boundary models

7/29/2019 Boundary Models

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Observations and Models of

Boundary-Layer Processes Over

Complex Terrain What is the planetary boundary layer (PBL)?

What are the effects of irregular terrain on the basic

PBL structure?

How do we observe the PBL over complex terrain?

What do models tell us?

What is our current understanding of the PBL and

what are the outstanding problems to be addressed?


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Effects of irregular terrain on PBL

structure Flow over hills (horizontal scale a few km;

vertical scale a few 10s of m up to a fraction

of PBL depth) Flow over heterogeneous surfaces (small-

scale variability with discontinuous changes

in surface properties)


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Flow over a hill (neutral stability)

Idealized profile (Witch of Agnesi profile):

(After Maria Agnesi; Milano, Italy, 1748)

2

1

1

h

z hx

L


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(Kaimal & Finnigan, 1994).


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Regions of Flow Over Hills

Inner layer region where turbulent stresses affect changes in

mean flow. Hunt et al. (1988) obtain the relation for:

Outer layer height at which shear in upwind profile ceases to

be important:

Forh = 10 m, Lh = 200 m and z0 = 0.02 m, = 10 m and

hm = 66 m

2

0

ln 2h

k

L z

1/ 2

0

ln hm h

Lh L

z


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Effects of horizontal heterogeneity in

surface properties Changes in surface roughness

Rough to smooth

Smooth to rough

Changes in surface energy fluxes Sensible heat flux

Latent heat flux

Changes in incoming solar radiation Cloudiness

Slope


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Scale of changes in PBL downwind

of discontinuity Confined to surface layer (10 to 50 m)

Entire PBL (10 to 100 km)

Mesoscale (geostrophic adjustment;> 100 km)


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Effects of variations in

surfaceroughness


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Changes in surface roughness

Characterized by change in roughness length

, where upwind

roughness length and downwind

roughness length

0z

01

02ln

z

M z01

z

02

z


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Surface-layer internal boundary layer

We define internal BL by (subscript for

temperature and cfor other scalars). The

simplest formulations for are of the form

(analogous to BL growth on a smooth flat plate

in wind tunnel experiments.)

i

0.8

1

02 02

ix

Az z

1 0.75 0.03A M ,


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Surface-layer internal boundary layer

A more sophisticated approach is to assume

vertical diffusion then,*2 ,u

02

*2 *21 , ( , ) ln .( , )

id u u z

B U x zdx U x z k z

With at02i z 0,x

1

02ln 1

i i

B kx z

With this gives reasonable agreement

With observations. (Works best from smooth to

rough).

1 1.25,B


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z02=1

z02= 0.1

z02=0.001

z02=0.01


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From Oke, T.R., 1987: Boundary Layer Climates


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Effects of changes in surface

energy fluxes


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The Surface Energy BudgetThe thermal energy balance at the bottom of the surface layer

is conventionally written as

Rn = H + eE + Gs,

whereRn is the net radiation: short- and long-wave incoming

minus outgoing,His the sensible heat flux, eEis the latent

heat flux, and Gs is the heat flux going into storage in the soil

or vegetation.


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(a) Surface energy budget termsfor clear skies over a moist, bare

soil in the summer at mid-lati-

tudes. (b) Temperatures at the

surface, at 1.2 m height in the air,

and at 0.2 m depth in the soil

(from Oke, 1987 after Novak and

Black, 1985).

(a)

Rn

eE

H

Gs


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Effects of changes in incoming

solar radiation


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Diurnal variation of direct-beam solar radiation

On surfaces with different angles of slope and

aspect ratio at 40 N latitude for:

(a) the equinoxes (21 March and 21 September)

(b) summer solstice (22 June)

(c) winter solstice (22 December)

(Oke, 1987)


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Total daily direct-beam solarRadiation incident upon

Slopes of differing angle and

Aspect ratio at 45 N at the

times of the equinoxes(21 March and 21

September).

Oke, 1987


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Time sequence of valley inversion destruction along with potential temperature

profile at valley center (left) and cross-section of inversion layer and motions(right).

(a) nocturnal valley inversion (b) start of sfc. warming after sunrise

(c) shrinking stable core & start of slope (d) end of inversion 3-5 hrs. after

breezes sunrise (Oke, 1987, based onWhiteman, 1982)


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Normalized surface-layer velocity standard deviations for near

neutral conditions in the Adige Valley in the northern Italy alpine

region. a is from Panofsky and Dutton, 1984; b the average values

from MAP; e/u*2

is the normalized turbulence kinetic energy(From de Franceschi, 2002).

u/u* v/u* w/u* e/u*2

Flat uniform

terrain

2.39 1.92 1.25 5.48

Rolling

terrain

2.654.50 2.003.80 1.201.24 6.2318.11

Along valley 2.19 2.13 1.55 5.88


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Suggestions for Further Reading

Main Reference Sources for these Lectures

Belcher, S.E. and J.C.R. Hunt, 1998: Turbulent flow over hills and waves.

Annu. Rev. Fluid Mech.. 30:507-538.

Blumen, W., 1990: Atmospheric Processes Over Complex Terrain.

American Meteorological Society, Boston, MA.

Geiger, R., R.H. Aron and P. Todhunter, 1961: The Climate Near the

Ground. Vieweg & Son, Braunschweig.

Kaimal, J.C. and J.J. Finnigan, 1994: Atmospheric Boundary Layer Flows.

Oxford Univ. Press, New York.

Oke, T.R., 1987: Boundary Layer Climates. Routledge, New York.

Venkatram, A. and J.C. Wyngaard, Eds.,1988: Lectures on Air Pollution

Modeling. American Meteorological Society, Boston MA.

Abstracts from the10th Conference on Mountain Meteorology, 17-21 June

2002, Park City, UT, American Meteorological Society, Boston.

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