The Ice Sheet State and Parameter Estimator (ICESEE) Library (v1.0.0): Ensemble Kalman Filtering for Ice Sheet Models

Abstract. ICESEE (ICE Sheet statE and parameter Estimator) is a Python-based, open-source data assimilation framework designed for seamless integration with ice-sheet and other Earth system models. ICESEE implements a parallel Ensemble Kalman Filter (EnKF) architecture with full Message Passing Interface (MPI) support, enabling scalable assimilation in both model state and parameter spaces. Its core algorithm employs a nonlinear, transformation-based update scheme originally proposed by Evensen (2003), which avoids explicit construction of the forecast error covariance matrix. This matrix-free formulation eliminates the need for localization while retaining robustness in high-dimensional, nonlinear systems. In addition to the core EnKF, ICESEE provides serial implementations of four alternative EnKF variants, including a localized formulation, offering flexibility for methodological testing and comparative studies. Beyond state estimation, ICESEE supports the indirect inference of unobserved or weakly constrained model parameters through a hybrid assimilation–inversion strategy. In this approach, ensemble-based data assimilation corrects the model state using available observations, while physics-based inverse methods are subsequently applied to infer parameters such as basal friction. The framework features modular coupling interfaces, adaptive state indexing, and efficient parallel input/output, making it readily extensible to a wide range of numerical modeling environments. ICESEE has been successfully coupled with several existing models, including the MATLAB/C++-based Ice Sheet and Sea-level System Model (ISSM), the Firedrake-based Python model Icepack, a one-dimensional flowline model, and the reduced-order Lorenz–96 system. In this study, we focus on applications with ISSM and Icepack to demonstrate ICESEE’s interoperability, numerical performance, scalability, and its ability to jointly improve state estimates and infer uncertain model parameters. Performance benchmarks show strong and weak scaling on high-performance computing platforms, underscoring ICESEE’s potential to enable long-term, observation-constrained reanalyses of ice-sheet evolution at continental scales.