## 1. Introduction

Bias correction is a popular technique for postprocessing the raw output from general circulation models (GCM), which usually suffers from biases due to uncertainty in parameterizing unresolved processes (Christensen *et al*., 2008). A realistic and reliable representation of future climate is crucial for impact and vulnerability assessment. Moreover, the importance of bias correction has been described in the special report of the Intergovernmental Panel on Climate Change (IPCC, Seneviratne and Nicholls, 2012). In recent years, much effort has been dedicated to investigating various postprocessing techniques, from simple additive and scaling corrections (Fowler and Kilsby, 2007) to more advanced quantile mapping approaches (e.g. Wood *et al*., 2002; Wood *et al*., 2004; Maurer and Hidalgo, 2008). The major advantage of quantile mapping is that it aims to adjust the cumulative distribution function (CDF) of a model simulation to agree with that of observations in a given reference period rather than to merely adjust the mean and variance of model output. Quantile mapping is a very efficient bias correction technique with many applications (e.g. Sharma *et al*., 2007; Piani *et al*., 2010). This method can be mathematically formulated as

Where is the quantile function (inverse CDF) corresponding to observations and *F*_{m − c} is the CDF of GCM outputs in the reference period. Briefly, a quantile of a random variable is a real number satisfying where *F* is the CDF. Accordingly, the quantile function expresses the quantile values as a function of probabilities (Gibbons and Chakraborti, 2011; Gilchrist, 2000). The underlying assumption of quantile mapping is that the future distribution of a variable of interest will remain similar to that in the reference period. However, this may not hold true, as argued by Li *et al*. (2010), who recently proposed the equidistant cumulative distribution function matching (EDCDF_{m}) method as an improvement to the traditional method. EDCDF_{m} explicitly considers the change of the distribution in the future. This improved quantile mapping method can be mathematically written as

where is the CDF of the model for a future projection period, and and are quantile functions for observations and model in the reference period, respectively. Figure 1(a) illustrates how EDCDF_{m} works. Though it incorporates the change in distribution, the fundamental assumption of this method is that the difference between modeled and observed values over the reference period will be preserved in a future period. By performing a synthetic experiment, Li *et al*. (2010) concluded that the EDCDF_{m} method is superior to the traditional method. Though recently proposed, it has been widely cited in scholarly articles. In addition, several other studies have used EDCDF_{m} to bias-correct precipitation (e.g. Sun *et al*., 2011). However, there are problems with this method when applied to bias-correcting precipitation, as described thoroughly in the following section. We applied this exact same method to precipitation data from phase five of the Coupled Model Inter-comparison Project (CMIP5) and found that numerous negative values result.