Tải bản đầy đủ - 0 (trang)
Chapter 7. Temperature and Energy Budgets

Chapter 7. Temperature and Energy Budgets

Tải bản đầy đủ - 0trang


7. Temperature and Energy Budgets

usually exhibit a temperature optimum. In Chapter 3, we discussed the

Boltzmann energy distribution, Arrhenius plots, and Q10, all of which involve the thermal energy of molecular motion. Light absorption (Chapter 4)

causes molecules to attain states that are simply too improbable to be

reached by collisions based on thermal energy. Transitions from an excited

state to another one at a lower energy or to the ground state can be radiationless, releasing energy as heat that is eventually shared by the surrounding molecules. The surface temperature of an object indicates both the

wavelengths where radiation from it will be maximal (Wien’s displacement

law, Eq. 4.4) and the total energy radiated (Stefan–Boltzmann law, Eq. 6.18).

The temperature of an object reflects the net result of all the ways that

energy can enter or exit from it. In this chapter, we examine these various

ways, especially for leaves. We will then be able to predict the temperatures

of leaves and more massive plant parts, based on the ambient environmental

conditions. Moreover, we can also appreciate the consequences of certain

adaptations of plants to their environment and identify the experimental

data needed for future refinements of our calculations.

We should emphasize at the outset that individual plants as well as

environmental conditions vary tremendously. Thus, in this and the next

two chapters we will indicate an approach to the study of plant physiology

and physiological ecology rather than providing a compendium of facts

suitable for all situations. Nevertheless, certain basic features should become

clear. For instance, CO2 uptake during photosynthesis is accompanied by a

water efflux through the stomata. This water loss during transpiration cools a

leaf. Also, energy influxes are balanced against effluxes by changes in leaf

temperature, which affects the amount of radiation emitted by a leaf as well

as the heat conducted to the surrounding air. Another generality is that the

temperatures of small leaves tend to be closer to those of the air than do the

temperatures of large leaves. To appreciate the relative contributions of

the various factors, we will use representative values for leaf and environmental parameters to describe the gas fluxes and the energy balance of leaves.

7.1. Energy Budget—Radiation

The law of conservation of energy (the first law of thermodynamics) states

that energy cannot be created or destroyed but only changed from one form

to another. We will apply this principle to the energy balance of a leaf, which

occurs in an environment with many energy fluxes. We can summarize the

various contributors to the energy balance of a leaf as follows:

Absorbed solar


Absorbed infrared

irradiation from


(including sky)

Energy into leaf

Emitted infrared


Heat convection,

Heat conduction,

Heat loss accompanying

water evaporation

− Energy out of leaf


Other metabolism,

Leaf temperature



Energy storage by leaf



7.1. Energy Budget—Radiation

Equation 7.1 describes the case in which the leaf temperature is greater than

the temperature of the air; when the leaf temperature is less than that of the

surrounding turbulent air, heat moves into a leaf. Also, when water condenses onto a leaf, the leaf gains heat. In such cases, the appropriate energy

terms in Equation 7.1 change sign.

The various terms in Equation 7.1 differ greatly in magnitude. For

instance, usually all of the energy storage terms are relatively small. As a

basis for comparison, we will consider the average amount of solar

irradiation incident on the earth’s atmosphere (the term “irradiation”

refers to incident radiation; see Chapter 4, Footnote 3, for radiation

terminology). This radiant flux density, the solar constant, averages

1366 W mÀ2 (Chapter 4, Section 4.1D). The solar irradiation absorbed

by an exposed leaf is often about half of this during the daytime. Hence,

any process under 7 W mÀ2 corresponds to less than 1% of the absorbed

solar irradiation for full sunlight, which usually cannot be measured to

an accuracy greater than 1%. How much energy is stored by photosynthesis? A typical net rate of CO2 fixation by a photosynthetically active

