Using predictions for the sea surface temperature (SST) generated by a Flexible Global Ocean‐Atmosphere‐Land System model of IAP/LASG (FGOALS‐g), the season‐dependent predictability of SST anomalies for El Nino/La Nina events is investigated by analyzing the forecast error growth in an imperfect model scenario. The results indicate that, for the predictions through the spring season in the growth phase of El Nino events, the prediction errors induced by both initial errors and model errors tend to have a prominent season‐dependent evolution and yield a prominent spring predictability barrier (SPB). For the decay‐phase predictions of El Nino events, a less prominent season‐dependent evolution of prediction errors and then a less prominent SPB are observed. For the growth‐ and decay‐phase predictions of La Nina events, the prediction errors do not exhibit a significant season‐dependent evolution and yield a less prominent SPB phenomenon. These results indicate that the SPB phenomenon depends remarkably on the ENSO events themselves, particularly the phases of the El Nino/La Nina events. We also report that the initial SST errors that correspond to a significant SPB for El Nino events tend to have the dominant modes in a large‐scale dipolar pattern with negative anomalies in the equatorial central‐western Pacific and positive anomalies in the eastern Pacific, or vice versa. We further demonstrate that the error growth related to a significant SPB for El Nino prediction generated by the FGOALS‐g model can result from two dynamical mechanisms: in one case, the prediction errors grow in a manner similar to El Niño; in the other, the prediction errors develop with a tendency opposite to El Niño. Copyright © 2012 Royal Meteorological Society

The approach of conditional nonlinear optimal perturbation (CNOP) was previously proposed to find the optimal initial perturbation (CNOP-I) in a given constraint. In this paper, we extend the CNOP approach to search for the optimal combined mode of initial perturbations and model parameter perturbations. This optimal combined mode, also named CNOP, has two special cases: one is CNOP-I that only links with initial perturbations and has the largest nonlinear evolution at a prediction time; while the other is merely related to the parameter perturbations and is called CNOP-P, which causes the largest departure from a given reference state at a prediction time. The CNOP approach allows us to explore not only the first kind of predictability related to initial errors, but also the second kind of predictability associated with model parameter errors, moreover, the predictability problems of the coexistence of initial errors and parameter errors. With the CNOP approach, we study the ENSO predictability by a theoretical ENSO model. The results demonstrate that the prediction errors caused by the CNOP errors are only slightly larger than those yielded by the CNOP-I errors and then the model parameter errors may play a minor role in producing significant uncertainties for ENSO predictions. Thus, it is clear that the CNOP errors and their resultant prediction errors illustrate the combined effect on predictability of initial errors and model parameter errors and can be used to explore the relative importance of initial errors and parameter errors in yielding considerable prediction errors, which helps identify the dominant source of the errors that cause prediction uncertainties. It is finally expected that more realistic models will be adopted to investigate this use of CNOP.

The National Center for Atmospheric Research Community Earth System Model is used to study the “spring predictability barrier” (SPB) problem for El Niño events from the perspective of initial error growth. By conducting perfect model predictability experiments, we obtain two types of initial sea temperature errors, which often exhibit obvious season-dependent evolution and cause a significant SPB when predicting the onset of El Niño events bestriding spring. One type of initial errors possesses a sea surface temperature anomaly (SSTA) pattern with negative anomalies in the central–eastern equatorial Pacific, plus a basin-wide dipolar subsurface temperature anomaly pattern with negative anomalies in the upper layers of the eastern equatorial Pacific and positive anomalies in the lower layers of the western equatorial Pacific. The other type consists of an SSTA component with positive anomalies over the southeastern equatorial Pacific, plus a large-scale zonal dipole pattern of the subsurface temperature anomaly with positive anomalies in the upper layers of the eastern equatorial Pacific and negative anomalies in the lower layers of the central–western equatorial Pacific. Both exhibit a La Niña-like evolving mode and cause an under-prediction for Niño-3 SSTA of El Niño events. For the former initial error type, the resultant prediction errors grow in a manner similar to the behavior of the growth phase of La Niña; while for the latter initial error type, they experience a process that is similar to El Niño decay and transition to a La Niña growth phase. Both two types of initial errors cause negative prediction errors of Niño-3 SSTA for El Niño events. The prediction errors for Niño-3 SSTA are mainly due to the contribution of initial sea temperature errors in the large-error-related regions in the upper layers of the eastern tropical Pacific and/or in the lower layers of the western tropical Pacific. These regions may represent ‘‘sensitive areas’’ for El Niño–Southern Oscillation (ENSO) predictions, thereby providing information for target observations to improve the forecasting skill of ENSO.

Conditional nonlinear optimal perturbation (CNOP) is the initial perturbation that satisfies a certain physical constraint and causes the largest nonlinear evolution at prediction time. To yield mutually independent initial perturbations in ensemble forecasts, orthogonal CNOPs are developed. Orthogonal CNOPs are then applied to a Lorenz-96 model to generate initial perturbations for ensemble forecasting, as compared with orthogonal singular vectors (SVs). When the initial analysis errors are fast growing, the ensemble forecasts generated by orthogonal CNOPs of the control forecasts perform much more skillfully. Nevertheless, for slow-growing initial analysis errors, the ensemble forecasts generated by orthogonal SVs achieve higher skill when the ensemble initial perturbations are large, whereas the ensemble forecasts generated by orthogonal CNOPs achieve almost the same forecast skill as those generated by orthogonal SVs when the ensemble initial perturbations are sufficiently small. The initial analysis errors that possess much faster growth behavior are easily influenced by nonlinearity, and extreme events (extreme here refers to strong), because of strong nonlinear instability, may be much more likely to cause fast growth of initial analysis errors. Therefore, the ensemble forecasts generated by orthogonal CNOPs may have higher skill than those generated by orthogonal SVs for extreme events; in particular, the ensemble forecasts generated by orthogonal CNOPs, compared with those generated by orthogonal SVs, require a much smaller number of ensemble members to achieve high skill. Therefore, orthogonal CNOPs may provide another useful technique to generate initial perturbations for ensemble forecasting.

In this paper, we emphasize the importance of accurate initial conditions in predicting high-impact ocean-atmospheric environmental events, such as El Niño-Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), tropical cyclone (TC), and Kuroshio large meander (KLM), by reviewing recent progresses toward target observations for improving the initialization of these events forecasting. Since field observations are costly and will never be dense enough to fully cover the vast space of these events, it is necessary to develop methodologies that guide the design of efficient and effective observation strategy. Of particular interest is a method called conditional non-linear optimal perturbation (CNOP), which has been shown to be very useful in determining the sensitive areas for target observations applicable to the predictions of ENSO, IOD, TC, and KLM. Further studies are needed to understand the predictability of these events under the influence of climate change, and to explore the possibility of implementing field programs of target observations. These studies are challenging but are crucially important for improving our forecast skill of the high-impact ocean-atmospheric environmental events, and thus for disaster prevention, climate change mitigation, and sustainable socio-economic development.