What's a billion cubic meters among friends: The impacts of quantile mapping bias correction on climate projections

Consider two views of climate change, the percent change in precipitation from the GCMs and the percent change from the same GCMs as bias-corrected using quantile mapping. There is emerging evidence that quantile mapping, a commonly used bias correction method, can alter the projections of future precipitation in a way that leads to a systematicaly wetter future for the Colorado River than is indicated by the percent-changes in the GCMs. The difference, about 3% in precipitation, when put through hydrology models, amounts to roughly a 6% shift in the average flows at Lees Ferry, or a little over a billion cubic meters (a million acre feet). On the one hand, the quantile mapping does not add any new physics to the GCM water budget, so the shifts in the mean from could be viewed as an unintended statistical artifact. On the other, what is sacrosanct about the percent change in the (biased) GCM water budget as an indicator of the future climate? We investigate the reasons that this shift arises by taking a closer look at quantile mapping in theory and for idealized (Gamma and Weibull) probability distributions. Heuristics are developed to understand when the shift is likely to arise for more realistic distributions, and to connect the idealized statistical examples to hypothetical water budgets.