Bias Correction of Simulated Precipitation by Quantile Mapping: Preserving Relative Changes in Quantiles and Extremes

Simulated precipitation outputs from global climate models (GCMs) and regional climate models (RCMs) can exhibit large systematic biases relative to observational datasets. As GCM and RCM precipitation series are used as inputs to process models and gridded statistical downscaling models, algorithms have been developed to correct and minimize these biases as sources of error in subsequent modelling chains. While not without controversy, statistical bias corrections are, in practice, a common component of climate change impacts studies. Corrections can be to the modelled mean, variance, and also higher moments of a distribution, with many methods now applying bias corrections to all quantiles. Recently, studies have highlighted a potentially serious problem with quantile mapping bias corrections, in particular when they are used to assess projected climate change impacts, namely that long-term changes in simulated series may not be preserved following quantile mapping. For GCMs, modifications of projected trends in seasonal mean precipitation by quantile mapping have, in some locations, been found to be as large as the original GCM-projected changes. In addition, quantile mapping can affect trends in extreme quantiles differently than trends in the mean. In the absence of additional information, should trends in bias corrected outputs match those of the model itself? For future projections, which are subject to large external forcing signals relative to natural variability, it has been argued that trends should be preserved so that the climate sensitivity of the model is not affected by bias correction. In the case of variables related to atmospheric moisture, like precipitation, preserving the relative change signal is also important for maintaining physical scaling relationships with model-projected temperature changes, for example as indicated by the Clausius-Clapeyron equation.

In the literature, algorithms have beed designed to preserve relative trends in mean precipitation, but it is unclear how trends in extremes might be affected. Other methods considered for precipitation projections modify historical observations by superimposing relative trends in quantiles from a climate model overtop the observed series. In this case, modelled trends in all quantiles, including in the tails, are preserved, but the algorithms do not explicitly bias correct the daily time series from the climate model, instead falling back to adjustment of the observed series. Additionally, preserving relative changes in quantiles does not mean that relative changes in the mean will be preserved. Tradeoffs that go along with the choice to preserve relative trends in the mean or in the quantiles of a bias corrected series have yet to be explored in a systematic manner. This presentation aims to assess these tradeoffs, and, more generally, to investigate the extent to which quantile mapping algorithms modify GCM-projected trends in mean precipitation and indices of extremes. First, we describe and demonstrate a ‘quantile perturbation quantile mapping' bias correction algorithm that preserves relative changes in quantiles, thus ensuring that the climate sensitivity of the underlying climate model, at least so far as quantiles are concerned, is unaffected by the bias correction. The algorithm is then compared against a detrended form of quantile mapping, which is designed to preserve trends in the mean, and standard quantile mapping. Methods are first demonstrated using synthetic data and are then applied to daily GCM-simulated precipitation outputs over Canada. In the latter case, the ability of the algorithms to correct historical biases and preserve relative changes in mean quantities and annual extremes, is assessed using (i) the suite of precipitation indices recommended by the World Meteorological Organization's Expert Team on Climate Change Detection and Indices (ETCCDI), and (ii) results from a generalized extreme value analysis applied to annual precipitation maxima. There are three important reasons for analyzing algorithm performance in terms of extremes. First, previous studies that have looked at the influence of bias correction on simulated precipitation changes over large spatial domains have focused on the mean rather than extremes. Second, while bias correction methods are calibrated on daily precipitation series, they are typically not explicitly tuned to replicate distributions of annual extremes, so this provides a stringent and somewhat independent test of their performance. Finally, in terms of providing relevant information for engineering planning, return period calculations are of key interest.