Chapter 7
CHAPTER 7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
Surface Energy Fluxes
SURFACE ENERGY FLUXES ...................................................................................... 1
INTRODUCTION ................................................................................................................................ 2
SURFACE ENERGY BUDGET .............................................................................................................. 2
LEAF TEMPERATURE AND FLUXES ................................................................................................... 8
SURFACE TEMPERATURE AND FLUXES ........................................................................................... 14
VEGETATED CANOPIES .................................................................................................................. 19
SURFACE CLIMATE ........................................................................................................................ 23
TABLES ......................................................................................................................................... 28
FIGURE LEGENDS .......................................................................................................................... 30
Ecological Climatology
7.1 Introduction
Energy is exchanged between the atmosphere and Earth surface. Solar radiation and atmospheric
longwave radiation warm the surface and provide energy to drive weather and climate. Some of this energy
is stored in the ground or oceans. Some of it is returned to the atmosphere, warming the air. The rest is
used to evaporate water. These surface energy fluxes are an important component of Earth’s global mean
energy budget. At the global scale, Earth’s energy budget shows the atmosphere has a deficit of energy
while the surface has a surplus (Figure 2.1). The atmosphere absorbs 67 W m-2 of solar radiation and 350
W m-2 of longwave radiation from the surface; it emits 195 W m-2 of longwave radiation to space and 324
W m-2 onto the surface. The excess loss of radiation compared with absorption is -102 W m-2. The surface,
in contrast, gains 168 W m-2 of solar radiation and 324 W m-2 of longwave radiation from the atmosphere
while emitting 390 W m-2 of longwave radiation. This gives the surface a net surplus of 102 W m-2. This
surplus energy is returned to the atmosphere as sensible heat (24 W m-2) and latent heat (78 W m-2). These
heat fluxes arise as winds carry heat (sensible heat) and moisture (latent heat) away from the surface. Over
land, sensible and latent heat are important determinants of microclimates. Microclimates are the climate
near the ground and represent local climates due to topography, vegetation, soils, landforms, and
structures. This chapter introduces the energy fluxes needed to understand microclimates. The next chapter
examines spatial patterns in landscapes and resulting microclimates.
7.2 Surface energy budget
Energy continually flows through the climate system. As solar radiation passes through the
atmosphere, some is absorbed, primarily by water vapor and clouds, and some is scattered, both upwards to
space and downwards onto the surface, by clouds, air molecules, and particles suspended in the air. This
downward scattered radiation, known as diffuse radiation, emanates from all directions of the sky. In
contrast, direct beam radiation is not scattered and originates from the Sun’s position in the sky. The Sun is
the principal source of radiant energy, but all objects with a temperature warmer than –273.15 °C (0
Kelvin) emit longwave radiation in proportion to their temperature raised to the fourth power.
2
Chapter 7 – Surface Energy Fluxes
These radiative sources of energy are depicted in Figure 7.1 for a person standing next to a wall.
In this case, direct beam radiation is received based on the Sun’s angle above the horizon and its location
with respect to compass direction. Diffuse radiation is received in all directions from solar radiation
reflected by the sky, surrounding ground, and the wall. Likewise, the sky, ground, and wall emit longwave
radiation that is absorbed by the person. Incident solar radiation varies with time of year, time of day,
cloudiness, and atmospheric turbidity. A typical midday summertime value for clear, dry sky at tropical
latitudes is as much as 1000 W m-2. With cloudy skies or when in shade (so that direct beam radiation is
blocked), this may be as little as 100 W m-2. Diffuse radiation is most important when scattering is high.
On overcast days, all the radiation is diffuse. The fraction of total radiation that is diffuse is also high when
the low solar altitude angle leads to a longer path through the atmosphere, such as in mornings, evenings,
winter, and at high latitudes. When the Sun is directly overhead, solar radiation travels through less of the
atmosphere than when it is at an angle and hence less is scattered. Consequently, diffuse radiation may
account for 25-50% of the total radiation when the Sun is low on the horizon, but only 10-20% when the
Sun is high in the sky. The proportion of the total radiation that is diffuse increases, often by a factor of
two, for cloudy, overcast, or polluted skies. Incident longwave radiation varies with temperature, humidity,
and cloudiness. Typical clear sky fluxes are 400 W m-2 at 30 °C and 200 W m-2 at 0 °C. Under cloudy
conditions, these fluxes can increase by 20% or so. During the day, solar radiation is the dominant flux
under clear, dry skies. Solar and longwave fluxes are both important with cloudy skies. At night, longwave
radiation is the sole source of radiant energy to the surface.
An object has five means to dissipate the radiant energy impinging on it (Figure 7.1). Some of the
incident solar radiation is reflected away from the object; the remainder is absorbed. Longwave radiation is
emitted in proportion to temperature to the fourth power. Heat is also transferred by direct contact with
another object (conduction), movement of air that carries heat away from the object (convection or sensible
heat), and latent heat exchange in which heat is dissipated through a change in water from liquid to gas.
The radiation that impinges on a surface or object must be balanced by the energy radiated back to the
atmosphere, energy lost or gained by sensible and latent heat, and heat storage. The energy balance is
(1 − r ) S ↓ + L ↓= L ↑ + H + λ E + G
3
Ecological Climatology
The left-hand side of this equation constitutes the radiative forcing (Qa), which is the sum of absorbed solar
radiation ( (1 − r ) S ↓ ) and longwave radiation (L↓), respectively. The right-hand side of the equation
consists of the emitted longwave radiation (L↑), sensible heat (H), latent heat (λE), and heat exchange by
conduction (G). Expressed in a different manner, the net radiation absorbed by an object is
R = (1 − r ) S ↓ +( L ↓ − L ↑) = H + λ E + G
n
Net radiation (Rn) is balanced by sensible, latent, and conduction heat fluxes. The effect of different
surfaces on microclimates can be understood by considering the various terms in the energy budget (Gates
1980; Grace 1983; Monteith and Unsworth 1990; Campbell and Norman 1998).
All surfaces except for the blackest reflect sunlight. This amount is equal to rS ↓ , where S↓ is the
incident radiation onto the surface and r is the albedo, defined as the fraction of S↓ that is reflected by the
surface. The remainder, (1 − r ) S ↓ , is the solar radiation absorbed by the surface. A perfect mirror has an
albedo of one (i.e., all the incoming light is reflected). An object that completely absorbs all radiation
incident upon its surface, known as a blackbody, has an albedo of zero (i.e., all light is absorbed). The
albedo of natural landscapes ranges from greater than 0.9 for fresh snow to less than 0.1 for some types of
vegetation.
Emission of longwave radiation is a second means of radiative cooling. Terrestrial objects emit
electromagnetic radiation in the infrared band at long wavelengths between 3 µm and 100 µm. This
emission is proportional to temperature raised to the fourth power. For temperatures in degrees Celsius,
(
L ↑= εσ T + 273.15
s
)
4
where Ts + 273.15 is absolute temperature in Kelvin (K) and σ = 5.67 × 10-8 W m-2 K-4 is the StefanBoltzmann constant (Figure 7.2). The emissivity (ε) of an object generally ranges from 0.95 to 1.0. A
blackbody has an emissivity equal to one. Most natural surfaces are ‘grey bodies’, with emissivity less than
one.
Movement of air carries heat and moisture away from an object. These exchanges are represented
as a diffusion process analogous to electrical networks (Figure 7.3). The electrical current between two
points on a conducting wire is equal to the voltage difference divided by the electrical resistance. Similarly,
4
Chapter 7 – Surface Energy Fluxes
the diffusion of materials is related to the concentration difference divided by a resistance to diffusion. For
example, the exchange of water vapor and CO2 between a leaf and the surrounding air depends on two
resistances connected in series: a stomatal resistance from inside the leaf to the leaf surface and a boundary
layer resistance from the leaf surface to the air. The overall leaf resistance is the sum of these two
resistances. If stomata are located on both sides of the leaf, the upper and lower resistances acting in
parallel determine the overall leaf resistance.
Convection is the transport of heat through air movements. A common example is the warmth felt
as warm air rises from a radiator or the cooling of a breeze on a hot summer day. This heat exchange is
called sensible heat. Sensible heat flux is represented through a resistance network in which heat flux is
directly proportional to the temperature difference between an object and the surrounding air and inversely
proportional to a transfer resistance
H = − ρC
(Ta −Ts )
p
rH
where Ts and Ta are the surface and air temperatures (°C), respectively. An object loses energy if its
temperature is warmer than the air (a positive flux); it gains energy when it is colder than the air (a
negative flux). The density of air (ρ, kg m-3) varies with temperature and humidity but ρ = 1.2 kg m-3 is
typical. The term Cp is the heat capacity of air and is approximately 1010 J kg-1 °C-1. The transfer resistance
rH (s m-1) depends on wind speed and surface characteristics. The larger the temperature difference, the
larger the heat flux (Figure 7.2). Larger transfer resistances result in less heat flux for a given temperature
gradient.
Heat is also lost from an object by evapotranspiration. Considerable energy is required to change
water from liquid to vapor. Evapotranspiration, therefore, involves a transfer of mass and energy to the
atmosphere. Transfer of mass is seen as wet clothes dry on a clothesline. Heat loss is why a person may
feel cold on a hot summer day when wet but hot after being dried with a towel. When water changes from
liquid to gas (vapor), energy is absorbed from the evaporating surface without a rise in temperature. This
latent heat of vaporization varies with temperature, but is 2.43 × 106 J kg-1 at 30 °C (Table 5.2). A typical
summertime rate of evapotranspiration is 5 mm of water per day, which with a density of water of 1000 kg
5
Ecological Climatology
m-3 is equivalent to 5 kg water per square meter (5 kg m-2/1000 kg m-3 = 0.005 m). With a latent heat of
vaporization of 2.43 × 106 J kg-1, a water loss of 5 kg m-2 day-1 is equivalent to a heat loss of
kg
1 day
J
J
×
× 2 430 000
= 141
)
141 W m-2 (i.e., 5 2
kg
m day 86 400 s
sm2
For comparison, the solar radiation over the same 24-hour period is about 200 W m-2 for a cloud-free sky.
This heat is transferred from the evaporating surface to the air, where it is stored in water vapor as latent
heat. It is released when water vapor condenses back to liquid.
Evaporation occurs when a moist surface is exposed to drier air. Water evaporates from the
surface, increasing the amount of water vapor in the surrounding air. When the air is saturated with water
vapor, evaporation ceases. Evaporation, therefore, is related to the vapor pressure deficit of air – the
difference between the actual amount of water in air and the maximum possible when saturated. Saturation
vapor pressure increases exponentially with warmer temperature (Figure 7.4). The actual amount of water
vapor in air is related to relative humidity. Relative humidity is the ratio of actual vapor pressure (ea) to
saturated vapor pressure evaluated at the air temperature (e*[Ta]) expressed as a percent
RH = 100 ea e∗[Ta ]
For a constant vapor pressure, relative humidity decreases as temperature and therefore saturated vapor
pressure increases. Specific humidity is another measure of atmospheric moisture. This is the mass of water
divided by the total mass of air. Specific humidity (qa, kg kg-1) is related to vapor pressure (ea, Pa) as
qa =
0.622ea
P − 0.378ea
where P is atmospheric pressure (Pa). At sea level, P = 101 325 Pa and because P >> ea , specific humidity
can be approximated as qa = 0.622 ea / P . The right axis in Figure 7.4 shows corresponding specific
humidity at saturation for various temperatures. One kilogram of air can hold about 6 g of water when
saturated at 7 °C, 18 g at 23.5 °C, and 36 g at 35.5 °C.
Latent heat flux is represented by a resistance network similar to sensible heat in which
λE = −
ρ C p ( ea −e∗[Ts ])
rW
γ
6
Chapter 7 – Surface Energy Fluxes
The term e*[Ts] represents the saturation vapor pressure (Pa) evaluated at the surface temperature Ts, and
the term ea is the vapor pressure of air (Pa). The difference between these, ( e∗ ⎡⎣Ts ⎤⎦ − ea ), is the vapor
pressure deficit between the evaporating surface, which is saturated with moisture, and air. The term rW is
a resistance (s m-1) analogous to rH . This resistance increases as the surface becomes drier (i.e., less
saturated) so that a wet site has a higher latent heat flux than a dry site, all other factors being equal. The
term γ is the psychrometric constant, which depends on heat capacity (Cp, J kg-1 °C-1), atmospheric pressure
(P, Pa), and latent heat of vaporization (λ, J kg-1) as γ = (C p P ) /(0.622λ ) . A typical value is 66.5 pascals
per degree Celsius (Pa °C-1.). This equation is analogous to that for sensible heat flux, and a positive flux
means loss of heat and water to the atmosphere (Figure 7.2).
The fifth way in which objects gain or lose energy is conduction. Conduction is the transfer of
heat along a temperature gradient from high temperature to low temperature but in contrast to convection
due to direct contact rather than movement of air. The heat felt when touching a steaming mug of coffee is
an example of conduction. The rate at which an object gains or loses heat via conduction depends on the
temperature gradient and thermal conductivity as
G = k ( ∆T / ∆z )
where k is thermal conductivity (W m-1 °C-1) and ∆T / ∆z is the temperature gradient between the two
objects (°C m-1) (Figure 7.2). Thermal conductivity is a measure of an object’s ability to conduct heat.
Differences in thermal conductivity can create perceptions of hot or cold when touching an object. A metal
spoon in a cup of hot soup feels warmer than a wooden spoon because it conducts heat from the soup to a
person’s hand much more rapidly than a wooden spoon.
The radiation that impinges on a surface or object must be balanced by the reflected and emitted
radiation and by energy lost or gained through sensible heat, latent heat, and conduction. This balance is
maintained by changing surface temperature. As an example, consider the temperature and energy balance
of an object on a summer day in which S↓ = 700 W m-2. With an albedo of r = 0.2, the object absorbs 560
W m-2 solar radiation. A typical downward longwave flux from the atmosphere is L↓ = 340 W m-2, which
gives a radiative forcing of Qa = 560 + 340 = 900 W m-2. If the surface temperature is Ts = 31.8 °C, the
7
Ecological Climatology
upward longwave flux is L↑ = 490 W m-2 with ε = 1. Air temperature is Ta = 29.4 °C, relative humidity is
50% (so that ea = 2049.6 Pa), rH = 25 s m-1, and rW = 100 s m-1. The sensible heat flux is H = 111 W m-2 and
the latent heat flux, with e∗ ⎡⎣Ts ⎤⎦ = 4701.6 Pa, is λE = 461 W m-2 (in this example, ρ = 1.15 kg m-3, Cp =
1005 J kg-1 °C-1, γ = 66.5 Pa °C-1). For convenience, assume there is no heat loss by conduction (i.e., G =
0). In this case, the surface energy imbalance is Qa − L↑− H −λ E =900− 490−111− 461=−162 W m-2: i.e., the
object loses 162 W m-2 more energy than it receives. Its temperature must decrease to restore the energy
balance. If surface temperature drops to Ts = 29.0 °C, with e∗ ⎡⎣Ts ⎤⎦ = 4005.5 Pa, the upward longwave,
sensible heat, and latent heat fluxes are L↑ = 473, H = -18, and λE = 340 W m-2, respectively. The object
gains 105 W m-2 more energy than it loses ( 900− 473−( −18) −340=105 ) . The true temperature of this object
under these conditions is somewhere between 29.0 °C and 31.8 °C.
7.3 Leaf temperature and fluxes
The manner in which energy fluxes determine microclimates can be illustrated by the energy
budget and temperature of a leaf. The leaf energy budget is
Qa = εσ (Tl + 273.15) 4 + ρ C p
(Tl −Ta ) ρ C p ( e∗[Tl ]−ea )
r /2
b
+
γ
rs + rb
Leaf temperature (Tl) is the temperature that balances the energy budget. The boundary layer resistance (rb)
governs heat flow from the leaf surface to the air around the leaf (Figure 7.5). Stomatal resistance (rs)
acting in series with boundary layer resistance regulates transpiration.
For a leaf, heat and moisture transfer are governed by a leaf boundary layer resistance, which
depends on leaf size (d, meters) and wind speed (u, m s-1) and is approximated per unit leaf area (onesided) as
r = 200 d / u
b
This resistance has units of seconds per meter (s m-1). Plant physiologists often use m2 s mol-1 instead of s
m-1. At sea level and 20 °C, 1 m2 s mol-1 = 41 s m-1 (Jones 1992, p. 357). The boundary layer resistance
represents the resistance to heat and moisture transfer between the leaf surface and free air above the leaf
8
Chapter 7 – Surface Energy Fluxes
surface. Wind flowing across a leaf is slowed near the leaf surface and increases with distance from the
surface (Figure 7.6). Full wind flow occurs only at some distance from the leaf surface. This transition
zone, in which wind speed increases with distance from the surface, is known as the leaf boundary layer. It
is typically 1 to 10 mm thick. The boundary layer is also a region of temperature and moisture transition
from a typically hot, moist leaf surface with bright sunlight to cooler, drier air away from the surface. The
boundary layer regulates heat and moisture exchange between a leaf and the air. A thin boundary layer
produces a small resistance to heat and moisture transfer. The leaf is closely coupled to the air and has a
temperature similar to that of air. A thick boundary layer produces a large resistance to heat and moisture
transfer. Conditions at the leaf surface are decoupled from the surrounding air and the leaf is several
degrees warmer than air. Boundary layer resistance increases with leaf size and decreases with wind speed
(Figure 7.7).
