User Tools

Site Tools


start:hype_file_reference:info.txt:criteria_equations

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
start:hype_file_reference:info.txt:criteria_equations [2019/08/28 14:57]
cpers [Criteria equations for a model domain (several stations)]
start:hype_file_reference:info.txt:criteria_equations [2024/01/25 11:37] (current)
Line 28: Line 28:
 |''​NRMSE''​|normalised root mean square error |//NE//| |''​NRMSE''​|normalised root mean square error |//NE//|
 |''​NSEW''​|Nash-Sutcliffe efficiency adjusted for bias|//​NSEW//​| |''​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//​|
 </​sortable>​ </​sortable>​
  
Line 33: Line 37:
  
 <​sortable>​ <​sortable>​
-^ Name ^ Code ^ Equation ID ^ +^ Name          ^ Code     ​^ Equation ID   ​
-|Regional NSE|''​RR2''​|//​REGNSE//​| +| Regional NSE  | ''​RR2'' ​ | //​REGNSE// ​   
-|Regional RA|''​RRA''​|//​REGRA//​| +| Regional RA   ​| ''​RRA'' ​ | //​REGRA// ​    ​
-|Regional RE|''​RRE''​|//​REGRB//​| +| Regional RE   ​| ''​RRE'' ​ | //​REGRB// ​    ​
-|Regional MAE|''​-''​|//​REGMAE//​| +| Regional MAE  | ''​-'' ​   | //​REGMAE// ​   
-|Average NSE|''​MR2''​|//​AVNSE//​| +| Average NSE   ​| ''​MR2'' ​ | //​AVNSE// ​    ​
-|Average RA|''​MRA''​|//​AVRA//​| +| Average RA    | ''​MRA'' ​ | //​AVRA// ​     
-|Average RE|''​MRE''​|//​AVRB//​| +| Average RE    | ''​MRE'' ​ | //​AVRB// ​     
-|Average RSDE|''​MRS''​|//​AVRSB//​| +| Average RSDE  | ''​MRS'' ​ | //​AVRSB// ​    ​
-|Average CC|''​MCC''​|//​AVCC//​| +| Average CC    | ''​MCC'' ​ | //​AVCC// ​     
-|Average ARE|''​MAR''​|//​AVARB//​| +| Average ARE   ​| ''​MAR'' ​ | //​AVARB// ​    | 
-|Spatial NSE|''​SR2''​|//​SPATNSE//​| +| Average KGE   | ''​AKG'' ​ | //​AVKGE// ​    | 
-|Spatial RA|''​RRA''​|//​SPATRA//​| +| Aver scalKGE ​ | ''​ASK'' ​ | //​ASCKGE// ​   ​
-|Spatial RE|''​-''​|//​SPATRB//​| +| Spatial NSE   ​| ''​SR2'' ​ | //​SPATNSE// ​  ​
-|Kendalls Tau|''​TAU''​|//​AVTAU//​| +| Spatial RA    | ''​RRA'' ​ | //​SPATRA// ​   
-|Median NSE|''​MD2''​|//​MEDNSE//​| +| Spatial RE    | ''​-'' ​   | //​SPATRB// ​   | 
-|Median RA|''​MDA''​|//​MEDRA//​| +| Spatial Bias  | ''​SMB'' ​ | //​SPATASB// ​  | 
-|Median KGE|''​MKG''​|//​MEDKGE//​| +| Spatial RMSE  | ''​SNR'' ​ | //​SPATRMSE//  ​
-|Median NRMSE|''​MNR''​|//​MEDNE//​| +| Kendalls Tau  | ''​TAU'' ​ | //​AVTAU// ​    ​
-|Mean NSEW|''​MNW''​|//​AVNSEW//​|+| Median NSE    | ''​MD2'' ​ | //​MEDNSE// ​   
 +| Median RA     ​| ''​MDA'' ​ | //​MEDRA// ​    ​
 +| Median KGE    | ''​MKG'' ​ | //​MEDKGE// ​   
 +| Median NRMSE  | ''​MNR'' ​ | //​MEDNE// ​    ​
 +| Mean NSEW     ​| ''​MNW'' ​ | //​AVNSEW// ​   |
 </​sortable>​ </​sortable>​
  
