Exploring the Phase-Strength Asymmetry of the North Atlantic Oscillation Using Conditional Nonlinear Optimal Perturbation

Negative-phase North Atlantic Oscillation（NAO） events are generally stronger than positive-phase ones, i.e., there is a phase-strength asymmetry of the NAO. In this work, we explore this asymmetry of the NAO using the conditional nonlinear optimal perturbation（CNOP） method with a three-level global quasi-geostrophic spectral model. It is shown that, with winter climatological flow forcing, the CNOP method identifies the perturbations triggering the strongest NAO event under a given initial constraint. Meanwhile, the phase-strength asymmetry characteristics of the NAO can be revealed. By comparing with linear results, we find that the process of perturbation self-interaction promotes the onset of negative NAO events, which is much stronger than during positive NAO onset. Results are obtained separately using the climatological and zonal-mean flows in boreal winter（December–February） 1979–2006 as the initial basic state. We conclude, based on the fact that NAO onset is a nonlinear initial-value problem, that phase-strength asymmetry is an intrinsic characteristic of the NAO.

A new approach to the generation of initial perturbations for ensemble prediction:Conditional nonlinear optimal perturbation

Conditional nonlinear optimal perturbation (CNOP),which is a natural extension of singular vector (SV) into the nonlinear regime,is applied to ensemble prediction study by using a quasi-geostrophic model under the perfect model assumption. SVs and CNOPs have been utilized to generate the initial pertur-bations for ensemble prediction experiments. The results are compared for forecast lengths of up to 14 d. It is found that the forecast skill of samples,in which the first SV is replaced by CNOP,is com-paratively higher than that of samples composed of only SVs in the medium range (day 6―day 14). This conclusion is valid under the condition that analysis error is a kind of fast-growing ones regardless of its magnitude,whose nonlinear growth is faster than that of SV in the later part of the forecast. Fur-thermore,similarity index and empirical orthogonal function (EOF) analysis are performed to explain the above numerical results.

Ensemble prediction experiments using conditional nonlinear optimal perturbation

Two methods for initialization of ensemble forecasts are compared, namely, singular vector (SV) and conditional nonlinear optimal perturbation (CNOP). The comparison is done for forecast lengths of up to 10 days with a three-level quasi-geostrophic (QG) atmospheric model in a perfect model scenario. Ten cases are randomly selected from 1982/1983 winter to 1993/1994 winter (from December to the following February). Anomaly correlation coefficient (ACC) is adopted as a tool to measure the quality of the predicted ensembles on the Northern Hemisphere 500 hPa geopotential height. The results show that the forecast quality of ensemble samples in which the first SV is replaced by CNOP is higher than that of samples composed of only SVs in the medium range, based on the occurrence of weather re-gime transitions in Northern Hemisphere after about four days. Besides, the reliability of ensemble forecasts is evaluated by the Rank Histograms. The above conclusions confirm and extend those reached earlier by the authors, which stated that the introduction of CNOP improves the forecast skill under the condition that the analysis error belongs to a kind of fast-growing error by using a barotropic QG model.