A small perturbation approximation for stochastic dynamic weather prediction

The stochastic dynamic method for optimum weather forecasting and forecast variance estimation suffers from computational complexity sufficient to obviate its utility as an operational tool. The present paper suggests the use of a linear approximation for a perturbed set of stochastic dynamic equations aimed at reducing computation time. The linearization is based upon an assumption of small departures of the stochastic dynamic solution from the usual deterministic forecast. The resultant linear scheme was tested by evaluating its predictions for a simple mathematical model of the atmosphere, that described by Lorentz's “minimum hydrodynamic equations”.

The linearization was found to be as effective as was the standard non-linear stochastic dynamics method, which approximates the exact stochastic dynamic solution by ignoring third-order moments. The problem of developing efficient numerical algorithms that take advantage of the simplification attendant upon linearization is not taken up in this paper, but will be reported upon as the work is pursued.