Comparisons of Adjoint Sensitivity, Leading Singular Vector, and Conditional Nonlinear Optimal Perturbations in the Identification of Sensitive Areas for Tropical-Cyclone-Targeted Observations

By analyzing how adjoint sensitivity (ADS), leading singular vector (LSV), and conditional nonlinear optimal perturbation (CNOP) methods are used to identify sensitive areas for target observation, the authors developed the concept of nonlinear degree. Moreover, the authors investigated the nonlinear degrees of straight and recurved types of typhoons. Subsequently, the sensitive areas identified using the three methods indicated earlier under different nonlinear degrees, together with the sensitive areas for straight and recurved types of typhoons, were analyzed. Finally, the sensitivity of the forecast to the initial values in the sensitive areas under different nonlinear degrees and for straight and recurved types of typhoons was explored. The results showed that the nonlinear degrees of recurved typhoons were quite different, either particularly strong or particularly weak, whereas negligible differences were observed among the nonlinear degrees of straight typhoons. For typhoons with weak nonlinearity, the sensitive areas identified using the three methods were similar, whereas for typhoons with strong nonlinearity, the sensitive areas identified by the LSV and ADS methods were similar, but they were quite different from those identified by the CNOP method. For recurved typhoons, the sensitive area was mainly located at the right front of its travel path, whereas for straight typhoons, the sensitive area was mainly located behind its travel path. The sensitivity test showed that the development of random perturbation in CNOP sensitive areas was the largest, regardless of whether the typhoon was strong nonlinear or not. In addition, the development of perturbation for weak nonlinear typhoons was greater than that for strong nonlinear typhoons. These results imply that the prediction for weak nonlinear typhoons is more sensitive to the initial uncertainty; thus, targeted observations for this kind of typhoon may be more effective.