leaf is 10 mmol mÀ2 sÀ1 (see Chapter 8, Section 8.4G). As indicated at the

beginning of Chapter 5, about 479 kJ of energy is stored per mole of CO2

fixed into photosynthetic products. Hence, photosynthesis by leaves

might store

ð10 Â 10À6 mol mÀ2 sÀ1 Þð479 Â 103 J molÀ1 Þ ¼ 5 J mÀ2 sÀ1 ¼ 5 W mÀ2

which is less than 1% of the rate of absorption of solar irradiation under the

same conditions. In some cases the rate of photosynthesis can be higher. Still,

we can generally ignore the contribution of photosynthesis to the energy

balance of a leaf. Other metabolic processes in a leaf, such as respiration and

photorespiration, are usually even less important on an energy basis than is

photosynthesis, so they too can generally be ignored.

We will now consider the amount of energy that can be stored because of

changes in leaf temperature. For purposes of calculation, we will assume that

a leaf has the high specific heat of water (4.18 kJ kgÀ1  CÀ1 at 20 C; Appendix I), where specific heat is the energy required to raise the temperature of

unit mass by one degree. We will further assume that the leaf is 300 mm thick

(e.g., Fig. 1-2) and has an overall density of 700 kg mÀ3 (0.7 g cmÀ3)—a leaf is

often 30% air by volume. Hence, the mass per unit leaf area in this case is

ð300 Â 10À6 mÞð700 kg m3 ị ẳ 0:21 kg m2

The energy absorbed per unit area and per unit time equals the specific heat

times the mass per unit area times the rate of temperature increase. Therefore, if 7 W mÀ2 were stored by temperature increases in such a leaf, its

temperature would rise at the rate of

7 J m2 s1 ị

ẳ 0:008 C s1

4180 J kg1  CÀ1 Þð0:21 kg mÀ2 Þ

ð0:5 C minÀ1 Þ

Because this is a faster temperature change than is sustained for long periods

by leaves, we can assume that very little energy is stored (or released) in the


7. Temperature and Energy Budgets

form of leaf temperature changes. Hence, all three energy storage terms in

Equation 7.1 usually are relatively small for a leaf.

When the energy storage terms in Equation 7.1 are ignored, the remaining contributors to the energy balance of a leaf are either radiation or heat

terms. We can then simplify our energy balance relation as follows:

Emitted infrared


Heat convection,

Heat conduction,

Heat loss accompanying

water evaporation

Absorbed solar


Absorbed infrared

irradiation from


Energy into leaf



Energy out of leaf

The heat conducted and then convected from leaves is sometimes referred to

as sensible heat, and that associated with the evaporation or the condensation of water is known as latent heat. In this chapter, we consider each of the

terms in Equation 7.2, which have units of energy per unit area and per unit

time; for example, J mÀ2 sÀ1, which is W mÀ2.

7.1A. Solar Irradiation

Solar irradiation, meaning all of the incoming wavelengths from the sun

(Fig. 4-5), can reach a leaf in many different ways, the most obvious being

direct sunlight (Fig. 7-1). Alternatively, sunlight can be scattered by

molecules and particles in the atmosphere before striking a leaf. Also,

both the direct and the scattered solar irradiation can be reflected by the

surroundings toward a leaf (the term “scattering” usually denotes the

irregular changes in the direction of light caused by small particles or

molecules; “reflection” refers to the change in direction of irradiation at

a surface). In Figure 7-1 we summarize these various possibilities that

lead to six different ways by which solar irradiation can impinge on a leaf.

The individual energy fluxes can involve the upper surface of a leaf, its

lower surface, or perhaps both surfaces—in Figure 7-1 the direct solar

irradiation (Sdirect) is incident only on the upper surface of the leaf. To

proceed with the analysis in a reasonable fashion, we need to make many

simplifying assumptions and approximations.

