Theoretical Skill of Monte Carlo Forecasts

The theoretical skill of Monte Carlo approximations to the stochastic dynamic forecasting technique proposed by Epstein is examined by means of an extension of earlier atmospheric predictability studies that used the test-field model of two-dimensional turbulence. The fundamental statistical hydrodynamical concept of an ensemble of phase paths evolving in a dynamical phase space is reviewed and used to define the statistical properties of a finite Monte Carlo sample. The application of a linear regression step to arrive at a final best estimate of the state of the atmosphere is also discussed. The resulting forecasts approach the climatological mean at forecast times so late that all skill has been lost. For an ideal case with an observing resolution, hopefully achievable in the 1980s with satellite-based sensors, it is found that the. Monte Carlo procedure leads to the greatest improvement in mean-square vector wind forecast skill in the 6- to 10-day range. For another case corresponding roughly to present operational resolution the wind forecast skill is improved considerably in the 2- to 5-day range. Much of the improvement in mean-square skill is a consequence of the optimal filtering nature of the procedure which damps erroneous small scale structure in favor of the more predictable large scales.