Chapter 1: Terrestrial Surface Energy Balance
1. Introduction
Solar radiation and atmospheric longwave radiation warm the surface and provide energy
to drive weather and climate. The energy is expended as follows
•
•
•
some of it is stored in the ground (or the oceans)
some of it is returned to the atmosphere, warming the air
the rest is used to evaporate water
These are the surface energy fluxes which we will be discussing in this chapter. Figure 1
below shows the global energy budget – this provides the proper context for the surface
fluxes of interest to us.
Figure 1: Global energy budget. Credit: IPCC (2000).
2. Surface Energy Budget
The surface energy balance equation is
(1-r)S↓ + L↓ = L↑ + H + λE + G ,
where r is the albedo of the surface (dimensionless), S↓ is the solar radiation incident on
the surface (W/m2), L↓ is the longwave radiation incident on the surface (W/m2), L↑ is
longwave radiation emitted by the surface (W/m2), H is sensible heat flux from the
surface (W/m2), λE is latent heat flux from the surface (W/m2) and G is heat conducted
away from the surface (W/m2).
The left hand side of the equation denotes the energy inputs to the surface – gain terms (also called the radiative forcing term, Qa). The right hand side of the equation denotes
energy outputs from the surface (loss terms).
Let us define net radiation as follows
Rn = (1-r)S↓ + (L↓ - L↑) ,
and rewrite the surface energy balance equation as
Rn = H + λE + G .
Thus, the energy balance equation is a statement of how net radiation is balanced by
sensible, latent and conduction heat fluxes.
Albedo: Aledo is the fraction of incident solar radiation reflected by a surface. It varies
between 0 and 1. The albedo of natural surfaces varies from about 0.1 (vegetated
surfaces) to greater than 0.9 (fresh snow). The albedo of a surface depends on the solar
zenith angle, that is, it changes during the day time.
Solar Radiation: Electromagnetic radiation from the sun is contained approximately
between 0.3 and 4 microns. The energy is inversely proportional to the wavelength. The
total solar radiation at the surface can be as high as 1000 W/m2 at midday on a sunny day.
A surface receives both direct and diffuse solar radiation. The amount of direct solar
radiation incident on a surface varies with the solar zenith angle. Diffuse solar radiation is
radiant energy that has interacted with the constituents of the atmosphere and thus has no
directionality. The fraction of diffuse radiation depends on the cloud conditions. On clear
days, the diffuse fraction is about 10-20% and varies with the solar zenith angle.
Longwave Radiation: Terrestrial objects emit electromagnetic radiation in the wavelength
range of 4 to 100 microns. The amount emitted is given by the Boltzmann’s law as
L↑ = εσ(Ts + 273.15)4 ,
where Ts + 273.15 is absolute temperature in degrees Kelvin, σ is Boltzmann’s constant
(5.67 x 10-8 Watts/m2/K4) and ε is the emissivity of the surface (between 0.95 and 1). For
example, see the top left panel of Figure 2.
Sensible Heat Flux: Movement of air carries heat and mass (water and carbon dioxide
molecules, for example) away from an object. This is called convection or sensible heat
transport. The heat flux can be represented as being directly proportional to the
temperature difference between the object and the air surrounding it and inversely
proportional to the transfer resistance (in analogy to Ohm’s law in electricity),
H = [-ρCp (Ta – Ts)] / (rH) ,
where ρ is density of air (about 1.2 kg/m3), Cp is heat capacity of the air (about 1010
Joules/kg/C), Ta and Ts are temperature of the air and the surface, respectively, and rH is
the transfer resistance (s/m), which depends on wind speed and surface characteristics.
An object loses energy if its temperature is warmer than the air surrounding it (a positive
flux) and vice versa (see Figure 2c).
Latent Heat Flux: Heat is also lost from an object through evaporation and/or
transpiration. This process involves transfer of mass and heat to the atmosphere from the
object. Clearly, a significant amount of energy is required to change the state of water
from liquid to gas. Importantly, this exchange does not involve temperature changes, that
is, as energy from the surface is released into the atmosphere, it does not result in an
increase in the temperature of the air surrounding the object. This latent heat of
vaporization varies with temperature (about 2.43 x 106 J/kg at 30C). This latent heat is
released when water vapor condenses back to liquid.
Example: A typical summertime evaporation rate of 5 mm of water per day per square
meter is equivalent to 5 kg of water per square meter (assuming the density of water to be
1000 kg per cubic meter). This evaporation rate is equivalent to about 141 Watts per
square meter – comparable to daily (24 hr) average solar radiation of about 200 Watts per
square meter on a clear day.
Evaporation is related to the vapor pressure deficit of air – the difference between the
actual amount of water in the air and the maximum possible when saturated. The
saturation vapor pressure increases exponentially with warmer temperature.
Relative Humidity: Ratio of actual vapor pressure (ea) to saturated vapor pressure
evaluated at the air temperature [e*(Ta)] and expressed as a percent.
Specific Humidity: Mass of water divided by total mass of air and is related to vapor
pressure as
qa = (0.622ea) / (P – 0.378ea)
where qa is specific humidity (kg/kg), ea is vapor pressure (Pa), and P is atmospheric
pressure (101325 Pa at sea level).
Figure 2: Top left: Emitted longwave radiation as a function of temperature for an emissivity of one. Top
right: Heat conduction as a function of temperature gradient at various conductivities. Bottom left: Sensible
heat transport as a function of temperature difference and resistance. Bottom right: Latent heat flux as a
function of vapor pressure deficit and resistance. In this example, ρ = 1.15 kg/m3, Cp = 1005 J/kg/C and γ =
66.5 Pa/C. Credits: After Bonan (2002). Figure prepared by Cory Pettijohn for GG 529, Fall 2005.
Latent heat flux can be represented using the Ohm’s law analogy in a manner similar to
sensible heat flux
λE = - [(ρCp) / (γ)] {[ea – e*(Ts)] / (rw)} .