This expression for bounday layer resistance is derived for a fluid moving smoothly across a
surface – a condition known as laminar forced convection (Gates 1980, pp. 268-303; Monteith and
Unsworth 1990, pp. 121-131; Campbell and Norman 1998, pp. 99-101). For a flat plate of length d
(meters), the resistance to heat transfer from one side of the plate is
r = ( ρ C d ) /( kNu)
b
p
where ρ is the density of the fluid (kg m-3), Cp is the specific heat of the fluid (J kg-1 °C-1), k is the thermal
conductivity of the fluid (W m-1 °C-1), and Nu is the dimensionless Nusselt number. For a flat plate with
laminar flow, this is given by
Nu = 0.66 Re
0.5
Pr
0.33
where Pr is the dimensionless Prandtl number and Re is the dimensionless Reynolds number. The
Reynolds number depends on fluid velocity (u, m s-1) and kinematic viscosity (ν, m2 s-1)
Re = (ud ) / ν
Combining equations,
( ρC p ν )
r =
b (0.66 k Pr 0.33 )
d
d
=a
u
u
9
Ecological Climatology
For air at 20 °C, ρ = 1.204 kg m-3, Cp = 1010 J kg-1 °C-1, ν = 15.5 × 10-6 m2 s-1, k = 0.026 W m-1 °C-1, and Pr
= 0.72 so that a = 312 s1/2 m-1 for a flat plate. Values of Nu for leaves are generally higher, so that rb is
lower, than that of a flat plate. The boundary layer resistance for flat plates must be divided by 1.4 for
leaves in the field (Campbell and Norman 1998, p. 224), giving a = 223 s1/2 m-1. Gates (1980, pp. 297-303)
recommended a value of 174 s1/2 m-1 for leaves. An approximate value for leaves is a = 200 s1/2 m-1. This
is the resistance for heat exchange from one side of a leaf. Sensible heat is exchanged from both sides of a
leaf so that heat exchange is regulated by two resistances (each defined by rb) in parallel (Figure 7.3) and
the effective resistance for heat transfer is rb / 2 (Figure 7.5). Gates (1980, pp. 27, 30, 351) used a value of
a = 133 s1/2 m-1 for sensible heat flux from a leaf. Campbell (1977, pp. 119-123) reduced rb by one-half for
sensible heat. Jones (1992, p. 63) also distinguished between one-sided and two-sided heat transfer.
Transpiration occurs when stomata open to allow a leaf to absorb CO2 during photosynthesis
(Figure 7.6). At the same time, water diffuses out of the saturated cavities within the foliage to the drier air
surrounding the leaf. The resistance for latent heat exchange, therefore, includes two terms: a stomatal
resistance (rs), which governs the flow of water from inside the leaf to the leaf surface, and the boundary
layer resistance, which governs the flow of water from the leaf surface to surrounding air. The total
resistance is the sum of these two resistances (Figure 7.5). Stomata open and close in response to a variety
of conditions (Chapter 9): they open with higher light levels; they close with temperatures colder or hotter
than some optimum; they close as the soil dries; they close if the surrounding air is too dry; and they vary
with atmospheric CO2 concentration. Stomatal resistance is a measure of how open the pores are and varies
from about 100 s m-1 when stomata are open to greater than 5000 s m-1 when stomata are closed. For
transpiration, the boundary layer resistance, which is formulated based on heat exchange from one side of a
leaf, is not reduced by one-half because stomata are typically, but not always, located on only one side of a
leaf whereas sensible heat exchange occurs on both sides. For example, Gates (1980, pp. 27, 30, 32, 351)
used a = 133 s1/2 m-1 for sensible heat and a = 200 s1/2 m-1 for latent heat. Campbell (1977, pp. 119-123)
reduced rb by one-half for sensible heat but not latent heat when stomata are on one side of the leaf. If
stomata are on both sides of the leaf, the resistances are in parallel (Figure 7.3) and the total resistance is
(r + r ) / 2 .
s b
10
Chapter 7 – Surface Energy Fluxes
Table 7.1 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. The leaf has a radiative forcing of 1000,
700, and 400 W m-2, which is representative of values for a clear sky at midday, a cloudy sky at midday,
and night, when solar radiation is zero and the leaf receives only longwave radiation. If longwave radiation
is the only means to dissipate this energy, the leaf has temperatures of 91 °C, 60 °C, 17 °C with high,
moderate, and low radiative forcings.
Heat loss by convection – sensible heat – cools the leaf (Table 7.1). Under calm conditions, with a
wind speed of 0.1 m s-1, sensible heat loss decreases leaf temperature by 38 °C (to a temperature of 53 °C)
with the high radiative forcing and by 20 °C (to a temperature of 40 °C) with the moderate forcing. Higher
wind speeds lead to even cooler temperatures. At 4.5 m s-1, the temperature of the leaf exposed to the high
radiative forcing has been reduced from 91 °C to 34 °C. At low radiative forcing, convection warms the
leaf because it is colder than the surrounding air and heat is transferred from the air to the leaf. This
example illustrates the powerful effect wind has in transporting heat away from an object, thereby cooling
the object.
Greenhouse microclimates are an example of the warm temperatures that can arise in the absence
of convective heat exchange (Avissar and Mahrer 1982; Mahrer et al. 1987; Oke 1987). It is generally
thought that greenhouses provide a warm environment to grow plants because glass or other translucent
coverings allow solar radiation to penetrate and warm the interior of the greenhouse while longwave
radiation emitted by these warm interior surfaces is trapped by the glass. Indeed, this is the analogy that
spawned the term ‘greenhouse effect’ by which increasing concentrations of CO2 in the atmosphere warm
Earth’s climate. While this can happen, the daytime warmth in greenhouses is largely a result of negligible
convective heat exchange with the outside environment. The sensible heat lost from the warm interior
surfaces is trapped within the greenhouse, warming the interior air.
Latent heat exchange also cools the leaf (Table 7.1). Under calm conditions (0.1 m s-1) and high
radiative forcing, transpiration cools the leaf an additional 14 °C, from a temperature of 53 °C with
longwave radiation and convection to a temperature of 39 °C. Higher winds result in even lower
temperatures. With a wind speed of 4.5 m s-1, the leaf temperature has been reduced from a lethal
11
Ecological Climatology
temperature of 91 °C with longwave radiation only to a more comfortable temperature of 31 °C. Cooling
by transpiration is greatest with large radiative forcings and decreases as radiation decreases. It is largest
for calm conditions and decreases as wind increases.
Figure 7.8 shows the cooling effect of transpiration in more detail over a range of air temperature
and relative humidity. Latent heat flux decreases and leaf temperature increases as relative humidity
increases. For example, with an air temperature of 45 °C and a relative humidity of 20%, the leaf
temperature is about 37.5 °C. This is 7.5 °C colder than the air. However, at 90% relative humidity, when
the latent heat flux is much smaller, the leaf temperature is approximately equal to the air temperature of 45
°C. The same is true for all air temperatures: as relative humidity increases, transpirational cooling
decreases, and leaf temperature increases. For air temperature greater than 21 °C, the relative humidity at
which the leaf is warmer than air increases with warmer air temperature. In a hot environment, the leaf is
cooler than air for all but the most humid conditions. In a cool environment, the leaf is warmer than air for
all but the most arid conditions. The cooling effect of evaporation is why we sweat, and it is why a person
may feel comfortable in dry climates, where low relative humidity results in rapid evaporation of sweat, but
hot and uncomfortable in humid climates, where evaporation is not as efficient.
In Chapter 5, Thornthwaite’s equation was introduced as a means to calculate evapotranspiration.
