Tellus,
52A, 300-322
Statistical methods for interpreting Monte Carlo ensemble forecasts
David B. Stephenson
Météo-France/CNRM, 42 Avenue Coriolis
31057 Toulouse Cedex, France
Francisco J. Doblas-Reyes
Centro de Astrobiología, INTA, Ctra. de Ajalvir, km
4
28850 Torrejón, Madrid, Spain
For complex dynamical systems such as the atmosphere, improved estimates of future behaviour can be
obtained by making ensembles of forecasts starting from a set of Monte Carlo perturbed initial
conditions. Ensemble forecasting, however, generates an overwhelming amount of data that is difficult
to analyse in detail. Fortunately, the main features of interest are often summarised by certain
statistics estimated from the sample of forecasts. By considering an ensemble of forecasts as a
realisation of a linear mapping from phase space to sample space, it is possible to construct two
types of sample covariance matrix. The ensemble covariance can be visualised by constructing
multidimensional scaling maps, which show at a glance the relative distances between the different
ensemble members. Multivariate skewness and kurtosis can also be estimated from ensemble of forecasts
and provide useful information on the reliability of the sample mean and covariance estimated from
the ensemble. They can also give useful information on the non-linearity of the evolution in
phase space. Entropy can also be defined for an ensemble of forecasts and shows a regular increase
due to the smooth and rapid loss of initial information in the first 3 days of a meteorological
forecast. These new tools for summarising ensemble forecasts are illustrated using a single ensemble
of 51 weather forecasts made at the European Centre for Medium-Range Weather Forecasts for the period
20-30 December 1997.