Normalized error can become very large when a
Mean Fractional Error (percent):
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.
Normalized Mean Bias (percent): This performance statistic is used as a normalization
to facilitate a range of concentration magnitudes. This statistic averages the difference
(model - observed) over the sum of observed values. Normalized mean bias is a useful
model performance indicator because it avoids over inflating the observed range of values.
Normalized Mean Error (percent): This performance statistic is used as a
normalization of the mean error to facilitate a range of concentration magnitudes. This
statistic averages the difference (model - observed) over the sum of observed values.
Normalized mean error is a useful model performance indicator because it avoid over
inflating the observed range of values.
Averaging Times: Note that units of time associated with model and observed
concentrations can be days (i.e., usually for particulate matter and its species), hours (i.e., usually
for species with continuous measurements, like ozone) or sometimes weeks (CASTNet filter pack
measurements). Also note that the preceding metrics may not be meaningful if the number of
modeled days with monitored data is limited at a site.
Since modeling for the PM2.5 NAAQS and regional haze will likely require modeling
different times of year, season-specific statistics and graphic displays are helpful for evaluating
and diagnosing model performance. Statistics and graphics can be averaged for various time
scales. For example, statistical metrics and scatterplots can show daily averaged ambientmodeled
pairs, monthly averaged pairs, quarterly (or seasonal averaged) pairs, or annual average
pairs. Each of these averaging times can provide useful information. We recommend a range of
different averaging times for annual or seasonal modeling. At a minimum, States should examine
daily averaged pairs and seasonal (or quarterly) averaged pairs. It should be noted that statistics
and plots tend to look “better” as the averaging time increases from daily to monthly to quarterly
to annual. As such, daily pairs should always be examined to ensure a detailed look at model
performance on the time scale of the FRM and STN measurements (24-hour average).
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