An ensemble forecast method combining CNOPs with BVs

Abstract

Numerical forecasting can estimate the future state of the atmosphere or oceans. Because the atmosphere and oceans are complex and nonlinear systems, very small errors in the initial field can be amplified nonlinearly during integration of the numerical model, which may ultimately result in large errors. The true initial field cannot be obtained, and it is not possible to construct a perfect model that simulates the development of the atmospheric or oceanic state. Therefore, initial uncertainties and system instabilities result in large forecast errors. However, ensemble forecasting can be used to estimate the forecasting uncertainty. The ensemble initial perturbation has a crucial impact on the ensemble forecasting result. To obtain the initial perturbation that can capture initial field uncertainties and system instabilities, conditional nonlinear optimal perturbation (CNOP) is applied to generate initial perturbations for ensemble forecasting. CNOP is the initial perturbation that satisfies certain physical constraints and causes the largest forecast error at forecast time. More specifically, it is a generalization of the singular vector (SV) in nonlinear field. Using the Lorenz-96 model, we generate initial perturbations by combining CNOPs and breeding vectors (BVs), and then compare it with the traditional breeding growing modes (BGM) method. The spectral projected gradient 2 (SPG2) optimal algorithm is used to compute CNOPs based on basic states, and we sort the BVs according to the corresponding L 2 norm magnitude. We design two ensemble samples for the forecast experiments: sample 1 (S1) and sample 2 (S2). Ensemble initial perturbations all consist of BVs in S1. CNOPs and BVs are combined to form ensemble initial perturbations in S2; we use CNOPs to replace the several larger BVs in S1 according to the BVs’ L 2 norm magnitude order, and keep the remaining BVs unchanged. Both S1 and S2 are consist of 17 ensemble members, including one control forecast. Under the perfect model assumption, many ensemble forecasting numerical experiments are run on the Lorenz-96 model. The root mean square error (RMSE) and anomaly correlation coefficient (ACC) are used to evaluate the forecast results. We find that the forecast skill of S2 is higher than that of S1 in most experiments. This result suggests that initial perturbations generated using the new method better overcome the adverse impact from initial field uncertainty and system instability, and provide higher ensemble forecasting skill than the BGM method. When the initial analysis errors are fast-growing, ensemble forecasts generated by the new method can improve the control forecasts results. Furthermore, the rate of improvement increases with increasing forecast time, and is more obvious in the medium range (6–14 d). Ensemble forecasts generated using the new method can extend the effective forecast time about four days relative to the control forecasts based on the standard that the effective ACC forecast is not <0.6. Nevertheless, for slowly-growing initial analysis errors, ensemble forecasts generated using the new and BGM method may be worse than the control forecasts. The initial analysis errors that show much faster growth behavior are easily influenced by nonlinearity, and extreme events due to strong nonlinear instability may be more likely to cause fast growth of initial analysis errors. Therefore, ensemble forecasts generated by combining CNOPs and BVs will have higher forecasting skill than the BGM method, and can improve the forecast effect of control forecast.