As an area has a larger probability of rainfall than a point, the wet fraction should be larger for a time series from Selleckchem LBH589 a GCM grid cell than from a station. The scale effect is, however, difficult to quantify and therefore we neglect it here and use the observed local wet fraction as a target for the GCM data. Thus simulated and observed daily rainfall was sorted in descending order and a cut-off value was defined as the threshold that reduced the percentage of wet days

in the GCM data to that of the observations. Days with rainfall amounts larger than the threshold value were considered as wet days and all other days as dry days (Yang et al., 2010). In the second step of DBS, the remaining non-zero rainfall was transformed to match the observed cumulative probability distribution in the reference data by

fitting gamma distributions to both observed and simulated daily rainfall. DBS applies a gamma distribution because of its documented ability to represent the typically asymmetrical and positively skewed distribution of daily rainfall intensities (Haylock et al., 2006). The density distribution of the two-parameter gamma distribution is expressed as: equation(1) f(x)=(x/β)α−1exp(−x/β))βΓ(x) x,α,β>0where α is the shape parameter, β is the scale parameter and Γ(x) is the gamma function. As the distribution of daily rainfall values is heavily skewed towards low intensities, distribution parameters estimated by e.g. maximum likelihood will be dominated by the most frequently occurring values and fail to accurately describe selleck inhibitor extremes.

To capture the characteristics Smoothened of normal rainfall as well as extremes, in DBS the rainfall distribution is divided into two partitions separated by the 95th percentile. Two sets of parameters – α, β representing non-extreme values and α95, β95 representing extreme values – were estimated from observations and the GCM output for the reference period 1975–2004. These parameter sets were in turn used to bias-correct daily rainfall data from GCM outputs for the entire projection period up to 2099 using the following equations: equation(2) PDBS=F−1(αObs,βObs,F(P,αCTL,βCTL))if P<95th percentile valuePDBS=F−1(αObs,95,βObs,95,F(P,αCTL,95,βCTL,95))if P≥95th percentile valuewhere P denotes daily precipitation values of the GCMs and PDBS stands for the DBS bias corrected daily precipitation data. The suffix Obs denotes parameters estimated from observations in the reference period and the suffix CTL denotes parameters estimated from the GCM output in the reference period. F represents the cumulative gamma probability distribution associated with the probability density function f (see equation 1). To take seasonal dependencies into account, the parameter sets were estimated for each season separately: pre-monsoon (March–May), Southwest monsoon (June–September), post-monsoon (October–November) and winter (December–February).