Application of conditional non-linear optimal perturbations to tropical cyclone adaptive observation using theWeather Research Forecasting (WRF) model

Abstract

Conditional non-linear optimal perturbation (CNOP), which is a natural extension of the linear singular vector into the non-linear regime, has been suggested to identify data-sensitive regions in the adaptive observation strategy. CNOP is the global maximum of a cost function, whereas, local CNOP is the local maximum of the cost function if the local maximum exists. The potential application of CNOPs to tropical cyclone adaptive observation is researched. The CNOPs and the first singular vector (FSV) are numerically obtained by a spectral projected gradient algorithm with the Weather Research Forecasting (WRF) model. This paper examines two tropical cyclone cases, a fast straight moving typhoon Matsa (2005) and a slow moving recurving typhoon Shanshan (2006). The CNOPs and FSVs are obtained using the norms of background error at initial time and total dry energy at final time with a 36-h optimization time interval. The spatial structures of CNOPs, their energies, non-linear evolutions and impacts on track simulations are compared with those of the FSVs. The results show that both the CNOPs and the FSVs are localized, and evolve into the verification area at the final time with the upscale growth of perturbations. However, the CNOPs are different from the FSVs in spatial patterns, wind maximum distribution, growth rate of energy and impact on track simulation. Compared to FSV, CNOP and local CNOP have greater impact on the forecast in the verification region at the final time in terms of total energy, and have larger, at least similar impact on track simulation too. This indicates the CNOP method with constraint of the norm of background error at initial time and total energy norm at final time is a reasonable candidate in tropical cyclone adaptive observation. Therefore, both CNOP and local CNOP are suggested to be considered in tropical cyclone adaptive observation.