Lagged average forecasting, an alternative to Monte Carlo forecasting

In order to use the information present in past observations and simultaneously to take advantage of the benefits of stochastic dynamic prediction we formulate the lagged average forecast (LAF) method. In a LAF, just as in a Monte Carlo forecast (MCF), sample statistics are calculated from an ensemble of forecasts. Each LAF ensemble member is an ordinary dynamical forecast (ODF) started from the initial conditions observed at a time lagging the start of the forecast period by a different amount. These forecasts are averaged at their proper verification times to obtain an LAF. The LAF method is operationally feasible since the LAF ensemble members are produced during the normal operational cycle.

To test the LAF method, we use a two-layer, f-plane, highly truncated spectral model, forced by asymmetric Newtonian heating of the lower layer. In the experiments, a long run is generated by the primitive equation version of the model which is taken to represent nature, while forecasts are made by the quasigeostrophic version of the model. On the basis of forecast skill, the LAF and MCF are superior to the ODF; this occurs principally because ensemble averaging hedges the LAF and MCF toward the climate mean. The LAF, MCF and ODF are all improved when tempered by a simple regression filter; this procedure yields different weights for the different members of the LAF ensemble. The tempered LAF is the most skillful of the forecast methods tested. The LAF and MCF can provide a priori estimates of forecast skill because there is a strong correlation between the dispersion of the ensemble and the loss of predictability. In this way the time at which individual forecasts lose their skill can be predicted.

The application of the LAF method to more realistic models and to monthly or seasonally averaged forecasts is briefly discussed.