Normalized Mean Error (percent): This performance statistic is used to normalize the mean

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

positive.

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)

PM 2.5: MFE = 50% ~ 85%, MFB = -55% ~ +60% (> 5 ug/m3)

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