Model-Independent Data Assimilation Package for Estimation of High Dimensional Model Parameters and Dynamic States Fields

Calibration of high-dimensional model input parameters at high resolution is largely hampered by the expensive computational cost required to compute the parameter-observation sensitivity matrix (Jacobian Matrix). Data assimilation-based (DA) methods, such as the Ensemble Smoother (ES), Ensemble Kalman Filter (EnKF), and Ensemble Kalman Smoother (EnKS), avoid the explicit computation of the Jacobian matrix by generating an ensemble of realizations for model input and response variables that are used by the DA procedure to update both model input parameters and output dynamic states given a set of observations. These methods have successfully estimated a large number of unknown parameters (~10⁶ ) using a relatively small number (~10²-10³) of forward model runs. Additionally, DA methods offer a unified framework in which both parameter estimation and uncertainty quantification are achieved simultaneously. This work presents an open-source Python implementation (PESTPP-ENK) of a wide range of data assimilation methods using the widely known PEST model-interface protocols. The tool leverages existing PEST++ protocols, primarily through three file types: the control file, template files, and instruction files. The implemented DA methods include both deterministic and stochastic versions of ES, EnKF, and EnKS. For the purpose of tool demonstration, a synthetic groundwater pumping test is simulated with MODLOW and the tool is used to estimate the unknown hydraulic conductivity field at the resolution of the finite difference grid with the best match to the hydraulic head observations.