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Documentation of the Evaluation of CALPUFF and Other Long ...

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Table ES‐2. ATMES‐II spatial <strong>and</strong> global statistical metrics.<br />

Statistical Metric Definition<br />

Spatial Statistics<br />

Figure <strong>of</strong> Merit in Space<br />

(FMS)<br />

AM<br />

∩ AP<br />

FMS = × 100%<br />

AM<br />

∪ AP<br />

False Alarm Rate (FAR)<br />

Probability <strong>of</strong> Detection<br />

(POD)<br />

Threat Score (TS)<br />

where,<br />

Factor <strong>of</strong> Exceedance<br />

(FOEX)<br />

Factor <strong>of</strong> α (FA2 <strong>and</strong> FA5)<br />

Normalized Mean Squared<br />

Error (NMSE)<br />

Pearson’s Correlation<br />

Coefficient (PCC or R)<br />

⎛ a ⎞<br />

FAR = ⎜ ⎟×<br />

100%<br />

⎝ a + b ⎠<br />

⎛ b ⎞<br />

POD = ⎜ ⎟×<br />

100%<br />

⎝ b + d ⎠<br />

⎛ b ⎞<br />

TS = ⎜ ⎟×<br />

100%<br />

⎝ a + b + d ⎠<br />

• “a” represents <strong>the</strong> number <strong>of</strong> times a condition that has<br />

been forecast, but was not observed (false alarm)<br />

• “b” represents <strong>the</strong> number <strong>of</strong> times <strong>the</strong> condition<br />

was correctly forecasted (hits)<br />

• “c” represents <strong>the</strong> number <strong>of</strong> times <strong>the</strong><br />

nonoccurrence <strong>of</strong> <strong>the</strong> condition is correctly<br />

forecasted (correct negative); <strong>and</strong><br />

• “d” represents <strong>the</strong> number <strong>of</strong> times that <strong>the</strong><br />

condition was observed but not forecasted (miss).<br />

Global Statistics<br />

⎡ N ( P ) ⎤<br />

i > Nii<br />

FOEX = ⎢ − 0 . 5⎥<br />

× 100%<br />

⎣ N ⎦<br />

⎡ N(<br />

y − y0<br />

= [ x − x0]<br />

α)<br />

⎤<br />

FAα<br />

=<br />

⎢<br />

⎥<br />

× 100<br />

⎣ N ⎦<br />

( ) 2<br />

1 = ∑ i − i M P<br />

NMSE<br />

N PM<br />

R =<br />

⎡<br />

⎢<br />

⎣<br />

∑<br />

∑<br />

i<br />

7<br />

( M − M ) • ( P − P)<br />

i<br />

2 ⎤⎡<br />

2 ⎤<br />

( M i − M ) ⎥⎢<br />

∑(<br />

Pi<br />

− P)<br />

⎥⎦<br />

Fraction Bias (FB) FB = 2 B ( P + M )<br />

Kolmogorov‐Smirnov (KS)<br />

Parameter<br />

⎦⎣<br />

( M ) C(<br />

P )<br />

KS = MaxC<br />

−<br />

2<br />

RANK RANK = R + ( 1−<br />

FB / 2 ) + FMS / 100+<br />

( 1−<br />

KS / 100)<br />

k<br />

i<br />

k<br />

Perfect<br />

Score<br />

100%<br />

0%<br />

100%<br />

100%<br />

0%<br />

100%<br />

0%<br />

1.0<br />

0%<br />

0%<br />

4.0

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