22Available Metrics
33=================
44
5- The metrics currently built into TEEHR are listed in the table below.
5+ The metrics currently built into TEEHR are listed in the tables below.
66Please note that some are still in development and planned for inclusion in future versions.
7- To download a pdf of the equations corresponding to the metrics listed in the table, see:
8- :download: `pdf <TEEHR Metrics_27May2024.pdf >`
97
8+ Signatures
9+ ==========
10+
11+ Signatures operate on a single field to characterize timeseries properties.
1012
1113.. list-table ::
1214 :header-rows: 1
@@ -16,137 +18,231 @@ To download a pdf of the equations corresponding to the metrics listed in the ta
1618 - Description
1719 - Short Name
1820 - Equation
21+ - API Reference
22+ * - :material-regular: `check;1.5em;sd-text-success `
23+ - Average
24+ - :math: `Average`
25+ - :math: `\frac {\sum (prim)}{count}`
26+ - `Average <https://rtiinternational.github.io/teehr/api/generated/teehr.SignatureMetrics.html#teehr.SignatureMetrics.Average >`__
27+ * - :material-regular: `check;1.5em;sd-text-success `
28+ - Count
29+ - :math: `Count`
30+ - :math: `count`
31+ - `Count <https://rtiinternational.github.io/teehr/api/generated/teehr.SignatureMetrics.html#teehr.SignatureMetrics.Count >`__
32+ * - :material-regular: `check;1.5em;sd-text-success `
33+ - Flow Duration Curve Slope
34+ - :math: `FDC\ Slope`
35+ - :math: `\frac {q85 -q25 }{p85 -p25 }`
36+ - `Flow Duration Curve Slope <https://rtiinternational.github.io/teehr/api/generated/teehr.SignatureMetrics.html#teehr.SignatureMetrics.FlowDurationCurveSlope >`__
37+ * - :material-regular: `check;1.5em;sd-text-success `
38+ - Max Value Time
39+ - :math: `Max\ Value\ Time`
40+ - :math: `peak\ time_{prim}`
41+ - `Max Value Time <https://rtiinternational.github.io/teehr/api/generated/teehr.SignatureMetrics.html#teehr.SignatureMetrics.MaxValueTime >`__
42+ * - :material-regular: `check;1.5em;sd-text-success `
43+ - Maximum
44+ - :math: `Max`
45+ - :math: `max(prim)`
46+ - `Maximum <https://rtiinternational.github.io/teehr/api/generated/teehr.SignatureMetrics.html#teehr.SignatureMetrics.Maximum >`__
47+ * - :material-regular: `check;1.5em;sd-text-success `
48+ - Minimum
49+ - :math: `Min`
50+ - :math: `min(prim)`
51+ - `Minimum <https://rtiinternational.github.io/teehr/api/generated/teehr.SignatureMetrics.html#teehr.SignatureMetrics.Minimum >`__
52+ * - :material-regular: `check;1.5em;sd-text-success `
53+ - Sum
54+ - :math: `Sum`
55+ - :math: `\sum (prim)`
56+ - `Sum <https://rtiinternational.github.io/teehr/api/generated/teehr.SignatureMetrics.html#teehr.SignatureMetrics.Sum >`__
57+ * - :material-regular: `check;1.5em;sd-text-success `
58+ - Variance
59+ - :math: `Variance`
60+ - :math: `\sigma ^2 _{prim}`
61+ - `Variance <https://rtiinternational.github.io/teehr/api/generated/teehr.SignatureMetrics.html#teehr.SignatureMetrics.Variance >`__
62+
63+
64+ Deterministic Metrics
65+ =====================
66+
67+ Deterministic metrics compare two timeseries, typically primary ("observed") vs. secondary ("modeled") values.
