The most sensitive initial error of sea surface height anomaly forecasts and its implication for target observations of mesoscale eddies

Abstract

Abstract We used the conditional nonlinear optimal perturbation (CNOP) approach to investigate the most sensitive initial error of sea surface height anomaly (SSHA) forecasts by using a two-layer quasigeostrophic model and revealed the importance of mesoscale eddies in initialization of the SSHA forecasts. Then, the CNOP-type initial errors for individual mesoscale eddies were calculated, revealing that the errors tend to occur in locations where the eddies present a clear high-to low-velocity gradient along the eddy rotation and the errors often have a shear SSHA structure present. Physically, we interpreted the rationality of the particular location and shear structure of the CNOP-type errors by barotropic instability from the perspective of the Lagrange expression of fluid motions. Numerically, we examined the sensitivity of the CNOP-type errors by using observing system simulation experiments (OSSEs). We concluded that if additional observations are preferentially implemented in the location where CNOP-type errors occur, especially with a particular array indicated by their shear structure, the forecast ability of the SSHA can be significantly improved. These results provide scientific guidance for the target observation of mesoscale eddies and therefore are very instructive for improving ocean state SSHA forecasts.