Averaging Techniques in Long-Range Weather Forecasting

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Abstract

A method is investigated for increasing the length of prediction time for intermediate-range forecasting (up to 30 days). The method is to use the ensemble average of a set of forecasts generated by random perturbations from an observed initial state. The effect of ensemble averaging on the predictability time is investigated by means of a simulation study utilizing a three-layer general circulation model. It is found that the technique of ensemble averaging can lead to an increased predictability time when compared either to a single forecast made from the observed state, or to climatological means.

It is found that 1) the distribution of forecasts made from states which am randomly perturbed is Gaussian, within the limits of the numerical experiment; 2) both amplitude (root-mean-square) and phase (correlation coefficient) predictability times are increased for the ensemble-average forecast when compared to the forecast made from the observed initial state; and 3) the number of forecasts necessary to constitute a usable ensemble lies between four and eight. In addition, the procedure of ensemble forecasting was applied to averages over space regions ranging from 4 × 106 to 107 km2, as well as time averages over periods of 5 days. Space-time averaging appears to emulate ensemble averaging in its effect on predictability time for ground temperatures, but not for surface pressure.

It should be emphasized that the results obtained here are based on a specific single initial weather situation and on a particular model’s response to that situation. A “perfect model” assumption is made, i.e., that the degradation of the forecasts is due to incorrect initial conditions and not to the model. However, the model used is imperfect. The results obtained here are indicative, but care must be exercised not to extrapolate the results beyond the circumstances and assumptions without further investigation.

Abstract

A method is investigated for increasing the length of prediction time for intermediate-range forecasting (up to 30 days). The method is to use the ensemble average of a set of forecasts generated by random perturbations from an observed initial state. The effect of ensemble averaging on the predictability time is investigated by means of a simulation study utilizing a three-layer general circulation model. It is found that the technique of ensemble averaging can lead to an increased predictability time when compared either to a single forecast made from the observed state, or to climatological means.

It is found that 1) the distribution of forecasts made from states which am randomly perturbed is Gaussian, within the limits of the numerical experiment; 2) both amplitude (root-mean-square) and phase (correlation coefficient) predictability times are increased for the ensemble-average forecast when compared to the forecast made from the observed initial state; and 3) the number of forecasts necessary to constitute a usable ensemble lies between four and eight. In addition, the procedure of ensemble forecasting was applied to averages over space regions ranging from 4 × 106 to 107 km2, as well as time averages over periods of 5 days. Space-time averaging appears to emulate ensemble averaging in its effect on predictability time for ground temperatures, but not for surface pressure.

It should be emphasized that the results obtained here are based on a specific single initial weather situation and on a particular model’s response to that situation. A “perfect model” assumption is made, i.e., that the degradation of the forecasts is due to incorrect initial conditions and not to the model. However, the model used is imperfect. The results obtained here are indicative, but care must be exercised not to extrapolate the results beyond the circumstances and assumptions without further investigation.

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