Some of the solar irradiation can be scattered or reflected from

clouds before being incident on a leaf. On a cloudy day, the diffuse

sunlight emanating from the clouds—Scloud, or cloudlight—is substantial,

whereas Sdirect may be greatly reduced. For instance, a sky overcast by a

fairly thin cloud layer that is 100 m thick might absorb or reflect away

from the earth about 50% of the incident solar irradiation and diffusely

scatter most of the rest toward the earth. A cloud layer that is 1 km thick

will usually scatter somewhat less than 10% of the Sdirect incident on it

toward the earth (the actual percentages depend on the type and the


7.1. Energy Budget—Radiation

S direct




S cloud




S sky








rS sky

rS cloud

rS direct

Figure 7-1.

Schematic illustration of eight forms of radiant energy incident on an exposed leaf, including six

that involve shortwave irradiation from the sun and contain the letter S and two that involve

infrared (IR) radiation incident on the upper and the lower leaf surfaces. Also illustrated is the

IR emitted by a leaf.

density of the clouds). Because the relative amounts of absorption, scattering, reflection, and transmission by clouds all depend on wavelength,

cloudlight has a somewhat different wavelength distribution than does

direct solar irradiation. Specifically, cloudlight is usually white or gray,

whereas direct sunlight tends to be yellowish.

Solar irradiation scattered by air molecules and airborne particles leads

to Ssky, or skylight. Such scattering is generally divided into two categories:

(1) Rayleigh scattering due to molecules, whose magnitude is approximately

proportional to 1/l4 (l is the wavelength); and (2) Mie scattering due to

particles such as dust, which is approximately proportional to 1/l. Because of

the greater scattering of the shorter wavelengths, skylight differs considerably from the wavelength distribution for Sdirect. In particular, Ssky is

enriched in the shorter wavelengths, because Rayleigh scattering causes

most of the wavelengths below 500 nm to be scattered out of the direct solar

beam and to become skylight (Fig. 7-2). This explains the blue color of the

sky (and its skylight) during the daytime, especially when the sun is nearly

overhead, and the reddish color of the sun at sunrise and sunset, when Sdirect

must travel a much greater distance through the earth’s atmosphere, leading

to more scattering of the shorter (bluish) wavelengths out of the direct solar

beam. In terms of energy, Ssky can be up to 10% of Sdirect for a horizontal leaf

(Fig. 7-1) on a cloudless day when the sun is overhead (Fig. 7-2) and can

exceed Sdirect when the sun is near the horizon.


7. Temperature and Energy Budgets

Wavelength (μm)








Relative radiant energy flux density

per unit wave number interval



Infrared radiation

emitted by leaf




Direct solar





3 × 106

Figure 7-2.

2 × 106

1 × 106

Wave number (m−1)


Wave number and wavelength distributions for direct solar irradiation, skylight, and radiation

emitted by a leaf at 25 C. Wave number (introduced in Problem 4.2) equals the reciprocal of

wavelength and thus is proportional to energy (see Eq. 4.2a; El = hn = hc/lvac). The areas under

the curves indicate the total energy radiated: Sdirect is 840 W mÀ2, Ssky is 80 W mÀ2, and the IR

emitted is 860 W mÀ2.

We refer to the direct sunlight plus the cloudlight and the skylight as the

global irradiation, S. Generally, Scloud + Ssky is referred to as diffuse shortwave irradiation, a readily measured quantity, whereas Scloud and Ssky are

difficult to measure separately. Sdiffuse can be comparable in magnitude to

Sdirect, even on cloudless days, especially at high latitudes. In any case, the

global irradiation equals the direct plus the diffuse solar irradiation:

S ẳ Sdirect ỵ Sdiffuse

ẳ Sdirect ỵ Scloud ỵ Ssky


The value of the global irradiation (Eq. 7.3) varies widely with the time of day,

the time of year, the latitude, the altitude, and atmospheric conditions. As

indicated previously, the maximum solar irradiation incident on the earth’s

atmosphere averages 1366 W mÀ2. Because of scattering and absorption of

solar irradiation by atmospheric gases (see Fig. 4-5), S on a cloudless day with

the sun directly overhead in a dust-free sky is about 1000 W mÀ2 at sea level.


