Available Metrics#
The metrics currently built into TEEHR are listed in the table below.
Please note that some are still in development and planned for inclusion in future versions.
To download a pdf of the equations corresponding to the metrics listed in the table, see:
pdf
Available |
Description |
Short Name |
Equation |
|---|---|---|---|
Mean Error |
\(Mean\ Error\) |
\(\frac{\sum(sec-prim)}{count}\) |
|
Relative Bias |
\(Relative\ Bias\) |
\(\frac{\sum(sec-prim)}{\sum(prim)}\) |
|
Multiplicative Bias |
\(Mult.\ Bias\) |
\(\frac{\mu_{sec}}{\mu_{prim}}\) |
|
Mean Square Error |
\(MSE\) |
\(\frac{\sum(sec-prim)^2}{count}\) |
|
Root Mean Square Error |
\(RMSE\) |
\(\sqrt{\frac{\sum(sec-prim)^2}{count}}\) |
|
Mean Absolute Error |
\(MAE\) |
\(\frac{\sum|sec-prim|}{count}\) |
|
Mean Absolute Relative Error |
\(Relative\ MAE\) |
\(\frac{\sum|sec-prim|}{\sum(prim)}\) |
|
Pearson Correlation Coefficient |
\(r\) |
\(r(sec, prim)\) |
|
Coefficient of Determination |
\(r^2\) |
\(r(sec, prim)^2\) |
|
Nash-Sutcliffe Efficiency |
\(NSE\) |
\(1-\frac{\sum(prim-sec)^2}{\sum(prim-\mu_{prim}^2)}\) |
|
Normalized Nash-Sutcliffe Efficiency |
\(NNSE\) |
\(\frac{1}{(2-NSE)}\) |
|
Kling Gupta Efficiency - original |
\(KGE\) |
\(1-\sqrt{(r(sec, prim)-1)^2+(\frac{\sigma_{sec}}{\sigma_{prim}}-1)^2+(\frac{\mu_{sec}}{\mu_{sec}/\mu_{prim}}-1)^2}\) |
|
Kling Gupta Efficiency - modified 1 (2012) |
\(KGE'\) |
\(1-\sqrt{(r(sec, prim)-1)^2+(\frac{\sigma_{sec}/\mu_{sec}}{\sigma_{prim}/\mu_{prim}}-1)^2+(\frac{\mu_{sec}}{\mu_{sec}/\mu_{prim}}-1)^2}\) |
|
Kling Gupta Efficiency - modified 2 (2021) |
\(KGE''\) |
\(1-\sqrt{(r(sec, prim)-1)^2+(\frac{\sigma_{sec}}{\sigma_{prim}}-1)^2+\frac{(\mu_{sec}-\mu_{prim})^2}{\sigma_{prim}^2}}\) |
|
Coming Soon |
Nash-Sutcliffe Efficiency of Log Flows |
\(NSE(log)\) |
\(1-\frac{\sum(log(prim)-log(sec))^2}{\sum(log(prim)-\mu(log(prim)))^2}\) |
Coming Soon |
Annual Peak Flow Relative Bias |
\(Ann\ PF\ Bias\) |
\(\frac{\sum(ann.\ peak_{sec}-ann.\ peak_{prim})}{\sum(ann.\ peak_{prim})}\) |
Coming Soon |
Spearman Rank Correlation Coefficient |
\(r_s\) |
\(1-\frac{6*\sum|rank_{prim}-rank_{sec}|^2}{count(count^2-1)}\) |
Coming Soon |
Flow Duration Curve Slope Error |
\(Slope\ FDC\ Error\) |
\(\frac{q66_{sec}-q33_{sec}}{33}-\frac{q66_{prim}-q33_{prim}}{33}\) |
Coming Soon |
Event Peak Flow Relative Bias |
\(Peak\ Bias\) |
\(\frac{\sum(peak_{sec}-peak_{prim})}{\sum(peak_{prim})}\) |
Coming Soon |
Event Peak Flow Timing Error |
\(Peak\ Time\ Error\) |
\(\frac{\sum(peak\ time_{sec}-peak\ time_{prim})}{count}\) |
Coming Soon |
Baseflow Index Error |
\(BFI\ Error\) |
\(\frac{\frac{\mu(baseflow_{sec})}{\mu(sec)}-\frac{\mu(baseflow_{prim})}{\mu(prim)}}{\frac{\mu(baseflow_{prim})}{\mu(prim)}}\) |
Coming Soon |
Rising Limb Density Error |
\(RLD\ Error\) |
\(\frac{count(rising\ limb\ events_{sec})}{count(rising\ limb\ timesteps_{sec})}-\frac{count(rising\ limb\ events_{prim})}{count(rising\ limb\ timesteps_{prim})}\) |
Coming Soon |
Mean Square Error Skill Score (generalized reference) |
\(MSESS\) |
\(1-\frac{\sum(prim-sec)^2}{\sum(prim-reference)^2}\) |
Coming Soon |
Runoff Ratio Error |
\(RR\ Error\) |
\(abs\left\|\frac{\mu(volume_{sec})}{\mu(precip\ volume)}-\frac{\mu(volume_{prim})}{\mu(precip\ volume)}\right\|\) |
Coming Soon |
False Alarm Ratio |
\(FAR\) |
\(\frac{n_{FP}}{n_{TP}+n_{FP}}\) |
Coming Soon |
Probability of Detection |
\(POD\) |
\(\frac{n_{TP}}{n_{TP}+n_{FN}}\) |
Coming Soon |
Probability of False Detection |
\(POFD\) |
\(\frac{n_{FP}}{n_{TN}+n_{FP}}\) |
Coming Soon |
Critical Success Index (Threat Score) |
\(CSI\) |
\(\frac{n_{TP}}{n_{TP}+n_{FN}+n_{FP}}\) |
Coming Soon |
Brier Score |
\(BS\) |
\(\frac{\sum(sec\ ensemble\ prob-prim\ outcome)^2}{n}\) |
Coming Soon |
Brier Skill Score |
\(BSS\) |
\(1-\frac{BS}{BS_{ref}}\) |
Coming Soon |
Continuous Ranked Probability Skill Score |
\(CRPSS\) |
\(1-\frac{CRPS}{CRPS_{ref}}\) |