The term e*(Ts) denotes saturation vapor pressure (Pa) evaluated at surface temperature
Ts, and ea is vapor pressure (Pa) of the air. The difference between the two is the vapor
pressure deficit between the evaporating surface, which is saturated with moisture, and
the air. The term rw is the transfer resistance (s/m) – this increases as the surface becomes
drier. The term γ is the psychrometric constant (66.5 Pa/C) – it depends on the heat
capacity, atmospheric pressure and latent heat of vaporization.
As in the case of sensible heat, a positive flux means loss of heat and water to the
atmosphere (see Figure 2d).
Conduction: Conduction is transfer of energy in solids, that is, transfer of heat along a
temperature gradient due to direct contact. The rate at which an object gains or loses heat
via conduction depends on the temperature gradient and thermal conductivity as
G = κ (∆T/∆Z)
where κ is thermal conductivity (W/m/C) – which is a measure of the ability of an object
to conduct heat (see Figure 2b).
3. Leaf Temperature and Fluxes
The leaf energy budget, on the assumption of negligible conductive heat transfer, is
(1-r)S↓ + L↓ = L↑ + H + λE ,
Qa = εσ(TL + 273.15)4 + [ρCp (TL – Ta)] / (rb /2) + [(ρCp) / (γ)] {[e*(TL) - ea] / (rs + rb)} ,
where TL is the leaf temperature that balances the energy budget, rb is the boundary layer
resistance that governs heat flow from the leaf surface to the air surrounding the leaf and
rs is the stomatal resistance acting in series regulating transpiration (Figure 3).
Stomata
Tl
el=e*(Tl)
rs
Leaf
Boundary
Layer
rb/2
rb
ea
es
1.65·rs 1.37·rb
cl
cs
ca
Total Resistance
Sensible Heat
rb/2
Latent Heat
(rs+rb)
Photosynthesis
(1.65· rs + 1.37· rb )
Figure 3. Resistances to sensible and latent heat transfer and CO2 uptake for an individual leaf. Sensible
heat is exchanged between the leaf (Tl) and air (Ta). Water vapor and CO2 are exchanged from inside the
stomatal cavity (ei, ci) to the leaf surface (es, cs) and then to air (ea, ca). Credits: After Bonan (2002).
Figure prepared by Yin Su for GG 529, Fall 2005.
Boundary layer resistance: The leaf boundary resistance (s/m) depends on leaf size (d in
meters) and wind speed (u in m/s) and may be approximated, per unit one-sided leaf area,
as
rb = 200 (d/u)0.5 .
Wind flowing across a leaf is slowed by the leaf, that is, wind speed increases with
distance from the leaf. Full wind flow occurs only at some distance downwind from the
leaf. This transition zone, where wind speed decreases with distance from leaf, is termed
the boundary layer, which could be 1 to 10 mm thick (Fig. 4).
High CO2
Dry Air
CO2
Leaf Cuticle
Guard
Cell
Guard Cell
Photosynthetically
Active Radiation
Chloroplast
0
High
Wind speed
rs
Low
CO2
Height
H2O
Boundary Layer
Thickness
rb 1 to 10 mm
Low
High
Temperature
Moist
Air
Light
CO2+2H2O→CH2O+O2+H2O
Figure 4. Leaf boundary layer processes. Left: Stomata and associated CO2 and water fluxes. These fluxes
are regulated by stomatal (rs) and boundary layer (rb) resistances. Right: Boundary layer thickness and
associated wind and temperature profiles. Credits: After Bonan (2002). Figure prepared by Yin Su for GG
529, Fall 2005.
The resistance to diffusive heat and moisture transport across this boundary layer
increases with leaf size and decreases with wind speed (Fig. 5). A small resistance means
a thin boundary layer, and the leaf is closely coupled to the air and therefore has a
temperature similar to that of air. A higher resistance means a thick boundary layer and
the leaf is decoupled from the surrounding air and could be several degrees warmer than
the air.
Sensible heat is exchanged from both sides of the leaf – heat exchange is thus regulated
by two resistances, each defined by rb in parallel, and therefore, the effective resistance is
0.5 rb .
Stomatal Resistance: Water escapes the leaf through small pores called stomata. These
pores open to allow carbon dioxide from the ambient air (high CO2 concentration) to
diffuse into the leaf (low CO2 concentration) for use in photosynthetic reactions (Fig. 4).
The resistance for latent heat exchange thus includes two terms – stomatal resistance
which governs the flow of water from inside the leaf to the leaf surface and boundary
layer resistance which governs the flow of water from the leaf surface to the ambient air.
The total resistance to water transport is the sum of these two resistances.
Figure 5. Boundary layer resistance in relation to leaf size and wind speed. Credits: After Bonan (2002).
Figure prepared by Matthew Adams for GG 529, Fall 2005.
Stomata open and close in response to a large number of factors, principally, light,
ambient air temperature and CO2 concentration and soil water content. Stomatal
resistance may vary from about 500 s/m when stomata are open to about 5000 s/m when
they are closed. If the stomata are located on only one side of a leaf, then the resistances
are not reduced by one-half. However, in some cases, stomata can be located on both
sides of a leaf, in which the total resistance to water exchange must be reduced by onehalf, in the expression above.
Cooling of leaf by Sensible and Latent Exchanges: The table below shows the
importance of sensible and latent heat in cooling leaf temperature under a variety of
radiative forcings and wind speeds for a summer day.
Table 1: Surface temperatures for radiative forcing of 1000, 700 and 400 W/m2 with (a) longwave radiation
only (L↑), (b) longwave radiation and convection only (L↑+H), and (c) longwave radiation, convection and
transpiration (L↑+H+λE).
