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 Earth system models. It implements a parallel Ensemble Kalman Filter (EnKF) with full MPI support for scalable assimilation in state and parameter spaces. ICESEE uses a matrix-free update scheme from Evensen (2003), which avoids explicit forecast error covariance construction and eliminates the need for localization in high-dimensional, nonlinear systems. ICESEE also supports four EnKF variants, including a localized version for methodological testing. It enables indirect inference of unobserved model parameters through a hybrid assimilation-inversion strategy. The framework features modular coupling interfaces, adaptive state indexing, and efficient parallel I/O, making it extensible to a variety of modeling environments. ICESEE has been successfully coupled with ISSM, Icepack, and other models. In this study, we focus on applications with ISSM and Icepack, demonstrating ICESEE's interoperability, performance, scalability, and ability to improve state estimates and infer uncertain parameters. Performance benchmarks show strong and weak scaling, highlighting ICESEE's potential for large-scale, observation-constrained ice sheet reanalyses.

Figures (10)

• Figure 1: Schematic of the Ensemble Kalman Filter (adapted from gillet2020assimilation) illustrating four assimilation cycles. The process begins with four ensemble members (black dots within the green oval) initialized at time $t_0$, after which the system state (green oval) is advanced through a forecast phase (indicated by the magenta dashed arrow), producing a predicted ensemble state (cyan box within the orange oval). Upon receiving an observation (red star), the state is updated to a new state (purple box inside the yellow oval) via the analysis step (red arrow). The cycle repeats for subsequent forecast and analysis phases, with blue dotted arrows indicating the trajectories of the individual ensemble realizations. Here, $k$ and $dt$ denote the timestep index and time increment, respectively.
• Figure 2: High-level structure of the ICESEE codebase, showing modular components for data assimilation, model interfaces, utilities, and parallelization.
• Figure 3: Overview of the ICESEE workflow illustrating the sequence of operations from the model initializations, observation loading and transformation to the model grid, ensemble initialization, model forecasting, and assimilation. Components shown in green, orange, magenta, and yellow represent the core ICESEE routines, while those in cyan and gray correspond to model-specific extensions configurable by the user.
• Figure 4: Left side: ($a_1$) shows the true ice thickness at time zero. ($b_1$) shows the difference between the simulation without assimilation and the true thickness at time zero. Panels ($c_1$–$e_1$) show the differences between the assimilated and true thickness fields after 5, 15, and 25 years, respectively. Right side: ($a_2$) shows the true velocity magnitude at time zero. ($b_2$) shows the difference between the velocity obtained without assimilation and the true velocity magnitude at time zero. Panels ($c_2$–$e_2$) show the differences between the assimilated and true velocity magnitudes after 5, 15, and 25 years, respectively. The magenta marker denotes the reference point at $(1.25~\mathrm{km},\,0.3~\mathrm{km})$, located within the perturbed (bump) region of the computational domain. $\Delta |u|$ denotes the signed difference in velocity magnitude.
• Figure 5: Temporal evolution of ice thickness (a), velocity (b), and surface mass balance (c) at the reference point indicated by the magenta marker in Figure \ref{['fig:hu_diff']}.