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	$M e a n E r r o r$	$\frac{\sum (s e c - p r i m)}{c o u n t}$
	Relative Bias	$R e l a t i v e B i a s$	$\frac{\sum (s e c - p r i m)}{\sum (p r i m)}$
	Multiplicative Bias	$M u l t . B i a s$	$\frac{μ_{s e c}}{μ_{p r i m}}$
	Mean Square Error	$M S E$	$\frac{\sum (s e c - p r i m)^{2}}{c o u n t}$
	Root Mean Square Error	$R M S E$	$\sqrt{\frac{\sum (s e c - p r i m)^{2}}{c o u n t}}$
	Mean Absolute Error	$M A E$	$\frac{\sum \| s e c - p r i m \|}{c o u n t}$
	Mean Absolute Relative Error	$R e l a t i v e M A E$	$\frac{\sum \| s e c - p r i m \|}{\sum (p r i m)}$
	Pearson Correlation Coefficient	$r$	$r (s e c, p r i m)$
	Coefficient of Determination	$r^{2}$	$r (s e c, p r i m)^{2}$
	Nash-Sutcliffe Efficiency	$N S E$	$1 - \frac{\sum (p r i m - s e c)^{2}}{\sum (p r i m - μ_{p r i m}^{2})}$
	Normalized Nash-Sutcliffe Efficiency	$N N S E$	$\frac{1}{(2 - N S E)}$
	Kling Gupta Efficiency - original	$K G E$	$1 - \sqrt{(r (s e c, p r i m) - 1)^{2} + (\frac{σ_{s e c}}{σ_{p r i m}} - 1)^{2} + (\frac{μ_{s e c}}{μ_{s e c} / μ_{p r i m}} - 1)^{2}}$
	Kling Gupta Efficiency - modified 1 (2012)	$K G E^{'}$	$1 - \sqrt{(r (s e c, p r i m) - 1)^{2} + (\frac{σ_{s e c} / μ_{s e c}}{σ_{p r i m} / μ_{p r i m}} - 1)^{2} + (\frac{μ_{s e c}}{μ_{s e c} / μ_{p r i m}} - 1)^{2}}$
	Kling Gupta Efficiency - modified 2 (2021)	$K G E^{″}$	$1 - \sqrt{(r (s e c, p r i m) - 1)^{2} + (\frac{σ_{s e c}}{σ_{p r i m}} - 1)^{2} + \frac{(μ_{s e c} - μ_{p r i m})^{2}}{σ_{p r i m}^{2}}}$
Coming Soon	Nash-Sutcliffe Efficiency of Log Flows	$N S E (l o g)$	$1 - \frac{\sum (l o g (p r i m) - l o g (s e c))^{2}}{\sum (l o g (p r i m) - μ (l o g (p r i m)))^{2}}$
Coming Soon	Annual Peak Flow Relative Bias	$A n n P F B i a s$	$\frac{\sum (a n n . p e a k_{s e c} - a n n . p e a k_{p r i m})}{\sum (a n n . p e a k_{p r i m})}$
Coming Soon	Spearman Rank Correlation Coefficient	$r_{s}$	$1 - \frac{6 * \sum \| r a n k_{p r i m} - r a n k_{s e c} \|^{2}}{c o u n t (c o u n t^{2} - 1)}$
Coming Soon	Flow Duration Curve Slope Error	$S l o p e F D C E r r o r$	$\frac{q 66_{s e c} - q 33_{s e c}}{33} - \frac{q 66_{p r i m} - q 33_{p r i m}}{33}$
Coming Soon	Event Peak Flow Relative Bias	$P e a k B i a s$	$\frac{\sum (p e a k_{s e c} - p e a k_{p r i m})}{\sum (p e a k_{p r i m})}$
Coming Soon	Event Peak Flow Timing Error	$P e a k T i m e E r r o r$	$\frac{\sum (p e a k t i m e_{s e c} - p e a k t i m e_{p r i m})}{c o u n t}$
Coming Soon	Baseflow Index Error	$B F I E r r o r$	$\frac{\frac{μ (b a s e f l o w_{s e c})}{μ (s e c)} - \frac{μ (b a s e f l o w_{p r i m})}{μ (p r i m)}}{\frac{μ (b a s e f l o w_{p r i m})}{μ (p r i m)}}$
Coming Soon	Rising Limb Density Error	$R L D E r r o r$	$\frac{c o u n t (r i s i n g l i m b e v e n t s_{s e c})}{c o u n t (r i s i n g l i m b t i m e s t e p s_{s e c})} - \frac{c o u n t (r i s i n g l i m b e v e n t s_{p r i m})}{c o u n t (r i s i n g l i m b t i m e s t e p s_{p r i m})}$
Coming Soon	Mean Square Error Skill Score (generalized reference)	$M S E S S$	$1 - \frac{\sum (p r i m - s e c)^{2}}{\sum (p r i m - r e f e r e n c e)^{2}}$
Coming Soon	Runoff Ratio Error	$R R E r r o r$	$a b s ‖ \frac{μ (v o l u m e_{s e c})}{μ (p r e c i p v o l u m e)} - \frac{μ (v o l u m e_{p r i m})}{μ (p r e c i p v o l u m e)} ‖$
Coming Soon	False Alarm Ratio	$F A R$	$\frac{n_{F P}}{n_{T P} + n_{F P}}$
Coming Soon	Probability of Detection	$P O D$	$\frac{n_{T P}}{n_{T P} + n_{F N}}$
Coming Soon	Probability of False Detection	$P O F D$	$\frac{n_{F P}}{n_{T N} + n_{F P}}$
Coming Soon	Critical Success Index (Threat Score)	$C S I$	$\frac{n_{T P}}{n_{T P} + n_{F N} + n_{F P}}$
Coming Soon	Brier Score	$B S$	$\frac{\sum (s e c e n s e m b l e p r o b - p r i m o u t c o m e)^{2}}{n}$
Coming Soon	Brier Skill Score	$B S S$	$1 - \frac{B S}{B S_{r e f}}$
Coming Soon	Continuous Ranked Probability Skill Score	$C R P S S$	$1 - \frac{C R P S}{C R P S_{r e f}}$

Available Metrics#

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