Qa
(W/m2)
L↑
1000
700
400
91
60
17
0.1 m/s
53
40
26
Leaf Temperature (deg C)
L↑ + H
L↑ + H + λE
0.9 m/s
4.5 m/s
0.1 m/s
0.9 m/s 4.5 m/s
39
34
39
33
31
34
32
32
29
29
28
29
23
26
27
Note: Air temperature is 29C, relative humidity is 50%, wind speeds are 0.1, 0.9 and 4.5 m/s. Stomatal
resistance is 100 s/m, leaf dimension is 5 cm.
At a radiative forcing of 1000 W/m2, typical of midday clear skies, leaf temperatures are
reduced from a lethal 91C (L↑ only) to moderate values due to cooling from sensible
(and latent heat) exchanges. The leaves are significantly cooled through sensible heat
exchange with increasing wind speeds.
At a radiative forcing of 400 W/m2, typical of night time, sensible heat warms the leaf as
the air is warmer than the leaf. This warming increases with wind speed, that is, wind
speed increases the effectiveness of air warming the leaf.
Cooling by transpiration is greatest with large radiative forcings and decreases as
radiation decreases. It is largest for calm conditions and decreases as wind speed
increases.
Relative Humidity and Latent Cooling: Latent heat flux decreases and leaf temperature
increases as relative humidity increases. For example, with an air temperature of 45C and
a relative humidity of 20%, the leaf temperature is about 37.5C, which is 7.5C cooler
than the air. However, at a relative humidity of 90%, when latent heat flux is much
smaller, the leaf temperature is approximately equal to the air temperature. Thus, as
relative humidity increases, latent heat flux decreases and leaf temperatures increase.
This results in the following interesting fact – in hot environments, the leaf is cooler than
air for all but the most humid conditions, and, in cool environments, the leaf is warmer
than air for all but the most arid conditions!
Penman-Monteith Formulation of Latent Heat Exchange: The equation for leaf λE
formulated above can be improvised as follows. The saturation vapor pressure at the leaf
temperature [e*(TL)] can be approximated as e*a + s(TL – Ta), where e*a is the saturation
vapor pressure evaluated at air temperature and the coefficient s is the slope of the
saturation vapor pressure versus temperature evaluated at Ta (s = de*/dT). Thus,
λE = [(ρCp) / (γ)] {[ e*a + s(TL – Ta) - ea] / (rs + rb)} .
From the definition of energy budget and sensible heat flux
(TL – Ta) = [(0.5rb) / (ρCp)] (Rn - λE - G) .
Substituting this expression in the equation for λE gives
λE = {(s Rn) + [(ρCp )/(0.5rb)] (e*a – ea)} / {s + γ [(rb+rs)/(0.5rb)]} .
This Penman-Monteith equation relates leaf transpiration to net radiation, the vapor
pressure deficit of the air and the boundary and stomatal resistances as follows - λE
increases as more net radiation is available to evaporate water and as the atmospheric
demand, indicated by the vapor pressure deficit, increases. This transpiration rate is
inversely proporational to the resistances.
Equilibrium transpiration rate: If the boundary layer resistance is very large, such that
the leaf is decoupled from the surrounding air, λE = (s Rn)/(s+γ), that is, transpiration is
independent of stomatal resistance, and is driven principally by net radiation available to
evaporate the water.
Imposed transpiration rate: If the boundary layer resistance is very small, such that the
leaf is closely coupled to the environment, the transpiration rate is at a rate imposed by
the stomata, λE = [ρCp (e*a – ea)] / (γ rs).
In reality, the transpiration rate happens at a rate in between these two extremes. The
degree of coupling depends on leaf size and wind speed. Small leaves with their low
boundary layer resistance, approach strong coupling. Large leaves with their high
boundary layer resistance, are weakly coupled. And, leaves in still air are decoupled from
the surrounding air, while moving air results in strong coupling.
4. Surface Temperature and Fluxes
The same principles that govern the exchange of energy, heat and mass for a leaf can be
applied to surfaces, whether bare or vegetated. Some details however are different and
these require a closer examination. The exchanges of sensible and latent heat between the
surface and atmosphere occur because of turbulent mixing of air and resultant transport
of heat and moisture. Turbulence is generated when wind blows over the surface. The
objects on the surface, which constitute its roughness, exert a retarding force on the fluid
motion of air. This frictional force imparted on air slows the air flow and transfers
momentum (mass times velocity) from the atmosphere to surface and creates turbulence
that transports heat and water from the surface to the atmosphere.
Buoyancy also generates turbulence. Strong solar heating of the surface provides a source
of buoyant energy. The rising air enhances mixing and transport of heat and water away
from the surface. At night time, longwave emission cools the surface more rapidly than
the air above it. Cold air is trapped near the surface as vertical motions are suppressed
and transport is reduced.
One-Resistor Analogy: The fluxes of momentum (τ in kg/m/s2), sensible heat (H in
W/m2) and water vapor (E in kg/m2/s) between the atmosphere, at some height z with
horizontal wind speed (ua in m/s), temperature (Ta in deg C) and specific humidity (qa in
kg/kg), and a bare ground, using a one-resistor analogy, can be formulated as
τ = ρ(ua – us)/ram ,
H = - ρCp(Ta – Ts)/rah ,
E = -ρ(qa – qs)/raw ,
where us, Ts and qs are the corresponding surface values. These fluxes are nearly constant
in the layer of the atmosphere close to the ground, about 50 m or so.
Turbulent Transport: A more physical formulation for these turbulent fluxes is provided
by the Monin-Obukhov similarity theory, which relates turbulent fluxes to mean vertical
gradients of horizontal wind, temperature and specific humidity,
τ = ρKM δu/δz ,
H = - ρCp KH δT/δz ,
E = -ρ KE δq/δz ,
where the turbulent transfer coefficients Ki are of the general form [κu*(z-d)/φi(ζ)]. Here
κ = 0.4 is the von Karman constant, z is height in the surface layer (m), and d is the
displacement height (m). The frictional velocity (u* in m/s) is given by τ = ρu*2.
