Feedbacks in the land-surface and mixed-layer energy budgets

A mixed-layer model of the surface energy budget and the planetary boundary layer (PBL) is developed, based on the prognostic equations for soil temperature, mixed layer potential temperature and specific humidity and the growth and abrupt collapse of the PBL. Detailed parameterizations of the longwave radiative fluxes are included. The feedbacks in the uncoupled (i.e. surface energy budget with non-responding PBL) and coupled land surface and atmospheric mixed-layer energy budgets are examined. A simplified, time continuous, version of the model, in which the specific humidity budget is the balance of evapotranspiration and dry-air entrainment, and the PBL height is given by the lifted condensation level, is shown to be in good agreement with the complete model. By forcing the simplified model with daily mean rather than periodic solar radiation, an equilibrium model state is achieved where the fluxes are in close agreement with the daily mean fluxes corresponding to the periodic forcing. The model also agrees favorably with measurements from the FIFE field experiment. Feedbacks are examined using the equilibrium model state. The uncoupled and coupled model sensitivities with respect to the minimal stomatal resistance and the atmospheric specific humidity not only differ in magnitude, but in sign as well. This results puts into question the extent to which uncoupled land-surface models that are forced with atmospheric variables may be used in sensitivity studies.