Solar Radiation and Productivity in Tropical EcosystemsSOLAR RADIATION AND PRODUCTIVITY IN TROPICAL ECOSYSTEMS* BY J. L. MONTEITH Department of Physiology and Environmental Studies,

SOLAR RADIATION AND PRODUCTIVITY IN TROPICAL ECOSYSTEMS*

BY J. L. MONTEITH

Department of Physiology and Environmental Studies, School of Agriculture, University of Nottingham

In thermodynamic terms, ecosystems are machines supplied with energy from an external source, usually the sun. When the input of energy to an ecosystem is exactly equal to its total output of energy, the state of equilibrium which exists is a special case of the First Law of Thermodynamics. The Second Law is relevant too. It implies that in every spontaneous process, physical or chemical, the production of 'useful' energy, which could be harnessed in a form such as mechanical work, must be accompanied by a simultaneous 'waste' of heat. No biological system can break or evade this law. The heat produced by a respiring cell is an inescapable component of cellular metabolism, the cost which Nature has to pay for creating biological order out of physical chaos in the environment of plants and animals.

Dividing the useful energy of a thermodynamic process by the total energy involved gives a figure for the efficiency of the process, and this procedure has been widely used to analyse the flow of energy in ecosystems. For example, the efficiency with which a stand of plants produces dry matter by photosynthesis can be defined as the ratio of chemical energy stored in the assimilates to radiant energy absorbed by foliage during the period of assimilation. The choice of absorbed energy as a base for calculating efficiency is convenient but arbitrary. To derive an efficiency depending on the environment of a particular site as well as oil the nature of the vegetation, dry matter production can be related to the receipt of solar energy at the top of the earth's atmosphere. This exercise was attempted by Professor William Thomson, later Lord Kelvin, in 1852. 'The author estimates the mechanical value of the solar heat which, were none of it absorbed by the atmosphere, would fall annually on each square foot of land, at 530 000 000 foot pounds; and infers that probably a good deal more, 1/1000 of the solar heat, which actually falls on growing plants, is converted into mechanical effect.'

Outside the earth's atmosphere, a surface kept at right angles to the sun's rays receives energy at a mean rate of 1360 W m-2 or 1f36 kJ m-2 s-1, a figure known as the solar constant. As the energy stored by plants is about 17 kJ per gram of dry matter, the solar constant is equivalent to the production of dry matter at a rate of about 1 g m-2 every 12 s, 7 kg m-2 per day, or 2 6 t m-2 year-'. The annual yield of agricultural crops ranges from a maximum of 30-60 t ha-' in field experiments to less than I t ha-' in some forms of subsistence farming. When these rates are expressed as a fraction of the integrated solar constant, the efficiencies of agricultural systems lie between 0-2 and 0 004%, a range including Kelvin's estimate of 0-1%.

Conventional estimates of efficiency in terms of the amount of solar radiation incident at the earth's surface provide ecologists and agronomists with a method for comparing plant productivity under different systems of land use and management and in different

* Opening paper read at IBP/UNESCO Meeting on Productivity of Tropical Ecosystems, Makerere University, Uganda, September 1970.

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748 Productivity in tropical ecosystems

climates (Holliday 1966; Penman 1968). Classifying ecosystems on the basis of energy conversion is becoming a popular form of taxonomy but it contributes little to our understanding of how plants respond to their environment. It is necessary to go a stage further, relating efficiences of dry matter production to the physical and biological factors that determine growth rates such as the fraction of radiation intercepted by a leaf canopy, the irradiance of individual leaves, the diffusion resistance of stomata and the behaviour of the photochemical system. This paper attempts to develop this approach, using examples taken from tropical ecosystems although the principles involved are general enough to be applied to any stand of plants growing in any climate.

COMPONENTS OF EFFICIENCY

The efficiency e with which crops or natural communities produce dry matter is defined here as the net amount of solar energy stored by photosynthesis in any period, divided by the solar constant integrated over the same period. This definition allows e to be expressed as the product of seven factors distinguished by appropriate subscripts: 6g determined by the geometry of the earth with respect to the sun; 6a determined by the transparency of the earth's atmosphere; es determined by the spectral composition of solar radiation and by the optical properties of foliage; 6q related to the number of light quanta needed in the photosynthetic process; sl fraction of radiation intercepted by a canopy; Ed determined by the finite rate at which carbon dioxide molecules can diffuse from the atmosphere to the surfaces of photosynthetic units in green cells; 6r the fraction of assimilate not used for respiration.

Then the efficiency for the whole system can be written as

8 = 8 (g, r) = 8gea8s8qeied8r

and the efficiency of any part of the system can be determined by multiplying the appropriate group of consecutive factors, e.g.

e (s, d) = 6s6q6i6d

The geometrical factor 6g

Knowing the solar constant, it is possible to calculate the rate at which radiant energy will be received outside the atmosphere on a plane parallel to the earth's surface. The factor e9 is defined as the ratio of this flux to the solar constant integrated over the same period and it depends only on latitude and on season. Fig. 1, derived from the Smith- sonian Meteorological Tables, shows that 6g is relatively constant through the year in the tropics having a biannual oscillation of +001 at the equator and an annual oscillation of +0-06 at latitude 200. The much larger seasonal change in temperate regions (e.g. 0-07-0-36 at latitude 500) is a major factor determining the pattern of world climate and the global distribution of plant and animal species. The annual average value of 6g

decreases from about 0 3 in the tropics to 0-2 in temperate latitudes.

Atmospheric transmission Solar radiation penetrating the earth's atmosphere is absorbed and scattered by gases,

by cloud, and by aerosols in the form of soil and salt particles, smoke, insects and spores. Knowing the amount of water vapour and ozone in the atmosphere, it is possible to calculate how much radiant energy would be received at the surface in the absence of



J. L. MONTEITH 749

0-3 ~~~~~~~~~~~0 I 0

20 1z, 0-2

-

50

J M M J S N

FIG. 1. Annual variation of geometrical factor eg at three latitudes (N or S).

cloud or of particulates and to express this flux as a fraction of the extraterrestrial radiation on a horizontal surface (i.e. 6g times the solar constant).

For three tropical stations, Samaru in Nigeria (11 N 80E), Kinshasa in the Congo (40S 1 5'E) and Muguga in Kenya (1'S, 370E) the water vapour content of the atmosphere was derived by interpolation from maps published by Bannon & Steele (1960) and the ozone content was assumed to be constant at 3 mm (Robinson 1966). A computer pro- gram developed by Dr M. H. