Comparison Of Ensemble Forecasting And Single Forecasting And Its Predictability Study Based On Lorenz Models

The atmosphere is a chaotic system,and a small error in the initial conditions will result in an enormous forecast uncertainty with time.The ensemble forecasting is a feasible method to reduce the forecast uncertainty and to improve the numerical prediction skills.Consequently,it has important scientific significance and application value to study the ensemble forecasting and relevant problems.In this paper,the nonlinear local Lyapunov vectors(NLLV)method and the bred growing mode(BGM)method are introduced to generate the initial perturbations for the ensemble forecasting.Taking different states of the Lorenz models as the experimental cases,the forecast performances of the ensemble forecasting and single forecasting are compared.The possible reasons of ensemble mean with small forecast error have been analyzed from the perspective of probability distribution.The Kullback-Leibler divergence(KLD)theory is also used to investigate the predictability from the perspective of ensemble forecasting.The results of predictability are compared with the results by nonlinear local Lyapunov exponent(NLLE)method based on the error growth theory.The main results are as following:(1)In the perspective of the overall average,both ensemble mean forecastings of NLLV and BGM are more skillful than the single forecasting in terms of the root mean square error(RMSE)and pattern anomaly correlation(PAC).In the early stage of forecasting,the results of the ensemble mean are close to the single forecast.But the ensemble mean will result in a better forecast performance in terms of the RMSE and the PAC with time.(2)For each experimental case,the performances of the ensemble forecasting and the single forecasting are different.In the early stage of forecasting,the forecast skills of the ensemble forecasting and the single forecasting are almost equal.The proportion of the ensemble forecasting better than single forecasting gradually increases with time in Lorenz models by both NLLV and BGM methods,respectively.(3)The probability distribution of the single forecasting states and the reference states are mainly consistent,which does not change with time.But the probability distribution of the forecasting states of the ensemble mean shows the characteristics of narrowing and peaking with time,which imply that the single forecasting tends to choose the random state on the attractor as the forecast state.However,the ensemble mean tends to select the random state on the subset of the attractor as the forecast state.This might be the reason why the forecast error of ensemble forecasting is less than that of the single forecasting.(4)For the Lorenz63 model,in whether the change of the predictability with initial error or the spatial distribution of the predictability,the results based on the ensemble forecasting are close to results by the NLLE method.It shows that the predictability of Lorenz system can be well studied based on the evolution of the probabilistic forecasting of the ensemble forecasting.