7.1. Energy Budget—Radiation

In the absence of clouds, S can be related to the solar constant

(1366 W mÀ2; Sc) and the atmospheric transmittance t (the fraction of sunlight transmitted when the sun is directly overhead), which ranges from 0.5

under hazy conditions at sea level to 0.8 for clear skies at higher elevations:

S ¼ Sc t1=sing sing


where g is the sun’s altitude, or angle above the horizon; g depends on the

time of day, the time of year, and the latitude. The dependence of g on the

time of day is handled by the hour angle, h, which equals 15 (t À 12), where t is

the solar time in hours and equals 12 at solar noon when the sun reaches its

highest daily point in the sky. The time of year is handled by the solar

declination, d, which equals À23.5 cos [(D + 10)360 /365.25], where D is

the day of the year (January 1 = 1) and À23.5 incorporates the tilt of the

earth’s axis relative to the plane of the earth’s orbit. Using these parameters,

sin g equals sin d sin l + cos h cos d cos l, where l is the latitude in degrees.

When the sun is directly overhead, g is 90 and sin g equals 1.00; S then equals

Sct by Equation 7.4, where t averages about 0.75 on clear days at sea level.

Sunlight may impinge on a leaf as direct solar irradiation, cloudlight, or

skylight. These three components of global irradiation may first be reflected

from the surroundings before striking a leaf (see Fig. 7-1). Although the

reflected global irradiation can be incident on a leaf from all angles, for a

horizontal exposed leaf it occurs primarily on the lower surface (Fig. 7-1).

The reflected sunlight, cloudlight, and skylight usually are 10 to 30% of the

global irradiation. A related quantity is the fraction of the incident shortwave irradiation reflected from the earth’s surface, termed the albedo, which

averages about 0.60 for snow, 0.35 for dry sandy soil, 0.25 for dry clay, but

only 0.10 for peat soil; the albedo is about 0.25 for most crops and 0.15 for

forests. The albedo generally varies with the angle of incidence of the direct

solar beam, being greater at smaller angles of incidence.

Each of these six forms of solar irradiation (direct as well as reflected

forms of sunlight, cloudlight, and skylight) can have a different variation

with wavelength. Because absorption depends on wavelength, the fraction

of each one absorbed (the absorptance) can also be different. Moreover, the

fraction reflected depends on wavelength. For simplicity, we will assume that

the same absorptance applies to Sdirect, Scloud, and Ssky, as well as to the

reflected forms of these irradiations. We will also assume that the same

reflectance applies to each component of the global irradiation. We can then

represent the absorption of direct, scattered, and reflected forms of solar

irradiation by a leaf as follows:

Absorbed solar irradiation

aSdirect ỵ Scloud ỵ Ssky ị ỵ arSdirect ỵ Scloud ỵ Ssky ị

ẳ a1 ỵ rịS


where the absorptance a is the fraction of the global radiant energy flux

density S absorbed by the leaf, and the reflectance r is the fraction of S

reflected from the surroundings onto the leaf. Absorptance is often called

absorptivity, and reflectance is called reflectivity, especially when dealing

with smooth surfaces of uniform composition.


7. Temperature and Energy Budgets

7.1B. Absorbed Infrared Irradiation

Besides the absorption of the various components of solar irradiation, additional infrared (IR), or thermal, radiation is also absorbed by a leaf (see

Eq. 7.2 and Fig. 7-1). Any object with a temperature above 0 K (“absolute

zero”) emits such thermal radiation, including a leaf’s surroundings as well

as the sky (see Fig. 6-11). The peak in the spectral distribution of thermal

radiation can be described by Wien’s displacement law, which states that the

wavelength for maximum emission of energy, lmax, times the surface temperature of the emitting body, T, equals 2.90 Â 106 nm K (Eq. 4.4b). Because

the temperature of the surroundings is generally near 290 K, lmax for radiation from them is close to

ð2:90 Â 106 nm Kị

ẳ 10; 000 nm ẳ 10 mm

290 Kị

Therefore, the emission of thermal radiation from the surroundings occurs

predominantly at wavelengths far into the infrared. Because of its wavelength distribution, we will also refer to thermal radiation as infrared radiation and as longwave radiation (over 99% of the radiant energy from the

surroundings occurs at wavelengths longer than 4 mm, and over 98% of the

solar or shortwave irradiation occurs at wavelengths shorter than this).