The functions, φi (i = m for momentum, H for heat and w for water), are universal
similarity functions that represent the effect of buoyancy on turbulence, where ζ = (zd)/L. Here L (in meters) is the Obukhov length scale which a measure of atmospheric
stability. These functions have a value of 1 when the atmosphere is neutral, less than 1
when the atmosphere is unstable and greater than 1 when the atmosphere is stable.
The turbulent transfer coefficients increase with height above the surface because of
larger eddies. To maintain a constant flux with respect to height, this increase in transport
with height must be balanced by a decrease in the vertical gradients (δu/δz , δT/δz ,
δq/δz). This has been observed experimentally.
Logarithmic Wind Profile: If we assume that the turbulent transfer coefficient for
momentum KM = κu*z , and make use of the relation τ = ρu*2 and integrate δu/δz =
u*/(κz) , we obtain the logarithmic wind profile equation,
uz = (u*/κ) ln (z/z0) ,
where z0 is a constant called the roughness length, such that u = 0 when z = z0. A more
general form of the logarithmic wind profile equation takes into account the height of
surface elements by assuming the existence of a zero plane at a height d such that the
distribution of shearing stress (that is, momentum transfer) over the elements is
aerodynamically equivalent to the imposition of the entire stress at height d. The
turbulent transfer coefficient for momentum is KM = κu*(z-d) and the wind profile
equation is uz = (u*/κ) ln [(z-d)/z0)].
These wind profile equations are valid only in the layer above the surface where the
fluxes are constant with height (that is, not valid deep inside vegetation canopies and
immediately above tall canopies). Note that the zero plane displacement is the equivalent
height for absorption of momentum and d+z0 is the equivalent height for zero wind
speed. Equivalent heights for heat and water sources can be similarly derived.
Aerodynamic Resistance: The aerodynamic resistance to momentum transfer, introduced
above, can be evaluated as
ram = (u2 - u1) / u*2 = ln [(z2 - d) / (z1 - d)] / (κu*) .
The resistance between a single height where the wind speed is u(z) and the level (z0+d)
where the extrapolated value of u is zero can be written in several equivalent forms,
ram = u(z)/u*2 = ln [(z - d)/z0] / (κu*) = ln [(z - d)/z0]2 / [κ2u(z)] .
Similar forms for the resistances to heat and water transfer can be written.
5. Vegetated Canopies
Stomatal control of transpiration is quantified by the stomatal resistance at the scale of a
single leaf. An aggregate measure of surface resistance to water loss is needed at the scale
of vegetation canopy to quantify evaporation from the soil and transpiration from the
canopy. This can be done in either of two ways.
In a bulk representation of the vegetated surface, evapo-transpiration is controlled by two
resistances acting in series: a surface resistance that combines foliage transpiration and
soil evaporation and an aerodynamic resistance that represents turbulent processes.
Alternately, evapo-transpiration can be partitioned into soil evaporation and foliage
transpiration. Soil evaporation is regulated by aerodynamic processes within the plant
canopy. Transpiration is regulated by a canopy resistance that is an integration of leaf
resistance over all leaves in the canopy.
Big Leaf Model: One means to estimate the canopy resistance is to represent the canopy
as one big leaf with a resistance representative of all leaves in the canopy (Fig. 6). In this
case, canopy resistance is leaf resistance divided by leaf area index, L (one-sided leaf
area per unit ground area). This would be more obvious if we were to use conductance,
the inverse of resistance. Canopy conductance per ground area is leaf conductance per
unit leaf area times leaf area per unit ground area. Leaf area indices vary from about 0.5
in sparse scrubby vegetated areas, about 1-2 in grasslands and about 3 in crops, to over 5
in dense forests. Greater leaf area increases the latent and sensible heat exchange with the
atmosphere by increasing the surface area from which these fluxes are emitted.
Canopy
Tv
rb/(2·L)
Atmosphere
Surface
Layer
ra
Tac
rs/L rb/L
ra
el=e*(Tv)
es
eac
1.65·rs/L 1.37·rb/L
cl
cs
ca
Ta
ea
Total Resistance
Sensible Heat
rb/(2·L)+ra
Latent Heat
(rs+rb)/L+ra
Photosynthesis
(1.65· rs +1.37· rb)/L
Figure 6. Resistances to sensible and latent heat transfer and CO2 uptake for a canopy of leaves. Sensible
heat is exchanged between the vegetation and surrounding air in the canopy (Tv - Tac) and between air
within the canopy and air above the canopy (Tac - Ta). Water vapor transfer is from inside the leaf to the
leaf surface (ev - es), leaf surface to surrounding air (es - eac), and air within the canopy to air above the
canopy (eac - ea). Credits: After Bonan (2002). Figure prepared by Yin Su for GG 529, Fall 2005.
The latent heat from a vegetated surface can be written as the sum of three component
fluxes as follows.
Flux one: Water is exchanged between leaves and air in the canopy,
λEv = - [(ρCp) / (γ)] {[eac – ev*(Tv)] / (rc)} ,
where eac is the vapor pressure in the air within the canopy and ev*(Tv) is saturation vapor
pressure of vegetation temperature (Tv) and rc is canopy resistance.
Flux two: Moisture is also lost from the ground as,
λEg = - [(ρCp) / (γ)] {[eac – eg*(Tg)] / (rac)} ,
where eg*(Tg) is saturation vapor pressure of ground temperature (Tg) and rac is an
aerodynamic resistance with in the canopy.
Flux three: Water vapor is also exchanged between the air within the canopy and air
above the canopy. This flux is,
λEa = - [(ρCp) / (γ)] {[ea – eac] / (ra)} ,
where ea is the vapor pressure in the air above the canopy and ra is the aerodynamic
resistance for transfer from within the canopy to above the canopy.
