Abstract. Negative glacier mass balances in most of Earth's glacierized regions contribute roughly one-quarter to currently observed rates of sea-level rise and have likely contributed an even larger fraction during the 20th century. The distant past and future of glaciers' mass balances, and hence their contribution to sea-level rise, can only be estimated using numerical models. Since, independent of complexity, models always rely on some form of parameterizations and a choice of boundary conditions, a need for optimization arises. In this work, a model for computing monthly mass balances of glaciers on the global scale was forced with nine different data sets of near-surface air temperature and precipitation anomalies, as well as with their mean and median, leading to a total of 11 different forcing data sets. The goal is to better constrain the glaciers' 20th century sea-level budget contribution and its uncertainty. Therefore, five global parameters of the model's mass balance equations were varied systematically, within physically plausible ranges, for each forcing data set. We then identified optimal parameter combinations by cross-validating the model results against in situ annual specific mass balance observations, using three criteria: model bias, temporal correlation, and the ratio between the observed and modeled temporal standard deviation of specific mass balances. These criteria were chosen in order not to trade lower error estimates by means of the root mean squared error (RMSE) for an unrealistic interannual variability. We find that the disagreement between the different optimized model setups (i.e., ensemble members) is often larger than the uncertainties obtained via the leave-one-glacier-out cross-validation, particularly in times and places where few or no validation data are available, such as the first half of the 20th century. We show that the reason for this is that in regions where mass balance observations are abundant, the meteorological data are also better constrained, such that the cross-validation procedure only partly captures the uncertainty of the glacier model. For this reason, ensemble spread is introduced as an additional estimate of reconstruction uncertainty, increasing the total uncertainty compared to the model uncertainty merely obtained by the cross-validation. Our ensemble mean estimate indicates a sea-level contribution by global glaciers (outside of the ice sheets; including the Greenland periphery but excluding the Antarctic periphery) for 1901–2018 of 69.2 ± 24.3 mm sea-level equivalent (SLE), or 0.59 ± 0.21 mm SLE yr−1. While our estimates lie within the uncertainty range of most of the previously published global estimates, they agree less with those derived from GRACE data, which only cover the years 2002–2018.
Gyre-scale atmospheric pressure variations and their relation to 19th and 20th century sea level rise
