SELEN<sup>4</sup> (SELEN version 4.0): a Fortran program for solving the gravitationally and topographically self-consistent sea-level equation in glacial isostatic adjustment modeling

Abstract

Abstract. We present SELEN4 (SealEveL EquatioN solver), an open-source program written in Fortran 90 that simulates the glacial isostatic adjustment (GIA) process in response to the melting of the Late Pleistocene ice sheets. Using a pseudo-spectral approach complemented by a spatial discretization on an icosahedron-based spherical geodesic grid, SELEN4 solves a generalized sea-level equation (SLE) for a spherically symmetric Earth with linear viscoelastic rheology, taking the migration of the shorelines and the rotational feedback on sea level into account. The approach is gravitationally and topographically self-consistent, since it considers the gravitational interactions between the solid Earth, the cryosphere, and the oceans, and it accounts for the evolution of the Earth's topography in response to changes in sea level. The SELEN4 program can be employed to study a broad range of geophysical effects of GIA, including past relative sea-level variations induced by the melting of the Late Pleistocene ice sheets, the time evolution of paleogeography and of the ocean function since the Last Glacial Maximum, the history of the Earth's rotational variations, present-day geodetic signals observed by Global Navigation Satellite Systems, and gravity field variations detected by satellite gravity missions like GRACE (the Gravity Recovery and Climate Experiment). The “GIA fingerprints” constitute a standard output of SELEN4. Along with the source code, we provide a supplementary document with a full account of the theory, some numerical results obtained from a standard run, and a user guide. Originally, the SELEN program was conceived by Giorgio Spada (GS) in 2005 as a tool for students eager to learn about GIA, and it has been the first SLE solver made available to the community.

Exploring the Drivers of Global and Local Sea‐Level Change Over the 21st Century and Beyond

“…Gregory et al (2019) refer to these effects collectively as GRD (Gravity, Rotation, Deformation), and we adopt their nomenclature here. We use three different estimates of GRD for the different ice mass terms following Slangen et al (2014), Spada and Melini (2019), and Klemann and Groh (2013) extended to include rotational deformation following Martinec and Hagedoorn (2014). We use a single GRD estimate for changes in land water storage based on the projections of Wada et al (2012), following Slangen et al (2014).…”

Mid- to late-Holocene sea-level evolution of the northeastern Aegean sea

“…Lambeck et al, 2003; Nakada and Lambeck, 1987), hereafter referred to as ANU. The ice-time history of these three GIA models was implemented in the Sea-Level Equation solver SELEN4 (Spada and Melini, 2019), which has been solved on a global grid to maximum harmonic degree Lmax = 256. For the ICE model, we adopted the viscosity profile given by the author, while for ANU we employed a lithospheric thickness of 90 km, an upper-mantle and lower-mantle viscosity of 0.5 × 10 21 Pa s and of 10 22 Pa s, respectively, according to the range of parameters provided in Lambeck et al (2017).…”

Late Holocene relative sea‐level fluctuations and crustal mobility at Bataneh (Najirum) archaeological site, Persian Gulf, Iran

“…The glacial isostatic adjustment (GIA) simulations performed in this study are based on model ICE‐6G (VM5a) of Peltier et al (2012, 2015). The Late‐Pleistocene ice sheets chronology of model ICE‐6G (VM5a) was implemented in the programme SELEN4 (Spada & Melini, 2019). SELEN4 solves the sea‐level equation by taking into account the horizontal migration of shorelines, for the transition from grounded to floating ice and for the effects of rotational feedback on sea level.…”