3.1.2. Ranking Based on Changes in Climate Extremes

To ascertain that preference will be given to those climate model runs that represent the full range of projected change in extremes, all 20 shortlisted model runs for each of RCP4.5 and RCP8.5, were further scrutinized and ranked based on their projected changes in climatic extremes. To that end, the ETCCDI indices [25] (Table 2) were used to evaluate changes in climatic extremes for air temperature, as well as precipitation. For the former, changes in the extremes were ranked and evaluated based on two indices—the warm spell duration index (WSDI), and the cold spell duration index (CSDI)—while for the latter, consecutive dry days (CDD) and the precipitation due to extremely wet days (R99pTOT) were considered.

To keep the work manageable, we only analyzed four indices in total, two indices to represent changes in precipitation extremes and two for changes in temperature extremes. Furthermore, as the intended use of the selected climate model ensemble was to force the hydrological model for assessing climate change impacts on both flows and extremes, we chose the four most obvious indicators of precipitation and temperature extremes.

The R99pTOT (precipitation due to extremely wet days (>99th percentile)) and CDD (consecutive dry days: maximum length of dry spell (P < 1 mm)) are appropriate indicators for precipitation extremes and suitable for assessment of associated hydrological extremes. R99pTOT is an important

indicator for wet spells in terms of their length and magnitude, which are both key influencing factors in shaping extreme hydrological events (floods and high flows). Similarly, CDD is an important indicator for dry spells that can provide a good opportunity for assessment of the associated low flow episodes. The two temperature-related extreme indices used, i.e., WSDI (count of days in a span of at least 6 days where TX > 90th percentile) and CSDI (count of days in a span of at least 6 days where TN < 10th percentile), seemed best suited for their effects on evapotranspiration and cryospheric processes. The snow and glacier melt/accumulation, as well as evapotranspiration dynamics, are very important in the highly glacierized study area.

The changes in these indices, averaged over the UIB and over 30 years, between the reference period (1976–2005) and the late 21st century projections (2071–2100), were calculated using the database available at the ETCCDI extremes indices archive (http://climexp.knmi.nl), constructed by [26,40].

Only the relevant index for the air temperature or for the precipitation was considered for each of the previously selected group of models (a set of four) initially shortlisted models for each corner or the center), so that for the models in the Wet-Warm corner, only the R99pTOT index for precipitation and the WSDI index for temperature were considered, because they were the only relevant indices, as R99pTOT indicates extreme precipitation events, while WSDI indicates warm spells (Table 2). The other two indices, i.e., CDD and CSDI, were not considered in this case; however, they were the only indices considered for models in the Dry-Cold corner. For each corner, the relevant indices were given scores based on the ratio of the extreme index to the mean of that index, for all four models in a corner. For example, in the Wet-Warm corner, the % change in R99pTOT for a single model is divided by the mean of the % change in R99pTOT for all four models in that corner. The same procedure was applied for WSDI and, finally, both scores were averaged to obtain a final score.


**Table 2.** List of ETCCDI extreme indices used during the GCM selection procedure.

For each of the extreme indices, a weighted rank/skill score *(SkEI)* was calculated, with the highest value among the group getting the highest weighted rank/skill score of 1, and the others getting a rank according to their difference from this highest value, i.e.,

$$Sk\_{EI} = 1 - \frac{EI\_h - EI\_t}{EI\_h} \tag{1}$$

where *Sk* is the weighted rank for the specific extreme index *EI*, *h* denotes the highest index value in a group, and *t* denotes the target index to be ranked.

Similarly, in the case of the change in means, i.e., Δ*T* ( ◦C) and Δ*P* (%), the ranking *(Skm)* was done based on the difference Δ*T* ( ◦C) or Δ*P* (%) shown by each member with the percentile value relevant to that group,

$$\text{Sk}\_{\text{fl}} = 1 - \frac{(\Delta \text{ } T \text{ or } \Delta \text{ } P)\_{10, 50 \text{ or } 90^{\text{th}} \text{percentile}} - (\Delta \text{ } T \text{ or } \Delta \text{ } P)\_{\text{target}}}{(\Delta \text{ } T \text{ or } \Delta \text{ } P)\_{10, 50 \text{ or } 90^{\text{th}} \text{percentile}}} \tag{2}$$
