Vapor flux associated with return flow over the Gulf of Mexico: A sensitivity study using adjoint modeling

The moisture flux associated with a return-flow event in the Gulf of Mexico is studied with the aid of a regional forecast model and its adjoint. The adjoint model allows us to determine the derivatives of some aspect of the model output (a scalar, J) with respect to elements of the control vector (initial and boundary conditions). We choose J to be the northward moisture flux through a vertical cross section in the northwestern corner of the Gulf at the time when the moisture surge in the US is a maximum. The sensitivities (∇J) are used in conjunction with a set of optimal perturbations to estimate the impact of each of the perturbations on the moisture flux. The perturbations are chosen to have the structure of the sensitivities (making them optimal as described in the next), with magnitudes based on the (assumed) uncertainties in the model's initial and boundary conditions. The linear impact estimate is simply the projection of the perturbation onto the sensitivity fields. In complementary fashion, we introduce perturbations into the nonlinear forecast model and decompose the actual impact on J into thermodynamic and dynamic components, in order to better understand the nature of the sensitivity. From this numerical experiment we conclude the following. J is more sensitive to the temperature field than to the other prognostic variables, roughly by a factor of 3 or 4, based on the optimal perturbations used here. The sensitivity to each of the 3-D prognostic variables peaks in the lower atmosphere near 85 k Pa. The sensitivity of J to the sea surface temperature (T_s, a fixed boundary condition) increases with forecast length. More than 30 h before the verification time, the impact of an optimal perturbation to T_S is comparable to the impact of an optimal perturbation to the whole 3-D air temperature field. The zones of sensitivity to the T_S are intimately tied to the trajectories of low-level air which terminate at the cross section. The impact of an optimal perturbation to the topography along the Sierra Madre Oriental mountains is comparable to the impact of optimal perturbations in each of the 3-D prognostic variables (except T).