Page 378 - Fundamentals of Air Pollution 3E

V. Model Performance, Accuracy, and Utilization 333
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A measure of the variability of the differences is the variance S , which is
the second moment of the distribution of these differences:

The square root of the variance is the standard deviation.
The mean absolute error MAE is

The mean square error MSB is

The root-mean-square error is the square root of the mean square error. Note
that since the root-mean-square error involves the square of the differences,
outliers have more influence on this statistic than on the mean absolute
error.
The fractional error FE (41) is

The mean fractional error MFE is

The fractional error is logarithmically unbiased; that is, an M which is k
times E produces the same magnitude fractional error (but of opposite sign)
as an M which is I Ik times E.
In addition to analyzing the residuals, it may be desirable to determine
the degree of agreement between sets of paired measurements and esti-
mates. The linear correlation coefficient r EM is

The slope b and intercept a of the least-squares line of best fit of the
relation M = a + bE are

Intercept:

Slope:

The temporal correlation coefficient at each monitoring location can be
calculated by analysis of the paired values over a time period of record.
The spatial correlation coefficient at a given time can be calculated by
analysis of the paired values from each station. For the spatial correlation