Sensitivity analysis deals with the calculation of the gradients of a model forecast aspect with respect to the model parameters. The model parameters might be model initial conditions, boundary conditions or other parameters. The adjoint method is an efficient approach to carry out sensitivity analysis. This method allows us to calculate the gradients of any forecast aspect with respect to all of the model input variables and parameters with only one integration of the forward nonlinear model and one backward integration of its adjoint model. The use of adjoint in sensitivity studies was initiated by the early work of Cacuci (1981a, b), who introduced a general sensitivity theory for nonlinear systems. Hall et al. (1982) applied the theory successfully to sensitivity of a climate radiative-convective model to some parameters. An in-depth review of the entire range of applications of sensitivity theory has been presented by Cacuci (1988). Later, Errico and Vukicevic (1992) indicated that the adjoint fields quantify the previous conditions that most affect a specified forecast aspect. Rabier et al. (1992) used the adjoint of a global primitive equation model to investigate the following question: to which aspects of the initial conditions is cyclogenesis most sensitive in a simple idealized situation? Zou et al. (1993c) examined the sensitivity of a blocking index in a two-layer isentropic model using a response functional depending on both space and time.
One of the applications of adjoint sensitivity is to trace back the geographical regions where large forecast errors originate. Since the numerical weather prediction model forecasts are generally sensitive to the small errors in the initial conditions, the errors in analyses might amplify rapidly in model forecasts, leading to large forecast errors. Some studies have been carried out recently applying adjoint sensitivity to targeted or adaptive observations. For instance, Morss et al. (1998) examined adaptive observation strategies using a multilevel quasi-geostrophic channel model and a realistic data assimilation scheme. Pu et al. (1998) applied the quasi-inverse linear and adjoint methods to targeted observations during FASTEX. Both of their results indicated that the adjoint method was useful in determining the locations for adaptive observations.
In this study, a sensitivity experiment using the adjoint method was carried out for a case on June 8, 1988 occurring during the Indian summer monsoon. We will explore the sensitivity of the 1-day forecast error over a localized region of interest with respect to the initial conditions, which will be taken as a diagnostic tool to identify possible regions where analysis problems are leading to large forecast errors, and we expect that the sensitivity analysis will provide us with an indication as to the placement of adaptive observations in the locations where they are most needed, i.e., adding observations in the areas of large uncertainty (Lorenz and Emanuel, 1997).