Line 61: Line 69:
 |''​rr2''​|regional Nash-Sutcliffe efficiency (data from all subbasins combined in one data series)|//​REGNSE//​| |''​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//​| |''​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 ​efficiencies ​for subbasins|//​AVNSE//​|+|''​mr2''​|average of Nash-Sutcliffe ​efficiency ​for subbasins|//​AVNSE//​|
 |''​rmae''​|regional mean absolute error (data from all subbasins combined in one data series)|//​REGMAE//​| |''​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//​| |''​sre''​|spatial relative bias (calculated on annual means for all subbasins)|//​SPATRB//​|
Line 75: Line 83:
 |''​mcc''​|Pearson correlation coefficient,​ average of all subbasins with observations|//​AVCC//​| |''​mcc''​|Pearson correlation coefficient,​ average of all subbasins with observations|//​AVCC//​|
 |''​mdkg''​|median of Kling-Gupta efficiency (MKG in [[start:​hype_file_reference:​info.txt|info.txt]]) for subbasins|//​MEDKGE//​| |''​mdkg''​|median of Kling-Gupta efficiency (MKG in [[start:​hype_file_reference:​info.txt|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 [[start:​hype_file_reference:​info.txt|info.txt]])|//​AVARB//​| |''​mare''​|average of absolute relative bias for subbasins (Note: fraction. not %) (MAR in [[start:​hype_file_reference:​info.txt|info.txt]])|//​AVARB//​|
-|''​mnr''​|median of normalised RMSE for subbasins|//​MEDNE//​|+|''​mdnr''​|median of normalised RMSE for subbasins|//​MEDNE//​|
 |''​mnw''​|average of Nash-Sutcliffe efficiencies adjusted for bias for subbasins|//​AVNSEW//​| |''​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//​|
 </​sortable>​ </​sortable>​
  
Line 89: Line 101:
 |//​c//​|computed value| |//​c//​|computed value|
 |//​r//​|recorded 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| |//​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| |//​mi//​|number of values in a time series of a station|
Line 99: Line 113:
 |//​cd//​|standard deviation of <m> c_{i}, i=1,mi </m> for a station| |//​cd//​|standard deviation of <m> c_{i}, i=1,mi </m> for a station|
 |//​rd//​|standard deviation of <m> r_{i}, i=1,mi </m> for a station| |//​rd//​|standard deviation of <m> r_{i}, i=1,mi </m> for a station|
 +|//​cmax//​|maximum value of <m> c_{i}, i=1,mi </m> for a station|
 +|//​rmax//​|maximum value of <m> r_{i}, i=1,mi </m> for a station|
 +|//​cmin//​|minimum value of <m> c_{i}, i=1,mi </m> for a station|
 +|//​rmin//​|minimum value of <m> r_{i}, i=1,mi </m> for a station|
 +|//​w//​|weight of station|
 </​sortable>​ </​sortable>​
  
Line 110: Line 129:
  
 <m> xd = sqrt{{1/mi} sum{i=1}{mi}{{x_{i}}^2}-xm^2} </​m> ​ //x=r// or //c// <m> xd = sqrt{{1/mi} sum{i=1}{mi}{{x_{i}}^2}-xm^2} </​m> ​ //x=r// or //c//
 +
 +Natural logaritm of value:
 +
 +<m> xl = LN(x) </​m> ​ //x=r// or //c// or //rm// or //cm//, //x>0//
  
  
Line 152: Line 175:
 Kling-Gupta efficiency (//KGE//): Kling-Gupta efficiency (//KGE//):
  
-<m> KGE = 1-sqrt{(CC-1)^2+(cd/​rd-1)^2+(cm/​rm-1)^2} </m>+<m> KGE = 1-sqrt{(CC-1)^2+(cd/​rd-1)^2+(cm/​rm-1)^2} </​m> ​ //​cm>​0//​ and //rm>0// and //cd>0// and //rd>0//
  
 Pearson correlation coefficient,​ Kling-Gupta efficiency part 1 (//CC//): Pearson correlation coefficient,​ Kling-Gupta efficiency part 1 (//CC//):
Line 180: Line 203:
 Nash-Sutcliffe Efficiency adjusted for bias (//NSEW//). Introduced in Lindström (2016): Nash-Sutcliffe Efficiency adjusted for bias (//NSEW//). Introduced in Lindström (2016):
  
-<m> NSEW = NSE-Bias^2/rd^2 </m>+<m> NSEW = NSE+Bias^2/rd^2 </m>
  
 where  where 
Line 194: Line 217:
 <m> n_{2} </m> = number of compared pairs that ties in the recorded values <m> n_{2} </m> = number of compared pairs that ties in the recorded values
  