68+
69+ .. list-table ::
70+ :header-rows: 1
71+ :class: metrics-table
72+
73+ * - Available
74+ - Description
75+ - Short Name
76+ - Equation
77+ - API Reference
1978 * - :material-regular: `check;1.5em;sd-text-success `
2079 - Mean Error
2180 - :math: `Mean\ Error`
2281 - :math: `\frac {\sum (sec-prim)}{count}`
82+ - `Mean Error <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.MeanError >`__
2383 * - :material-regular: `check;1.5em;sd-text-success `
2484 - Relative Bias
2585 - :math: `Relative\ Bias`
2686 - :math: `\frac {\sum (sec-prim)}{\sum (prim)}`
87+ - `Relative Bias <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.RelativeBias >`__
2788 * - :material-regular: `check;1.5em;sd-text-success `
2889 - Multiplicative Bias
2990 - :math: `Mult.\ Bias`
3091 - :math: `\frac {\mu _{sec}}{\mu _{prim}}`
92+ - `Multiplicative Bias <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.MultiplicativeBias >`__
3193 * - :material-regular: `check;1.5em;sd-text-success `
3294 - Mean Square Error
3395 - :math: `MSE`
3496 - :math: `\frac {\sum (sec-prim)^2 }{count}`
97+ - `Mean Square Error <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.MeanSquareError >`__
3598 * - :material-regular: `check;1.5em;sd-text-success `
3699 - Root Mean Square Error
37100 - :math: `RMSE`
38101 - :math: `\sqrt {\frac {\sum (sec-prim)^2 }{count}}`
102+ - `Root Mean Square Error <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.RootMeanSquareError >`__
39103 * - :material-regular: `check;1.5em;sd-text-success `
40104 - Mean Absolute Error
41105 - :math: `MAE`
42106 - :math: `\frac {\sum |sec-prim|}{count}`
107+ - `Mean Absolute Error <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.MeanAbsoluteError >`__
43108 * - :material-regular: `check;1.5em;sd-text-success `
44109 - Mean Absolute Relative Error
45110 - :math: `Relative\ MAE`
46111 - :math: `\frac {\sum |sec-prim|}{\sum (prim)}`
112+ - `Mean Absolute Relative Error <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.MeanAbsoluteRelativeError >`__
47113 * - :material-regular: `check;1.5em;sd-text-success `
48114 - Pearson Correlation Coefficient
49115 - :math: `r`
50116 - :math: `r(sec, prim)`
117+ - `Pearson Correlation Coefficient <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.PearsonCorrelationCoefficient >`__
51118 * - :material-regular: `check;1.5em;sd-text-success `
52119 - Coefficient of Determination
53120 - :math: `r^2 `
54121 - :math: `r(sec, prim)^2 `
122+ - `Coefficient of Determination <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.RSquared >`__
55123 * - :material-regular: `check;1.5em;sd-text-success `
56124 - Nash-Sutcliffe Efficiency
57125 - :math: `NSE`
58126 - :math: `1 -\frac {\sum (prim-sec)^2 }{\sum (prim-\mu _{prim}^2 )}`
127+ - `Nash-Sutcliffe Efficiency <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.NashSutcliffeEfficiency >`__
59128 * - :material-regular: `check;1.5em;sd-text-success `
60129 - Normalized Nash-Sutcliffe Efficiency
61130 - :math: `NNSE`
62131 - :math: `\frac {1 }{(2 -NSE)}`
132+ - `Normalized Nash-Sutcliffe Efficiency <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.NormalizedNashSutcliffeEfficiency >`__
63133 * - :material-regular: `check;1.5em;sd-text-success `
64134 - Kling Gupta Efficiency - original
65135 - :math: `KGE`
66136 - :math: `1 -\sqrt {(r(sec, prim)-1 )^2 +(\frac {\sigma _{sec}}{\sigma _{prim}}-1 )^2 +(\frac {\mu _{sec}}{\mu _{sec}/\mu _{prim}}-1 )^2 }`
137+ - `Kling Gupta Efficiency - original <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.KlingGuptaEfficiency >`__
67138 * - :material-regular: `check;1.5em;sd-text-success `
68139 - Kling Gupta Efficiency - modified 1 (2012)
69140 - :math: `KGE'`
70141 - :math: `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 }`
142+ - `Kling Gupta Efficiency - modified 1 <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.KlingGuptaEfficiencyMod1 >`__
71143 * - :material-regular: `check;1.5em;sd-text-success `
72144 - Kling Gupta Efficiency - modified 2 (2021)
73145 - :math: `KGE''`
74146 - :math: `1 -\sqrt {(r(sec, prim)-1 )^2 +(\frac {\sigma _{sec}}{\sigma _{prim}}-1 )^2 +\frac {(\mu _{sec}-\mu _{prim})^2 }{\sigma _{prim}^2 }}`
75- * - `Coming Soon `
76- - Nash-Sutcliffe Efficiency of Log Flows
77- - :math: `NSE(log)`
78- - :math: `1 -\frac {\sum (log(prim)-log(sec))^2 }{\sum (log(prim)-\mu (log(prim)))^2 }`
