Converting geodetic ice volume to mass change: a global-scale assessment

The potential of surface altimetry and photogrammetry for assessing the volume change of glaciers is tremendous and the scope of available data sets is increasing at a rapid pace. Surface elevation changes are now available for all glaciers globally and the time periods that can be resolved by these data are becoming shorter. However, most glaciological and hydrological studies rely on glacier mass change instead of volume change, thus necessitating a conversion accounting for the density of the gained or lost ice, firn or snow. While glaciers gain or lose volume, their firn coverage simultaneously changes, both in terms of extent, thickness and density, complicating the estimation of the conversion factor. Often, geodetic studies use a density of volume change equal to 850 kg m^-3 which has been found to be valid for a wide range of cases. Nevertheless, particular situations, e.g. changes in mass balance gradients related to abrupt accelerations or decelerations of local atmospheric warming might result in significant departures of the conversion factor from this reference value. This probably represents the most important uncertainty factor in regional to global-scale assessments of geodetic glacier mass change.

Here, we substantially update the assessment of the optimal conversion between volume and mass change by Huss (2013) and apply the same firn densification model to all roughly 200'000 glaciers globally. Local annual surface mass balance over the period 2000-2019 is prescribed by the global glacier model GloGEM. The model is driven by ERA5 climate re-analysis data, and cumulative modelled mass balance is constrained to match observations of geodetic elevation change for each individual glacier for 2000-2019. By comparing mass balance and computed glacier volume changes resulting from the firn density model, a volume-to-mass change conversion factor is derived for each glacier and any period over the last two decades. Our assessment thus accounts for local changes in climate and, hence, shifts in the properties of the firn coverage, as well as the observed changes of each individual glacier.

A considerable variance in the factors necessary to convert geodetic ice volume change to mass change is found, both at the regional scale but also for different time periods of the same region. For many regions, the estimate of 850±60 kg m^-3 for the density of ice volume change is valid, encompassing most of the investigated periods within 2000-2019. However, for some - mostly high-latitude - regions significantly lower and higher conversion factors have been found, related to particular long-term changes in firn density and thickness. Various assumptions and simplifications are involved in this global-scale assessment. Nevertheless, we consider our results as a helpful guideline for estimating volume-to-mass conversion factors in geodetic studies around the world over arbitrary time periods.