However, this method is not based on the surface energy budget and instead uses air temperature as a
surrogate for the energy available to evaporate water. The Penman-Monteith equation is an alternative
formulation of evapotranspiration based on the energy budget. It combines the surface energy balance with
physiological and aerodynamic controls of heat transfer. The Penman-Monteith equation is derived from
the energy balance and the expressions for sensible and latent heat. In this equation, the saturation vapor
pressure at the leaf temperature ( e*s ), which is a non-linear function of temperature (Figure 7.4), is
approximated by e*s =e*a + s (Ts −Ta ) where e*a is the saturation vapor pressure evaluated at the air
temperature (Ta) and s = de* / dT is the slope of the saturation vapor pressure versus temperature evaluated
at Ta. Substituting this expression for e*s into λE gives
12
Chapter 7 – Surface Energy Fluxes
*
ρ C p ( ea + s (Ts − Ta ) − ea )
λE =
rW
γ
Then, from the definition of the surface energy budget and sensible heat flux,
Ts − Ta = (rH / ρ Cp ) ( Rn − λ E − G )
Substituting this expression for Ts −Ta into the latent heat flux gives, after algebraic manipulation,
λE =
s ( Rn − G ) +
ρ Cp
(e
rH
s + γ (rW / rH )
*
a
− ea
)
For a leaf, G = 0, rH = rb / 2 , and rW = rs + rb so that
λE =
sRn +
ρ Cp
(e
r /2
*
a
− ea
)
b
⎛r +r ⎞
s +γ ⎜ b s ⎟
⎝ rb / 2 ⎠
This equation relates transpiration to net radiation (Rn), the vapor pressure deficit of air ( e*a −ea ), and the
boundary layer and stomatal resistances. Evapotranspiration increases as more net radiation is available to
evaporate water and as the atmospheric demand (i.e., vapor pressure deficit) increases.
The role of stomata in regulating leaf transpiration can be seen in the two limiting cases when leaf
boundary layer resistance is very large or very small (Jarvis and McNaughton 1986). If the leaf boundary
layer resistance becomes very large, so that the leaf is decoupled from the surrounding air by a thick
boundary layer,
λ E = sR /( s + γ )
n
which is known as the equilibrium evaporation rate. In this case, transpiration is independent of stomatal
resistance and depends chiefly on the net radiation available to evaporate water. If the boundary layer
resistance is small, so that there is strong coupling between conditions at the leaf surface and outside the
leaf boundary layer, transpiration is at a rate imposed by stomatal resistance
λ E = ρC
p
(e*a − ea ) /(γ rs )
13
Ecological Climatology
In this case, an increase or decrease in stomatal resistance causes a proportional decrease or increase in
transpiration. In between these two extremes of equilibrium and imposed transpiration, intermediate
degrees of stomatal control prevail. The degree of coupling between a leaf and surrounding air depends on
leaf size and wind speed (Figure 7.7). Small leaves, with their low boundary layer resistance, approach
strong coupling. Large leaves, with the high boundary layer resistance, are weakly coupled. Leaves in still
air are decoupled from the surrounding air while moving air results in strong coupling.
7.4 Surface temperature and fluxes
The same principles that determine the temperature and energy fluxes of a leaf also determine the
temperature and energy fluxes of land surfaces. Consider, for example, the energy balance of a forest
(Figure 7.9). The forest absorbs and reflects solar radiation, absorbs and emits longwave radiation, and
exchanges latent and sensible heat with the atmosphere. Sensible heat flux is directly proportional to the
difference in air temperature (Ta) and the effective surface temperature (Ts) and varies inversely in relation
to an overall resistance. Latent heat flux is directly proportional to the difference in vapor pressure of air
(ea) and the saturated vapor pressure of the surface (e*[Ts]) and is inversely related to an overall resistance.
The exchanges of sensible and latent heat between land and atmosphere occur because of
turbulent mixing of air and resultant heat and moisture transport. The movement of air can be represented
as discrete parcels of air, each with its own temperature, humidity, and momentum (mass times velocity),
moving vertically and horizontally. As the parcels of air move, they carry with them their heat, moisture,
and momentum. Wind mixes air and transports heat and water vapor in relation to the temperature and
moisture of the parcels of air being mixed. The importance of wind in mixing air in the atmospheric
boundary layer near the surface is illustrated with two simple examples. Over the course of a summer day,
productive vegetation can absorb enough CO2 during photosynthesis to deplete all the CO2 in the air to a
height of 30 m (Monteith and Unsworth 1990, p. 146). In practice, however, CO2 is not depleted because
wind mixes the air and replenishes the absorbed CO2. Likewise, productive vegetation can transpire 10 kg
m-2 (10 mm) of water on a hot summer day (Campbell and Norman 1998, p. 63). This would increase the
moisture in the first 100 m of the atmosphere by 100 g m-3 if it were not transported away. This is much
14
Chapter 7 – Surface Energy Fluxes
more water than the atmosphere can hold when saturated (about 17 g m-3 at 20 °C). Instead, wind replaces
the moist air with drier air.
Turbulence is generated when wind blows over Earth’s surface (Figure 7.10). The ground, trees,
grasses, and other objects exert a retarding force on the fluid motion of air. The frictional drag imparted on
air as it encounters rough surfaces slows the flow of air near the ground. The reduction in wind speed
transfers momentum from the atmosphere to the surface, creating turbulence that mixes the air and
transports heat and water from the surface into the lower atmosphere. With greater height above the
surface, eddies are larger so that transport of momentum, heat, and moisture is more efficient with height
above the surface.
The derivation of surface fluxes can be understood in a one-resistor formulation such as for bare
ground (Figure 7.11). Momentum (τ, kg m-1 s-2), sensible heat (H, W m-2), and water vapor (E, kg m-2 s-1)
fluxes between the atmosphere at some height z with horizontal wind (ua, m s-1), temperature (Ta, °C), and
specific humidity (qa, kg kg-1) and the ground are
τ = ρ (ua − us ) / ram
H = − ρ C p (Ta − Ts ) / rah
E = − ρ (qa − qs ) / raw
where us, Ts , and qs are corresponding surface values. The resistances ram, rah, and raw are aerodynamic
resistances (s m-1) to momentum, heat, and moisture, respectively, and represent turbulent processes. (This
derivation of evapotranspiration is in terms of water vapor (E, kg m-2 s-1) not heat (λE, J m-2 s-1) and
specific humidity nor vapor pressure. Substitution of qa = 0.622ea / P and multiplying both sides of the
equation by latent heat of vaporization (λ) gives the previously defined latent heat flux.)
These fluxes are nearly constant with height in the layer of the atmosphere near the surface
(lowest 50 m or so). Monin-Obukhov similarity theory (Brutsaert 1982; Arya 1988) relates turbulent fluxes
in the surface or constant flux layer to mean vertical gradients of horizontal wind (u), temperature (T), and
specific humidity (q) as
15
Ecological Climatology
⎡ ku* ( z − d ) ⎤ ∂u
⎥
⎣ φm (ζ ) ⎦ ∂z
τ =ρ⎢
⎡ ku ( z − d ) ⎤ ∂T
H = − ρC p ⎢ *
⎥
⎣ φh (ζ ) ⎦ ∂z
⎡ ku ( z − d ) ⎤ ∂q
E = −ρ ⎢ *
⎥
⎣ φw (ζ ) ⎦ ∂z
where k = 0.4 is the von Karman constant, z is height in the surface layer (m), and d is the displacement
height (m). The functions φm(ζ), φh(ζ), and φw(ζ) are universal similarity functions that relate the constant
fluxes of momentum, sensible heat, and water vapor to the mean vertical gradients of wind, temperature,
and moisture in the surface layer. The friction velocity (u*, m s-1) is given by
τ = ρ u*2
The terms in brackets in each equation are turbulent transfer coefficients for momentum, heat, and
moisture. These coefficients increase with height above the surface (z) because of larger eddies. To
maintain a constant flux with respect to height, increases in transport with greater height must be balanced
by corresponding decreases in the vertical gradient ( ∂u / ∂z , ∂T / ∂z , ∂q / ∂z ). Indeed, observations show that
in the surface layer, mean vertical gradients in horizontal wind, temperature, and specific humidity
decrease with height so that greater turbulent transfer is balanced by decreased vertical gradient and fluxes
are constant (e.g., Figure 7.10). Turbulent mixing also increases with greater wind speed, and hence the
coefficients increase with greater wind speed. This is represented by the friction velocity (u*). Greater
turbulence results in a weaker vertical gradient.
In addition to surface friction, buoyancy generates turbulence. In daytime, the surface is typically
warmer than the atmosphere and strong solar heating of the land provides a source of buoyant energy.
Warm air is less dense than cold air, and rising air enhances mixing and the transport of heat and moisture
away from the surface. In this unstable atmosphere, sensible heat flux is positive, temperature decreases
with height, and vertical transport increases with strong surface heating. At night, longwave emission
generally cools the surface more rapidly than the air above. The lowest levels of the atmosphere become
stable, with cold, dense air trapped near the surface and warmer air above. Sensible heat flux is negative
(i.e., toward the surface). Under these conditions, vertical motions are suppressed, and transport is reduced.
