Atmospheric Boundary-Layer Dynamics with Constant Bowen Ratio |
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| Authors: | Amilcare Porporato |
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| Institution: | (1) Department of Civil and Environmental Engineering, Duke University, Durham, NC, USA;(2) EFLUM-EPFL, Lausanne, Switzerland |
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| Abstract: | Motivated by the observation that the diurnal evolution of sensible and latent heat fluxes tends to maintain a constant Bowen
ratio, we derive approximate solutions of the ordinary differential equations of a simplified atmospheric boundary-layer (ABL)
model. Neglecting the early morning transition, the potential temperature and specific humidity of the mixed layer are found
to be linearly related to the ABL height. Similar behaviour is followed by the inversion strengths of temperature and humidity
at the top of the ABL. The potential temperature of the mixed layer depends on the entrainment parameter and the free-atmosphere
temperature lapse rate, while the specific humidity also depends on the free-atmosphere humidity lapse rate and the Bowen
ratio. The temporal dynamics appear only implicitly in the evolution of the height of the boundary layer, which in turn depends
on the time-integrated surface sensible heat flux. Studying the limiting behaviour of the Bowen ratio for very low and very
large values of net available energy, we also show how the tendency to maintain constant Bowen ratio during midday hours stems
from its relative insensitivity to the atmospheric conditions for large values of net available energy. The analytical expression
for the diurnal evolution of the ABL obtained with constant Bowen ratio is simple and provides a benchmark for the results
of more complex models. |
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| Keywords: | Atmospheric boundary layer Bowen ratio Evaporation Mixed layer Slab model |
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