processes using a coupled numerical,stochastic approach

The impact of three-dimensional subsurface heterogeneity in the saturated hydraulic conductivity on hillslope runoff generated by excess infiltration (so-called Hortonian runoff) is examined. A fully coupled, parallel subsurface–overland flow model is used to simulate runoff from an idealized hillslope. Ensembles of correlated, Gaussian random fields of saturated hydraulic conductivity are used to create uncertainty in spatial structure. A large number of cases are simulated in a parametric manner with the variance of the hydraulic conductivity varied over orders of magnitude. These cases include rainfall rates above, equal and below the geometric mean of the hydraulic conductivity distribution. These cases are also compared to theoretical representations of runoff production based on simple assumptions regarding (1) the rainfall rate and the value of hydraulic conductivity in the surface cell using a spatially-indiscriminant approach; and (2) a percolation-theory type approach to incorporate so-called runon. Simulations to test the ergodicity of hydraulic conductivity on hillslope runoff are also performed. Results show that three-dimensional stochastic representations of the subsurface hydraulic conductivity can create shallow perching, which has an important effect on runoff behavior that is different than previous two-dimensional analyses. The simple theories are shown to be very poor predictors of the fraction of saturated area that might runoff due to excess infiltration. It is also shown that ergodicity is reached only for a large number of integral scales (∼30) and not achieved for cases where the rainfall rate is less than the geometric mean of the saturated hydraulic conductivity.