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

Abstract

The moisture flux associated with a return-flow event in the Gulf ofMexico is studied with the aidof a regional forecastmodel and its adjoint.The adjointmodel allows us to determine the derivativesof 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 avertical cross section in the northwestern corner of the Gulf at the time when the moisture surgein the US is a maximum. The sensitivities (VJ) are used in conjunction with a set of optimalperturbations to estimate the impact of each of the perturbations on the moisture flux. The perturbationsare chosen to have the structure of the sensitivities (making them optimal as describedin the text), with magnitudes based on the (assumed) uncertainties in the model’s initial andboundary conditions. The linear impact estimate is simply the projection of the perturbation ontothe sensitivity fields. In complementary fashion, we introduce perturbations into the nonlinearforecast 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 experimentwe conclude the following. J is more sensitive to the temperature field than to the other prognosticvariables, roughly by a factor of 3 or 4, based on the optimal perturbations used here. The sensitivityto each of the 3-D prognostic variables peaks in the lower atmosphere near 85 kPa. The sensitivityof 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 comparableto the impact of an optimal perturbation to the whole 3-D air temperature field. The zonesof sensitivity to the T_s are intimately tied to the trajectories of low-level air which terminate at thecross section. The impact of an optimal perturbation to the topography along the Sierra MadreOriental mountains is comparable to the impact of optimal perturbations in each of the 3-Dprognostic variables (except T ).