FastEarth3D

A state-of-the-art but simple and fast 3D solid-Earth model — a visco-elastic deformation model coupled with the sea-level equation — intended as an open-source replacement for VILMA within the CLIMBER-X climate model.

The method is a clean-room reimplementation of the spectral–finite-element, time-domain approach of Martinec (2000): spherical harmonics horizontally, finite elements radially, an incompressible Maxwell rheology integrated explicitly in time, a self-consistent sea-level equation with migrating coastlines, and rotational feedback. It is built 3D-ready from the start (laterally varying viscosity) and validated against the published GIA benchmarks.

Documentation: https://fesmc.github.io/FastEarth3D/ (physics, discretization, benchmarks, install & run), rendered from the Quarto sources under docs/; see doc/design.md for the design rationale and method comparison, and doc/vilma-backend.md for the optional VILMA backend (&fe3d solver = "vilma"), which drives VILMA itself through this model's driver, namelist, forcing, remap and output for a like-for-like comparison. It is off by default and is not a dependency: it needs an explicit make fastearth vilma=1 VILMAROOT=<install> and a hand-installed VILMA.

Status

The full model is implemented and validated: the spectral–finite-element solver core, viscoelastic time stepping, the self-consistent migrating-coastline sea-level equation, rotational feedback (polar motion), and laterally varying (3D) viscosity — plus restart, spin-up, online lon-lat→Gauss remapping, and a host-coupling API. A second response operator, a reduced modal solver, offers a tunable, faster approximation that converges back to the full solver.

Validated against the Spada et al. (2011) and Martinec et al. (2018) community benchmarks (radial Love numbers, disc-load response, sea-level equation) and Spada test 3/2 (rotation). Cross-code validation of the 3D path and the modal-vs-VE accuracy/cost study are ongoing.

Install

Dependencies are fesm-utils (branch coords-dev, providing FFTW, SHTns, the fesmutils helper and the coords module) plus a system netCDF. configme clones/links the dependencies and generates the machine/compiler Makefile:

configme install FastEarth3D                 # resolve machine/compiler, clone deps
configme install FastEarth3D -m macbook -c gfortran
configme install FastEarth3D --link fesm-utils=/abs/path/to/fesm-utils   # reuse a checkout

Build

make fastearth        # -> bin/fastearth.x        (standalone forced-run driver)
make fastearth_mkref  # -> bin/fastearth_mkref.x  (build a Gauss-grid reference)
make fastearth_remap  # -> bin/fastearth_remap.x  (offline lon-lat -> Gauss remap)
make check            # build + run the test suite

make switches: debug=0|1|2, openmp=0|1 (default 1; build openmp=1 for the threaded degree loop at production resolutions).

Configure & run

All runtime parameters live in a single namelist group &fe3d, loaded into the fe_param_class record by fe_par_load. fastearth.nml is the complete, documented defaults set; a run can pass a sparse file overlaid on it (yelmo defaults_file convention), overriding only what it needs. Time fields (dt_*, time_*) are given in years and converted to SI seconds on load.

• Earth structure — earth: a named built-in (e.g. "M3-L70-V01") or "custom" to assemble from the surface-first layer arrays.
• Response solver — earth_response: "ve" (full viscoelastic, default), "modal" (reduced, with n_modes / mode_rank), "elastic", "null".
• Time scheme — scheme = "fe" (1st-order explicit) or "trap" (2nd-order adaptive), advanced by the fe_timestep controller.
• 3D viscosity / spin-up / restart — l_visc_3d, dt_equil, spinup_1d, restart_in_file.
• Rotation — rotation (TPW feedback): on by default; .false. for the non-rotating benchmarks.

Run the standalone driver directly (sparse overlay + complete defaults):

./bin/fastearth.x examples/deglac_lgm.nml fastearth.nml

It reads a reference state and an ice-thickness forcing (file_forcing, h_ice(lon,lat,time); remapped from lon-lat on the fly by default), marches the model across the forcing, and writes the diagnostic surface fields (rsl, z_bed, …) to file_out.

Or stage/submit runs and ensembles with runme (-r run, -s submit; comma-lists in -p define ensemble dimensions):

runme -o runs/deglac -e main --omp 8 -r -p fe3d.lmax=128 fe3d.earth_response=ve

The scripts/run_modal_vs_ve.sh launcher stages the full modal-vs-VE accuracy/cost sweep through runme.

Embedding the model in a host (the CLIMBER-X coupling path) uses the same API behind a single use fastearth3d:

use fastearth3d
type(fe_param_class) :: par
type(solid_earth)    :: se
call fe_par_load(par, "fastearth.nml")
call solid_earth_init(se, par, sht, z_bed_eq, h_ice_ref)
call solid_earth_update(se, h_ice, dt)   ! advance time -> time+dt; reads se%rsl, se%z_bed