16
Chapter 7 – Surface Energy Fluxes
The effect of buoyancy on turbulence is represented by the similarity functions φm(ζ), φh(ζ), and φw(ζ),
where
ζ = (z − d ) / L
and L (m) is the Obukhov length scale (a measure of atmospheric stability). These functions have values
of one when the atmosphere is neutral, <1 when the atmosphere is unstable, and >1 when the atmosphere is
stable. As a result, the vertical profile is weaker in unstable conditions than in stable conditions (Figure
7.12).
Integrating
u2 − u1 =
∂u / ∂z between two arbitrary heights ( z2 > z1 ) gives
u* ⎡ ⎛ z2 − d ⎞
⎛ z2 − d ⎞
⎛ z1 − d ⎞ ⎤
⎢ln ⎜
⎟ −ψ m ⎜
⎟ +ψ m ⎜
⎟⎥
k ⎣ ⎝ z1 − d ⎠
⎝ L ⎠
⎝ L ⎠⎦
⎛ z1 − d ⎞
⎟ = 0 so that wind speed at height z is
⎝ L ⎠
The surface is defined as u1 = 0 at z1 = z0 m + d and ψ m ⎜
uz =
u*
k
⎡ ⎛ z−d ⎞
⎤
⎢ln ⎜
⎟ − ψ m (ζ ) ⎥
⎢⎣ ⎝ z0 m ⎠
⎥⎦
The height z0m +d is known as the apparent sink of momentum. The roughness length (z0m, m) is the
theoretical height at which wind speed is zero. A typical value is 5 cm or less for bare ground and as large
as 1 m for tall forests. The displacement height (d, m) is the vertical displacement caused by surface
elements. This displacement height is zero for bare ground and greater than zero for vegetation. Similarly,
∂T / ∂z and ∂q / ∂z can be integrated between height z and the surface as
Tz − Ts =
−H
k ρ C p u*
q z − qs =
−E
k ρ u*
⎡ ⎛ z−d ⎞
⎤
⎢ ln ⎜
⎟ − ψ h (ζ ) ⎥
⎢⎣ ⎝ z0 h ⎠
⎥⎦
⎡ ⎛ z−d ⎞
⎤
⎢ln ⎜
⎟ − ψ w (ζ ) ⎥
⎢⎣ ⎝ z0 w ⎠
⎥⎦
For temperature and specific humidity, surface values are defined as Ts at height z = z0h + d and qs at
z = z0w + d . Similar to momentum, the effective heights at which heat and moisture are exchanged with
the atmosphere are defined by the heights z0h + d and z0w + d , where z0h and z0w are the roughness
17
Ecological Climatology
lengths for heat and moisture, respectively. These heights are known as the apparent sources of heat and
moisture. The functions ψm(ζ), ψh(ζ), and ψw(ζ) account for the influence of atmospheric stability on
turbulent fluxes. They have negative values when the atmosphere is stable, positive values when the
atmosphere is unstable, and equal zero under neutral conditions.
These equations describe logarithmic vertical profiles of mean wind, temperature, and moisture in
the atmosphere. Figure 7.13 illustrates wind profiles under neutral atmospheric conditions
(i.e., ψ m (ζ ) = 0 ) that might be found over grassland and forest. In the grassland, wind speed decreases
sharply close to the ground surface, attaining a value of zero at z = z0m + d = 40 cm. For forest, wind
speed attains a value of zero at z = z0m + d = 8 m. At any height above the vegetation, wind is stronger
over the smooth grassland surface than over the rougher forest, and in general wind speed at a given height
decreases as roughness length increases. The logarithmic wind profile is valid only for heights
z > z0m + d and does not describe wind within plant canopies or close to the surface. The height
z = z0m + d is the height where the wind profile extrapolates to zero. In reality, however, wind does blow
within plant canopies. Also, it only applies to an extensive uniform surface of 1 km2 or more. Similar
logarithmic profiles can be constructed for temperature and moisture. When sensible heat and
evapotranspiration are positive, so that heat and water vapor are exchanged into the atmosphere,
temperature and specific humidity decrease with height. This typically occurs during the day. At night,
when sensible heat is negative (i.e., towards the surface), temperature increases with height. Similar to
wind, these profiles only apply to extensive homogenous terrain.
The aerodynamic resistances to momentum, heat, and moisture transfer between height z and the
surface are found by relating the profile equations to the flux equations to give
⎡ ⎛ z −d ⎞
⎤ ⎡ ⎛ z −d ⎞
⎤
1
⎢ln ⎜
=
−ψ m (ζ ) ⎥ ⎢ln ⎜
−ψ m (ζ ) ⎥
r
⎟
⎟
am
k 2u a ⎢⎣ ⎝ z0 m ⎠
⎦⎥ ⎣⎢ ⎝ z0 m ⎠
⎦⎥
1
r =
ah k 2u
a
⎡ ⎛ z −d ⎞
⎤ ⎡ ⎛ z −d ⎞
⎤
⎢ln ⎜
⎟−ψ m (ζ ) ⎥ ⎢ln ⎜
⎟ −ψ h (ζ ) ⎥
⎢⎣ ⎝ z0 m ⎠
⎥⎦ ⎢⎣ ⎝ z0 h ⎠
⎥⎦
1
r =
aw k 2u
a
⎡ ⎛ z −d ⎞
⎤ ⎡ ⎛ z −d ⎞
⎤
⎢ln ⎜
⎟−ψ m (ζ ) ⎥ ⎢ln ⎜
⎟−ψ w (ζ ) ⎥
⎥⎦
⎣⎢ ⎝ z0 m ⎠
⎦⎥ ⎣⎢ ⎝ z0 w ⎠
18
Chapter 7 – Surface Energy Fluxes
where ua is wind speed (m s-1) at height z. These resistances are less than the neutral value when the
atmosphere is unstable, resulting in a large flux for a given vertical gradient, and more than the neutral
value when the atmosphere is stable, resulting in a smaller flux for the same vertical gradient.
7.5 Vegetated canopies
At the scale of an individual leaf, stomatal control of transpiration is quantified by stomatal
resistance. At the scale of a canopy of leaves, an aggregated measure of surface conductance is required to
account for evaporation from soil and transpiration from foliage. In particular, the stomatal physiology of
individual leaves, which is directly measurable in terms of the response of stomata to light, water,
temperature, and other environmental factors, must be scaled over all leaves to the canopy, where
photosynthesis and transpiration can only be measured for the aggregate canopy (Figure 7.14, color plate).
The relationship between the bulk surface resistance obtained from canopy-scale micrometeorological
measurements to leaf resistance, a biological parameter obtained directly from leaf gas exchange, is the
subject of considerable research.
Whereas stomatal resistance describes the transpiration resistance of an individual leaf, canopy or
surface resistance describes the aggregate resistance of a canopy of leaves. This can be done as a single
bulk representation of the effective surface for moisture exchange or by partitioning evapotranspiration
into ground and vegetation, represented as one layer of leaves or multiple layers (Figure 7.11). In a bulk
representation of a vegetated canopy, evapotranspiration is controlled by two resistances acting in series: a
surface resistance that represents the combined foliage transpiration and soil evaporation and an
aerodynamic resistance that represents turbulent processes. Alternatively, evapotranspiration can be
partitioned into soil evaporation and 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 the leaves in a canopy. For very dense canopies, soil evaporation is negligible and the
distinction between surface resistance and canopy resistance is not important.
One means to estimate canopy resistance is to represent the canopy as a ‘big leaf’ with a
resistance representative for all the leaves in the canopy (Figure 7.5). Canopy resistance is then the leaf
19
Ecological Climatology
resistance divided by leaf area index. If rb / 2 and (rs + rb ) are the leaf resistances for sensible and latent
heat, respectively, the corresponding canopy resistances are rb /(2 L ) and ( rs + rb ) / L where L is leaf area
index. Leaf area index is the total one-sided or projected area of leaves per unit ground area. A square
centimeter of ground covered by a leaf with an area of 1 cm2 has a leaf area index of one. The same area
covered by two leaves, each with an area of 1 cm2, has a leaf area index of two. Canopy exchange is
perhaps more obvious in terms of conductance. Canopy conductance per unit ground area is the leaf
conductance per unit leaf area times leaf area index. A typical leaf area index for a productive forest is 4-6
m2 m-2. Greater leaf area index increases latent heat exchange with the atmosphere by increasing the
surface area from which moisture is lost. The same is true for sensible heat flux.
