Performance criteria are used in several files. Different criterion is given in subass.txt and simass.txt files. In addition criteria can be selected in info.txt. Below is listed the code/heading used in each file together with the equation identificator. Further down all the equations are defined.
Equation IDs for subbasin assessment criteria (subassX.txt):
Heading | Description | Equation ID |
---|---|---|
NSE | Nash-Sutcliffe efficiency | NSE |
CC | Pearson correlation coefficient (Kling-Gupta efficiency, part 1) | CC |
RE(%) | relative bias in percent | RE% |
RSDE(%) | relative error in standard deviation in percent | RS% |
Sim | average of simulated variable | cm |
Rec | average of observed variable | rm |
SDSim | standard deviation of simulated variable | cd |
SDRec | standard deviation of observed variable | rd |
MAE | mean absolute error | MAE |
RMSE | root mean square error | RMSE |
Bias | bias | Bias |
SDE | Error of standard deviation | ES |
KGE | Kling-Gupta efficiency | KGE |
KGESD | Kling-Gupta efficiency, part 2 | KGESD |
KGEM | Kling-Gupta efficiency, part 3 | KGEM |
NRMSE | normalised root mean square error | NE |
NSEW | Nash-Sutcliffe efficiency adjusted for bias | NSEW |
MinRec | minimum of observed variable | rmin |
MaxRec | maximum of observed variable | rmax |
MinSim | minimum of simulated variable | cmin |
MaxSim | maximum of simulated variable | cmax |
Equation IDs for simulation assessment criteria (simass.txt):
Name | Code | Equation ID |
---|---|---|
Regional NSE | RR2 | REGNSE |
Regional RA | RRA | REGRA |
Regional RE | RRE | REGRB |
Regional MAE | - | REGMAE |
Average NSE | MR2 | AVNSE |
Average RA | MRA | AVRA |
Average RE | MRE | AVRB |
Average RSDE | MRS | AVRSB |
Average CC | MCC | AVCC |
Average ARE | MAR | AVARB |
Average KGE | AKG | AVKGE |
Aver scalKGE | ASK | ASCKGE |
Spatial NSE | SR2 | SPATNSE |
Spatial RA | RRA | SPATRA |
Spatial RE | - | SPATRB |
Spatial Bias | SMB | SPATASB |
Spatial RMSE | SNR | SPATRMSE |
Kendalls Tau | TAU | AVTAU |
Median NSE | MD2 | MEDNSE |
Median RA | MDA | MEDRA |
Median KGE | MKG | MEDKGE |
Median NRMSE | MNR | MEDNE |
Mean NSEW | MNW | AVNSEW |
Equation IDs for calibration simulation assessment criteria (bestsims.txt and allsim.txt):
Heading | Description | Equation ID |
---|---|---|
rr2 | regional Nash-Sutcliffe efficiency (data from all subbasins combined in one data series) | REGNSE |
sr2 | spatial Nash-Sutcliffe efficiency, calculated using annual means for all subbasins (requires at least 5 years and 5 subbasins with data) to form one data series to calculate the Nash-Sutcliffe efficiency on | SPATNSE |
mr2 | average of Nash-Sutcliffe efficiency for subbasins | AVNSE |
rmae | regional mean absolute error (data from all subbasins combined in one data series) | REGMAE |
sre | spatial relative bias (calculated on annual means for all subbasins) | SPATRB |
rre | regional relative bias (data from all subbasins combined in one data series) | REGRB |
mre | average of the relative bias for all subbasins (Note: fraction, not %) | AVRB |
rra | regional RA, similar to regional NSE, RA is a Nash-Sutcliffe like criterion where the square in the Nash-Sutcliffe formula is exchanged with a coefficient value | REGRA |
sra | spatial RA, similar to spatial NSE, RA is a Nash-Sutcliffe like criterion where the square in the Nash-Sutcliffe formula is exchanged for a coefficient value | SPATRA |
mra | average value of RA for subbasins, RA is a Nash-Sutcliffe like criterion where the square in the Nash-Sutcliffe formula is exchanged with a coefficient value | AVRA |
tau | average of Kendall's Tau value for subbasins | AVTAU |
md2 | median of Nash-Sutcliffe efficiency for subbasins | MEDNSE |
mda | median of all subbasins’ RA (Nash-Sutcliffe like criteria where the square is exchanged with a coefficient value) | MEDRA |
mrs | average of error in standard deviation for subbasins | AVRSB |
mcc | Pearson correlation coefficient, average of all subbasins with observations | AVCC |
mdkg | median of Kling-Gupta efficiency (MKG in info.txt) for subbasins | MEDKGE |
akg | average of Kling-Gupta efficiency for subbasins | AVKGE |
asckg | average of Kling-Gupta efficiency rescaled to interval [-1,1] (C2M criteria applied to KGE, Mathevet et al. 2006) | ASCKGE |
mare | average of absolute relative bias for subbasins (Note: fraction. not %) (MAR in info.txt) | AVARB |
mdnr | median of normalised RMSE for subbasins | MEDNE |
mnw | average of Nash-Sutcliffe efficiencies adjusted for bias for subbasins | AVNSEW |
snr | spatial root mean square error | SPATRMSE |
smb | spatial mean absolute scaled bias on natural log transformed values | SPATASB |
Equation IDs for performance criteria set in info.txt are tabled here.
