Stochastic dynamic prediction

Abstract

Stochastic dynamic prediction assumes the laws governing atmospheric behavior are entirely deterministic, but seeks solutions corresponding to probabilistic statements of the initial conditions, thus recognizing the impossibility of exact or sufficiently dense observations. The equation that must be solved is the continuity equation for probability. For practical reasons only approximate solutions to this equation are possible in general. Deterministic forecasts represent a very low order of approximation. More exact methods are developed and some of the attributes and advantages of stochastic dynamic predictions are illustrated by applying them to a low order set of dynamic equations. Stochastic dynamic predictions have significantly smaller mean square errors than deterministic procedures, and also give specific information on the nature and extent of the uncertainty of the forecast. Also the range of time over which useful forecasts can be obtained is extended. However, they also require considerably more extensive calculations. The question of analysis to obtain the initial stochastic statement of the atmospheric state is considered and one finds here too a promise of significant advantages over present deterministic methods. It is shown how the stochastic method can be used to assess the value of new or improved data by considering their influence on the decrease in the uncertainty of the forecast. Comparisons among physical‐numerical models are also made more effectively by applying stochastic methods. Finally the implications of stochastic dynamic prediction on the question of predictability are briefly considered, with the conclusion that some earlier estimates have been too pessimistic.

Evaluation of a Short-Range Multimodel Ensemble System

“…A suitable measure of the accuracy for probabilistic categorical forecasts is the ranked probability score (Epstein 1969;Murphy 1971;Wilks 1995), which compares the cumulative distribution functions of the forecast and verification. The RPS is negatively oriented: an RPS ϭ0 denotes a perfect forecast with the worst possible score being J Ϫ 1, where J is the number of mutually exclusive, collectively exhaustive categories.…”

Lyapunov, Floquet, and singular vectors for baroclinic waves

“…Of particular practical interest is the problem of numerical weather prediction. One apCorrespondence to: R. M. Samelson (rsamelson@coas.oregonstate.edu) proach to this problem involves the use of ensemble forecasting techniques, which attempt to improve a single atmospheric forecast by combining multiple model predictions (Epstein, 1969;Leith, 1974).…”

Inclusion of potential vorticity uncertainties into a hydrometeorological forecasting chain: application to a medium size basin of Mediterranean Spain

“…For the driven discharge volumes, the scores are calculated using only the hourly data produced at each sub-basin that is non-zero in at least one of the two compared series in order to prevent an artificial improvement of the ROC values. It is worth to remark that the ensemble mean, statistically, should provide a better forecast that any individual ensemble member, because errors in the individual forecasts tend to cancel when averaged (Epstein, 1969;Leith, 1974). Therefore, statistical scores for the ensemble means of rainfall and runoff volumes have also been computed in order to highlight the possible benefits of a simple ensemble average in comparison with the control experiments.…”