The generation of orthogonal nonlinear ensemble perturbations in the China Meteorological Administration‐Global Ensemble Prediction System: Method and preliminary tests

To capture the fast‐growing initial perturbation with nonlinear growth characteristics, this paper develops orthogonal nonlinear ensemble perturbation within the China Meteorological Administration (CMA)‐Global Ensemble Prediction System (GEPS) by leveraging the existing moist singular vectors (MSVs). By applying the ensemble projection algorithm and imposing orthogonality constraints, we are able to derive a larger number of orthogonal conditional nonlinear optimal perturbations (O‐CNOPs), which subsequently serve as the basis for constructing ensemble members. A comparative analysis between O‐CNOPs and MSVs is conducted in terms of the structure of the perturbations, their growth characteristics and their performance in ensemble forecast experiments. Results show that the information encapsulated in the O‐CNOPs cannot be fully expressed by the combination of MSVs. In contrast, six out of the 15 MSVs, including the first two leading vectors, can be well expressed through the linear combination of O‐CNOPs. Regarding perturbation growth, while the difference total energy (DTE) of MSV01 is the largest among all MSVs, it is still smaller than that of O‐CNOPs. Notably, the DTE of certain MSVs grows very slowly in the nonlinear model, whereas each member of O‐CNOPs demonstrates substantial growth. The ensemble forecast results show that, with the same number of samples, the ensemble forecasts with samples generated by O‐CNOPs can achieve superior improvements throughout the entire forecast period compared to those with samples generated by MSVs. Moreover, when the sample size of O‐CNOPs is much smaller than that of MSVs, appropriate adjustments to the empirical parameters can be made, enabling the forecasts to approximate the results obtained with larger MSV sample sizes.