linked research is being used to improve the ice sheet model
Not according to the abstract. The authors explored an ambitious approach but found the mathematical obstacles insuperable. The details of why things didn't work out will prove very interesting to others in the field but ultimately nothing has been learned about geothermal heat flux under Greenland that will improve understanding of the past, present or future of this ice sheet.
Meanwhile, there has been quite a bit of experimental progress reported lately on geothermal heat flux and the equally important melt state of the bottom ice. Ultimately the lack of data on matters such as temperature, hydration state and topography of basal till are essential boundary conditions. PDEs propagate from there, they can't go anywhere without them.
Not that I have any desire to over-sell the value of "Inversion of Geothermal Heat Flux in a Thermo-Mechanically Coupled Nonlinear Stokes Ice Sheet Model"; however, the abstract does state: "Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.” Therefore, the research did provide some guidance in certain "optimized" circumstances. Thus even if these finds are of little practical value for either the GIS or the EAIS; they may well be of some value for the WAIS (which is currently more critical, w.r.t. collapse risk); as the following references indicate that the geothermal heat flux beneath portions of the WAIS (particularly near the West Antarctic Rift System (WARS) and the Marie Byrd Land Dome (MBLD). Also, for what is worth, ACME continues to provide funding for this research; thus what is impracticable today, may (with more findings) be practicable in the not too distant future:
C. Ramirez, A. Nyblade, S.E. Hansen, D.A. Wiens, S. Anandakrishnan, R.C. Aster, A.D. Huerta, P. Shore and T. Wilson (March, 2016) "Crustal and upper-mantle structure beneath ice-covered regions in Antarctica from S-wave receiver functions and implications for heat flow", Geophys. J. Int., 204 (3): 1636-1648. doi: 10.1093/gji/ggv542https://gji.oxfordjournals.org/content/204/3/1636.refs?related-urls=yes&legid=gji;204/3/1636
Abstract: "S-wave receiver functions (SRFs) are used to investigate crustal and upper-mantle structure beneath several ice-covered areas of Antarctica. Moho S-to-P (Sp) arrivals are observed at ∼6–8 s in SRF stacks for stations in the Gamburtsev Mountains (GAM) and Vostok Highlands (VHIG), ∼5–6 s for stations in the Transantarctic Mountains (TAM) and the Wilkes Basin (WILK), and ∼3–4 s for stations in the West Antarctic Rift System (WARS) and the Marie Byrd Land Dome (MBLD). A grid search is used to model the Moho Sp conversion time with Rayleigh wave phase velocities from 18 to 30 s period to estimate crustal thickness and mean crustal shear wave velocity. The Moho depths obtained are between 43 and 58 km for GAM, 36 and 47 km for VHIG, 39 and 46 km for WILK, 39 and 45 km for TAM, 19 and 29 km for WARS and 20 and 35 km for MBLD. SRF stacks for GAM, VHIG, WILK and TAM show little evidence of Sp arrivals coming from upper-mantle depths. SRF stacks for WARS and MBLD show Sp energy arriving from upper-mantle depths but arrival amplitudes do not rise above bootstrapped uncertainty bounds. The age and thickness of the crust is used as a heat flow proxy through comparison with other similar terrains where heat flow has been measured. Crustal structure in GAM, VHIG and WILK is similar to Precambrian terrains in other continents where heat flow ranges from ∼41 to 58 mW m−2, suggesting that heat flow across those areas of East Antarctica is not elevated. For the WARS, we use the Cretaceous Newfoundland–Iberia rifted margins and the Mesozoic-Tertiary North Sea rift as tectonic analogues. The low-to-moderate heat flow reported for the Newfoundland–Iberia margins (40–65 mW m−2) and North Sea rift (60–85 mW m−2) suggest that heat flow across the WARS also may not be elevated. However, the possibility of high heat flow associated with localized Cenozoic extension or Cenozoic-recent magmatic activity in some parts of the WARS cannot be ruled out."
Andrew T. Fisher et. al. (July 2015), "High geothermal heat flux measured below the West Antarctic Ice Sheet", Science Advances 1(6):e1500093-e1500093, DOI: 10.1126/sciadv.1500093 http://advances.sciencemag.org/content/1/6/e1500093http://advances.sciencemag.org/content/advances/1/6/e1500093.full.pdf
Abstract: "The geothermal heat flux is a critical thermal boundary condition that influences the melting, flow, and mass balance of ice sheets, but measurements of this parameter are difficult to make in ice-covered regions. We report the first direct measurement of geothermal heat flux into the base of the West Antarctic Ice Sheet (WAIS), below Subglacial Lake Whillans, determined from the thermal gradient and the thermal conductivity of sediment under the lake. The heat flux at this site is 285 ± 80 mW/m(2), significantly higher than the continental and regional averages estimated for this site using regional geophysical and glaciological models. Independent temperature measurements in the ice indicate an upward heat flux through the WAIS of 105 ± 13 mW/m(2). The difference between these heat flux values could contribute to basal melting and/or be advected from Subglacial Lake Whillans by flowing water. The high geothermal heat flux may help to explain why ice streams and subglacial lakes are so abundant and dynamic in this region."
Theresa M. Damiani, Tom A. Jordan, Fausto Ferraccioli, Duncan A. Young, and Donald D. Blankenship, (2014), "Variable crustal thickness beneath Thwaites Glacier revealed from airborne gravimetry, possible implications for geothermal heat flux in West Antarctica", Earth and Planetary Science Letters Volume 407, 1, Pages 109–122, DOI: 10.1016/j.epsl.2014.09.023http://www.sciencedirect.com/science/article/pii/S0012821X14005780