In the absence of vapor storage in the canopy space, these three fluxes are related as λEa
= λEg + λEv . Soil evaporation is minimal in a very dense canopy, so the latent heat flux is
the sum of vegetation and canopy air fluxes,
λE = λEv + λEa = - [(ρCp) / (γ)] {[ea – ev*(Tv)] / (rc + ra)} .
That is, the latent heat exchange between a dense canopy of leaves and the atmosphere is
governed by two resistances acting in series – a canopy resistance that regulates
transpiration and an aerodynamic resistance. Water vapor must first diffuse out of the leaf
interior to the leaf surfaces, governed by the resistance (rs/L), and then from the leaf
surfaces to the canopy air environment about the leaves, governed by the resistance
(rb/L), and then to the air above the canopy (ra).
Penman-Monteith Formulation: The Penman-Monteith equation applied to a canopy of
leaves provides insights into surface and canopy resistances and their relationship to leaf
resistances. For a canopy, the formulation is,
λE = {[s (Rn – G)] + [(ρCp )/(ra)] (e*a – ea)} / {s + γ [(rc+ra)/(ra)]} ,
or equivalently, in terms of conductances,
λE = {[s (Rn – G)] + ρCp ga (e*a – ea)} / {s + γ [1+ga/gc)]} ,
where rc is canopy or surface resistance, ra is aerodynamic resistance for water vapor, and
gc and ga are the respective conductances. By measuring evapo-transpiration and if the
other terms are known, this equation can be used to estimate canopy conductance.
Canopy Conductance: Canopy conductance increases linearly with leaf area index at low
leaf area. It reaches an asymptotic value depending on leaf conductance at high leaf area.
This is because leaves deep in the dense canopy experience low light levels and close
their stomata.
Surface Conductance: Surface conductance approaches canopy conductance as leaf area
increases because soil evaporation becomes negligible in dense canopies. Surface
conductance significantly exceeds canopy conductance only for leaf area index values
less than 3, where soil evaporation is significant. The maximum surface conductance
increases linearly with maximum leaf conductance with a slope of approximately 3.
There general relations have been confirmed with empirical observations.
As with an individual leaf, vegetation has different degrees of coupling to the atmosphere
as determined by the magnitude of the aerodynamic resistance. Tall forest vegetation is
aerodynamically rough, creates turbulence more efficiently, thus has a low aerodynamic
resistance, and is therefore, closely coupled to the atmosphere. Evapo-transpiration
approaches a rate imposed by the canopy resistance,
λE = [ρCp (e*a – ea)] / (γrc) .
Short vegetation such as a grassland is aerodynamically smooth, creates turbulence less
efficiently, and thus has a large aerodynamic resistance, and is therefore, decoupled from
the atmosphere. Evapo-transpiration rate is dependent on the energy available with little
canopy influence,
λE = [s(Rn – G)] / (s + γ) .
Sensible heat exchanges are similarly impacted in tall and short vegetation. Thus, the
temperature of leaves in a tall forest canopy are closer to the air temperature. And, the
temperature of leaves in a short canopy are warmer than the air temperature. Thus, in
cold climates, short stature has the advantage of keeping leaves warmer than the air. The
effect of wind speed to decrease aerodynamic resistance is greater for short vegetation
compared to tall vegetation.
6. Surface Climate
General: Several atmospheric variables affect surface fluxes (Table 2). Incoming solar
and longwave radiation determine net radiation. Air temperature and atmospheric
humidity determine the diffusion gradients for sensible and latent heat transfer. Wind
speed affects fluxes of momentum, heat and mass through turbulence. Precipitation
determines soil waters and thus latent heat. Snow on the ground affects surface albedo
and thus net radiation. Soil temperature affects heat flow in the soil. In addition, solar
radiation, air temperature, atmospheric humidity, atmospheric CO2 and soil water
determine stomatal functioning and thus mass fluxes. In turn, these atmospheric variable
are themselves affected by the surface fluxes. Thus, there is this coupling between the
state of atmosphere and land.
Table 2a: Principal Meteorological Forcings and Surface Processes. Credits: Bonan (2002).
Meteorological Forcing
Surface Process
Incoming solar radiation
Net radiation, Stomatal resistance
Incoming longwave radiation
Net radiation
Air temperature
Sensible heat flux, Stomatal resistance
Atmospheric humidity
Latent heat flux, Stomatal resistance
Wind speed
Sensible, Latent and Momentum fluxes
Atmospheric CO2
Stomatal Resistance
Precipitation – Soil water
Latent heat flux, Stomatal resistance
Precipitation - Snow
Albedo
Soil temperature
Ground Heat
Table 2b: Principal Surface Forcings and Surface processes. Credits: Bonan (2002).
Surface Forcing
Surface Process
Albedo
Reflected solar radiation, Net radiation
Emissivity
Emitted longwave radiation, Net radiatioon
Soil texture – Hydraulic properties
Soil water, Latent heat
Soil texture – Thermal properties
Ground heat flux
Roughness length
Sensible, Latent and Momentum fluxes
Displacement height
Sensible, Latent and Momentum fluxes
Stomatal physiology
Latent heat
Leaf dimension
Leaf area index
Rooting depth
Topography
Sensible and Latent heat
Canopy resistance, Albedo, Sensible & Latent heat
Stomatal resistance, Latent heat
Radiation balance, Temperature, Soil water
Annual Averages: The annual average values of surface fluxes and related variables over
land as computed by the NCAR Common Land Model (CLM Version 3) are shown in
Table 3. About 74% of the incoming solar radiation is absorbed by the land, which means
that the average land albedo is 25.6%. The longwave exchanges are significant, and in
general, the land has a longwave radiation deficit (-67.7 W/m2). Thus, net radiation is
less than absorbed solar radiation. The sensible and latent heat fluxes are comparable, and
together account for nearly all of the net radiation – meaning, ground heat flux and
energy used to melt snow is negligible. Of the three components of latent heat fluxes,
evaporation from the ground is nearly 59% of the latent heat flux. Transpiration from the
leaves accounts for only 13% of the total latent heat flux. The average air temperature at
2 m height that results from these fluxes is 282 K (9 C).