 +Scaled bias (//​ScBias//​):​
  
 +<m> ScBias = {sum{i=1}{mi}{delim{|}{{(c_{i}-r_{i})}/​{(c_{i}+r_{i})}}{|}}}/​mi </m>
 +
 +Scaled KGE (//​SCKGE//​):​
 +
 +<m> SCKGE = KGE/{2-KGE} </m>
  
 ====Criteria equations for a model domain (several stations)==== ====Criteria equations for a model domain (several stations)====
  
-Average Nash-Sutcliffe efficiency (//​AVNSE//​):​+Average Nash-Sutcliffe efficiency (//​AVNSE//​): ​
  
-<m> AVNSE = {1/mj sum{j=1}{mj}{NSE_{j}}} </m>+//AVNSE// arithmetric mean 
 + 
 +<m> AVNSE = {1/mj sum{j=1}{mj}{NSE_{j}}} </m>  
 + 
 +or //AVNSE// weighted average 
 + 
 +<m> AVNSE = {sum{j=1}{mj}{w_{j}*NSE_{j}}}/​{sum{j=1}{mj}{w_{j}}} </m>
  
 Median Nash-Sutcliffe efficiency (//​MEDNSE//​):​ Median Nash-Sutcliffe efficiency (//​MEDNSE//​):​
Line 213: Line 248:
  
 <m> REGNSE = 1-{sum{ij=1}{mij}{(c_{ij}-r_{ij})^2}}/​{sum{ij=1}{mij}{(r_{ij}-{1/​mij} sum{ij=1}{mij}{r_{ij}})^2}} </m> <m> REGNSE = 1-{sum{ij=1}{mij}{(c_{ij}-r_{ij})^2}}/​{sum{ij=1}{mij}{(r_{ij}-{1/​mij} sum{ij=1}{mij}{r_{ij}})^2}} </m>
 +
 +Average Nash-Sutcliffe efficiency adjusted for bias (//​AVNSEW//​):​
 +
 +//AVNSEW// arithmetric mean
 +
 +<m> AVNSEW = {1/mj sum{j=1}{mj}{NSEW_{j}}} </m>
 +
 +or //AVNSEW// weighted average
 +
 +<m> AVNSEW = {sum{j=1}{mj}{w_{j}*NSEW_{j}}}/​{sum{j=1}{mj}{w_{j}}} </m>
  
 Average efficiency with coefficient a (//AVRA//): Average efficiency with coefficient a (//AVRA//):
 +
 +//AVRA// arithmetric mean
  
 <m> AVRA = {1/mj sum{j=1}{mj}{RA_{j}}} </m> <m> AVRA = {1/mj sum{j=1}{mj}{RA_{j}}} </m>
 +
 +or //AVRA// weighted average
 +
 +<m> AVRA = {sum{j=1}{mj}{w_{j}*RA_{j}}}/​{sum{j=1}{mj}{w_{j}}} </m>
  
 Median efficiency with coefficient a (//​MEDRA//​):​ Median efficiency with coefficient a (//​MEDRA//​):​
Line 231: Line 282:
  
 Average relative bias (//AVRB//): Average relative bias (//AVRB//):
 +
 +//AVRB// arithmetric mean
  
 <m> AVRB = {1/mj sum{j=1}{mj}{RB_{j}}} </m> <m> AVRB = {1/mj sum{j=1}{mj}{RB_{j}}} </m>
 +
 +or //AVRB// weighted average
 +
 +<m> AVRB = {sum{j=1}{mj}{w_{j}*RB_{j}}}/​{sum{j=1}{mj}{w_{j}}} </m>
  
 Regional relative bias (//​REGRB//​):​ Regional relative bias (//​REGRB//​):​
Line 243: Line 300:
  
 Average Kling-Gupta efficiency (//​AVKGE//​):​ Average Kling-Gupta efficiency (//​AVKGE//​):​
 +
 +//AVKGE// arithmetric mean
  
 <m> AVKGE = {1/mj sum{j=1}{mj}{KGE_{j}}} </m> <m> AVKGE = {1/mj sum{j=1}{mj}{KGE_{j}}} </m>
 +
 +or //AVKGE// weighted average
 +
 +<m> AVKGE = {sum{j=1}{mj}{w_{j}*KGE_{j}}}/​{sum{j=1}{mj}{w_{j}}} </m>
  
 Median Kling-Gupta efficiency (//​MEDKGE//​):​ Median Kling-Gupta efficiency (//​MEDKGE//​):​
  
