The First-Order Comprehensive Sensitivity Analysis Methodology (1st-CASAM) for Scalar-Valued Responses: I. Theory

This work presents the first-order comprehensive adjoint sensitivity analysis methodology (1st-CASAM) for computing efficiently, exactly, and exhaustively, the first-order sensitivities of scalar-valued responses (results of interest) of coupled nonlinear physical systems characterized by imprecisely known model parameters, boundaries and interfaces between the coupled systems. The 1st-CASAM highlights the conclusion that response sensitivities to the imprecisely known domain boundaries and interfaces can arise both from the definition of the system’s response as well as from the equations, interfaces and boundary conditions defining the model and its imprecisely known domain. By enabling, in premiere, the exact computations of sensitivities to interface and boundary parameters and conditions, the 1st-CASAM enables the quantification of the effects of manufacturing tolerances on the responses of physical and engineering systems. Ongoing research will generalize the methodology presented in this work, aiming at computing exactly and efficiently higher-order response sensitivities for coupled systems involving imprecisely known interfaces, parameters, and boundaries.

The Sensitive Regions Identified by CNOPs of Three Typhoon Events

In this paper, several sets of observing system simulation experiments (OSSEs) were designed for three typhoon cases to determine whether or not the additional observation data in the sensitive regions identified by conditional nonlinear optimal perturbations (CNOPs) could improve the short-range forecast of typhoons. The results show that the CNOPs capture the sensitive regions for typhoon forecasts, which implies that conducting additional observation in these specific regions and eliminating initial errors could reduce forecast errors. It is inferred from the results that dropping sondes in the CNOP sensitive regions could lead to improvements in typhoon forecasts.

Identifying the sensitive area in adaptive observation for predicting the upstream Kuroshio transport variation in a 3-D ocean model

Using the conditional nonlinear optimal perturbation(CNOP) approach, sensitive areas of adaptive observation for predicting the seasonal reduction of the upstream Kuroshio transport(UKT) were investigated in the Regional Ocean Modeling System(ROMS). The vertically integrated energy scheme was utilized to identify sensitive areas based on two factors: the specific energy scheme and sensitive area size. Totally 27 sensitive areas, characterized by three energy schemes and nine sensitive area sizes, were evaluated. The results show that the total energy(TE) scheme was the most effective because it includes both the kinetic and potential components of CNOP. Generally, larger sensitive areas led to better predictions. The size of 0.5% of the model domain was chosen after balancing the effectiveness and efficiency of adaptive observation. The optimal sensitive area OSen was determined accordingly. Sensitivity experiments on OSen were then conducted, and the following results were obtained:(1) In OSen, initial errors with CNOP or CNOP-like patterns were more likely to yield worse predictions, and the CNOP pattern was the most unstable.(2) Initial errors in OSen rather than in other regions tended to cause larger prediction errors. Therefore, adaptive observation in OSen can be more beneficial for predicting the seasonal reduction of UKT.