Table 3. Annual average surface energy balance. Credits: NCAR-CLM- Website
Variable
Annual Mean over Land
Incoming solar radiation (W/m2)
184.6
Absorbed solar radiation (W/m2)
137.4
Incoming longwave radiation (W/m2)
304.0
Emitted longwave radiation (W/m2)
371.7
Net radiation (W/m2)
69.8
Sensible Heat (W/m2)
30.5
Latent Heat (W/m2)
38.6
Transpiration (W/m2)
5.2
Canopy evaporation (W/m2)
10.9
Ground evaporation (W/m2)
22.6
Ground heat flux + Snow melt (W/m2)
0.6
Air temperature at 2 m height (K)
282.0
Seasonal Cycle: The seasonal variation of the components of surface radiation balance
for all land area in the Northern Hemisphere is shown in Fig. 7. Albedo decreases in the
summer due to (1) increased greenness of the lands and (2) lower solar zenith angles.
Nevertheless, the annual course of absorbed radiation follows that of incoming solar
radiation, that is, maximum in the summer months and minimum in the winter months.
There is a similar seasonality in the longwave fluxes. Therefore, net radiation shows
similar seasonality. The opposite is seen in the seasonal course of variables for land areas
in the Southern Hemisphere.
Figure 7. Seasonal variation of land surface radiation balance in the Northern Hemisphere as simulated
by the CLM3. Credits: NCAR CLM Web site.
The surface fluxes follow the seasonality of net radiation (Fig. 8). Most of the net
radiation is expended as sensible and latent heat – the ground heat flux is nearly
negligible. Evaporation from the ground and plants accounts for a large fraction of the
latent heat flux. The opposite seasonality is seen for land areas in the Southern
Hemisphere.
Figure 8. Seasonal variation of land surface energy balance in the Northern Hemisphere as simulated by
the CLM3. Credits: NCAR CLM Web site.
Diurnal Cycle: Surface fluxes also vary over the course of a day due to the diurnal cycle.
As more radiation is received from the sun, the land warms and more energy is dissipated
as sensible and latent heat. In addition, stomata open to allow CO2 to diffuse into the leaf
and in the process, water is transpired. The diurnal course of surface fluxes for a
vegetated surface is shown in Fig. 9. The surface has a negative radiation balance in the
night time – there is no solar radiation and longwave radiation is being emitted. The
stomates are closed and there is no latent heat flux. As the sun shines, solar radiation is
absorbed and net radiation become positive – absorbed solar radiation is greater than net
longwave radiation loss. The surface begins to warm up, and some of this energy is
returned to the atmosphere as sensible heat flux. The stomates open and there is a latent
heat flux to the atmosphere, thus cooling the surface. At mid-day, more than 50% of the
net radiation is expended as latent heat, significantly cooling the surface. The ground heat
flux is a small negligible component of the surface energy balance.
Figure 9. Diurnal course of net radiation, sensible, latent and ground heat fluxes over a vegetated surface.
Credits: sheba.geo.vu.nl/.../mmVeggie/index_mmVeggie.html
7. Key Literature (based on Buermann’s PhD dissertation, BU, 2002)
The importance of vegetation control on the exchange of energy, mass and momentum
between the land surface and the atmosphere has been the focus of several efforts [Betts
and Beljaars, 1993; LeMone et al., 2000; Sellers et al., 1995; Shuttleworth et al., 1991;
amongst others]. Many field experiments at different spatial and temporal scales have
been conducted to test the sensitivity of climate to changes in land surface conditions
[e.g., Bastable et al., 1993; Betts et al., 1996, 1999; Schwartz and Karl, 1990). Their
findings and results from model investigations, recently summarized in Pielke et al.
[1998], indicate that the effect of vegetation dynamics on climate might not be
insignificant compared to other forcings resulting from changes in atmospheric
composition, ocean circulation and orbital perturbations.
In many studies involving atmospheric general circulation models (GCMs), a 'case'
simulation is typically performed with modified land surface characteristics and then
compared to a 'control' simulation. Such sensitivity studies have identified the
significance of key land surface parameters such as albedo [Sud and Fennessey, 1982],
evapotranspiration [Shukla and Mintz, 1982], surface roughness [Sud et al., 1988] and
stomatal conductance [Henderson-Sellers et al., 1995; Pollard and Thompson, 1995;
Sellers et al., 1996; Martin et al., 1999] on land-atmosphere exchange processes.
Model investigations with changes in global LAI [Chase et al., 1996] and replacement of
entire biomes at regional [tropical in the case of Dickinson and Henderson-Sellers, 1988;
Lean and Warrilow, 1989; Nobre et al., 1991; Zhang et al., 1996a, 1996b; and boreal in
the case of Bonan et al., 1992; Chalita and Le Treut, 1994] and global [Kleidon et al.,
2000] scale indicate dramatically the importance of vegetation on regional and global
climate.
Albedo: The average albedo over ocean areas, without sea ice, is about 8-10%. Over
barren land surfaces, it may vary between 20-35% for deserts, and 35-90% for snow. The
albedo over vegetated surfaces may vary from very low values (10-15%) over humid
tropical forests to somewhat larger values over shrubs (15-20%) [Hartmann, 1994]. The
vegetation albedo is a function of plant-specific structural and optical properties and the
leaf area index (LAI) [Dickinson, 1983]. Generally, surface albedo decreases as LAI
increases due to increased canopy absorption and decreased reflection from the generally
brighter ground below the vegetation. It were the pioneering studies of Charney [1977]
and Sud and Fennessy [1982] that first identified surface albedo as an important
parameter in land-surface processes. The results of these sensitivity studies substantiated
the famous Charney hypothesis [Charney, 1975] that in sup-tropical desert-margin
regions, the radiative heat loss caused by high albedos from diminished vegetation
contributes to sinking and drying air aloft, leading to a further reduction in precipitation,
which partially explains the recurrence of droughts. In a similar vein, Foley et al. [1994]
showed, in a palaeoclimatic model study, that lower albedos associated with a northward
shift of boreal forests [Bonan et al., 1992] replacing the tundra during the Mid-Holocene
period (about 6000 years ago) gave rise to an additional warming, larger in magnitude
than that due to orbital perturbation alone, thus documenting a dramatic positive
vegetation feedback.
