*2.7. Metrics for Hydrological Simulations*

An additional set of cross-validation statistics was calculated for the hydrological indexes. First, quantile distributions of river discharge *Q* (i.e., flow-duration curves) were estimated at the outflow sub-basin of each of the sub-models. The average of the four predicting distributions was then compared against the pseudo-reality distribution using a logarithmic accuracy ratio (LAR10) defined as

$$\text{LAR10} = A \left\langle \left| \log\_{10} \left( \frac{\pounds\_{\text{pred}}^{-1}(i)}{F\_{\text{ver}}^{-1}(i)} \right) \right| \right\rangle \right. \tag{6}$$

where *A* has the same meaning as in Equation (4). The statistic is symmetric in the sense that the same value is assigned for under- and overestimation of the same relative magnitude [17]. This alleviates the issue of most other relative accuracy measures penalizing overestimation more strongly than underestimation. In addition to distribution-averaged statistics, LAR10 was also inspected individually for the 5th (Q5) and 99th (Q99) percentile of the flow duration curve to see how the relative performance of the selected MOS methods varies in the tails of the monthly flow duration curves.

The analysis of river discharges is complemented by evaluating a set of individual flux and storage elements, which affect the overall water balance and river discharge generation. To this end, MAE was calculated for the monthly mean values of total runoff (R), evapotranspiration (E), soil moisture (S) and snow water equivalent (SWE) in a similar manner as for daily mean temperature and precipitation. MAE in the mean annual maximum SWE (SWEmax) was also calculated to evaluate how method differences are reflected in the simulation of highest snow pack depths. This allows us to make inferences on how the remaining errors in daily mean temperature and precipitation and in their inter-variable correlations affect the different hydrological elements, as well as to gain insights on the relative performance of the selected bias adjustment methods in terms of hydrological modeling results.