Most of the thermal radiation from the sky comes from H2O, CO2, and

other molecules in the atmosphere that emit considerable radiation from 5 to

8 mm and above 13 mm. Moreover, the concentration of these gases varies, so

the effective temperature of the sky, Tsky (as judged from its radiation), also

varies. For instance, clouds contain much water in the form of vapor, droplets,

or crystals, which leads to a substantial emission of infrared radiation, so Tsky

can be as high as 280 K on a cloudy day or night. On the other hand, a dry,

cloudless, dust-free atmosphere might have a Tsky as low as 220 K.

We will now consider the thermal (IR) irradiation absorbed by an

unshaded leaf. We will suppose that the infrared irradiation from the surroundings, acting as a planar source at an effective temperature of Tsurr, is

incident on the lower surface of the leaf, and that the upper surface of the

leaf is exposed to the sky, which acts as a planar source with an effective

temperature of Tsky (Fig. 7-1). In Chapter 6 (Section 6.5A) we introduced the

Stefan–Boltzmann law, which indicates that the amount of radiation emitted

by a body depends markedly on its surface temperature (Eq. 6.18a; Maximum radiant energy flux density = sT4). The Stefan–Boltzmann law predicts the maximum rate of energy radiation by a perfect radiator, a so-called

“blackbody” (Figs. 6-11 and 7-3). Here we will use effective temperature in

the sense that the actual radiant energy flux density equals s(Teffective)4. For

instance, Tsky is not the temperature we would measure at some particular

location in the sky, although s(Tsky)4 does equal the actual amount of

radiant energy from the sky, which we can readily measure. By the Stefan–

Boltzmann law, with effective temperatures to give the radiation emitted by

the surroundings and the sky, the IR absorbed by a leaf is

IR irradiation absorbed ¼ aIR sẵT surr ị4 ỵ T sky ị4



7.1. Energy BudgetRadiation


Infrared radiation emitted (W m )















Surface temperature (ºC)

Figure 7-3.

Rate of emission of infrared (longwave) radiation per unit area by a blackbody (eIR = 1.00)

versus its surface temperature, as predicted by the Stefan–Boltzmann law (Eq. 6.18).

where the absorptance aIR is the fraction of the energy of the incident IR

irradiation absorbed by the leaf.

7.1C. Emitted Infrared Radiation

Infrared or thermal radiation is also emitted by a leaf. Such radiation occurs

at wavelengths far into the IR because leaf temperatures, like those of its

surroundings, are near 300 K. This is illustrated in Figure 7-2, in which the

emission of radiant energy from a leaf at 25 C is plotted in terms of both

wavelength and wave number. Using the wave number scale makes it easier

to illustrate the spectral distribution of radiation from the sun and a leaf in

the same figure; moreover, the area under a curve is then proportional to the

total radiant energy flux density. The lmax for sunlight is in the visible region

near 600 nm; for a leaf lmax for thermal radiation is in the IR near 10 mm.

Figure 7-2 also indicates that essentially all of the thermal radiation emitted

by a leaf has wave numbers less than 0.5 Â 106 mÀ1, corresponding to IR

wavelengths greater than 2 mm.

We will express the IR emitted by a leaf at a temperature Tleaf using the

Stefan–Boltzmann law (Eq. 6.18a), which describes the maximum rate of

radiation emitted per unit area. For the general emission case we incorporate a coefficient known as the emissivity, or emittance (e), which takes on its

maximum value of 1 for a perfect, or blackbody, radiator. The actual radiant

energy flux density equals es(Tactual)4 (Eq. 6-18b), which is the same as

s(Teffective)4. We will use emissivities and actual temperatures to describe


7. Temperature and Energy Budgets

the energy radiated by leaves; effective temperatures are usually employed

for thermal radiation from the surroundings and the sky because their

temperatures are difficult to measure or, indeed, hypothetical (empirical

equations incorporating the influence of air temperature, water vapor content, and clouds can be used to predict the IR radiation from the sky).

