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The mean error (ME) of forecasts (f)
relative to analyses (a) can be defined as
where the over-bar denotes an average over a
large sample in time and space. A perfect score, ME=0, does not
exclude very large errors of opposite signs which cancel each other out. If the mean errors are independent of the
forecast and vary around a fixed value, this constitutes an
“unconditional bias”. If the ME is flow dependent i.e. if the errors are dependent on the
forecast itself or some other parameter, then we are dealing with
systematic errors of “conditional bias”
type; in this case, variations in
the ME from one month to another might not necessarily reflect
changes in the model but in the large-scale flow patterns
(see Figure 60 below).
Figure
60: A convenient way to
differentiate between “unconditional” and
“conditional” biases is to plot scatter diagrams, with
forecasts vs. forecast errors or observations (analyses) vs.
forecast error. From the slope and direction of the scatter
in these diagrams it is also possible to find out if the forecasts
are over- or under-variableIn this case the colder the
forecasts the larger the positive error, the warmer the forecast
the larger the negative error. This implies that cold anomalies are
not cold enough and warm anomalies not warm enough, i.e. the
forecasts are under-variable.
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