ON STOCHASTIC DYNAMIC PREDICTION

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Abstract
The stochastic dynamic equations, as investigated in part I of this two-part study, can be applied to any time-dependent set of differential equations which are, at most, nonlinear quadratic. In this study, they are used to explore various aspects of the question of atmospheric predictability. The growth of uncertainty due to ill-defined initial conditions in the nonlinear advection field is viewed by considering a simple barotropic model. A wave number is defined to be “unpredictable” when the “uncertain” energy associated with that wave becomes as large as the “certain” energy associated with it. The predictability of wave number 12 is used as a reference point and as an arbitrary minimum requirement for useful synoptic forecasts. It is found that, based upon the average root-mean-square vector error in the wind field today, such a wave number has a predictability value of about 1.5 days. If this error could be reduced by a factor of 4 (i.e., down to 1 m/s), this value would be approximately 5 ... Abstract The stochastic dynamic equations, as investigated in part I of this two-part study, can be applied to any time-dependent set of differential equations which are, at most, nonlinear quadratic. In this study, they are used to explore various aspects of the question of atmospheric predictability. The growth of uncertainty due to ill-defined initial conditions in the nonlinear advection field is viewed by considering a simple barotropic model. A wave number is defined to be “unpredictable” when the “uncertain” energy associated with that wave becomes as large as the “certain” energy associated with it. The predictability of wave number 12 is used as a reference point and as an arbitrary minimum requirement for useful synoptic forecasts. It is found that, based upon the average root-mean-square vector error in the wind field today, such a wave number has a predictability value of about 1.5 days. If this error could be reduced by a factor of 4 (i.e., down to 1 m/s), this value would be approximately 5 ...

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