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

We present SELEN 4 (a 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 pseudospectral approach complemented by a spatial discretization on an icosahedron-based spherical geodesic grid, SELEN 4 solves a generalised "Sea Level Equation" (SLE) for a spherically symmetric Earth with linear viscoelastic rheology, taking the migra-5 tion 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. Program SELEN 4 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, 10

On Some Properties of the Glacial Isostatic Adjustment Fingerprints

“…Here we briefly introduce the essentials of the SLE theory, necessary to illustrate the geometry of the GIA fingerprints in Section 4 below. The reader is referred to Spada and Melini [33] (hereinafter SM19) and to its supplement for a more detailed and self-contained presentation. The paper SM19 and its supplement are presently (August 2019) submitted to Geoscientific Model Development (GMD), the interactive open-access journal of the European Geosciences Union at https://www.geosci-mod el-dev-discuss.net/gmd-2019-183/.…”

“…Although oversimplified, it is historically important and it has the merit of demostrating the important role of gravitational attraction in shaping the sea surface, with a sea-level change departing from the spatially uniform eustatic solution both nearby the melting ice sheets and in their far field. [33] have recently released a general open-source Fortran program called SELEN 4 (SELEN version 4.0) that solves the SLE in its full form; this shall be employed in next sections to study the geometry of the GIA fingerprints associated with the melting of past ice sheets. SELEN 4 is the current stage of the evolution of program SELEN which was originally published in 2007 by Spada and Stocchi [41] based upon the theory detailed in Spada and Stocchi [42].…”

“…a (GIA model dependent) value closely matching the value of −0.3 mm year −1 , often adopted as a rule of thumb to correct the altimetric absolute sea-level trend for the effects of past GIA (see [31,34] and references therein). Since during the altimetry era (1992-today) the rate of global mean sea-level rise has well exceeded ∼3 mm year −1 [69,70], using the average (33) to perform the GIA correction is certainly justified. However, spatial trends ofṄ (ω) at a regional scale may become important when one considers the effects of present land ice on absolute sea level change, as done by Ponte et al [71].…”

New relative sea-level (RSL) indications from the Eastern Mediterranean: Middle Bronze Age to the Roman period (~3800–1800 y BP) archaeological constructions at Dor, the Carmel coast, Israel

“…In this work, we model the RSL variations along the coasts of Israel using an improved version of the open source Sea-Level Equation (SLE) solver SELEN4 of Spada and Melini [69]. In SELEN4, the SLE is solved adopting a global, topographically and gravitationally self-consistent pseudo-spectral approach, taking rotational effects into account, and allowing for the migration of the shorelines.…”

“…progressively developed at the Australian National University by Kurt Lambeck and collaborators, hereinafter referred to as ANU (the specific ice history adopted here was kindly provided to GS by Anthony Purcell in November 2016). All these models are implemented into SELEN4, so that the outputs obtained may differ slightly from the results published by other authors, due to differences in the resolutions adopted, in the assumptions about the rheological layering and its discretization, and in the rotational theories adopted (see [69]).…”