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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) |
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|''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> | ||
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<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> | ||
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|''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//| | ||
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|''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> | ||
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|//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| | ||
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|//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> | ||
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<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// | ||
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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//): | ||
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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 | ||
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<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//): | ||
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<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//): | ||
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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//): | ||
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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//): | ||
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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//): | ||
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<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. | ||