*3.3. Temporal and Spatial Variations in the Cross-Validation Statistics*

Seasonal and spatial variations in both the relative performance of the studied methods and contributions of different hydrological processes are reflected in the cross-validation statistics for the hydrological simulations. To better infer the reasons for these variations, Figures 8 and 9 show matrices of cross-validated MAE for different aspects of the joint distribution of temperature and precipitation and the distributed hydrological variables in winter and summer seasons in the four sub-models (see Figures S6 and S7 for the same statistics in spring and autumn seasons). In absolute terms the largest MAE values for temperature are seen in Tornio in both seasons, while for precipitation the MAE is generally largest in Sava. The pattern is less clear for the correlation measures, which show larger variations between the four regions. The numeric values in the panels denote the percentage difference to M1. These values indicate that methods M2–M4 perform better than M1 in most cases in winter, while in summer the temperature is relatively well captured by M1. On the other hand, the statistics for both correlation measures indicate that M2 has systematically poorer performance than the other methods and the relative difference is particularly large in Tornio and Ems. The most striking feature

in Figure 8 is the consistently better performance of M1 in capturing the empirical copula density when compared to the other methods, regardless of region or season; apart from M4, which has a relatively similar performance in winter, M1 outperforms the other methods by a large margin.

When the cross-validation statistics for temperature and precipitation are compared against the statistics for the hydrological variables, it is evident that the relative differences between the methods are mostly explained by their capability to adjust the marginal distributions of temperature and precipitation, particularly in those regions and seasons, where snow processes play a less important role in the hydrological cycle. Backing up the previous conclusions, the added value of the adjustment of temperature and precipitation dependence structure, as indicated by differences between methods M2 and M4, is most visible in Tornio and Sava sub-models, where M4 systematically improves the simulation of SWE. The link between the improved simulation of SWE and improvements in total runoff and soil moisture is apparent, as M4 has a smaller MAE than M2 in both variables. Tornio and Sava also show the largest differences between pseudo-reality approaches V0 and V1, as SWE has substantial errors remaining even in summer in Tornio, when V0 is used.

Results from the previous section suggest that quantile mapping applied as a delta change method (M1) has a relatively robust performance from a hydrological modeling perspective. On sub-model scale this is only partially true, as M2 and M4 tend to have better performance in the northern sub-models, while M1 performs particularly well in Sava catchment. However, the relative differences are small in many cases also in other regions, which suggests that the delta change approach might be a good alternative for bias correction. From individual methods, M3 has largest variations in its relative performance between the four sub-models and two seasons. These variations seem not to be solely due to issues with the marginal distributions, and in Tornio, for example, failures to capture the full dependence structure in winter (cf. Figure 2) might deteriorate the statistics for M3.

**Figure 8.** Panels showing the cross-validated MAE (colors) of (**a**) daily mean temperature, (**b**) daily precipitation, (**c**) Pearson correlation coefficient and (**d**) empirical copula density separately for each method (panel rows) at each hydrological sub-domain (panel columns) in years 2061–2090, when two-month time window has been used to estimate simulated changes or model biases. Values for the pseudo-reality approach V0 (V1) are plotted in the upper (lower) triangle of each cell and are shown separately for (**top**) winter and (**bottom**) summer months. In addition, percentage differences to M1 are shown as numeric values for each element.

**Figure 9.** As in Figure 8 but shown for monthly mean (**a**) total runoff, (**b**) evapotranspiration, (**c**) soil moisture and (**d**) snow water equivalent.