79- * - `Coming Soon `
80- - Annual Peak Flow Relative Bias
147+ - `Kling Gupta Efficiency - modified 2 <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.KlingGuptaEfficiencyMod2 >`__
148+ * - :material-regular: `check;1.5em;sd-text-success `
149+ - Annual Peak Relative Bias
81150 - :math: `Ann\ PF\ Bias`
82151 - :math: `\frac {\sum (ann.\ peak_{sec}-ann.\ peak_{prim})}{\sum (ann.\ peak_{prim})}`
83- * - `Coming Soon `
152+ - `Annual Peak Relative Bias <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.AnnualPeakRelativeBias >`__
153+ * - :material-regular: `check;1.5em;sd-text-success `
84154 - Spearman Rank Correlation Coefficient
85155 - :math: `r_s`
86156 - :math: `1 -\frac {6 *\sum |rank_{prim}-rank_{sec}|^2 }{count(count^2 -1 )}`
157+ - `Spearman Rank Correlation Coefficient <https://rtiinternational.github.io/teehr/api/generated/teehr.DeterministicMetrics.html#teehr.DeterministicMetrics.SpearmanCorrelation >`__
87158 * - `Coming Soon `
88159 - Flow Duration Curve Slope Error
89160 - :math: `Slope\ FDC\ Error`
90161 - :math: `\frac {q66 _{sec}-q33 _{sec}}{33 }-\frac {q66 _{prim}-q33 _{prim}}{33 }`
162+ - `N/A `
91163 * - `Coming Soon `
92164 - Event Peak Flow Relative Bias
93165 - :math: `Peak\ Bias`
94166 - :math: `\frac {\sum (peak_{sec}-peak_{prim})}{\sum (peak_{prim})}`
167+ - `N/A `
95168 * - `Coming Soon `
96169 - Event Peak Flow Timing Error
97170 - :math: `Peak\ Time\ Error`
98171 - :math: `\frac {\sum (peak\ time_{sec}-peak\ time_{prim})}{count}`
172+ - `N/A `
99173 * - `Coming Soon `
100174 - Baseflow Index Error
101175 - :math: `BFI\ Error`
102176 - :math: `\frac {\frac {\mu (baseflow_{sec})}{\mu (sec)}-\frac {\mu (baseflow_{prim})}{\mu (prim)}}{\frac {\mu (baseflow_{prim})}{\mu (prim)}}`
177+ - `N/A `
103178 * - `Coming Soon `
104179 - Rising Limb Density Error
105180 - :math: `RLD\ Error`
106181 - :math: `\frac {count(rising\ limb\ events_{sec})}{count(rising\ limb\ timesteps_{sec})}-\frac {count(rising\ limb\ events_{prim})}{count(rising\ limb\ timesteps_{prim})}`
182+ - `N/A `
107183 * - `Coming Soon `
108184 - Mean Square Error Skill Score (generalized reference)
109185 - :math: `MSESS`
110186 - :math: `1 -\frac {\sum (prim-sec)^2 }{\sum (prim-reference)^2 }`
187+ - `N/A `
111188 * - `Coming Soon `
112189 - Runoff Ratio Error
113190 - :math: `RR\ Error`
114191 - :math: `abs\left \|\frac {\mu (volume_{sec})}{\mu (precip\ volume)}-\frac {\mu (volume_{prim})}{\mu (precip\ volume)}\right \|`
192+ - `N/A `
115193 * - `Coming Soon `
116194 - False Alarm Ratio
117195 - :math: `FAR`
118196 - :math: `\frac {n_{FP}}{n_{TP}+n_{FP}}`
197+ - `N/A `
119198 * - `Coming Soon `
120199 - Probability of Detection
121200 - :math: `POD`
122201 - :math: `\frac {n_{TP}}{n_{TP}+n_{FN}}`
202+ - `N/A `
123203 * - `Coming Soon `
124204 - Probability of False Detection
125205 - :math: `POFD`
126206 - :math: `\frac {n_{FP}}{n_{TN}+n_{FP}}`
207+ - `N/A `
127208 * - `Coming Soon `
128209 - Critical Success Index (Threat Score)
129210 - :math: `CSI`
130211 - :math: `\frac {n_{TP}}{n_{TP}+n_{FN}+n_{FP}}`
212+ - `N/A `
213+
214+
215+ Probabilistic Metrics
216+ =====================
217+
218+ Probabilistic metrics compare a value against a distribution of predicted values, such as ensemble forecasts.
219+
220+ .. list-table ::
221+ :header-rows: 1
222+ :class: metrics-table
223+
224+ * - Available
225+ - Description
226+ - Short Name
227+ - Equation
228+ - API Reference
229+ * - :material-regular: `check;1.5em;sd-text-success `
230+ - Continuous Ranked Probability Score
231+ - :math: `CRPS`
232+ - :math: `\int _{-\infty }^{\infty } (F(x) - \mathbf {1 }_{x \geq y})^2 dx`
233+ - `Continuous Ranked Probability Score <https://rtiinternational.github.io/teehr/api/generated/teehr.ProbabilisticMetrics.html#teehr.ProbabilisticMetrics.ContinuousRankedProbabilityScore >`__
131234 * - `Coming Soon `
132235 - Brier Score
133236 - :math: `BS`
134237 - :math: `\frac {\sum (sec\ ensemble\ prob-prim\ outcome)^2 }{n}`
238+ - `N/A `
135239 * - `Coming Soon `
136240 - Brier Skill Score
137241 - :math: `BSS`
138242 - :math: `1 -\frac {BS}{BS_{ref}}`
243+ - `N/A `
139244 * - `Coming Soon `
140245 - Continuous Ranked Probability Skill Score
141246 - :math: `CRPSS`
142247 - :math: `1 -\frac {CRPS}{CRPS_{ref}}`
143-
144-
145-
146-
147-
148-
149-
150-
151-
152-
248+ - `N/A `
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