Conditional nonlinear optimal perturbation: Applications to stability, sensitivity, and predictability

Abstract

Conditional nonlinear optimal perturbation (CNOP) is a nonlinear generalization of linear singular vector (LSV) and features the largest nonlinear evolution at prediction time for the initial perturbations in a given constraint. It was proposed initially for predicting the limitation of predictability of weather or climate. Then CNOP has been applied to the studies of the problems related to predictability for weather and climate. In this paper, we focus on reviewing the recent advances of CNOP's applications， which involves the ones of CNOP in problems of ENSO amplitude asymmetry, block onset, and the sensitivity analysis of ecosystem and ocean's circulations, etc. Especially, CNOP has been primarily used to construct the initial perturbation fields of ensemble forecasting, and to determine the sensitive area of target observation for precipitations. These works extend CNOP's applications to investigating the nonlinear dynamical behaviors of atmospheric or oceanic systems, even a coupled system, and studying the problem of the transition between the equilibrium states. These contributions not only attack the particular physical problems, but also show the superiority of CNOP to LSV in revealing the effect of nonlinear physical processes. Consequently, CNOP represents the optimal precursors for a weather or climate event; in predictability studies, CNOP stands for the initial error that has the largest negative effect on prediction; and in sensitivity analysis, CNOP is the most unstable (sensitive) mode. In multi-equilibrium state regime, CNOP is the initial perturbation that induces the transition between equilibriums most probably. Furthermore, CNOP has been used to construct ensemble perturbation fields in ensemble forecast studies and to identify sensitive area of target observation. CNOP theory has become more and more substantial. It is expected that CNOP also serves to improve the predictability of the realistic predictions for weather and climate events plays an increasingly important role in exploring the nonlinear dynamics of atmospheric, oceanic and coupled atmosphere-ocean system. optimal perturbation, predictability, stability, sensitivityOne of the central problems in atmospheric and oceanic sciences is the predictability for weather and climate, in which estimating the prediction uncertainty is very important. Tennekes [1] proclaimed that no forecast was complete without an estimate of the prediction error. This perspective can be traced back to Thompson [2] . Since then, operational weather forecasting has progressed to the point of explicit attempts to quantifying the evolution of initial uncertainty during each forecast [3][4][5] , which, furthermore, has been permeated through coupled model forecasts. Some understandings of the predictability of the tropical ocean-atmosphere system have been gained by studying the growth of errors and uncertainties during forecasts [6][7][8][9][10] .Despite the consensus on the best approach for predicting large dynamical systems like the Earth's atmos-

Optimal nonlinear excitation of decadal variability of the North Atlantic thermohaline circulation

“…This method has been used in predictability of ENSO events (Duan et al, 2004;Mu et al, 2007a, b;Duan et al, 2008Duan et al, , 2012Yu et al, 2012a, b), predictability of the Kuroshio Large Meander (Wang et al, 2011(Wang et al, , 2013, adaptive observations for tropical cyclones Qin and Mu, 2011a, b), sensitivity and decadal variability of THC in box models Sun et al, 2005;Wu and Mu, 2009), ecosystem sensitivity (Sun and Mu, 2011), and the study of ensemble forecast ( Jiang et al, 2009). For a review of the application of CNOP, we refer to Duan and Mu (2009).…”

Nonlinear optimal moisture perturbations as excitation of primary MJO events in a hybrid coupled climate model

“…In the past 15 years, the CNOP method has shown good advantages to linear methods across various fields of atmospheric and oceanic sciences (refer to the reviews by Mu and Duan 2005;Duan and Mu 2009;Mu et al 2015). For example, it has been successfully used to explore the "spring predictability barrier" and target observation problems of ENSO (e.g., Mu et al 2007Mu et al , 2014Tao et al 2018), the stability of thermohaline circulation (Sun et al 2005) and ecosystem (Sun andMu 2011, 2016), the ensemble forecast of the tropical cyclones (Wang et al 2011), and the optimally growing initial errors associated with the seasonal prediction of Kuroshio large mender .…”

Contribution of the location and spatial pattern of initial error to uncertainties in El Niño predictions

“…Note that the local CNOP error and CNOP error for a given optimization experiment are both related to one particular El Niño event and one particular start month, but that two types of CNOP errors in Figure 2 are composited from many CNOP errors obtained from various combinations of 8 El Niño events and 12 start months. Meanwhile, the CNOP also possesses clear physical meanings [ Duan and Mu , 2009]. Apart from acting as an initial error that has the largest negative effect on the prediction result at the prediction time, CNOP can also be used to be superimposed on the climatological basic state acts as the initial anomaly mode that is most likely to evolve into an El Nino event and represents the optimal precursor of El Nino [ Duan et al , 2004; Duan and Mu , 2006; Duan et al , 2008].…”