c | computed value |
r | recorded value |
cl | log transform of computed value, natural logarithm |
rl | log transform of recorded value, natural logarithm |
i | index for time steps with observations in a time series of a station |
mi | number of values in a time series of a station |
j | index of stations |
mj | number of stations |
ij | index over time steps with observations for all stations |
mij | number of time steps with obsevations for all stations |
cm | average value of for a station |
rm | average value of for a station |
cd | standard deviation of for a station |
rd | standard deviation of for a station |
cmax | maximum value of for a station |
rmax | maximum value of for a station |
cmin | minimum value of for a station |
rmin | minimum value of for a station |
w | weight of station |
Average value for a time series of a station:
x=r or c
Standard deviation of a time series of a station:
x=r or c
Natural logaritm of value:
x=r or c or rm or cm, x>0
Nash-Sutcliffe Efficiency (NSE or R2):
Efficiency with coefficient a (RA):
Bias:
Relative bias (RB or RE):
Relative bias in percent (RE%):
Error of standard deviation (ES):
Relative error of standard deviation (RS):
Relative error of standard deviation in percent (RS%):
Mean absolute error (MAE):
Kling-Gupta efficiency (KGE):
cm>0 and rm>0 and cd>0 and rd>0
Pearson correlation coefficient, Kling-Gupta efficiency part 1 (CC):
Kling-Gupta efficiency part 2 (KGESD):
Kling-Gupta efficiency part 3 (KGEM):
Root mean square error (RMSE):
Normalised root mean square error (NE):
Kendalls rank correlation coefficient, tau-b, with adjustments for ties (TAU):
Nash-Sutcliffe Efficiency adjusted for bias (NSEW). Introduced in Lindström (2016):
where
= number of concordant pairs ()
= number of discordant pairs ()
= number of compared pairs
= number of compared pairs that ties in the computed values
= number of compared pairs that ties in the recorded values
Scaled bias (ScBias):
Scaled KGE (SCKGE):
Average Nash-Sutcliffe efficiency (AVNSE):
AVNSE arithmetric mean
or AVNSE weighted average
Median Nash-Sutcliffe efficiency (MEDNSE):
Spatial Nash-Sutcliffe efficiency (SPATNSE):
Regional Nash-Sutcliffe efficiency (REGNSE):
Average Nash-Sutcliffe efficiency adjusted for bias (AVNSEW):
AVNSEW arithmetric mean
or AVNSEW weighted average
Average efficiency with coefficient a (AVRA):
AVRA arithmetric mean
or AVRA weighted average
Median efficiency with coefficient a (MEDRA):
Spatial efficiency with coefficient a (SPATRA):
Regional efficiency with coefficient a (REGRA):
Average relative bias (AVRB):
AVRB arithmetric mean
or AVRB weighted average
Regional relative bias (REGRB):
Spatial relative bias (SPATRB):
Average Kling-Gupta efficiency (AVKGE):
AVKGE arithmetric mean
or AVKGE weighted average
Median Kling-Gupta efficiency (MEDKGE):
Average scaled Kling-Gupta efficiency (ASCKGE):
ASCKGE arithmetric mean
or ASCKGE weighted average
Spatial root mean square error (SPATRMSE):
Median of Normalised root mean square error (MEDNE):
Average of absolute relative bias (AVARB):
AVARB arithmetric mean
or AVARB weighted average
Average Pearson correlation coefficient (AVCC):
AVCC arithmetric mean
or AVCC weighted average
Average relative error of standard deviation (AVRSB):
AVRSB arithmetric mean
or AVRSB weighted average
Average Kendalls rank correlation coefficient (AVTAU):
AVTAU arithmetric mean
or AVTAU weighted average
Regional mean absolute error (REGMAE):
Spatial mean absolute scaled bias on log transformed values (SPATASB):
Lindström, G., 2016. Lake water levels for calibration of the S-HYPE model. Hydrology Research 47.4:672-682. doi: 10.2166/nh.2016.019.
Mathevet et al. 2006. A bounded version of the Nash-Sutcliffe criterion for better model assessment on large sets of basins. In: Large Sample Basin Experiments for Hydrological Model Parameterization: Results of the Model Parameter Experiment–MOPEX. IAHS Publ. 307, 2006, p. 211-219.