ALPS: A Unified Framework for Modeling Time Series of Land Ice Changes

Modeling time series (TS) is a research focus in cryospheric sciences because of the complexity and multiscale nature of events of interest. Highly nonuniform sampling of measurements from different sensors with different levels of accuracy, as is typical for measurements of ice sheet elevations, makes the problem even more challenging. In this article, we propose a spline-based approximation framework (ALPS—Approximation by Localized Penalized Splines) for modeling TS of land ice changes. The localized support of the B-spline basis functions enable robustness to nonuniform sampling, a considerable improvement over other global and piecewise local models. With features like discrete-coordinate-difference-based penalization and two-level outlier detection, ALPS further guarantees the stability and quality of approximations. ALPS incorporates rigorous model uncertainty estimates with all approximations. As demonstrated by examples, ALPS performs well for a variety of data sets, including TS of ice sheet thickness, elevation, velocity, and terminus locations. The robust estimation of TS and their derivatives facilitates new applications, such as the reconstruction of high-resolution elevation change records by fusing sparsely sampled TS of ice sheet thickness changes with modeled firn thickness changes, and the analysis of the relationship between different outlet glacier observations to gain new insights into processes and forcing.