A one-layer formulation of latent heat from a plant canopy illustrates the processes controlling
canopy fluxes (Figure 7.11). Total latent heat is the sum of three fluxes. Water vapor is exchanged between
the leaves and air in the canopy. This flux is
λ Ev =
ρ C p (ev −eac )
rc
γ
where eac is the vapor pressure of canopy air, ev is the saturated vapor pressure of the vegetation, and rc is
the canopy resistance. Moisture is also lost from the ground as
λ Eg =
ρ C p ( eg −eac )
γ
rac
where eg is the vapor pressure at the ground and rac is an aerodynamic resistance within the canopy. Water
vapor is also exchanged between the air within the canopy and air above the canopy. This flux is
λ Ea =
ρ C p (eac −ea )
ra
γ
where ea is the vapor pressure of air above the canopy and ra is the aerodynamic resistance to moisture
transfer from within the canopy to above the canopy (Section 7.4). If there is no storage of water vapor in
the canopy air, these three fluxes are related as
λ E a = λ E g + λ Ev
20
Chapter 7 – Surface Energy Fluxes
In a very dense canopy, soil evaporation is minimal so that total latent heat is the sum of the vegetation and
canopy air fluxes
λ E = λ Ev + λ Ea =
ρ C p ( ev −ea )
rc + ra
γ
That is, latent heat exchange between a canopy of leaves and the atmosphere is the sum of two resistances
acting in series: a canopy resistance that regulates transpiration and an aerodynamic resistance (Figure 7.5).
Water vapor must first diffuse out of stomata to the leaf surface, governed by the resistance rs / L , then
from the leaf surface to canopy air surrounding the leaf ( rb / L ), and then to air above the canopy (ra).
This additional canopy resistance is seen in derivations of bulk vegetation parameters obtained
from measurements of sensible and latent heat fluxes over vegetated canopies. For example, roughness
length can be derived from measured fluxes if all other terms in the flux equations are known. Such
derivations show that the roughness lengths for heat and moisture in a bulk aerodynamic formulation of
vegetated surfaces are typically 20% that for momentum (Campbell and Norman 1998, p. 96). That is, the
apparent sources of heat and moisture in general occur at a lower height in the canopy than the apparent
sink of momentum, and the aerodynamic resistances for sensible heat and water vapor are greater than that
for momentum. This is most obvious under neutral conditions, when the ψ functions have a value of zero.
In this case, the aerodynamic resistance for heat is
r =
ah
ln[ ( z − d ) / z0 h ] ln[ ( z − d ) / z0 m ] ln[ z0 m / z0 h ]
*
=
+
=r +r
am b
ku*
ku*
ku*
where u* = u a k / ln[( z − d ) / z0 m ] . The term rb is the additional boundary layer resistance for sensible
*
heat exchange from the canopy (Monteith and Unsworth 1990, p. 248).
The Penman-Monteith equation applied to a canopy of leaves gives insights to surface and canopy
resistances and their relationship with leaf resistance (Kelliher et al. 1995). For a canopy,
λE =
s ( Rn − G ) +
ρ Cp
ra
(e
*
a
⎛r +r ⎞
s +γ ⎜ c a ⎟
⎝ ra ⎠
− ea
)
=
(
s ( Rn − G ) + ρ Cp g a ea* − ea
s + γ (1 + g a / g c )
21
)
Ecological Climatology
where rc is canopy or surface resistance, ra is the aerodynamic resistance for water vapor, and gc and ga are
the corresponding conductances. By measuring evapotranspiration from a canopy and if all other terms are
known, the Penman-Monteith equation can be solved for canopy or surface resistance. Theory suggests
that canopy conductance increases linearly with leaf area index at low leaf area (Figure 7.15). Canopy
conductance is relatively constant at a value largely determined by leaf conductance at high leaf area.
Canopy conductance becomes constant with high leaf area because low light levels on leaves deep in the
canopy close stomata. Surface conductance approaches canopy conductance as leaf area increases because
soil evaporation becomes negligible in a dense canopy. Surface conductance significantly exceeds canopy
conductance only for low leaf area index less than about 3 m2 m-2, where soil evaporation is more
important. For a given leaf conductance, surface conductance is nearly independent of leaf area because the
tendency for canopy conductance to decrease with low leaf area is counteracted by increasing proportion of
soil evaporation.
Across a variety of forests, grasslands, and croplands, surface and canopy conductances derived
from the Penman-Monteith equation show relationships similar to that predicted from theory (Figure 7.15).
Maximum surface conductance in relation to leaf area index is within the bounds determined by three
values of leaf conductance representative of woody plants, natural herbaceous plants, and agricultural
crops (Table 5.3). Maximum surface conductance increases linearly with maximum leaf conductance with
a slope of approximately 3. This is consistent with theory, which predicts that for any leaf conductance
surface conductance is constrained within limits set by leaf area and that surface conductance is largely
determined by leaf conductance at high leaf area.
As with an individual leaf, vegetation has degrees of coupling to the atmosphere determined by
the magnitude of the aerodynamic resistance (Jarvis and McNaughton 1986). Tall forest vegetation has a
low aerodynamic resistance and is closely coupled to the atmosphere. Evapotranspiration approaches a rate
imposed by canopy resistance
λ E = ρ C p (ea* − ea ) /(γ rc )
22
Chapter 7 – Surface Energy Fluxes
Short vegetation such as grassland has a large aerodynamic resistance and is decoupled from the
atmosphere. Evapotranspiration approaches an equilibrium rate dependent on available energy with little
canopy influence
λ E = s ( R − G ) /( s + γ )
n
This coupling and decoupling with the atmosphere can be seen in leaf temperature. By influencing
aerodynamic resistance, the height of plants has a large influence on leaf temperature. Tall vegetation is
aerodynamically rough. Heat is readily exchanged with the atmosphere, and the temperature of leaves is
closely coupled to that of the air. In contrast, short vegetation is aerodynamically smooth and dissipates
heat less effectively. The leaves of short vegetation experience warmer temperatures than that of air. In
cold climates, short stature may convey an advantage by warming leaf temperature (Wilson et al. 1987;
Grace 1988; Grace et al. 1989). Figure 7.16 illustrates this for alpine forest and shrub vegetation. For both
types of vegetation the leaf-to-air temperature difference increases with greater net radiation. In the tall
forest, the slope of this relationship is near zero (0.001-0.004 °C per W m-2). Leaf temperatures are similar
to air temperature, with a maximum excess of 5 °C. In the dwarf shrub vegetation, the slope is larger
(0.013-0.023 °C per W m-2) and declines with increasing wind speed. The maximum temperature excess is
19 °C in bright sunshine and low wind speed. These results are explained by the effect of wind and
vegetation height on the efficiency with which heat is carried away from leaves. The aerodynamic
resistance increases with shorter vegetation and weaker winds (Figure 7.7). The effect of wind speed to
decrease resistance is greater for short vegetation than for tall vegetation.
7.6 Surface climate
Several atmospheric variables affect surface fluxes (Table 7.2). Incoming solar and longwave
radiation determine net radiation. Air temperature and atmospheric humidity determine the diffusion
gradients for sensible and latent heat, respectively. Wind speed affects sensible heat, latent heat, and
momentum fluxes through turbulence. Precipitation determines soil water, and through this, latent heat.
Snow on the ground affects surface albedo. Soil temperature affects the amount of heat flowing into the
soil. In addition, solar radiation, air temperature, atmospheric humidity, atmospheric CO2, and soil water
23
Ecological Climatology
determine stomatal resistance and therefore influence latent heat. In turn, these atmospheric variables are
themselves affected by surface fluxes. There is a coupling between the state of the atmosphere and the
land.
Surface fluxes vary over the course of a day in response to the diurnal cycle. As more radiation is
received from the Sun, the land warms and more energy must be dissipated as sensible and latent heat. In
addition, stomata open to allow CO2 uptake, but in doing so plants lose water during evapotranspiration.
Figure 7.17 illustrates these cycles for a deciduous forest on a typical summer day. In early morning, the
forest has a negative radiative balance – no solar radiation is absorbed but longwave radiation is lost.