Canopy Conductance: Evapotranspiration from the land may be divided into evaporation
from wet leaf surfaces, transpiration from leaves and evaporation from the soil. The
wetness of leaves, that is, the interception storage capacity, is a direct function of LAI,
leading to enhanced plant evaporation from the leaf surfaces, as LAI increases. Tiny little
openings on the leaf surface, called stomates, provide the path between the atmosphere
and the water saturated cellular tissues inside the leaves to facilitate the exchange of mass
[Sellers et al., 1997]. Depending on environmental conditions, stomates act to optimize
the uptake of atmospheric CO2 and loss of water vapor, and, thus directly control
transpiration of vegetated surfaces. With increasing leaf area, more sunlight is absorbed
which in turn increases the uptake of CO2 and loss of water to the atmosphere, resulting
generally in increased canopy conductance, or transpiration rates.
The results of a sensitivity study by Shukla and Mintz [1982] first documented the
importance of land surface evapotranspiration in land surface processes at global scale
affecting climate fields of rainfall, temperature and motions. Based on observations,
Schwartz and Karl [1990] showed that the increase of mean temperature in the spring in
the eastern United States is markedly damped as vegetation leafs out due to a shift in the
surface energy budget from sensible to latent heating. Results from a model simulation of
the climate of the Sahara in the early and Mid-Holocene suggest that the replacement of
deserts with grasslands and associated increase in evapotranspiration provided an
important positive feedback to the climatic response of the African summer monsoon to
orbital forcing, resulting in a farther northward shift of the grasslands [Kutzbach et al.,
1996]. The findings of a series of model based Amazonian deforestation studies [e.g.,
Nobre et al., 1991] also confirm the strong impact of vegetation related changes in
evapotranspiration on near-surface climate. The replacement of tropical forests by pasture
generally causes a decrease in evapotranspiration, precipitation and surface runoff
accompanied by warmer surface temperatures. Recently, the maximum possible influence
of vegetation on global climate was evaluated by comparing the simulated fields of a
model run with all vegetation removed ('desert world') to one with all land surfaces being
forested ('green planet') [Kleidon et al., 2000]. The results indicated that the largest
impact on the global climate is due to changes in evapotranspiration and not surface
albedo.
Surface Roughness: The surface roughness affects the exchanges of sensible and latent
heat fluxes, and the exchange of momentum between the land surface and the overlying
air. Increases in vegetation height or LAI enhance the transport of sensible and latent heat
away from the surface while exerting a larger drag force on the atmospheric boundary
layer [Sellers et al., 1997]. The impact study by Sud et al. [1988] demonstrated that the
height of the earth's vegetation cover, which is the main determinant of land surface
roughness, plays a significant role in near-surface climate, affecting in particular water
vapor transport convergence and rainfall distribution.
Text Books
(1) The material in Sections 1 through 6 are based on Chapter 7: Surface Energy Fluxes
in Ecological Climatology by Bonan (2002).
(2) Class handouts on background material are chapters from Principles of Environmental
Physics by Monteith and Unsworth (1990).
Key Papers
Bonan, G.B., D. Pollard and S.L. Thompson, 1992: Effects of boreal forest vegetation on
global climate. Nature, 359, 716-718, 1992.
Chase, T.N., R.A. Pielke, T.G.F. Kittel, R. Nemani, and S.W. Running, Sensitivity of a
general circulation model to global changes in leaf area index. J. Geophys. Res., 101,
7393-7408, 1996.
Kleidon, A., K. Fraedrich, and M. Heimann, A green planet versus a desert world:
Estimating the maximum effect of vegetation on the land surface climate. Clim. Change,
44, 471-493, 2000.
Nobre, C.A., P.J. Sellers, and J. Shukla, Amazonian deforestation and regional climate
change. J. Climate, 4, 957-988, 1991.
Pielke, R.A., R. Avissar, M. Raupach, A.J. Dolman, Y. Xeng, and S. Denning,
Interactions between the atmosphere and terrestrial ecosystems: Influence on weather and
climate. Global Change Biol., 4, 461-475, 1998.
Sellers, P.J., R.E. Dickinson, D.A. Randall, A.K. Betts, F.G. Hall, J.A. Berry, G.J.
Collatz, A.S. Denning, H.A. Mooney, C.A. Nobre, N. Sato, C.B. Field, and A.
Henderson-Sellers, Modeling the exchanges of energy, water, and carbon between
continents and the atmosphere, Science, 275, 502-509, 1997.
Shukla, J., and Y. Mintz, The influence of land-surface evapotranspiration on the earth's
climate. Science, 247, 1322-1325, 1982.
General References
Bastable, H.G., W.J. Shuttleworth, R.L.G. Dallarosa, G. Fisch, and C.A. Nobre,
Observations of climate, albedo and surface radiation over cleared and undisturbed
amazonia forest. Int. J. Climatol., 13, 783-796, 1993.
Betts, A.K., and A.C.M. Beljaars, Estimation of effective roughness length for heat and
moment um from FIFE dat a. Atmos. Research, 30, 251-261, 1993.
Betts, A.K., J.H. Ball, A.C.M. Beljaars, M.J. Miller, and P.A. Viterbo, The land
surfaceatmosphere interaction: A review based on observational and global modeling
perspectives. J. Geophys. Res., 101, 7209-7225, 1996.