Because IR radiation is emitted by both sides of a leaf (see Fig. 7-1), the

factor 2 is necessary in Equation 7.7 to describe its energy loss by thermal


IR radiation emitted ẳ J IR ẳ 2eIR sT leaf ị4


As for our other flux density relations, Equation 7.7 is expressed on the basis

of unit area for one side of a leaf. The substantial temperature dependency of

emitted IR is depicted in Figure 7-3.

7.1D. Values for a, aIR, and eIR

The parameters a, aIR, and eIR help determine the energy balance of a leaf.

We will first consider how the absorptance of a leaf depends on wavelength

and then indicate the magnitude of the leaf emittance for infrared radiation.

Figure 7-4 shows that the leaf absorptance at a particular wavelength, al,

varies considerably with the spectral region. For example, al averages about

0.8 in the visible region (0.40–0.74 mm; Table 4-1). Such relatively high

fractional absorption by a leaf is mainly due to the photosynthetic pigments.

The local minimum in al near 0.55 mm (550 nm, in the green region) is where

chlorophyll absorption is relatively low (Fig. 5-3) and thus a larger fraction of

Wavelength (μm)

















Reflected fraction

Transmitted fraction





2 × 106

1 × 106

Wave number (m

Figure 7-4.




Representative fractions of irradiation absorbed (shaded region), reflected, and transmitted by

a leaf as a function of wave number and wavelength. The sum al + rl + tl equals 1.

7.1. Energy Budget—Radiation


the incident light is reflected or transmitted; this leads to the green color (see

Table 4-1) of leaves, as seen both from above (reflected light) and from

below (transmitted light). Figure 7-4 indicates that al is small from about

0.74 mm up to nearly 1.2 mm. This is quite important for minimizing the

energy input into a leaf, because much global irradiation occurs in this

interval of the IR. The fraction of irradiation absorbed becomes essentially

1 for IR irradiation beyond 2 mm. This does not lead to excessive heating of

leaves from absorption of global irradiation, because very little radiant

emission from the sun occurs beyond 2 mm (see Fig. 7-2).

We have used two absorptances in our equations: a (in Eq. 7.5) and aIR

(in Eq. 7.6). In contrast to al, these coefficients represent absorptances for a

particular wavelength region. For example, a refers to the fraction of the

incident solar energy absorbed (the wavelength distributions for direct sunlight and skylight are presented in Fig. 7-2). For most leaves, a is between 0.4

and 0.6. The shortwave absorptance can differ between the upper and the

lower surfaces of a leaf, and a also tends to be lower for lower sun angles in

the sky (such as at sunset), because the shorter wavelengths are then scattered more (Fig. 7-2) and the al’s for the relatively enriched longer wavelengths are lower (Fig. 7-4). For wavelengths in the region 0.40 to 0.70 mm

(designated the “photosynthetic photon flux,” or PPF, in Chapter 4, Section

4.1C), the overall leaf absorptance is usually 0.75 to 0.90. Figure 7-4 shows

that nearly all of the IR irradiation beyond 2 mm is absorbed by a leaf. In fact,

aIR for leaves is usually 0.94 to 0.98, and we will use a value of 0.96 for

purposes of calculation.

Because the emission of radiation is the reverse of its absorption, the

same sort of electronic considerations that apply to the absorption of electromagnetic radiation (see Chapter 4, Section 4.2) also apply to its emission.

