A simple two-system-parameter model for surface-effected warming of the planetary boundary layer

Research paper by J. Otterman

Indexed on: 01 May '90Published on: 01 May '90Published in: Boundary-Layer Meteorology


The heat input into the planetary boundary layer (PBL) resulting from surface-atmosphere interactions under extremely arid conditions is formulated as a linear differential equation. The forcing for this heat input is the product of the shortwave (solar) absorption at the surface and the surface-to-PBL heat transfer efficiency, η. This efficiency is determined by five variables: the turbulent heat transfer coefficient, the soil heat conductance, the surface longwave emissivity, the surface temperature, and the fraction of the longwave flux from the surface absorbed within the PBL. The first two variables may vary by orders of magnitude, while the others vary much less.If a simplifying assumption is made that these variables and the thickness of the PBL do not vary with time, and that the shortwave absorption by the surface is given by a half-sine wave, then the PBL temperature cycle can be explicitly expressed (by exponential and trigonometric functions) as dependent on only two system parameters: (i) the system time constant and (ii) the transfer efficiency η divided by the thermal capacity of the PBL. The shape of this diurnal cycle depends solely on the system time constant, which is a simple function of the thermal capacity of the PBL, the PBL temperature, and the same variables that define η. For a small time constant, the peak PBL temperature will occur near noon, while for large values it will occur close to sunset. The amplitude of this diurnal cycle is proportional to the product of η and the peak (noon) shortwave absorption at the surface, and also depends very strongly on the system time constant.A concept of trans-absorptivity, that specifies the heat input into the PBL resulting from the shortwave absorption by the surface, is introduced and discussed in terms of the governing equations. The trans-absorptivity is given as the product of the surface absorptivity (the co-albedo) and the efficiency η. It is suggested that climatic effects of surface changes, such as removal of vegetation, should be formulated in terms of changes in the trans-absorptivity.