In-line processing of ensemble distributions in a simple model

Forecast ensemble "post-processing" is the statistical correction of the raw numerical forecast distribution based upon a database of past forecast performance. The statistically corrected forecast distributions are never dynamically evolved, and hence they may not fully describe the forecast distributions' state-dependent evolution. To provide a stronger link between the statistically corrected distributions and state-dependent dynamical evolution, here the idea of imbedding the statistical processing step within the numerical integration is examined in a simple-model setting. Monte Carlo experiments are undertaken using the three-variable Lorenz model in conjunction with the “reforecasting” post-processing technique. A three-way comparison is made between perfect-model forecast distributions, traditionally post-processed imperfect-model forecast distributions, and in-line post-processed imperfect-model forecast distributions.