Anderson, J. L., 1996: A method of producing and evaluating
probabilistic forecasts from ensemble model integrations. Journal of
Climate, 9 (7), 1518-1530.
The binned probability ensemble (BPE) technique is presented
as a method for producing forecasts of the probability distribution of
a variable using an ensemble of numerical model integrations. The ensemble
forecasts are used to partition the real line into a number of bins, each
of which has an equal probability of containing the "true" forecast. The
method is tested for both a simple low-order dynamical system and a general
circulation model (GCM) forced with observed sea surface temperatures (an
ensemble of Atmospheric Model Intercomparison Project integrations). The
BPE method can also be used to calculate the probability that probabilistic
ensemble forecasts are consistent with the verifying observations. The
method is not sensitive to the fact that the characteristics of the forecast
probability distribution may change drastically for different initial condition
(or boundary condition) probability distributions. For example, the method
is capable of evaluating whether the variance of a set of ensemble forecasts
is consistent with the verifying observed variance. Applying the method
to the ensemble of boundary-forced GCM integrations demonstrates that the
GCM produces probabilistic forecasts with too little variability for upper-level
dynamical fields. Operational weather prediction centers including the
U.K. Meteorological Office, the European Centre for Medium-Range Forecasts,
and the National Centers for Environmental Prediction have been applying
this method, referred to by them as Talagrand diagrams, to the verification
of operational ensemble predictions. The BPE method only evaluates the
consistency of ensemble predictions and observations and should be used
in conjunction with additional verification tools to provide a complete
assessment of a set of probabilistic forecasts.