The Role of Orthogonal Conditional Nonlinear Optimal Perturbations (O-CNOPs) in Ensemble Forecasting of Extreme Rainfall: Improvement and Physical Perturbation Mechanisms

From 17 to 22 July 2021, Henan Province in China experienced an exceptionally severe rainfall event (hereafter referred to as the “7·21” rainstorm). In particular, record-breaking local hourly precipitation occurred in Zhengzhou on 20 July, posing an unprecedented challenge to mesoscale numerical weather prediction (NWP) systems. Uncertainty is inherent in NWP, and ensemble forecasting has increasingly become the consensus approach for quantifying such uncertainty. The use of growing initial perturbations is essential for achieving high ensemble forecast skill. To investigate the influence of initial perturbations on forecast errors during this extreme rainfall event, this study applies the orthogonal conditional nonlinear optimal perturbation method (O-CNOP-Is) to construct an ensemble perturbation strategy tailored to the Henan rainstorm. The aim is to improve the representation of extreme precipitation and its associated forecast uncertainty, thereby providing new technical support for the prediction and early warning of similar high-impact events in the future.

The O-CNOP-Is represent a set of mutually orthogonal growing initial perturbations that satisfy prescribed physical constraints and exhibit the maximum nonlinear evolution at the forecast time. In this study, an O-CNOP-Is computation framework is established using the regional mesoscale Weather Research and Forecasting (WRF) model. The Global Ensemble Forecast System (GEFS) provided by the National Centers for Environmental Prediction is used as the source ensemble of initial perturbation samples. An ensemble projection algorithm is employed to derive a set of O-CNOP-Is perturbation fields specifically targeted at the “7·21” rainfall event, fully accounting for the nonlinear evolution of the model. These O-CNOP-Is are then superimposed onto the background field to generate an ensemble whose members embody the strongest features of uncertainty growth. The resulting ensemble forecasts are compared with those from the GEFS to assess the effectiveness of CNOP-type perturbations in ensemble forecasting of extreme precipitation.

The numerical results indicate that the initial perturbations provided by O-CNOP-Is are physically reasonable for regional ensemble prediction. The perturbation amplitudes increase with time, and their spatial structures effectively reflect the baroclinic instability characteristics of the evolving atmosphere. Compared with GEFS perturbations, O-CNOP-Is contain more uncertainty information at the initial time and exhibit stronger perturbation growth at the forecast time. Throughout the forecast period, the O-CNOP-Is ensemble displays larger ensemble spread that better matches the forecast errors. Moreover, the ensemble mean forecast shows notable improvements in reproducing both the location and peak intensity of extreme precipitation centers.

Overall, the results demonstrate that the conditional nonlinear optimal perturbation approach is a highly promising method for capturing the dominant error growth modes in the Henan rainstorm. It effectively enhances ensemble forecast skill for high-impact, strongly nonlinear extreme weather events such as the “7·21” Henan rainfall, and provides a solid scientific basis and practical foundation for the development of regional mesoscale ensemble forecasting systems.