16B.3 PLANETARY BOUNDARY LAYER FEEDBACK AND ITS ROLE IN THE CLIMATE CHANGE Igor N. Esau Nansen Environmental and Remote Sensing Center and Bjerknes Centre for Climate Research, Thormohlensgt. 47, 5006 Bergen, Norway; e-mail: igore@nersc.no 1. INTRODUCTION An energy balance model of the Earth’s Climate System (ECS) could be written as (Schwartz, 2007) L S dt d C a − = / θ (1) where C is the ECS heat capacity (per unit area); a θ is the ECS temperature, which could be associated with the surface (potential) air temperature (a popular characteristic of climate); and L S − is the balance of incoming and outgoing radiation at the top of the atmosphere. In majority of climate publications, C is taken as given property of the ECS. It is assumed that the system heat capacity is probably known with uncertainty (Hansen et al., 1985) but neither changing significantly with climate nor imposing significant feedbacks on the ECS. Hence the main attention of climatologists is focused on processes and feedbacks directly or indirectly affecting the radiation balance L S − . The formulation (1) could be further specified for an atmospheric column as C Q dt d a / / = θ (2) where Q is the heat flux divergence in the column, which includes also the divergence of the horizontal heat fluxes, the heat storage in the soil/ocean and the balance of the latent heat fluxes due to condensation and evaporation. If the vertical turbulent mixing in the planetary boundary layer (PBL) of thickness, h , is faster than the other dynamical or radiation processes, then the vertical temperature gradient, z a ∂ ∂ / θ , is height independent inside the PBL and smaller than the gradient in the free atmosphere. In well mixed convective PBL, this quantity is z a ∂ ∂ / θ = 0. Then the temperature evolution will be determined by a trivial equation ( ) h c Q C Q dt d p a ρ θ / / / = = (3) where p c , ρ are air density and the air specific heat at constant pressure. Integration of Eq. (3) over climatological time scales would give the mean surface air temperature in the ECS. There is however an important difficulty, the global and even more so the regional heat capacity of the ECS is determined by the PBL thickness h . This quantity varies by several orders of magnitude on daily and seasonal time scales depending on the atmospheric stability, measured, in the case of small baroclinicity, with the Brunt-Vaisala frequency z g N a ∂ ∂ = / θ β , where g =9.81 [m s -2 ] is the acceleration due to gravity and β =0.003 [K -1 ] is the thermal expansion coefficient. The PBL thickness ) (t h is an integral measure of the vertical turbulent mixing in the PBL. This quantity and its evolution depend on a number of control parameters, including Q as well as characteristics of the atmospheric circulation such as the large-scale wind speed U . Early studies did not include ) (t h or the turbulent mixing directly, but apply a convective adjustment procedure. The procedure adjusted the vertical temperature gradient in a model to the observed one, i.e. z a ∂ ∂ / θ > z obs ∂ ∂ / θ , and in this sense implicitly accounted for the turbulent mixing. Manabe and Strikler (1965) were probably the first who recognized the role of the turbulent mixing in the ECS. In their continuously heated radiation-convection model, this role was strongly negative and lowered the surface temperature by 44 o K relative to the ECS radiation equilibrium. This and following studies with the radiation- convective models (e.g. Cunnington and Mitchell, 1990; Moraes et al., 2005) were not very realistic as they studied the conditions of continues heating in the ECS. Contrary, as Eq. (3) suggests, the largest response on variations of Q , which includes changes in the radiation balance due to the accumulation of the greenhouse gases, should be found in the thinnest PBL. The latter ones are typical for the conditions of the net radiation cooling, i.e. in nocturnal and long-lived wintertime high-latitude PBL. Up to my knowledge, Manabe and Wetherald (1975) were first who has attributed the amplified a θ response in high latitudes on doubling CO2 concentration in simulations with GFDL climate model to the restrictions on the vertical turbulent mixing in a more statically stable polar atmosphere. This effect is quoted as the polar amplification of the global