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