Feedback between the Land Surface Energy Balance and Atmospheric Boundary Layer Diagnosed through a Model and Its Adjoint

In this paper, the differences in (daytime) sensitivity of surface turbulent fluxes to states and parameters for a coupled land–atmospheric boundary layer model in coupled and uncoupled modes are investigated using an adjoint framework. The adjoint approach yields diagnostic insight into sensitivity pathways that is not readily obtained when using a traditional forward sensitivity framework. It is shown that the corresponding uncoupled adjoint model is a special case of the coupled adjoint model in which the atmospheric feedback pathways are “closed.” These closed sensitivity pathways are directly responsible for the differences in sensitivity between the uncoupled and coupled models. Integrating the adjoint models about a consistent and common trajectory provided by the forward model yields the sensitivities of the surface turbulent fluxes to all of the model states and parameters, which are shown to be significantly different because of the boundary layer feedbacks. Furthermore, the adjoint sensitivity approach allows the estimation of time-varying parameter sensitivities, which are shown to be important for this system with its strong diurnal component. The results from this study clearly show the importance of using a coupled model when trying to determine sensitivities of land–atmosphere interactions to surface state variables and parameters and also indicate that “offline” land surface model intercomparison sensitivity studies can be incomplete and misleading.