# The application of the orthogonal conditional nonlinear optimal perturbations method to typhoon track ensemble forecasts

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## Abstract

The orthogonal conditional nonlinear optimal perturbations (CNOPs) method, orthogonal singular vectors (SVs) method and CNOP+SVs method, which is similar to the orthogonal SVs method but replaces the leading SV (LSV) with the first CNOP, are adopted in both the Lorenz-96 model and Pennsylvania State University/National Center for Atmospheric Research (PSU/NCAR) Fifth-Generation Mesoscale Model (MM5) for ensemble forecasts. Using the MM5, typhoon track ensemble forecasting experiments are conducted for strong Typhoon Matsa in 2005. The results of the Lorenz-96 model show that the CNOP+SVs method has a higher ensemble forecast skill than the orthogonal SVs method, but ensemble forecasts using the orthogonal CNOPs method have the highest forecast skill. The results from the MM5 show that orthogonal CNOPs have a wider horizontal distribution and better describe the forecast uncertainties compared with SVs. When generating the ensemble mean forecast, equally averaging the ensemble members in addition to the anomalously perturbed forecast members may contribute to a higher forecast skill than equally averaging all of the ensemble members. Furthermore, for given initial perturbation amplitudes, the CNOP+SVs method may not have an ensemble forecast skill greater than that of the orthogonal SVs method, but the orthogonal CNOPs method is likely to have the highest forecast skill. Compared with SVs, orthogonal CNOPs fully consider the influence of nonlinear physical processes on the forecast results; therefore, considering the influence of nonlinearity may be important when generating fast-growing initial ensemble perturbations. All of the results show that the orthogonal CNOP method may be a potential new approach for ensemble forecasting.

## Keywords

Ensemble forecasts Initial perturbation Conditional nonlinear optimal perturbation Singular vector Typhoon track## Notes

### Acknowledgements

The FNL data used in this study can be obtained from http://rda.ucar.edu/datasets/ds083.2/. The historical tropical cyclone data are available at http://tcdata.typhoon.org.cn/en/zjljsjj_zlhq.html. This work was sponsored by the National Natural Science Foundation of China (Grant Nos. 41525017 & 41475100), the National Programme on Global Change and Air-Sea Interaction (Grant No. GASI-IPOVAI-06), and the GRAPES Development Program of China Meteorological Administration (Grant No. GRAPES-FZZX-2018).

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