From Boundary Layer Climates, T.R. OKE

1. Pabitra Gurung
CHAPTER 4
CLIMATES OF
VEGETATED
SURFACES

2. CONTENTS
1. Special features
(a) Energy and water storage in vegetation
systems
(b) Photosynthesis and carbon dioxide exchange
(c) Effects of stand architecture
2. Leaves
(a) Radiation budget
(b) Energy balance
(c) Climate
3. Plant covers and crops
(a) Mass balances
(b) Radiation budget
(c) Energy balance
(d) Climate
4. Orchards and forests
(a) Mass balances
(b) Radiation budget
(c) Energy balance
(d) Climate
5. Comparison of low plant and forest water use

3. Schematic depiction of fluxes involved in (a) the energy
and (b) the water balances of a soil-plant-air volume
1. SPECIAL FEATURES
Energy and water storage in vegetation systems
 Energy balance:
𝑄∗
= 𝑄 𝐻 + 𝑄 𝐸 + ∆𝑄 𝑆 + ∆𝑄 𝑃 + ∆𝑄 𝐴,
Where,
∆𝑄 𝑃 = Biochemical energy storage due to
photosynthesis
∆𝑄 𝐴 = net horizontal energy transfer due to advection
 Water balance:
𝑝 = 𝐸 + ∆𝑟 + ∆𝑆 + ∆𝐴,
Where,
∆𝑆 = net water storage in the air and soil
∆𝐴 = net horizontal moisture exchange due to
advection

4. 1. SPECIAL FEATURES
Photosynthesis and carbon dioxide exchange
Plant growth is tied to the supply of solar radiation and carbon dioxide through the processes
of photosynthesis and respiration.
 Gross photosynthesis (𝑃) [kg m-2 s-1]
𝐶𝑂2 + 𝐻2 𝑂 + 𝐿𝑖𝑔ℎ𝑡 𝑒𝑛𝑒𝑟𝑔𝑦 → 𝐶𝐻2 𝑂 𝑜𝑟 𝐶6 𝐻12 𝑂6 + 𝑂2
 Respiration (𝑅) [kg m-2 s-1]
𝐶𝐻4 𝑜𝑟 𝐶6 𝐻12 𝑂6 + 𝑂2 → 𝐶𝑂2 + 𝐻2 𝑂 + 𝐶𝑜𝑚𝑏𝑢𝑠𝑡𝑖𝑜𝑛 𝑒𝑛𝑒𝑟𝑔𝑦
 Net rate of photosynthesis, ∆𝑃 = 𝑃 − 𝑅 [kg m-2 s-1]
 Energy stored due to net photosynthesis, ∆𝑄 𝑃 = ∅∆𝑃, Where ∅ = Heat of assimilation
of carbon ≈ 1.15 × 107 𝐽 𝑘𝑔−1 ≈ 3.2 𝑊 𝑚−2 𝑝𝑒𝑟 𝑔𝑚−2ℎ−1 of 𝐶𝑂2 assimilation
 By day, the crop is a net 𝐶𝑂2 sink because 𝑃 > 𝑅 and ∆𝑃 is positive
 By night, the crop is a net 𝐶𝑂2 source because 𝑃 < 𝑅 and ∆𝑃 is negative

5. 1. SPECIAL FEATURES
 Leaf stomate: passageway between the atmosphere
and the interior of the plant and tree
 Transpiration – latent heat is a major means of
dissipating the energy load on leaves
 The length of stomata depend on species (10 – 30
μm)
 Width of stomata: 0 when closed to 10 μm when fully
open
 Area covered by stomata: 0.3-1% of the total leaf
area
 Stomata density: 50 – 500 per mm2
(a) View of a partially open stomate on a wheat leaf, (b) Schematic cross-
section through a portion of a leaf illustrating the exchanges of water
vapour and CO2 through a stomate, and of heat from the leaf
Photosynthesis and carbon dioxide exchange

6. 1. SPECIAL FEATURES
Effects of stand architecture
 Foliage density and Canopy
 Foliage density: Concentrated in the overall height of the stand, near the top of the stand,
and near to the base of the stand
Typical wind profile measured above a vegetation
stand of height h, illustrating the concept of a zero
plane displacement at the height d
 Zero plane displacement, 𝑑 =
2
3
ℎ, for closely-
spaced stands
 𝑑 also depend on the drag elements and wind
speed
 𝑢 𝑧 =
𝑢∗
𝓀
𝑙𝑛
𝑧−𝑑
𝑧0
, where 𝑢 𝑧 is mean wind speed (m
s-1) at the height 𝑧, 𝑢∗ is friction velocity (m s-1),𝓀 is
von Karman’s constant (≈ 0.40), 𝑧0 is roughness
length (m)

