A New Method to Statistically Combine Ice Sheet Mass Balance Estimates
Abstract
We explore how to statistically combine multiple datasets estimating a common physical quantity. Three main methods are used to estimate the mass balance of the polar ice sheets: gravimetry, altimetry, and the input-output method. These yield different results, which leads to the question of how to combine them into one “best” mass balance estimate. Such measurement aggregation is a form of “meta-analysis”, which is a mature area of statistics. Using real-world data, we find that prominent meta-analysis methods, originally developed within medicine and social sciences, should not always be applied to problems in the physical sciences; that is, because their assumptions are too strong, they can yield intervals which are too narrow and understate our uncertainty. We propose new methods for meta-analysis with weaker assumptions that are more likely to be met in reality. The Ice sheet Mass Balance Inter-comparison Exercise (IMBIE) statistically aggregates mass balance estimates through a simple error-weighted mean and provides uncertainties which consider neither the heterogeneity between estimates nor the correlation in errors across time and between ice sheets. To sidestep the issue of error correlation, we estimate all final quantities (for example, mass trend in a given window for a given ice sheet) individually for the different mass balance time series datasets. We then perform a meta-analysis on the level of the final estimate using our proposed methods, and show illustrative results. Finally, we ask whether we should try to statistically reconcile different results in the first place, and on what basis we might trust the results.