Betts, A.K., M. Goulden, and S. Wofsy, Controls on Evaporation in a Boreal Spruce
Forest. J. Climate, 12, 1601-1618, 1999.
Bonan, G.B., D. Pollard and S.L. Thompson, 1992: Effects of boreal forest vegetation on
global climate. Nature, 359, 716-718, 1992.
Chalita, S., and H. Le Treut, The albedo of temperate and boreal forest and the northern
hemisphere climate - A sensitivity experiment using the LMD-GCM. Climate Dyn., 10,
231-240, 1994.
Chase, T.N., R.A. Pielke, T.G.F. Kittel, R. Nemani, and S.W. Running, Sensitivity of a
general circulation model to global changes in leaf area index. J. Geophys. Res., 101,
7393-7408, 1996.
Charney, J.G., Dynamics of deserts and drought in the Sahel. Quart. J. Roy. Meteor. Soc.,
101, 193, 1975.
Charney, J.G., and Coauthors, A comparative study of the effects of albedo change on
drought in semi-arid regions, J. Atmos. Sci., 34, 1366, 1977.
Dickinson, R.E., Land surface processes and climate-surface albedos and energy balance.
Adv. Geophys., 25, 305-353, 1983.
Dickinson, R.E., and A. Henderson-Sellers, Modeling tropical deforestation: A study of
GCM land-surface parameterizations. Quart. J. Roy. Meteor. Soc, 114, 439-462, 1988.
Foley, J.A., J.E. Kutzbach, M.T. Coe, and S. Levis, Feedbacks between climate and
boreal forests during the Holocene epoch, Nature, 371, 52-54, 1994.
Hartmann, D.L., in Global Physical Climatology, Academic Press, San Diego, p.411,
1994.
Henderson-Sellers, A., K. McGuffie, and C. Gross, Sensitivity of global climate model
simulations to increased stomatal resistance and CO2 increases. J. Climate, 8, 17381756,
1995.
Kleidon, A., K. Fraedrich, and M. Heimann, A green planet versus a desert world:
Estimating the maximum effect of vegetation on the land surface climate. Clim. Change,
44, 471-493, 2000.
Kutzbach, J., G. Bonan, J. Foley, and S.P. Harrison, Vegetation and soil feedbacks on the
response of the African monsoon to orbital forcing in the early and middle Holocene,
Nature, 384, 623-626,1996.
LeMone, M. A., and Coauthors, Land-atmosphere interaction research, early results, and
opportunities in the Walnut River Watershed in southeast Kansas: CASES and ABLE.
Bull. Amer. Meteor. Soc., 81, 757-779, 2000.
Lean, J., and D. A. Warrilow, Simulation of the regional climatic impact of Amazon
deforestation. Nature, 342, 411-413, 1989.
Martin, M., R.E. Dickinson, and Z.L. Yang, Use of coupled land surface general
circulation model to examine the impacts of stomatal resistance on the water resources of
the American Southwest. J. Climate, 12, 3359-3375, 1999.
Nobre, C.A., P.J. Sellers, and J. Shukla, Amazonian deforestation and regional climate
change. J. Climate, 4, 957-988, 1991.
Pielke, R.A., R. Avissar, M. Raupach, A.J. Dolman, Y. Xeng, and S. Denning,
Interactions between the atmosphere and terrestrial ecosystems: Influence on weather and
climate. Global Change Biol., 4, 461-475, 1998.
Pollard, D., and S.L. Thompson, Use of a land-surface transfer scheme (LSX) in a global
climate model: The response to doubling stomatal resistance. Glob. Plan. Change, 10,
129-162, 1995.
Schwartz, M.D., and T.R. Karl, Spring phenology: Nature's experiment to detect the
effect of 'green up' on surface maximum temperatures. Mon. Wea. Rev., 118, 883890,
1990.
Sellers, P.J., and Coauthors, The Boreal Ecosystem-Atmosphere Study (BOREAS): An
overview and early results from the 1994 field year. Bull. Amer. Meteor. Soc., 76, 15491577, 1995.
Sellers, P.J., and Coauthors, Comparison of radiative and physiological effects of doubled
atmospheric CO2 on climate. Science, 271, 1402-1406, 1996.
Sellers, P.J., R.E. Dickinson, D.A. Randall, A.K. Betts, F.G. Hall, J.A. Berry, G.J.
Collatz, A.S. Denning, H.A. Mooney, C.A. Nobre, N. Sato, C.B. Field, and A.
Henderson-Sellers, Modeling the exchanges of energy, water, and carbon between
continents and the atmosphere, Science, 275, 502-509, 1997.
Shukla, J., and Y. Mintz, The influence of land-surface evapotranspiration on the earth's
climate. Science, 247, 1322-1325, 1982.
Shuttleworth, W.J., J.H. C. Gash, J.M. Roberts, C.A. Nobre, L.C.B. Molion, and M.D.G.
Ribeiro, Post -deforestation amazonian climate: Anglo-Brazilian research to improve
prediction. J. Hydrology, 129, 71-85, 1991.
Sud, Y.C., and M. Fennessey, A study of the influence of surface albedo on July
circulation in semi-arid regions using t he CLAS GCM. J. Climatol., 2, 105-128, 1982.
Sud, Y.C., J. Shukla, and Y. Mintz, Influence of land-surface roughness on atmospheric
circulation and precipitation: A sensitivity study with a general circulation model. J.
Appl. Meteor., 27, 1036-1054, 1988.
Zhang, H., A. Henderson-Sellers and K. McGuffie, Impacts of tropical deforestation. Part
I: Process analysis of local climatic change. J. Climate, 9, 1497-1517, 1996a.
Zhang, H., K. McGuffie, and A. Henderson-Sellers, Impacts of tropical deforestation.
Part II: The role of large-scale dynamics. J. Climate, 9, 2498-2521, 1996b.