7. Idealized relation between wavelength and the reflectivity (α),
transmissivity (Ψ) and absorptivity (ζ) of a green leaf
2. LEAVES
Radiation budget
 The deposition of incident radiation is given by Ψ + 𝛼 + ζ = 1
 Photosynthetically active radiation (PAR) [0.4 -0.7 μm] and Photosynthesis photon flux density (PPFD)
 Leaves are full radiators if 𝜀 = 0.94 to 0.99
 𝑄𝑙𝑒𝑎𝑓
∗
= 𝐾𝑙𝑒𝑎𝑓
∗
+ 𝐿𝑙𝑒𝑎𝑓
∗
= 𝐾(𝑡)
∗
+ 𝐾(𝑏)
∗
+ 𝐿(𝑡)
∗
+ 𝐿(𝑏)
∗
= ζ 𝐾𝑖𝑛 𝑡 + 𝐾𝑖𝑛 𝑏 + 𝐿𝑖𝑛 𝑡 − 𝐿 𝑜𝑢𝑡(𝑡) + 𝐿𝑖𝑛(𝑏) − 𝐿 𝑜𝑢𝑡 𝑏
Where 𝛹 𝑎𝑛𝑑 𝛼 are assumed equal for the top and bottom sides of the leaf
Schematic depiction of the fluxes involved in the
radiation budget of an isolated leaf

8. 2. LEAVES
Energy balance
 𝑄𝑙𝑒𝑎𝑓
∗
= 𝑄 𝐻(𝑙𝑒𝑎𝑓) + 𝑄 𝐸(𝑙𝑒𝑎𝑓)
= 𝑄 𝐻(𝑡) + 𝑄 𝐻(𝑏) + 𝑄 𝐸(𝑡) + 𝑄 𝐻(𝑏) ,
Where both the physical and biochemical heat storage has been
neglected.
 Sensible heat transfer between the leaf surface and the air, 𝑄 𝐻 =
𝑄 𝐻(𝑙𝑒𝑎𝑓) = 𝐶 𝑎
𝑇0−𝑇 𝑎
𝑟 𝑏
, where 𝑇0 is the leaf surface temperature, &
𝑟𝑏 is the diffusive resistance of the laminar sub-layer adhering to the
leaf.
 By solving above two equations, 𝑇0 = 𝑇𝑎 +
𝑟 𝑏
𝐶 𝑎
𝑄(𝑙𝑒𝑎𝑓)
∗
−
Schematic depiction of the fluxes involved in the
energy balance of an isolated leaf
Schematic cross-section through a portion of a leaf
illustrating the exchanges of water vapour and CO2 through
a stomate, and of heat from the leaf

9. 2. LEAVES
Climate
 A large sunlit leaf is 5 to 10°C warmer than the
surrounding air
 The leaf temperature excess increases from the
windward to the leeward side
 In the leading edge: Thinnest insulation, Greatest heat
loss and Lowest temperature
 In the trailing edge: Thickest insulation, Least heat loss
and Highest temperature
 This influences patterns of leaf ‘burn’, fungal growth and
insect activity on the leaf
 Desert plants have large leaves to maintain a thick
insulating layer (high 𝑟𝑏)
Variation of temperature over the surface of a bean leaf with a wind speed
0.7 ms-1. Values are the amount by which leaf exceeds the air
temperature (°C). [𝑇𝑎= 25.6°C, 𝑄∗
= 150 W m-2, 𝑟𝑏=400 to 1300 s m-1.

10. 3. PLANT COVERS AND CROPS
Mass balances (Water)
 The resistance offered to moisture extraction: by
the soil rsoil, by extension of root development
rroot, by the vascular system of the xylem
rxylem, by the diffusion within the leaf rleaf, by
the laminar boundary layer rb𝑜𝑢𝑛.𝑙𝑎𝑦𝑒𝑟 or rb, and
by the turbulent layers (aerodynamic) rair or r 𝑎
 Canopy resistance, 𝑟𝑐 =
𝜌 𝑣(𝑇 𝑐)
∗
−𝜌 𝑣0
𝐸
≈
𝑟𝑠𝑡
𝐴1
, where
𝜌 𝑣(𝑇𝑐)
∗
is the saturation vapour density at the
canopy surface temperature (𝑇𝑐), and 𝐴1 is the
leaf area index of the canopy. [In the case of a
wetted leaf 𝑟𝑐= 0 because the stomata play no
regulatory role] The water balance and internal flows of water in a soil-plant-atmosphere
system. At the right is an electrical analogue of the flow of water from the soil
moisture store to the atmospheric sink via the plant system
 p = E + ∆r + ∆S + ∆A, where ∆S = net water storage in the air and soil, and ∆A = net horizontal moisture
exchange due to advection

