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).

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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).

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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 one-half, 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).

Leaf Temperature (deg C) L↑ + H L↑ + H + λE Qa

(W/m2) L↑ 0.1 m/s 0.9 m/s 4.5 m/s 0.1 m/s 0.9 m/s 4.5 m/s 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 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 = (z-d)/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.

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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 Sensible and Latent heat Leaf area index Canopy resistance, Albedo, Sensible & Latent heat Rooting depth Stomatal resistance, Latent heat Topography 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, 1549-1577, 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.