Sensible and latent heat fluxes are small. Stomata are closed, and trees do not absorb CO2 during
photosynthesis. Carbon dioxide is, however, lost during respiration, and there is a net flux of CO2 from the
forest to the atmosphere. As the Sun rises and solar radiation is absorbed by the forest, there is a net gain of
radiation at the surface – solar absorption exceeds longwave losses. The forest begins to warm and some
of this energy is returned to the atmosphere as sensible heat. Stomata open, allowing for net CO2 uptake
during photosynthesis and water loss during evapotranspiration. Latent heat exchange is an important
means of dissipating the energy absorbed by the forest. At midday, about one-half the net radiation
absorbed by the forest is returned to the atmosphere as latent heat. This is over twice the sensible heat flux,
indicating a well-watered site. Fluxes are strongest in early to middle afternoon and decrease late in the
afternoon when solar radiation diminishes.
The diurnal cycle of surface energy fluxes imparts a diurnal cycle to air temperature (Figure 7.18).
As the Sun’s intensity increases during the day, incoming solar radiation exceeds the net loss of longwave
radiation from the surface. At this point, there is a net gain of radiation and the ground begins to warm. Air
in contact with the ground is heated by conduction. This heating is greatest near the surface because air is a
poor conductor of heat. Turbulence carries heat from the surface upward into the atmosphere. As a result,
air temperature also begins to warm. At local noon, the Sun is at its highest point in the sky and, provided
there are no clouds, the ground receives the most intense radiation of the day. Then as the Sun becomes
lower in the sky, incoming solar radiation decreases. However, so long as the incoming solar radiation
exceeds the net loss of longwave radiation, surplus energy is gained and temperature warms. This creates a
time lag between maximum solar radiation and warmest air temperature. The exact time of maximum
24
Chapter 7 – Surface Energy Fluxes
temperature varies. Under clear skies, the maximum temperature typically occurs in late afternoon between
1500 and 1700 hours. When the afternoon is cloudy or a cold front passes through, warmest temperatures
can occur earlier in the day. When the outgoing longwave radiation exceeds solar radiation, temperature
decreases. This cooling continues through the night because no energy is gained from the Sun but energy is
lost through terrestrial longwave radiation. Coldest temperatures typically occur just before sunrise.
Figure 7.19 shows observed diurnal cycles of solar radiation, temperature, relative humidity, and
wind for several summer days in Colorado. Solar radiation has a pronounced diurnal cycle. Peak values
typically occur near noon, but there is considerable variability as clouds pass overhead (e.g., July 25). Air
temperature varies in relation to solar radiation. Coldest temperatures typically occur near sunrise; warmest
temperatures occur in middle to late afternoon. Clouds reduce the solar radiation received at the surface
and reduce surface warming (compare July 23 and 28). Conversely, nighttime clouds reduce surface
cooling by re-radiating onto the surface terrestrial longwave radiation. The effect of clouds, therefore, is to
greatly diminish the diurnal temperature range – the difference between daily maximum and minimum
temperatures. Relative humidity has a strong diurnal cycle related to surface heating. The amount of water
vapor in the air often is lowest early in the morning, increasing to a maximum during daylight hours when
evapotranspiration moistens the atmosphere. However, relative humidity is generally highest at night, when
air is cool, and decreases during the day, when air is warm. Wind speed also has a diurnal cycle. Heating of
the surface during the day provides buoyant energy that mixes the near-surface air and creates winds. At
night, longwave emission of radiation typically cools the surface. The near-surface air becomes stable, with
cold, dense air trapped near the surface. Under these conditions, turbulence and vertical mixing are
suppressed. Hence, winds over land normally reach maximum speeds in early afternoon and decrease at
night.
Precipitation can also have a strong diurnal cycle. As air near the ground is warmed during the
day, it rises. The air cools, and water vapor condenses into clouds. If conditions are right and clouds grow
large enough, rain occurs in the form of afternoon thunderstorms. In the United States, precipitation has a
large diurnal cycle over many areas, especially during warm seasons (Dai et al. 1999a). The strongest
diurnal cycle occurs in summer in the Rocky Mountain region and the Southeast, when late-afternoon
thunderstorms produce maximum hourly precipitation that is greater than the 24-hour mean. In these
25
Ecological Climatology
regions, it is more than twice as likely to rain during summer from 1500 to 1800 hours than any other time
of day.
As shown in Figure 7.19, the amount of solar radiation reaching the ground is an important
determinant of the surface climate. The partitioning of net radiation into sensible and latent heat is also
strongly influenced by soil water (Figure 7.20). Over the course of a typical summer day, the majority of
net radiation is dissipated as latent heat for a well-watered site. In contrast, a dry site dissipates much less
energy via latent heat and more as sensible heat. As a result, the wet surface is colder than the dry surface.
In general, most of net radiation is dissipated as latent heat when water does not limit evapotranspiration.
As a result, the air is cooler and moister than in the absence of evapotranspiration. As soil dries, less water
is available for evapotranspiration, canopy resistance increases, and more energy is dissipated as sensible
heat or stored in the ground. Because most of the net radiation is dissipated as sensible heat, the lower
atmosphere is likely to be warm and dry. Typical values of the Bowen ratio (defined as the ratio of sensible
to latent heat, i.e., β = H / λ E ) are: 0.1 to 0.3 for tropical rain forests, where high annual rainfall keeps soil
wet year-round; 0.4 to 0.8 for temperate forests and grasslands, where less rainfall causes drier soils; 2.0 to
6.0 for semi-arid regions with extremely dry soils; and greater than 10.0 for deserts (Oke 1987, p. 70).
The energy balance at the surface varies seasonally due to changes in incoming solar radiation and
precipitation. Figure 7.21 illustrates monthly surface fluxes for six geographic regions of North America.
At all sites, net radiation is highest in summer and lowest in winter. Middle latitude sites have a higher
summer net radiation than northern Canada or Alaska. The processes by which this radiation is balanced
differ among locations. Moist sites (southeast, central, and northeast United States, northern Canada) have
high summertime latent heat flux and lower sensible heat flux. Cool sites (northeast United States, northern
Canada) sustain high rates of evapotranspiration throughout the summer and most of the net radiation is
dissipated as latent heat. At the warm sites (central and southeast United States), evapotranspiration peaks
in June and then declines so that latent heat and sensible heat are equally important by late summer. This
suggests soil water is becoming depleted. In contrast to the moist sites, southwest United States has little
evapotranspiration. Most of the net radiation is returned to the atmosphere as sensible heat. The cold tundra
site has the highest soil heat flux because much of the net radiation is used in late spring to melt snow and
warm frozen soil.
26
Chapter 7 – Surface Energy Fluxes
The diurnal heating of land varies seasonally and geographically depending on variations in solar
geometry, cloudiness, and the amount of dust, pollution, and moisture in the air. In the United States, the
arid West has the largest diurnal temperature range (greater than 15 °C) in summer (Figure 7.22, color
plate). Extremely dry regions such as Nevada have a diurnal temperature range in excess of 20 °C. The dry
air allows intense penetration of radiation through the atmosphere and provides little longwave heating at
night. Humid regions of eastern United States, where the hazy sky prevents strong solar heating during the
day and warms temperature at night, have a lower diurnal temperature range (less than 14 °C). Coastal
areas have a lower diurnal temperature range (less than 10 °C) because of greater haziness and the
moderating influence of water. Similar geographic patterns occur in winter, but less intense winter solar
radiation precludes strong daytime heating of the land. Clouds have a large effect on diurnal temperature
range (Dai et al. 1999b). Clouds reduce daytime heating by decreasing the amount of solar radiation that
reaches the ground and they warm nighttime temperatures by enhancing downward longwave radiation.
Wet soils also reduce diurnal temperature range by increasing daytime evaporative cooling. As soils dry,
evapotranspiration decreases and daytime temperatures become hotter as a result of the decreased cooling
(Durre et al. 2000).
27
Ecological Climatology
7.7 Tables
Table 7.1. Surface temperatures for radiative forcings of 1000, 700, and 400 W m-2 with (a) longwave
radiation only (L↑), (b) longwave radiation and convection (L↑ + H), and (c) longwave radiation,
convection, and transpiration (L↑ + H + λE)
Temperature (°C)
L↑ + H + λE
L↑ + H
Qa (W m-2)
L↑
0.1 m s-1
0.9 m s-1
4.5 m s-1
0.1 m s-1
0.9 m s-1
4.5 m s-1
1000
91
53
39
34
39
33
31
700
60
40
34
32
32
29
29
400
17
26
28
29
23
26
27
Note: Air temperature is 29 °C, relative humidity is 50%, and wind speeds are 0.1, 0.9, and 4.5 m s-1.
Stomatal resistance is 100 s m-1 and leaf dimension is 5 cm. In this example, ρ = 1.15 kg m-3, Cp = 1005 J
kg-1 °C-1, γ = 66.5 Pa °C-1, and ε = 1.