A good absorber of radiation is thus a good emitter. In more precise language, the absorptance al equals the emittance el when they refer to the

same wavelength (referred to as Kirchhoff’s radiation law)—for a blackbody, al and el are both equal to 1.00 at all wavelengths. Because the IR

irradiation from the surroundings and the sky occurs in essentially the same

IR region as that emitted by a leaf, eIR is about the same as aIR (e.g., 0.96).1

1. We can relate el and al to radiation quantities introduced in Chapter 4. The amount of radiant

energy emitted by a blackbody per unit wavelength interval is proportional to lÀ5/(ehc/lkT À 1),

as predicted by Planck’s radiation distribution formula (Eq. 4.3b). When we multiply this

maximum radiation by el at each wavelength, we obtain the actual spectral distribution of the

emitted thermal radiation. The absorptance al is related to the absorption coefficient el. Equation 4.19a indicates that log J0/Jb equals elcb, where c is the concentration of the absorbing

species, b is the optical path length, J0 is the incident flux density, and Jb is the flux density of the

emergent beam when only absorption takes place (i.e., in the absence of reflection and scattering). The fraction of irradiation absorbed at a particular wavelength, (J0 À Jb)/J0, is the absorptance, al. Thus al equals 1 À Jb/J0, which is 1 À 10Àelcb, so the absorptance tends to be higher for

wavelengths where the pigments absorb more (higher el), for leaves with higher pigment concentrations (higher c), and for thicker leaves (higher b).


7. Temperature and Energy Budgets

7.1E. Net Radiation

We have now considered each of the terms that involve radiation in the

energy balance of a leaf (Eqs. 7.1 and 7.2). These quantities comprise the net

radiation balance for the leaf:

Net radiation ẳ Absorbed solar irradiation ỵ Absorbed IR from

surroundings À Emitted IR radiation


Using Equations 7.5 through 7.7, we can express the net radiation balance as

Net radiation ẳ a1 ỵ rịS ỵ aIR sẵT surr ị4 ỵ ðT sky Þ4 Š À 2eIR sðT leaf Þ4


Before continuing with our analysis of the energy balance of a leaf, we will

examine representative values for each of the terms in the net radiation.

7.1F. Examples for Radiation Terms

We will consider a horizontal leaf exposed to full sunlight (Fig. 7-1) at sea

level where the global irradiation S is 840 W mÀ2. We will assume that the

absorptance of the leaf for global irradiation a is 0.60 and that the reflectance

of the surroundings r is 0.20. By Equation 7.5, the direct plus the reflected

sunlight, cloudlight, and skylight absorbed by the leaf then is

a1 ỵ rịS ẳ 0:60ị1:00 ỵ 0:20ị840 W m2 ị

ẳ 605 W mÀ2

To calculate the IR irradiation absorbed by the leaf, we will let aIR be 0.96,

the temperature of the surroundings be 20 C, and the sky temperature be

À20 C. Using Equation 7.6 with a Stefan–Boltzmann constant (s) of

5.67 Â 10À8 W mÀ2 KÀ4 (see Appendix I), the absorbed IR is

aIR s½ðT surr ị4 ỵ T sky ị4 ẳ 0:96ị5:67 108 W m2 K4 ịẵ293 Kị4 ỵ 253 Kị4

ẳ 624 W mÀ2

Hence, the total irradiation load on the leaf is 605 W mÀ2 plus 624 W mÀ2, or

1229 W mÀ2.

The rate of energy input per unit leaf area (1229 W mÀ2) here is nearly

the size of the solar constant (1366 W mÀ2). About half is contributed by the

various forms of irradiation from the sun (605 W m À2) and half by IR

irradiation from the surroundings plus the sky (624 W mÀ2). Because the

sky generally has a much lower effective temperature for radiation than does

the surroundings, the upper surface of an exposed horizontal leaf usually

receives less IR than does the lower one: aIRs(Tsky)4 here is 223 W mÀ2, and

the IR absorbed by the lower surface of the leaf, aIRs(Tsurr)4, is 401 W mÀ2,

which is nearly twice as much (see Fig. 7-3). Changes in the angle of an

exposed leaf generally have a major influence on the absorption of direct

solar irradiation but less influence on the total irradiation load, because the

scattered, the reflected, and the IR irradiation received by a leaf come from

Tài liệu bạn tìm kiếm đã sẵn sàng tải về

Chapter 7. Temperature and Energy Budgets

Tải bản đầy đủ ngay(0 tr)