11. 3. PLANT COVERS AND CROPS
Mass balances (Carbon dioxide)
 During night: 𝐹𝐶 is directed away from the vegetation into the atmosphere (loss of CO2 from the system by
respiration from plant top)
Diurnal variation of carbon dioxide concentration in the air
at a rural site in Ohio for different months
Diurnal variation of the vertical flux of carbon dioxide
(𝐹𝐶 ) over a prairie grassland at monthly intervals
during the growing season (Data are 10-day averages)
 The seasonal decrease in 𝐹𝐶: due to soil moisture depletion
 The midday minimum: due to increase in canopy resistance (the
effects of temperature and stomatal closure)
 Growing seasons (May – July): Highest 𝐹𝐶 in the plant system and
Highest C02 concentration in the air

12. 4. ORCHARDS AND FORESTS
Mass balances
 Forest can retain a larger proportion of the precipitation as interception storage
Deciduous forest: 10% – 25% of annual precipitation
Coniferous forest: 15% - 40% of annual precipitation
The relation between the rainfall interception efficiency of tropical and
temperature forests and the amount of rain precipitated by a storm
 Interception depend on the nature of
rainstorm
 Maximum storage capacity
For rain: 0.5 – 2 mm for all forest types
For snow: 2 to 6 mm for all forest types
 Evapotranspiration (Evaporation >
Transpiration)
 The principal features of CO2 balance of
forests are same as for other vegetation

13. 3. PLANT COVERS AND CROPS
Radiation budget
 Beer’s Law: 𝐾 ↓(𝑧)= 𝐾 ↓0 𝑒−𝑎𝐴1(𝑧), where 𝑎 is extinction coefficient of plant leaves and 𝐴1(𝑧) is the leaf area
accumulated from the top of the canopy down to the level 𝑧.
Relation between the albedo of vegetation and its
height. Vertical lines: two standard deviations, &
horizontal lines: seasonal range of canopy height.
Measured profiles of (a) incoming solar (𝐾 ↓), and
(b) net all-wave radiation (𝑄∗
) in a 0.2 m stand of
native grass at Matador, Sask. Relation between the albedo of vegetation and solar
altitude on sunny days.
 Albedo and vegetation height relation is for: 1) Green vegetation surface
2) Midday period
 Albedo depends on the radiative
properties of the surfaces, stand
architecture of the plant, and the
angle of solar incidence

14. 4. ORCHARDS AND FORESTS
Radiation budget
 The principal radiative exchanges occur at the canopy
layer (upper and lower boundary)
 Approximate attenuation of SW with height is given Beer’s
law
 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

15. 4. ORCHARDS AND FORESTS
Radiation budget
 The canopy also affects diffuse radiation (𝐷) and its spectral composition
 Net all-wave radiation (𝑄∗
) is similar to other vegetation
Component fluxes of the radiation budget of a 28 m stand of
Douglas fir (coniferous forest) at Cedar River, Washington
(47°N) on the 10 August 1972
SW radiation measured above the canopy, and at one point on the
floor of a 23 m stand of Loblolly pine near Durham, N.C. (36°N) on
October 1965
Low albedo (0.09)
 𝐿 ↑ varies with the canopy surface temperature
 𝑄∗
varies with stand height, density, species & solar
altitude

16. 3. PLANT COVERS AND CROPS
Energy balance
 Net long-wave radiation budget (𝐿∗
) of vegetation is
almost always negative, as with most other surfaces.
However, the reduction of the sky view factor is reason
behind the net loss.
 Day time energy dissipating was dominated by 𝑄 𝐸 and
some occasions 𝑄 𝐸 > 𝑄∗
due to the flow of heat from the
atmosphere to the crop in the morning and afternoon
 𝑟𝑐 is very small in the morning due to dew, is almost
constant for most of the day and is high in the late
afternoon due to decreasing light intensity and increasing
water stress
(a) The radiation budget, (b) energy balance and (c) canopy resistance of a
barley field at Rothamsted, England (52°N) on 23 July 1963. [On the day
with clear skies, mostly sunny day, wind < 2.5 ms-1 & light rain at night]

