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Role of advection and penetrative convection in affecting the mixing-height variations over an idealized metropolitan area

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Abstract

This study deals with the variability of mixing height during daylight hours in the summer months for weak wind regimes. A two-dimensional model was employed using simulated input variables which are quite representative of conditions found over the midwestern United States in late summer and early fall. With the aid of this model and various analytical techniques, the dependence of the urban mixing height on such factors as horizontal advection, downward heat flux across the stable mixing-layer interface, lapse rate in the stable layer, etc., was delineated and compared with actual mixing height variations observed in St. Louis, Missouri during selected days for August, 1972.

The experiment indicated the following: (1) A spatially symmetric surface heating profile over a city is accompanied by a similarly symmetric mixing-height profile in the absence of vertical wind shear; (2) When the same heating assumption is invoked and vertically variable wind profiles are introduced, the model-generated mixing-height contours become increasingly asymmetric with vertical wind shear; (3) The modelled mixing heights are more sensitive to temperature fluctuations than to those of wind over the range of speeds studied (wind speeds ⩽4ms−1); (4) Present operational methods of predicting the time of erosion of an inversion (based upon forecast surface temperature ranges and adiabatic diagram considerations) underestimate breakup time by a factor which is proportional to the amount of available downward heat flux from the stable layer into the mixed layer below.

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Abbreviations

a :

amplitude of heating

D :

total distance (=200 km)

F H :

a quantity proportional to the downward flux of sensible heat from the stable layer as measured at the top of the mixing layer

Fs :

a quantity proportional to the flux of sensible heat from the Earth's surface as measured at the top of the surface layer

H :

height of the mixing layer minus the height of the surface layer (approximated in this study to be the height of the mixing layer)

H 0 :

initial height of the mixing layer

k :

refers to individual grid numbers

K :

the total number of grid points

l :

refers to the individual time steps

L :

the total number of time steps

R :

a combination of constants R≡α/(α+1)γ s

t :

an independent variable, time; also the time step

u :

wind component along thex axis at the inversion interface

u 1 :

wind speed in the mixing layer

w :

wind speed along theZ axis

W H :

vertical motion due to subsidence

x :

a horizontal grid distance (5 km)

X :

an independent variable signifying the direction paralleling the mean wind flow

Z :

vertical coordinate, usually height

α :

ratio of the magnitudes of downward to upward sensible heat fluxes into the mixing layer

γ s :

lapse rate in the stable inversion air

θ :

potential temperature

()′:

turbulent component of () in the mixing layer

()* :

indicates a dimensionless quantity

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Author notes

  1. Dale C. Barnum (Lt. Colonel, USAF)

    Present address: HQ 6th WEA WG, Andrews AFB, Md., USA

Authors and Affiliations

  1. HQ Air Weather Service (MAC), Scott Air Force Base, Ill., USA

    Dale C. Barnum (Lt. Colonel, USAF)

  2. Dept. of Earth and Atmospheric Sciences, Saint Louis University, Saint Louis, Mo., USA

    Gandikota V. Rao

Authors
  1. Dale C. Barnum
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  2. Gandikota V. Rao
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Barnum, D.C., Rao, G.V. Role of advection and penetrative convection in affecting the mixing-height variations over an idealized metropolitan area. Boundary-Layer Meteorol 8, 497–514 (1975). https://doi.org/10.1007/BF02153567

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  • DOI: https://doi.org/10.1007/BF02153567

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