28
Chapter 7 – Surface Energy Fluxes
Table 7.2. Principal meteorological and surface variables that affect energy, moisture, and momentum
fluxes
Meteorological
Surface process
Surface forcing
Surface process
Incoming solar
Net radiation
Albedo
Reflected solar radiation
radiation
Stomatal resistance
Incoming longwave
Net radiation
forcing
Net radiation
Emissivity
radiation
Air temperature
Emitted longwave radiation
Net radiation
Sensible heat
Soil texture
Stomatal resistance
• Hydraulic properties
Soil water → Latent heat
• Thermal properties
Ground heat
Atmospheric
Latent heat
Roughness length
Sensible heat
humidity
Stomatal resistance
Displacement height
Latent heat
Momentum
Wind speed
Sensible heat
Stomatal physiology
Latent heat
Leaf dimension
Sensible heat
Latent heat
Momentum
Atmospheric CO2
Stomatal resistance
Latent heat
Precipitation
• Soil water
Leaf area index
Canopy resistance
Latent heat
Latent heat
Stomatal resistance
Sensible heat
• Snow
Albedo
Albedo
Soil temperature
Ground heat
Rooting depth
Stomatal resistance
Latent heat
Topography
Incoming solar radiation
Net radiation
Temperature
Soil water
29
Ecological Climatology
7.8 Figure Legends
Figure 7.1. Energy balance of a person. Top: Sources of energy. Bottom: Means to dissipate energy.
Figure 7.2. Means to dissipate energy. Top left: Emitted longwave radiation as a function of temperature
for an emissivity of one. Top right: Heat transfer by conduction in relation to temperature gradient (∆T/∆z)
and thermal conductivity (k). Bottom left: Sensible heat flux in relation to temperature difference (Ts-Ta)
and resistance ( rH ). Bottom right: Latent heat flux in relation to vapor pressure deficit ( e∗ ⎡⎣Ts ⎤⎦ − ea ) and
resistance ( rW ). In this example, ρ = 1.15 kg m-3, Cp = 1005 J kg-1 °C-1, and γ = 66.5 Pa °C-1.
Figure 7.3. Electrical network analogy for heat, water, and CO2 exchange by leaves. Left: Resistance (r)
and conductance (g) for two resistances in series and parallel. Also shown is the total resistance (R) and
conductance (G). Right: Heat, water, and CO2 exchange as a network of leaf boundary layer (rb) and
stomatal (rs) resistances for upper and lower leaf surfaces.
Figure 7.4. Saturation vapor pressure as a function of temperature. The left axis shows vapor pressure in
pascals. The right axis shows specific humidity, which is the mass of water divided by the mass of air.
Dashed lines show vapor pressure at 18.5 °C and 30 °C. In this example, a parcel of air with a vapor
pressure of 2122 Pa has a relative humidity of 100% at 18.5 °C and 50% at 30 °C.
Figure 7.5. Resistances to sensible and latent heat transfer and CO2 uptake for an individual leaf (top) and
a canopy of leaves (bottom). 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). Canopy: 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).
30
Chapter 7 – Surface Energy Fluxes
Figure 7.6. 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.
Figure 7.7. Resistances to heat transfer. Top: Leaf boundary layer resistance in relation to leaf size and
wind speed. Bottom: Aerodynamic resistance in relation to vegetation height and wind speed.
Figure 7.8. Leaf temperature (top) and latent heat flux (bottom) in response to air temperature ranging
from 16 °C to 49 °C and relative humidity ranging from 0% to 100%. The gray region shows combinations
of air temperature and relative humidity where the leaf is warmer than the air. The radiative forcing is Qa =
700 W m-2, winds are light (u = 0.9 m s-1), leaf dimension is d = 0.05 m, and stomatal resistance is rs = 100
s m-1. In this example, ρ = 1.15 kg m-3, Cp = 1005 J kg-1 °C-1, γ = 66.5 Pa °C-1, and ε = 1.
Figure 7.9. Energy balance and momentum transfer for a forest.
Figure 7.10. Conceptual diagram of momentum, heat, and water vapor transfer. Momentum is transferred
to the surface. Heat and water are generally exchanged from the surface to the atmosphere. Heat and
moisture are transferred towards the surface when it is colder than the atmosphere or when dew forms.
Figure 7.11. Resistance networks for sensible heat (top) and latent heat (bottom). Networks are for bare
ground and vegetation with a bulk surface formulation, one vegetation layer, and two vegetation layers.
Bare ground: The surface is the ground and fluxes are regulated by an aerodynamic resistance (ra). Bulk
surface: This is based on an effective surface temperature (Ts) and vapor pressure (es) that combines
vegetation and ground. The overall resistance is a surface resistance (rs) acting in series with an
aerodynamic resitance (ra). One-layer vegetation: Fluxes are partitioned into vegetation and ground based
on vegetation (Tv, ev) and ground (Tg, eg) temperature and vapor pressure. The resistance rac accounts for
aerodynamic processes within the canopy. The canopy resistance rc accounts for exchange from the
vegetation to air within the canopy (Tac, eac). For latent heat, this also includes stomatal resistance. Twolayer vegetation: The vegetation is partitioned into an upper (u) and lower (l) canopy.
Figure 7.12. Effect of atmospheric stability on the vertical gradient of wind speed.
31
Ecological Climatology
Figure 7.13. Effect of surface roughness on wind. Wind speeds are given as a percent of the winds at a
height of 30 m. Left: Grassland with a roughness length z0 = 5 cm and a displacement height d = 35 cm.
Right: Forest with a roughness length z0 = 1 m and a displacement height d = 7 m.
Figure 7.14. Scaling of photosynthesis and transpiration for an individual leaf to a canopy. An individual
leaf has measurable CO2 and water vapor exchange in response to light (photosynthetic photon flux
density) regulated by stomatal and boundary layer resistances. At the scale of a plant, one common
approach is to recognize two types of leaves (sunlit and shaded) that differ in stomatal physiology. Canopy
resistance is based on these two leaves acting in parallel. Individual plants in the canopy differ in leaf
physiology. In this case, canopy resistance can be derived from micrometeorological measurements of
fluxes above the canopy.
Figure 7.15. Relationships among maximum leaf, canopy, and surface conductance when vegetation is not
stressed by low soil water and other environmental conditions. Left: Theoretical relationships among
maximum leaf conductance (gsmax), canopy conductance (Gc), and surface conductance (Gs) with increasing
leaf area index for gsmax = 8 mm s-1. Relationships are for particular values of net radiation, vapor pressure
deficit, aerodynamic conductance, and response of stomata to light. Middle: Observed maximum surface
conductance (Gsmax) in relation to leaf area index for a variety of grasslands, forests, and croplands. The
solid lines show the expected relationship for three values of gsmax. Right: Observed Gsmax in relation to
gsmax for several grasslands, forests, and croplands. The dashed lines show the upper and lower limits of
Gsmax expected from theory with leaf area index of 10 and 2 m2 m-2. Adapted from Kelliher et al. (1995).
Figure 7.16. Relationship between daytime leaf-air temperature difference and net radiation for four wind
speed categories. Left: Forest, 15-18 m tall. Right: Shrub, 0.1 m tall. Data from Grace et al. (1989).
Figure 7.17. Fluxes of net radiation, sensible heat, latent heat, and carbon dioxide for a boreal deciduous
forest on a typical summer day. Fluxes towards the atmosphere are positive. Negative values show fluxes
towards the surface. Data from Bonan et al. (1997).
32
Chapter 7 – Surface Energy Fluxes
Figure 7.18. Idealized relationship over the course of a day between air temperature (top) and surface
radiation (bottom).
Figure 7.19. Diurnal variation in solar radiation (top left), air temperature (top right), relative humidity
(bottom left), and wind speed (bottom right) measured in Boulder County, Colorado. Tick marks are 0600,
1200, 1800, and midnight.
Figure 7.20. Energy balance and temperature of wet and dry forested surfaces on a typical summer day.
Top: Wet surface fluxes. Middle: Dry surface fluxes. Bottom: Temperatures for wet and dry surfaces. From
a model of surface energy fluxes and soil temperature using the principles outlined in this chapter and
Chapter 6.
Figure 7.21. Monthly surface energy fluxes for various locations in North America. Data from the National
Center for Atmospheric Research Community Climate Model (Bonan 1998).
Figure 7.22. Diurnal temperature range. Top: Winter. Bottom: Summer. Data from Rosenbloom and Kittel
(1996) and provided by the National Center for Atmospheric Research (Boulder, Colorado).
33