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Mixed-layer heat advection and entrainment during the sea breeze

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Abstract

A model is developed to simulate the potential temperature and the height of the mixed layer under advection conditions. It includes analytic expressions for the effects of mixed-layer conditions upwind of the interface between two different surfaces on the development of the mixed layer downwind from the interface. Model performance is evaluated against tethersonde data obtained on two summer days during sea breeze flow in Vancouver, Canada. It is found that the mixed-layer height and temperature over the ocean has a small but noticeable effect on the development of the mixed layer observed 10 km inland from the coast. For these two clear days, the subsidence velocity at the inversion base capping the mixed layer is estimated to be about 30 mm s−1 from late morning to late afternoon. When the effects of subsidence are included in the model, the mixed-layer height is considerably underpredicted, while the prediction for the mean potential temperature in the mixed layer is considerably improved. Good predictions for both height and temperature can be obtained when values for the heat entrainment ratio,c, 0.44 and 0.68 for these two days respectively for the period from 1000 to 1300 LAT, were used. These values are estimated using an equation including the additional effects on heat entrainment due to the mechanical mixing caused by wind shear at the top of the mixed layer and surface friction. The contribution of wind shear to entrainment was equal to, or greater than, that from buoyant convection resulting from the surface heat flux. Strong wind shear occurred near the top of the mixed layer between the lower level inland flow and the return flow aloft in the sea breeze circulation.

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Abbreviations

c :

entrainment parameter for sensible heat

c p :

specific heat of air at constant pressure, 1010 J kg−1 K−1

d 1 :

the thickness of velocity shear at the mixed-layer top, m

Q H :

surface sensible heat flux, W m−2

u m :

mean mixed-layer wind speed, m s−1

u * :

friction velocity at the surface, m s−1

w :

subsidence velocity, m s−1

W :

subsidence warming,oC s−1

w e :

entrainment velocity, m s−1

w * :

convection velocity in the mixed layer, m s−1

x :

downwind horizontal distance from the water-land interface, m

y :

dummy variable forx, m

Z :

height above the surface, m

Z i :

height of capping inversion, m

Z m :

mixed-layer depth, i.e.,Z i−Zs, m

Z s :

height of the surface layer, m

γ⊙ :

lapse rate of potential temperature aboveZ i, K m−1

Δ⊙ :

potential temperature step atZ i, K

Δu h :

velocity step change at the mixed-layer top

⊙ m :

mean mixed-layer potential temperature, K

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Author notes

  1. J. M. Chen

    Present address: Global Monitoring Section, Canada Centre for Remote Sensing, 588 Booth Street, 4th Floor, K1A 0Y7, Ottawa, Ontario, Canada

Authors and Affiliations

  1. Department of Geography, University of British Columbia, V6T 1Z2, Vancouver, B.C., Canada

    J. M. Chen & T. R. Oke

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  1. J. M. Chen
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Chen, J.M., Oke, T.R. Mixed-layer heat advection and entrainment during the sea breeze. Boundary-Layer Meteorol 68, 139–158 (1994). https://doi.org/10.1007/BF00712668

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