Observations and Models of Boundary-Layer Processes Over Complex Terrain What is the planetary boundary layer (PBL)? What are the effects of irregular.

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?

Effects of irregular terrain on PBL structure

• Flow over hills (horizontal scale a few km; vertical scale a few 10’s of m up to a fraction of PBL depth)

• Flow over heterogeneous surfaces (small-scale variability with discontinuous changes in surface properties)

Flow over a hill (neutral stability)

• Idealized profile (Witch of Agnesi profile):

(After Maria Agnesi; Milano, Italy, 1748)

2

1

1h

z hxL

(Kaimal & Finnigan, 1994).

(Kaimal & Finnigan, 1994).

(Kaimal & Finnigan, 1994).

(Kaimal & Finnigan, 1994).

Regions of Flow Over Hills

• Inner layer – region where turbulent stresses affect changes in mean flow. Hunt et al. (1988) obtain the relation for ℓ:

• Outer layer – height at which shear in upwind profile ceases to be important:

• For h = 10 m, Lh = 200 m and z0 = 0.02 m, ℓ = 10 m and hm = 66 m

2

0

ln 2h

kL z

1/ 2

0

ln hm h

Lh L

z

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

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)

Effects of variations in surface roughness

Changes in surface roughness

• Characterized by change in roughness length –

• , where upwind

roughness length and downwind roughness length

0z01

02

lnz

Mz

01z

02z

Surface-layer internal boundary layer

We define internal BL by (subscript θ for temperature and c for 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

102 02

i xA

z z

1 0.75 0.03A M ,

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 at 02i z 0,x

102

ln 1i i B kx z

With this gives reasonable agreement With observations. (Works best from smooth to rough).

1 1.25,B

0 200 400 600 800 1000

xm0

20

40

60

80

100

im z2.001

z2.01

z2.1

z21z02=1

z02= 0.1

z02=0.001

z02=0.01

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

Effects of changes in surface energy fluxes

The Surface Energy Budget

The thermal energy balance at the bottom of the surface layer is conventionally written as Rn = H + λeE + Gs ,where Rn is the net radiation: short- and long-wave incomingminus outgoing, H is the sensible heat flux, λeE is the latentheat flux, and Gs is the heat flux going into storage in the soilor vegetation.

(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 andBlack, 1985).

(a)

Rn

λeE

H

Gs

Effects of changes in incoming solar radiation

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)

Total daily direct-beam solar Radiation 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

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. afterbreezes sunrise (Oke, 1987, based on Whiteman, 1982)

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 valuesfrom MAP; e/u*

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

σu /u* σv /u* σw /u* e /u*2

Flat uniform terrain

2.39 1.92 1.25 5.48

Rolling terrain

2.65±4.50 2.00±3.80 1.20±1.24 6.23±18.11

Along valley 2.19 2.13 1.55 5.88

Suggestions for Further ReadingMain 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.