*3.3. Power Transformation of Precipitation and Variance Scaling of Temperature*

The power transformation of precipitation has been implemented in smaller domains in Europe, such as the basin of the river Meuse [40] and the mesoscale catchments of Sweden [30], where the precipitation is significant. In our work, the power value of precipitation was calculated with Brent's root-finding algorithm [48]. It is possible that the mean value of precipitation is near zero in the dryer regions. This zero mean value may have caused an invalid value in the coefficient of variation of precipitation that stopped the root-finding algorithm and produced incorrect K-G zones (this is not shown). To get around this issue, we applied two conditions before running the root-finding algorithm. The first condition was to ignore the RCM precipitation values if they were missing values. The second was to ignore the RCM precipitation values if their mean value was zero, as this causes an invalid value. Thanks to the above-mentioned conditions, the power transformation of precipitation combined with the variance scaling of temperature created the correct K-G classification in each RCM. Negligible differences were seen between the observed and simulated K-G zones (Figure 5). The difference in the frequency of occurrence of climate zones between observations and simulations was zero in each region with the exception of ALADIN. ALADIN simulated larger Cfb and smaller Csb extension in the Iberian Peninsula and in the Mediterranean regions where the difference from the observations was only 2%. Due to these facts, power transformation of precipitation and variance scaling of temperature appear to be the most suitable for climate classification in the whole pan-European domain.

**Figure 5.** Simulated K-G climate classification according to E-OBS (**A**) and power transformation of precipitation and variance scaling of temperature correction in ALADIN (**B**), HIRHAM (**C**), RegCM (**D**), RAMCMO2 (**E**) and RCA (**F**).

The value of residual precipitation bias was similar in each RCM, with the exception of HIRHAM, where the residual bias values were zero (Table 5.). Furthermore, the bias was almost identical, except for HIRHAM, which means that power transformation is not dependent on the RCMs. The modelled temperature was almost commensurate with the observed data when variance scaling correction was implemented.


**Table 5.** Residual bias of seasonal amount of simulated precipitation in the case of power transformation of the precipitation bias correction method in eight different regions: the Alps (AL), the British Isles (BI), Eastern Europe (EA), France (FR), the Iberian Peninsula (IP), the Mediterranean (MD), Mid-Europe (ME) and Scandinavia (SC) in DJF and JJA. The bias values are in %.