17. 3. PLANT COVERS AND CROPS
Energy balance
Water relations of a field of alfalfa at Phoenix,
Arizona (33°N)
 The crop field was flooded by irrigation on 27 May.
 Soil water potential (ψ) increased with time
 After 20 June, the role of canopy resistance (𝑟𝑐) began
 On 28 June, near the limit for moisture availability for
plants (ψ = −1.1 𝑀𝑃𝑎)
 𝑟𝑐 became very large during the middle of the day
 In day time: 𝑟𝑐(31 𝑑𝑎𝑦𝑠) > 𝑟𝑐(23 𝑑𝑎𝑦𝑠) whereas
𝐸(31 𝑑𝑎𝑦𝑠) < 𝐸(23 𝑑𝑎𝑦𝑠)
(a) Daily average soil moisture potential and canopy resistance, and (b) diurnal variation of
the evaporation rate and canopy resistance at period of 23 and 31 days after irrigation.
Water stress and high leaf
temperature

18. 4. ORCHARDS AND FORESTS
Energy balance
 The principal energy budget is similar to other
vegetation
 Some nocturnal cloud at Thetford (00 to 05 h) and
some daytime cloud at Haney (11 to 20 h)
 Albedo, day length & cloud → Net radiative surplus
for the day
Diurnal energy balance of (a) a Scots and Corsican pine forest at Thetford, England (52°N) on 7 July 1971, and (b) a
Douglas fir forest at Haney, BC (49°N) on 10 July 1970, including (c) the atmospheric vapour pressure deficit
Albedo (0.08)
Albedo (0.09)

19. 4. ORCHARDS AND FORESTS
Energy balance
 The higher 𝑟𝑎 at Haney in the evening due to
local wind stagnation
 Generally, 𝑟𝑎 values are low in forests due to
roughness (more turbulent atmosphere than
the other natural surfaces, excluding
topographic effects)
 𝑟𝑐 at Thetford >> 𝑟𝑐 at Haney
 𝑟𝑐 >>> 𝑟𝑎
 𝑟𝑐 are larger in the afternoon
Diurnal variation of (a) the canopy and (b)
aerodynamic resistance of coniferous forests

20. CLIMATE
Orchards and forests
Profiles of (a) wind speed, (b) temperature, (c) vapour pressure and (d) carbon dioxide
concentration in and above a barley field at Rothamsted, England on 23 July 1963
Typical mean hourly profiles of climatological properties in a Sitka
spruce forest at Fetteresso near Aberdeen (57°N) on a sunny day in
July 1970 at midday. Also included is the profile of the leaf area
showing the vertical distribution of foliage density. The characterize
conditions above the canopy at a reference height of 13 m above the
ground: 𝐾 ↓ = 605 W m-2, 𝑄∗
= 524 W m-2, 𝑇 = 11.8°C, 𝑒 = 1,110 Pa,
𝜌 𝑐 = 315.4 ppm, 𝑢= 3.9 m s-1
Plant covers and crops

21. 5. COMPARISON OF LOW PLANT & FOREST WATER USE
 𝐸𝑡(𝑐𝑟𝑜𝑝) =
𝜌 𝑣(𝑇 𝑐)
∗
−𝜌 𝑣𝑎
𝑟 𝑐+𝑟 𝑎𝑉
 𝐸𝑡(𝑓𝑜𝑟𝑒𝑠𝑡) =
𝜌 𝑣𝑎
∗ −𝜌 𝑣𝑎
𝑟 𝑐
=
𝑣𝑑𝑑 𝑎
𝑟 𝑐
 𝐸𝑡(𝑐𝑟𝑜𝑝) > 𝐸𝑡(𝑓𝑜𝑟𝑒𝑠𝑡)
 𝐸𝑖(𝑐𝑟𝑜𝑝 𝑜𝑟 𝑓𝑜𝑟𝑒𝑠𝑡) =
𝜌 𝑣(𝑇 𝑐)
∗
−𝜌 𝑣𝑎
𝑟 𝑎𝑉
 𝐸𝑖(𝑐𝑟𝑜𝑝) < 𝐸𝑖(𝑓𝑜𝑟𝑒𝑠𝑡)
 Evapotranspiration, 𝐸 = 𝐸𝑡 + 𝐸𝑖
 In temperate climates it is common to
have wet;
Windy winters when 𝐸𝑐𝑟𝑜𝑝 < 𝐸𝑓𝑜𝑟𝑒𝑠𝑡
Less rainy summer when 𝐸𝑐𝑟𝑜𝑝 > 𝐸𝑓𝑜𝑟𝑒𝑠𝑡
Observed mean annual water and energy balances for two catchments in Wales, UK: (a) Wye catchment
(grassed)
∆𝑟
𝑝
= 0.83 𝑎𝑛𝑑
𝑄 𝐸
𝑄∗ = 0.58 (b) Severn catchment (forested)
∆𝑟
𝑝
= 0.61 𝑎𝑛𝑑
𝑄 𝐸
𝑄∗ = 1.15 .
Grass
Forest

22. THANK YOU