We use several metrics and hydrological signatures to evaluate model simulations, including the general performance of discharge simulations, the reproduction of hydrological responses by model simulations, and long-term water balances. Table 2 summarizes all the metrics and signatures.
Performance metrics and hydrological signatures
| Metric & signature | Equation | Description | Reference |
|---|---|---|---|
| Kling-Gupta efficiency (KGE [–]) |   | Describes the model performance. KGE ranges from − to 1, with optimum at 1.  ,  and r indicates variability, bias and linear correlation, respectively | Gupta et al. (2009) |
Baseflow index ( [–]) |  | Characterizes the proportion of baseflow of the total discharge | Sawicz et al. (2011) |
R-B Flashness index ( [–]) |  | Describes the frequency and rapidness of changes in discharge over a given time | Baker et al. (2004) |
Inter-annual correlation coefficient ( [–]) |  | Describes the linear correlation between observed and simulated annual average discharge | – |
Intra-annual correlation coefficient ( [–]) |  | Describes the linear correlation between observed and simulated long-term monthly mean discharge (mean of specific month over a period) | – |
Runoff ratio ( [–]) |  | Characterizes the separation of precipitation to discharge and evapotranspiration | Yadav et al. (2007) |
Relative error of long-term mean discharge ( [–]) |  | Characterizes relative error of the long-term water balance | – |
Rainfall index ( [–]) |  | Characterizes spatial variability of precipitation in a catchment | Smith et al. (2004) |
Location index ( [–]) |  | Characterizes the variability of the precipitation fields | Smith et al. (2004) |
Mean interquartile range ( [–]) |  | Characterizes the uncertainty associated with different parameter sets | – |
Mean standard deviation ( [–]) |  | Characterizes the uncertainty associated with different parameter sets | – |
Mean variance ( [–]) |  | Characterizes the uncertainty associated with different parameter sets | – |
| Metric & signature | Equation | Description | Reference |
|---|---|---|---|
| Kling-Gupta efficiency (KGE [–]) | | Describes the model performance. KGE ranges from − to 1, with optimum at 1. , and r indicates variability, bias and linear correlation, respectively | Gupta et al. (2009) |
| Baseflow index ( [–]) | | Characterizes the proportion of baseflow of the total discharge | Sawicz et al. (2011) |
| R-B Flashness index ( [–]) | | Describes the frequency and rapidness of changes in discharge over a given time | Baker et al. (2004) |
| Inter-annual correlation coefficient ( [–]) | | Describes the linear correlation between observed and simulated annual average discharge | – |
| Intra-annual correlation coefficient ( [–]) | | Describes the linear correlation between observed and simulated long-term monthly mean discharge (mean of specific month over a period) | – |
| Runoff ratio ( [–]) | | Characterizes the separation of precipitation to discharge and evapotranspiration | Yadav et al. (2007) |
| Relative error of long-term mean discharge ( [–]) | | Characterizes relative error of the long-term water balance | – |
| Rainfall index ( [–]) | | Characterizes spatial variability of precipitation in a catchment | Smith et al. (2004) |
| Location index ( [–]) | | Characterizes the variability of the precipitation fields | Smith et al. (2004) |
| Mean interquartile range ( [–]) | | Characterizes the uncertainty associated with different parameter sets | – |
| Mean standard deviation ( [–]) | | Characterizes the uncertainty associated with different parameter sets | – |
| Mean variance ( [–]) | | Characterizes the uncertainty associated with different parameter sets | – |
Note: (
, 
) and (
, 
): mean and standard deviation of observations and simulations, respectively; VB and V: volumes of baseflow and total discharge, respectively [m3]. Qt: discharge at time t [m3/s]; (
, 
), (
, 
), and (
, 
): mean of simulated and observed annual, long-term monthly, and entire discharge, respectively [m3/s]; q: long-term areal mean discharge [mm]; P: long-term areal mean precipitation [mm]; 
: daily precipitation at time step t [mm]; 
: standard deviation of precipitation at one time step [–]; 
: rainfall centroid ratio at one time step [–]; 
, 
and 
: interquartile range, standard deviation and variance of standardized discharge per catchment based on all parameter sets at one time step, respectively [–].