From Boundary Layer Climates, T.R. OKE

1. Pabitra Gurung
CHAPTER 5
CLIMATES OF NON-
UNIFORM TERRAIN

2. CONTENTS
1. Effects of spatial inhomogeneity
(a)Advective effects
(b)Thermal circulation systems
2. Effects of topography
(a)Radiation loading effects
(b)Topographically-generated winds
(c)Topographically-modified winds

3. 1. EFFECTS OF SPATIAL INHOMOGENEITY
Moisture advection from a dry to a wet surface. (a) Evaporation rates and the vapour balance of a
surface air layer, (b) Surface evaporation rate (𝐸0), and mean water vapour concentration of the air
layer, (c) Vertical profile of water vapour in relation to the developing boundary layer
The development of an internal boundary layer as air flows from a
smooth, hot, dry, bare soil surface to a rougher, cooler and
more moist vegetation surface
A = the rate of horizontal moisture
transport
Advective effects
 Clothesline effect: The flow of air through a vegetative
canopy
 Leading-edge or fetch effect: Air passes from one surface-
type to a new and climatically different surface
 Oasis effect: Due to evaporation cooling, an isolated
moisture source always cooler than its surroundings (Desert
oasis)

4. 1. EFFECTS OF SPATIAL INHOMOGENEITY
(a) Adjustment of surface sensible heat flux (𝑄 𝐻0
) and mean air temperature ( 𝑇) as air passes from a hot to a cooler surface. (b)
Change in surface shearing stress (𝜏0) and mean wind speed ( 𝑢) as air flows from a smooth to a rougher surface. Associated
modification of the vertical profiles of (c) air temperature, and (d) wind speed at different distances downward of the leadi ng edge
Advective effects
 Clothesline effect: The flow of air through a vegetative
canopy
 Leading-edge or fetch effect: Air passes from one surface-
type to a new and climatically different surface
 Oasis effect: Due to evaporation cooling, an isolated
moisture source always cooler than its surroundings (Desert
oasis)
The development of an internal boundary layer as air flows from a
smooth, hot, dry, bare soil surface to a rougher, cooler and
more moist vegetation surface

5. (a) Horizontal profile of surface radiation temperature, and (b) hot and cold
‘plumes” over a diverse prairie landscape. Based on aircraft observations on
the afternoon of 6 August 1968 near Brooks, Alberta
1. EFFECTS OF SPATIAL INHOMOGENEITY
Average daily energy balance of an alfalfa crop in June 1964
near Phoenix, Arizona (33°N), The crop was irrigated by flooding
in late May and this followed by drought throughout June
Advective effects
 Clothesline effect: The flow of air through a vegetative
canopy
 Leading-edge or fetch effect: Air passes from one surface-
type to a new and climatically different surface
 Oasis effect: Due to evaporation cooling, an isolated
moisture source always cooler than its surroundings (Desert
oasis)

6. 1. EFFECTS OF SPATIAL INHOMOGENEITY
Thermal circulation systems
 Land and sea (Lake) breezes
o Water allows transmission of SW radiation to
considerable depths
o Water is able to transfer heat by convection
and mixing
o Water converts much of its energy surplus
into latent rather than sensible heat
o Water has large thermal inertia due to its
higher heat capacity
 Other thermal breezes
o A city can generate ‘country breezes’ Land and sea (lake) breeze circulations across a shoreline
(a) by day and (b) at night, during anticyclonic weather

7. 2. EFFECTS OF TOPOGRAPHY
Radiation loading effects
The diurnal variation of direct-beam solar radiation upon surfaces with different
angles of slope and aspect at latitude 40°N for (a) the equinoxes (21 Mar, 21
Sep), (b) summer solstice (22 Jun), and (c) winter solstice (22 Dec)
(a) Diagrammatic representation of the angle 𝜃 between the surface and the incident
direct-beam short-wave radiation, 𝑆, (b) The form of the cosine law of illumination
𝑺 = 𝑺𝒊 𝒄𝒐𝒔 𝜽
Total daily direct-beam solar
radiation ( 𝑆) incident upon slopes
of differing angle and aspect at
latitude 45°N at the times of the
equinoxes

8. 2. EFFECTS OF TOPOGRAPHY
Topographically-generated winds
 By day: The slopes and floor of the valley will be heated. [Anabatic winds: Unstable upslope flow]
 By night: The lower air layers cool and slide down-slope under the influence of gravity. [Katabatic winds]
Mountain and valley wind system viewed with the reader looking up-valley. (a) By day slope winds are anabatic, and the valley
wind fills the valley and move upstream with the anti-valley wind coming downstream. (b) At night the slope winds are katabatic
and reinforce the mountain wind which flows downstream, with the anti-mountain wind flowing in the opposite direction above.
Time sequence of valley inversion destruction including potential temperature
profile at valley centre (left) and cross-section of inversion layer and motions
(right), at each time. (a) Nocturnal valley inversion, (b) start of surface
warming after sunrise, (c) shrinking stable core and start of slope breezes,
(d) end of inversion 3-5 h after sunrise.

9. 2. EFFECTS OF TOPOGRAPHY
Topographically-generated winds
The vertical distribution of along-valley winds in a 1 km deep valley on
Mt. Rainer, Washington. Horizontal scale is graduated in units of wind
speed and separated into two wind directions (up and down valley)
Variation of air temperature with distance along a traverse route over hilly terrain in the
early morning following a good radiation night. Note the correspondence of elevation
and temperature. The vertical distance scale is exaggerated to aid comparison.

