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Tao Lingjiang and Duan Wansuo

Abstract

Nonlinear forcing singular vector (NFSV)-based assimilation is adopted to determine the model tendency errors that represent the combined effect of different kinds of model errors; then, an NFSV-tendency error forecast model is formulated. This error forecast model is coupled with an intermediate complex model (ICM) and makes the ICM output closer to the observations; finally, an NFSV-ICM forecast model for ENSO is constructed. The competing aspect of the NFSV-ICM is to consider not only model errors but also the interaction between model errors and initial errors because of the mathematical nature of the NFSV-tendency errors. Based on the prediction experiments for tropical SSTAs during either the training period (1960–96; i.e., when the NFSV-ICM is formulated) or the cross-validation period (1997–2016), the NFSV-ICM is determined to have a much higher forecast skill in predicting ENSO that, specifically, extends the skillful predictions of ENSO from a lead time of 6 months in the original ICM to a lead time of 12 months. The higher skill of the NFSV-ICM is especially reflected in the predictions of SSTAs in the central and western Pacific. For the well-known spring predictability barrier (SPB) phenomenon that greatly limits ENSO forecasting skill, the NFSV-ICM also shows great abilities in suppressing its negative effect on ENSO predictions. Although the NFSV-ICM is presently only involved with the NFSV-related assimilation of SSTs, it has shown its usefulness in predicting ENSO. It is clear that the NFSV-based assimilation approach is effective in dealing with the effect of model errors on ENSO forecasts.

Open access
Wansuo Duan and Zhenhua Huo

Abstract

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.

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Yanshan Yu, Mu Mu, and Wansuo Duan

Abstract

Within the framework of the Zebiak–Cane model, the approach of conditional nonlinear optimal perturbation (CNOP) is used to study the effect of model parameter errors on El Niño–Southern Oscillation (ENSO) predictability. The optimal model parameter errors are obtained within a reasonable error bound (i.e., CNOP-P errors), which have the largest effect on the results of El Niño predictions. The resultant prediction errors were investigated in depth. The CNOP-P errors do not cause a noticeable prediction error of the sea surface temperature anomaly averaged over the Niño-3 region and do not show an obvious season-dependent evolution of the prediction errors. Consequently, the CNOP-P errors do not cause a significant spring predictability barrier (SPB) for El Niño events. In contrast, the initial errors that have the largest effect on the results of the predictions (i.e., the CNOP-I errors) show a season-dependent evolution, with the largest error increase in spring, and also cause a large prediction error, thereby generating a significant SPB. The initial errors play a more important role than the parameter errors in generating a significant SPB for El Niño events. To further validate this result, the authors investigated the situation in which CNOP-I and CNOP-P errors are simultaneously superimposed in the model, which may be a more credible approach because the initial errors and model parameter errors coexist under realistic predictions. The combined mode of CNOP-I and CNOP-P errors shows a similar season-dependent evolution to that of CNOP-I errors and yields a large prediction error, thereby inducing a significant SPB. The inference, therefore, is that initial errors play a more important role than model parameter errors in generating a significant SPB for El Niño predictions of the Zebiak–Cane model. This result helps to clarify the roles of the initial error and parameter error in the development of an SPB, and highlights the role of initial errors, which demonstrates that the SPB could be markedly reduced by improving the initial conditions. The results provide a theoretical basis for improving data assimilation in ENSO predictions.

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Jianping Li, Richard Swinbank, Ruiqiang Ding, and Wansuo Duan
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Qian Zhou, Lei Chen, Wansuo Duan, Xu Wang, Ziqing Zu, Xiang Li, Shouwen Zhang, and Yunfei Zhang

Abstract

Using the latest operational version of the ENSO forecast system from the National Marine Environmental Forecasting Center (NMEFC) of China, ensemble forecasting experiments are performed for El Niño–Southern Oscillation (ENSO) events that occurred from 1997 to 2017 by generating initial perturbations of the conditional nonlinear optimal perturbation (CNOP) and climatically relevant singular vector (CSV) structures. It is shown that when the initial perturbation of the leading CSV structure in the ensemble forecast of the CSVs scheme is replaced by those of the CNOP structure, the resulted ensemble ENSO forecasts of the CNOP+CSVs scheme tend to possess a larger spread than the forecasts obtained with the CSVs scheme alone, leading to a better match between the root-mean-square error and the ensemble spread, a more reasonable Talagrand diagram, and an improved Brier skill score (BSS). All these results indicate that the ensemble forecasts generated by the CNOP+CSVs scheme can improve both the accuracy of ENSO forecasting and the reliability of the ensemble forecasting system. Therefore, ENSO ensemble forecasting should consider the effect of nonlinearity on the ensemble initial perturbations to achieve a much higher skill. It is expected that fully nonlinear ensemble initial perturbations can be sufficiently yielded to produce ensemble forecasts for ENSO, finally improving the ENSO forecast skill to the greatest possible extent. The CNOP will be a useful method to yield fully nonlinear optimal initial perturbations for ensemble forecasting.

Open access
Hongdou Fan, Lin Wang, Yang Zhang, Youmin Tang, Wansuo Duan, and Lei Wang

Abstract

Based on 36-yr hindcasts from the fifth-generation seasonal forecast system of the European Centre for Medium-Range Weather Forecasts (SEAS5), the most predictable patterns of the wintertime 2-m air temperature (T2m) in the extratropical Northern Hemisphere are extracted via the maximum signal-to-noise (MSN) empirical orthogonal function (EOF) analysis, and their associated predictability sources are identified. The MSN EOF1 captures the warming trend that amplifies over the Arctic but misses the associated warm Arctic–cold continent pattern. The MSN EOF2 delineates a wavelike T2m pattern over the Pacific–North America region, which is rooted in the tropical forcing of the eastern Pacific-type El Niño–Southern Oscillation (ENSO). The MSN EOF3 shows a wavelike T2m pattern over the Pacific–North America region, which has an approximately 90° phase difference from that associated with MSN EOF2, and a loading center over midlatitude Eurasia. Its sources of predictability include the central Pacific-type ENSO and Eurasian snow cover. The MSN EOF4 reflects T2m variability surrounding the Tibetan Plateau, which is plausibly linked to the remote forcing of the Arctic sea ice. The information on the leading predictable patterns and their sources of predictability is further used to develop a calibration scheme to improve the prediction skill of T2m. The calibrated prediction skill in terms of the anomaly correlation coefficient improves significantly over midlatitude Eurasia in a leave-one-out cross-validation, implying a possible way to improve the wintertime T2m prediction in the SEAS5.

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