Interpretation of the Structure and Evolution of Adjoint-Derived Forecast Sensitivity Gradients

A 36-h adjoint-based forecast sensitivity study of three response functions defined in the lower troposphere—average temperature in an isolated region of the upper Midwest (R1), meridional temperature difference (R2), and average zonal component of the wind (R3)—is conducted with the goal of providing a synoptic and dynamic interpretation of the sensitivity gradient structure and evolution. In addition to calculating and interpreting the sensitivity gradients with respect to basic model variables along the model forecast trajectory, a technique is outlined that allows for the calculation of the sensitivity gradients with respect to variables derivable from the model state vector (including geopotential, relative vorticity, and divergence), and a method for visualizing the sensitivities with respect to the horizontal components of the wind is proposed and demonstrated. The sensitivity of R1 to all model and derived variables revealed that R1 was controlled by nearly adiabatic processes associated with the addition or generation of temperature perturbations upstream of the region in which R1 was defined. For R2, the sensitivity gradients revealed the well-known influence of confluent horizontal flow and vertical tilting of isentropes to increase the north–south temperature gradient over the region within which R2 was defined. The sensitivity of R3 to the components of the horizontal wind reveals that simply adding or generating an upstream zonal wind perturbation is insufficient to change the zonal wind at 36 h as these wind perturbations upstream of the domain within which R3 is defined are torqued by the Coriolis force as they are advected toward the domain. These results suggest adjoint-derived sensitivities of quasi-conserved response functions may be more easily interpretable than sensitivities calculated for nonconserved response functions.