Application of the Conditional Nonlinear Optimal Perturbation Method to the Predictability Study of the Kuroshio Large Meander

A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations. The results show that the model was able to capture the essential features of these path variations. We used one simulation of the model as the reference state and investigated the effects of errors in model parameters on the prediction of the transition to the Kuroshio large meander （KLM） state using the conditional nonlinear optimal parameter perturbation （CNOP-P） method. Because of their relatively large uncertainties, three model parameters were considered： the interracial friction coefficient, the wind-stress amplitude, and the lateral friction coefficient. We determined the CNOP-Ps optimized for each of these three parameters independently, and we optimized all three parameters simultaneously using the Spectral Projected Gradient 2 （SPG2） algorithm. Similarly, the impacts caused by errors in initial conditions were examined using the conditional nonlinear optimal initial perturbation （CNOP-I） method. Both the CNOP-I and CNOP-Ps can result in significant prediction errors of the KLM over a lead time of 240 days. But the prediction error caused by CNOP-I is greater than that caused by CNOP-P. The results of this study indicate not only that initial condition errors have greater effects on the prediction of the KLM than errors in model parameters but also that the latter cannot be ignored. Hence, to enhance the forecast skill of the KLM in this model, the initial conditions should first be improved, the model parameters should use the best possible estimates.

Identifying sensitive areas of adaptive observations for prediction of the Kuroshio large meander using a shallow-water model

Sensitive areas for prediction of the Kuroshio large meander using a 1.5-layer,shallowwater ocean model were investigated using the conditional nonlinear optimal perturbation(CNOP) and first singular vector(FSV) methods.A series of sensitivity experiments were designed to test the sensitivity of sensitive areas within the numerical model.The following results were obtained:(1) the effect of initial CNOP and FSV patterns in their sensitive areas is greater than that of the same patterns in randomly selected areas,with the effect of the initial CNOP patterns in CNOP sensitive areas being the greatest;(2) both CNOP- and FSV-type initial errors grow more quickly than random errors;(3) the effect of random errors superimposed on the sensitive areas is greater than that of random errors introduced into randomly selected areas,and initial errors in the CNOP sensitive areas have greater effects on final forecasts.These results reveal that the sensitive areas determined using the CNOP are more sensitive than those of FSV and other randomly selected areas.In addition,ideal hindcasting experiments were conducted to examine the validity of the sensitive areas.The results indicate that reduction(or elimination) of CNOP-type errors in CNOP sensitive areas at the initial time has a greater forecast benefit than the reduction(or elimination) of FSVtype errors in FSV sensitive areas.These results suggest that the CNOP method is suitable for determining sensitive areas in the prediction of the Kuroshio large-meander path.

Identifying the sensitive areas in targeted observation for predicting the Kuroshio large meander path in a regional ocean model

With the Regional Ocean Modeling System(ROMS),this paper investigates the sensitive areas in targeted observation for predicting the Kuroshio large meander(LM)path using the conditional nonlinear optimal perturbation approach.To identify the sensitive areas,the optimal initial errors(OIEs)featuring the largest nonlinear evolution in the LM prediction are first calculated;the resulting OIEs are localized mainly in the upper 2500 m over the LM upstream region,and their spatial structure has certain similarities with that of the optimal triggering perturbation.Based on this spatial structure,the sensitive areas are successfully identified,located southeast of Kyushu in the region(29°–32°N,131°–134°E).A series of sensitivity experiments indicate that both the positions and the spatial structure of initial errors have important effects on the LM prediction,verifying the validity of the sensitive areas.Then,the effect of targeted observation in the sensitive areas is evaluated through observing system simulation experiments.When targeted observation is implemented in the identified sensitive areas,the prediction errors are effectively reduced,and the prediction skill of the LM event is improved significantly.This provides scientific guidance for ocean observations related to enhancing the prediction skill of the LM event.

Optimal precursor of the transition from Kuroshio large meander to straight path

We used the conditional nonlinear optimal perturbation(CNOP) method to explore the optimal precursor of the transition from Kuroshio large meander(LM) to straight path within a barotropic inflowoutflow model,and found that large amplitudes of the optimal precursor are mainly located in the east of Kyushu,which implies that perturbations in the region are important for the transition from LM to straight path.Furthermore,we investigated the transition processes caused by the optimal precursor,and found that these processes could be divided into three stages.In the first stage,a cyclonic eddy is advected to the formation region of the Kuroshio large meander,which enhances the LM path and causes a cyclonic eddy to shed from the Kuroshio mainstream.This process causes the LM path to change into a small meander path.Subsequently,the small meander is maintained for a period because the vorticity advection is balanced by the beta effect in the second stage.In the third stage,the small meander weakens and the straight path ultimately forms.The positive vorticity advecting downstream is responsible for this process.The exploration of the optimal precursor will conduce to improve the prediction of the transition processes from LM path to straight path,and its spatial structure can be used to guide Kuroshio targeted observation studies.

Impact of nonlinear processes on formation of the Kuroshio large meander path in a barotropic inflow-outflow model

Based on a barotropic inflow-outflow model,we examine the formation of the Kuroshio large meander(LM) using conditional nonlinear optimal perturbation(CNOP) method.Both linear and nonlinear evolutions of such perturbations obtained by this method are investigated.The results show that the nonlinear evolution can result in the Kuroshio transition from a straight to LM path,whereas the linear evolution cannot.This implies that nonlinearity plays an important role in the formation of the Kuroshio LM path.The nonlinearity exists as advection in the evolution equations of the perturbation derived from the barotropic inflow-outflow model,namely the nonlinear advection of the perturbation by the perturbation(NAPP).By examining the role of this nonlinearity,we find that the NAPP tends to move the cyclonic eddy induced by the CNOP-type perturbation westward.Together with the beta effect,this offsets part of the eastward advection caused by the interaction between the perturbation and the background flow.Hence,the eastward movement of the cyclonic eddy is significantly weakened,effectively causing the eddy to develop.The sufficient evolution of this cyclonic eddy leads to the formation of the Kuroshio LM.

Comparison of the seven large meanders of the Kuroshio

In this paper, a comparison among the seven large meanders of the Kuroshio is made in order to probe into their similarity and differences. The major results are described as follows.1. Although the three phases for the seven large meanders such as their formations, maturity, as well as decline are very similar to one another, each meander has its own trivial difference in detail.2.The paths of the first six large meanders in the mature phase may be classified into ten types: U1, V1, U2, V2, U1', V1', U2', V2',φ and W.3.The seven large meanders may be grouped into two patterns, i. e. , pattern Ⅰ and pattern Ⅱ. Pattern Ⅰ includes the first and the fourth large meanders, and pattern Ⅱ includes the rest of the above meanders.4. Four standards for identifying the large meanders of the Kuroshio are put forward.