This performance statistic is used to normalize the mean
Normalized Mean Error (percent):
error relative to the observations. This statistic averages the difference (model - observed) over
the sum of observed values. Normalized mean error is a useful model performance indicator
because it avoids over inflating the observed range of values.
Mean Fractional Error (percent): Normalized error can become very large when a minimum
threshold is not used. Therefore fractional error is used as a substitute. It is similar to the
fractional bias except the absolute value of the difference is used so that the error is always
Correlation Coefficient (R2): This performance statistic measures the degree to which two
variables are linearly related. A correlation coefficient of 1 indicates a perfect linear
relationship; whereas a correlation coefficient of 0 means that there is no linear relationship
between the variables.
1. Boylan, J., VISTAS, “PM Model Performance Goal and Criteria”, National RPO Modeling
Meeting, Denver, CO, 2005a.
• Based on benchmarking with a combination of data from a number of PM modeling
studies (SAMI, VISTAS, WRAP, EPA, MANE-NU, EPRI, and Midwest RPO).
Proposed performance goals (close to best achievable) and performance criteria
(acceptable) for these metrics and showed where the modeling studies fall for the
various components of PM.
• Proposed to use mean fractional bias (MFB) and mean fractional error (MFE) as the
standard performance metrics.
Goal: MFE <= 50%, MFB <= +-30%
Criteria: MFE <= 75%, MFB <= +-60%
Less abundant species should have
less stringent goal & criteria
• Proposed to use asymptotically approaching goals & criteria when data are greater than
2.5 um, approaching +200% MFE and +-200% MFB for extreme small model &
observed data (formula of logarithmic MFB & MFE are proposed)
• Based on combined modeling studies described above, for more abundant conditions,
MFE and MFB are typical in the range of
Sulfate: MFE = 30% ~ 77%, MFB = -45% ~ +51% (> 2 ug/m3)
Nitrate: MFE = 55% ~ 125%, MFB = +3% ~ +82% (> 1 ug/m3)
Organic: MFE = 35% ~ 95%, MFB = -70% ~ +35% (> 1.5 ug/m3)
EC: MFE = 50% ~ 95%, MFB = -45% ~ +50% (> 0.5 ug/m3)
PM2.5: MFE = 50% ~ 85%, MFB = -55% ~ +60% (> 5 ug/m3)
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