Add corrected diagnostic for sea level contribution

[talbrecht]

Reference: Goelzer et al., 2020 (https://doi.org/10.5194/tc-14-833-2020)

PISM uses the commonly used definition of volume above flotation and writes this as sea-level_rise_potential to the timeseries. This is fine, but as pointed out by Goelzer et al., 2020, there are effects of the external sea level forcing (ESLF, Sect. 6) and by the vertical displacement of the bed (Sect. 4), which result in incorrectly diagnosed sea level contributions (SLC). Goelzer and colleagues propose a simple correction, which estimates the contribution of the ice sheet in an ice sheet model to global-mean geocentric sea-level rise (avoiding the effect of ESLF). Such a correction could be easily implemented in geometry/Geometry.cc as additional diagnostic sea-level_rise_contribution, for instance. However, a reference state or value needs to be indicated (e.g. from Bedmap2).

I tested the correction and found for an Antarctic present-day configuration (Bedmap2) as compared to an LGM state (best fit paleo ensemble member), a sea level contribution of SLC_corr = -5.9 m SLE as compared to the volume above flotation (VAF) approach with SLC_af = -8.0 m SLE (same in PISM when comparing sea-level_rise_potential). The difference in this specific example is a result of the volume above flotation with respect to the present-day sea level SLC_af0 = -4.7 m SLE, the bed uplift contribution SLC_pov0 = -0.84 m SLE and by the density correction SLC_den = -0.35 m SLE. So this is about 26% less than in the current PISM diagnostic.

See also tests in https://nbviewer.jupyter.org/url/www.pik-potsdam.de/~albrecht/notebooks/compare_sea_level_contributions.ipynb#goelzer

[flocolleoni]

Hi Torsten,

I think it is important that this variable is correct in the outputs of PISM.

• It could be corrected as you mentioned and reference state to BEDMAP2 (or BEDMachine) has to be explicitely mentioned within the variable history. For paleo studies, most of the AIS contribution is anyway reported to present-day state for sea level rise estimates.

• for paleo studies of times older than the Pliocene, however, this could be a problem. This calculation mostly depends on the Ocean area that might vary in the times older than Pliocene already, thus for the Miocene up to the EOT.