The Impact Of Initial Error On Predictability Of Double-gvre Variability

With the1.5-layer shallow water model, the predictability of the double-gyrevariability is studied by using the conditional nonlinear optimal perturbations (CNOP)method. The main findings are as follows:Firstly, the results of simulating wind-driven double-gyre circulation show thatthis model can simulate the double-gyre circulation and its variations very well. Itshows that as the kinetic energy grows, the double-gyre flow will change from theelongated mode into the contracted mode. Based on the numerical modeling results,we establish the nonlinear optimization system, by which we use to compute theconditional nonlinear optimal initial perturbations (CNOP) and the first singularvector (FSV) under different perturbation constraints. Through comparing CNOPs’and FSVs’ spatial structure and the value of their objective function, we find thatwhen under small perturbation constraints, CNOPs have high similarity with FSVs inspatial structure. However, when coming with large perturbation constraints, theirspatial structures begin to become different. Moreover, the nonlinear evolution of theCNOPs at prediction time is always lager than that of the FSVs and as perturbationconstraints grow, the difference of their objective function values also becomes larger.It implies that the effects of the nonlinearity on the initial error growths cannot beignored. Hence, when considering the predictability of the double-gyre variability, theCNOP method is prior to the FSV method.Besides, we consider the process when the flow is changing from the elongatedmode into the contracted mode as the background flow, and then study the initialerror’s impact on the double-gyre circulation with the CNOP method. We get twokinds of optimal initial errors: the CNOP and the LCNOP. The results show that theCNOP and the LCNOP have nearly opposite effects on the double-gyre variability.After looking into their evolution, we find that the CNOP promotes the formation of the double-gyre eastward jet’s meander, and makes the eddy shedding60days earlierthan that of the background flow; while the LCNOP delays the formation of thedouble-gyre eastward jet’s meander, and makes the eddy shedding90days later thanthat of the background flow. In addition, during the prediction time the CNOP alwaysresults in greater prediction error than the LCNOP, which makes the prediction skillsof double-gyre variability become worse. We also find the areas where the optimalinitial error gets quick evolution generally have large velocity shear and potentialvorticity extremum. The reason is that barotropic instability probably exists in thoseareas. As a result, the initial error could continuously get energy from the backgroundflow and then develop into big eddies.