Efficient Approximation of Initial Conditions for Global Sensitivity Analysis and History Matching of Transient Numerical Groundwater Models

Numerical groundwater models are essential tools for simulating and understanding subsurface hydrological processes, supporting water resource management and environmental decision-making. Global sensitivity analysis (GSA) and history matching (HM) are critical methods for evaluating the influence of uncertain model parameters and calibrating models to observed data. However, applying these methods to transient, computationally expensive, large-scale groundwater models presents significant challenges.

A key obstacle arises from the requirement to adapt initial conditions for every model input parameter set during GSA and HM. Unlike steady-state models, transient groundwater systems often lack equilibrium, requiring initialization that reflects the dynamic nature of the system. Traditional approaches, such as performing a warmup simulation for each parameter set, ensure accurate initialization but are computationally infeasible for highly parameterized models.

To address this limitation, we propose a novel method to approximate suitable initial conditions for each parameter set without the need for costly warmup simulations. Our approach utilizes the fact that, after a system-specific relaxation time, the simulation becomes independent of the initial condition. Using a toy model as a test case, we demonstrate that the approximated initial conditions are sufficiently accurate for practical applications, with minimal impact on the outcomes of GSA and HM. The computational savings achieved through this method are substantial, making it particularly advantageous for large-scale systems with many parameters.

We also provide an analysis of the trade-offs between accuracy and efficiency and show that the inaccuracy introduced by the approximation is negligible. Finally, we outline a roadmap for extending this method to real-world groundwater models, addressing the computational barriers that may currently limit the application of GSA and HM in transient systems.