 <m> MEDKGE = median delim{lbrace}{{KGE_{j}},​{j=1..mj}}{rbrace} </m> <m> MEDKGE = median delim{lbrace}{{KGE_{j}},​{j=1..mj}}{rbrace} </m>
 +
 +Average scaled Kling-Gupta efficiency (//​ASCKGE//​):​
 +
 +//ASCKGE// arithmetric mean
 +
 +<m> ASCKGE = {1/mj sum{j=1}{mj}{SCKGE_{j}}} </m>
 +
 +or //ASCKGE// weighted average
 +
 +<m> ASCKGE = {sum{j=1}{mj}{w_{j}*SCKGE_{j}}}/​{sum{j=1}{mj}{w_{j}}} </m>
 +
 +Spatial root mean square error (//​SPATRMSE//​):​
 +
 +<m> SPATRMSE = sqrt{{1/mj sum{j=1}{mj}{({cm_{j}}-{rm_{j}})^2}}} </m>
  
 Median of Normalised root mean square error (//​MEDNE//​):​ Median of Normalised root mean square error (//​MEDNE//​):​
Line 255: Line 332:
  
 Average of absolute relative bias (//​AVARB//​):​ Average of absolute relative bias (//​AVARB//​):​
 +
 +//AVARB// arithmetric mean
  
 <m> AVARB = {1/mj sum{j=1}{mj}{delim{|}{RB_{j}}{|}}} </m> <m> AVARB = {1/mj sum{j=1}{mj}{delim{|}{RB_{j}}{|}}} </m>
 +
 +or //AVARB// weighted average
 +
 +<m> AVARB = {sum{j=1}{mj}{w_{j}*{delim{|}{RB_{j}}{|}}}}/​{sum{j=1}{mj}{w_{j}}} </m>
  
 Average Pearson correlation coefficient (//AVCC//): Average Pearson correlation coefficient (//AVCC//):
 +
 +//AVCC// arithmetric mean
  
 <m> AVCC = {1/mj sum{j=1}{mj}{CC_{j}}} </m> <m> AVCC = {1/mj sum{j=1}{mj}{CC_{j}}} </m>
 +
 +or //AVCC// weighted average
 +
 +<m> AVCC = {sum{j=1}{mj}{w_{j}*CC_{j}}}/​{sum{j=1}{mj}{w_{j}}} </m>
  
 Average relative error of standard deviation (//​AVRSB//​):​ Average relative error of standard deviation (//​AVRSB//​):​
 +
 +//AVRSB// arithmetric mean
  
 <m> AVRSB = {1/mj sum{j=1}{mj}{RS_{j}}} </m> <m> AVRSB = {1/mj sum{j=1}{mj}{RS_{j}}} </m>
 +
 +or //AVRSB// weighted average
 +
 +<m> AVRSB = {sum{j=1}{mj}{w_{j}*RS_{j}}}/​{sum{j=1}{mj}{w_{j}}} </m>
  
 Average Kendalls rank correlation coefficient (//​AVTAU//​):​ Average Kendalls rank correlation coefficient (//​AVTAU//​):​
 +
 +//AVTAU// arithmetric mean
  
 <m> AVTAU = {1/mj sum{j=1}{mj}{TAU_{j}}} </m> <m> AVTAU = {1/mj sum{j=1}{mj}{TAU_{j}}} </m>
 +
 +or //AVTAU// weighted average
 +
 +<m> AVTAU = {sum{j=1}{mj}{w_{j}*TAU_{j}}}/​{sum{j=1}{mj}{w_{j}}} </m>
  
 Regional mean absolute error (//​REGMAE//​):​ Regional mean absolute error (//​REGMAE//​):​
Line 274: Line 375:
 <m> REGMAE = {sum{ij=1}{mij}{delim{|}{c_{ij}-r_{ij}}{|}}}/​mij </m> <m> REGMAE = {sum{ij=1}{mij}{delim{|}{c_{ij}-r_{ij}}{|}}}/​mij </m>
  
-Average Nash-Sutcliffe efficiency adjusted for bias (//AVNSEW//):+Spatial mean absolute scaled ​bias on log transformed values ​(//SPATASB//): 
 + 
 +<m> SPATASB = {sum{j=1}{mj}{delim{|}{{cml_{j}-rml_{j}}/​{cml_{j}+rml_{j}}}{|}}}/​{mj} </m>
  
-<m> AVNSEW = {1/mj sum{j=1}{mj}{NSEW_{j}}} </m> 
  
 ==== References ==== ==== References ====
 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. 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.
  
start/hype_file_reference/info.txt/criteria_equations.1566997029.txt.gz · Last modified: 2023/11/16 14:28 (external edit)