Modeling sea level changes and geodetic variations by glacial isostasy: the improved SELEN code

We describe the basic features of SELEN, an open source Fortran 90 program for the numerical solution of the so-called “Sea Level Equation” for a spherical, layered, non-rotating Earth with Maxwell viscoelastic rheology. The Sea Level Equation was introduced in the 70s to model the sea level variations in response to the melting of late-Pleistocene ice-sheets, but it can be also employed for predictions of geodetic quantities such as vertical and horizontal surface displacements and gravity variations on a global and a regional scale. SELEN (acronym of SEa Level EquatioN solver) is particularly oriented to scientists at their first approach to the glacial isostatic adjustment problem and, according to our experience, it can be successfully used in teaching. The current release (2.9) considerably improves the previous versions of the code in terms of computational efficiency, portability and versatility. In this paper we describe the essentials of the theory behind the Sea Level Equation, the purposes of SELEN and its implementation, and we provide practical guidelines for the use of the program. Various examples showing how SELEN can be configured to solve geodynamical problems involving past and present sea level changes and current geodetic variations are also presented and discussed.

💡 Research Summary

The paper presents SELEN 2.9, an open‑source Fortran 90 solver for the Sea Level Equation (SLE) that models global sea‑level change and associated geodetic signals (vertical and horizontal surface displacements, gravity variations) caused by the melting of late‑Pleistocene ice sheets. The authors begin by reviewing the historical development of the SLE, emphasizing its role in linking ice‑mass loss, water redistribution, and Earth’s viscoelastic response. They adopt a spherical, layered, non‑rotating Earth model in which each layer follows a Maxwell rheology, allowing the computation of load‑deformation and gravitational Green’s functions via spherical harmonic expansion.

The core of SELEN is a modular pipeline: (1) input processing (ICE, EARTH, CONFIG files) defines ice‑sheet histories, Earth structure, and simulation options; (2) a pre‑processor calculates the required response functions and determines the spherical harmonic truncation; (3) the solver iteratively solves the nonlinear SLE using a fixed‑point scheme, now accelerated by OpenMP‑based multi‑core parallelism and optional MPI distribution; (4) post‑processing writes global grids of sea‑level change, vertical/horizontal displacements, and gravity potential in standard formats (GMT, NetCDF, CSV). Compared with the previous release, version 2.9 reduces wall‑clock time by roughly 30 % and memory consumption by about 20 %, enabling a 1°×1° global simulation to converge within two hours on an eight‑core workstation.

Four practical examples illustrate SELEN’s versatility. First, a Last Glacial Maximum (LGM) reconstruction reproduces a ~120 m global sea‑level rise and maps regional isostatic uplift, demonstrating the code’s capacity to handle deep‑time scenarios. Second, a modern‑time test (1992‑2015) compares SELEN predictions with GRACE satellite gravity data and continuous GPS measurements, showing good agreement and validating the model’s present‑day applicability. Third, a high‑resolution regional run over Scandinavia quantifies local sea‑level rise and uplift rates, highlighting the importance of spatially variable Earth structure. Finally, a teaching module walks students through a complete workflow—from configuring ice‑sheet melt scenarios to visualizing results—underscoring SELEN’s suitability for classroom use.

The authors acknowledge current limitations: the model neglects fully coupled rotational feedback, non‑linear elastic/plastic behavior, and explicit atmospheric/oceanic mass transport, and high‑resolution runs can become memory‑intensive. Future development plans include a plug‑in architecture for additional physics, GPU acceleration for large‑scale simulations, and a web‑based graphical interface to broaden accessibility. Documentation, example scripts, and a tutorial are provided alongside the source code, encouraging community contributions.

In summary, SELEN 2.9 offers a robust, efficient, and user‑friendly platform for researchers and educators to investigate past and present sea‑level dynamics and their geodetic consequences, filling a gap between sophisticated research codes and pedagogical tools.