# Evaluating CHIRPS and ERA5 for Long-Term Runoff Modelling with SWAT in Alpine Headwaters
## 2 Materials and Methods
### Evaluation Methods
The scale discrepancy between the rain gauges and the GPPs is typical, and the location of the rain gauges usually does not coincide with the GPP grid centers. The common practice in evaluation studies is to upscale/downscale the rain gauge data to the grid scale of the GPP [51]. Two preprocessing approaches were tested in this study: (a) spatial algorithmic averaging and (b) single gauge precipitation. In the first approach, the gauges adjacent to each grid point were identified and then the spatially averaged precipitation was obtained. In the second process, the double mass curves for each of the adjacent gauges to grid points were evaluated, and the gauge with the best-fitting curve was selected as the reference. The double mass curve was similarly used in the assessment of gauged precipitation datasets during the assessment of GPPs [111]. The double mass curves bias for the spatially averaged precipitation were significantly higher than for the selected single gauges. Due to the considerable elevation differences in the pilot area and the higher bias from spatial averaged precipitation, the selected pairs of gauge and grid points were used in further assessment. Table 5 shows the selected pairs of gauges and grid points from the considered GPPs. The following metrics were used to evaluate long-term variations in climate (\(TG\), \(P\), \(SD\)) and runoff (\(Q\)) indices: (i) 11-year moving averages, (ii) the slope of linear regression (\(LinT\)), and (iii) the trend significance using the non-parametric Mann-Kendall test [112, 113]. The breakpoint in the trend was identified using the (iv) Rescaled Adjustment Partial Sums (RAPS) method, as the visualization approach can compensate for small systematic fluctuations in the record [114]. To evaluate the performance of the GPPs in the point-to-point and hydrological modelling approaches, the following statistical metrics were used: bias (\(B\)), percent bias (\(PB\)), relative mean absolute error (\(RMAE\)), coefficient of determination (\(R^{2}\)), standard deviation of error (\(\sigma\)) and Nash-Sutcliffe efficiency (\(NSE\)) for the hydrological model only (see Table 6 for details). \begin{table}
\begin{tabular}{c c} \hline \hline
**Statistical Metric** & **Equation** & **Optimal Value** \\ \hline Bias (\(B\)) & \(B=\frac{\sum_{i=1}^{n}(S_{i}-Q_{i})}{\sum_{i=1}^{n}}\) & 0 \\ Percent bias (\(PB\)) & \(PB=\frac{\sum_{i=1}^{n}(S_{i}-Q_{i})}{\sum_{i=1}^{n}}\) (\(\%\)) & 0 \\ Mean absolute error (\(MAE\)) & \(MAE=\frac{\sum_{i=1}^{n}(S_{i}-Q_{i})}{\sum_{i=1}^{n}Q_{i}}\) & 0 \\ Relative mean absolute error (\(RMAE\)) & \(RMAE=\frac{\sum_{i=1}^{n}(S_{i}-Q_{i})}{\sum_{i=1}^{n}Q_{i}}\) & 0 \\ Coefficient of determination (\(R^{2}\)) & \(R^{2}=\left(\frac{\sum_{i=1}^{n}(Q_{i}-\overline{Q})(S_{i}-\overline{S})}{ \sqrt{\sum_{i=1}^{n}(S_{i}-\overline{S})^{2}}}\right)^{2}\) & 1 \\ Nash–Sutcliffe efficiency (\(NSE\)) & \(NSE=1-\frac{\sum_{i=1}^{n}(S_{i}-Q_{i})^{2}}{\sum_{i=1}^{n}(Q_{i}-\overline{Q })^{2}}\) & 1 \\ \hline \hline \end{tabular} Note(s): \(n\) refers to the number of samples; \(S_{i}\) means the precipitation estimates from GPPs or the simulated runoff from hydrological model; \(Q_{i}\) means observed precipitation by rain gauge or observed runoff at hydrological station.  
\end{table} 
Table 6: List of the statistical metrics used in the evaluation of GPPs. \begin{table}
\begin{tabular}{c c|c c c|c c c|c c c|c c} \hline \hline  & **Calculated** & **M.** & **Sall** & **M.** & **M.** & **Datasets** & **M.** & **Iail** & & & **Average Disc. (m.s. )** \\ \hline \multirow{2}{*}{**Categories**} & **Name** & **Dressler** & **S**-**d**e**m**  
In this study, the warm season comprises the months of May to October, and the period from November to April is considered the cold season. In addition to the analysis at the gauging stations, the performance was also assessed in terms of catchment averaged results (vertical averaging) for comparison between catchments, and horizontal averaging (in elevation bands) to account for the orographic influence on the GPPs [16].