10. 2. EFFECTS OF TOPOGRAPHY
Topographically-modified winds
 Flow over moderate topography
 Flow over steep topography
 Flow over roughness changes
Typical patterns of airflow over moderate
topography. The point maximum (●) and
minimum (○) is also indicated [Slope ≤17°]
Typical patterns of
airflow over steep
topography [Slope >17°]
(a) Wind from rough to smooth, (b) Wind from smooth to rough, (c) Wind parallel to the boundary
with the rougher area to the right of the wind, (d) Wind parallel to the boundary with the smoother
area to the right of the wind, and (e) Airflows across an isolated area of greater roughness

11. 2. EFFECTS OF TOPOGRAPHY
Topographically-modified winds
 Flow over moderate topography
 Flow over steep topography
 Flow over roughness changes
Problems of pollution dispersal on the windward slope of a steep sided valley. In (a) plume contents
are trapped in the lee eddy, and in (b) are forced to ground level by ‘downwash’

12. ADDITIONAL SLIDES FROM PREVIOUS CHAPTERS

13. o Diurnal variation of the important radiation budget
components
o Diffusion of radiation (Cloud, water vapour haze,
smoggy areas, distance between sun and
atmosphere)
o Net radiation budget
Net SW radiation, 𝐾∗
= 𝐾 ↓ −𝐾 ↑= 1 − 𝛼 𝐾 ↓
Net LW radiation, 𝐿∗ = 𝐿 ↓ −𝐿 ↑= 𝜀 𝐿 ↓ −𝜎𝑇0
4
o Total net radiation budget on the earth surface
(𝑄∗)
At day time, 𝑄∗
= 𝐾∗
+ 𝐿∗
At night time, 𝑄∗
= 𝐿∗
Radiation budget components for 30July1971, at Matador,
Saskatchewan over a 0.2 m stand of native grass in cloudless
[𝐾 ↑= 𝛼𝐾 ↓]
[𝐿 ↑= 𝜀𝜎𝑇0
4
+ 1 − 𝜀 𝐿 ↓]
DIURNAL ENERGY BALANCES AND RADIATION BUDGET
AT AN ‘IDEAL’ SITE

14. ANNUAL ENERGY BALANCES AND RADIATION BUDGET
OF E-A SYSTEM
 Energy exchanges between the earth, the
atmosphere and space
o For single wavelength
𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑣𝑖𝑡𝑦(ψλ) + 𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑣𝑖𝑡𝑦(𝛼λ)
+ 𝐴𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑣𝑖𝑡𝑦(ζλ) = 1
 Most of natural surfaces: 𝜀 ≈ 1
 Earth mean annual temp. ≈ 288 K
 Energy emitted by earth surface
= 𝜀𝜎𝑇0
4
≤ 390 𝑊𝑚−2
 Solar input (100%)
= 𝑆𝑊 𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 28% + 𝐿𝑊 𝐸𝑚𝑖𝑠𝑠𝑖𝑜𝑛(72%)
 Equilibrium: the E-A system and the E-A sub-
system
 Annual net sub-surface storage is zero
 Net 𝑄 𝐺 in annual balance is also zero
𝐾 𝐸𝑥 = 𝐾 ↑(𝐴𝑐)+ 𝐾 ↑(𝐴𝑎)+ 𝐾
∗
(𝐴𝑐)+𝐾
∗
(𝐴𝑎) +𝐾 ↑(𝐸) +𝐾
∗
(𝐴𝐸)
100% = 19% + 6% + 5% + 20% + 3% + 47%
𝐾 𝐸𝑥 = Spatial mean energy input ≈ 338 W m-2
(Values are in %)

15. RADIATION BUDGET: ORCHARDS AND FORESTS
 The principal radiative exchanges occur at the canopy
layer (upper and lower boundary)
 Approximate attenuation of SW with height is given Beer’s
law [𝐾 ↓ 𝑧= 𝐾 ↓0 𝑒−𝑎𝑧
]
 Amount of SW transmission depend on the height, density
and species of the stand, the angle of solar incidence
(generally 5% - 20% of flux 1 reaches floor of a stand)
Schematic model of radiation exchanges above and within a forest.
(𝐊 ↓) (𝐊 ↑)
(𝐋 ↑)(𝐋 ↓)
(𝐊 ↓)
(𝐊 ↑)
(𝐋 ↓) (𝐋 ↑)
SW radiation budget of (a) an orange orchard, and (b)
a single-layer mosaic of fresh orange leaves. All values
expressed as percentages of the incident radiation

16.  Dry adiabatic lapse rate (Γ): Constant (9.8 ℃ 𝑘𝑚−1) for dry/unsaturated air
 Environmental lapse rate (ELR): Based on actual observed temperature structure
above a given location
 (a) Unstable (ELR > Γ), (b) Stable (ELR < Γ), & (c) Neutral (ELR = Γ)
Lapse rates and stability
Warmer
Colder
Warmer
Colder
 With fine weather: Unstable by day
and Stable by night
 Over high latitude snow surfaces in
winter: Stable boundary layer for
longer period
 Over tropical ocean surfaces:
Unstable boundary layer for longer
period
Height vs temperature (a) unstable atmosphere on
sunny days and (b) stable atmosphere at night
SURFACE LAYER CLIMATES & EXCHANGES

17. THANK YOU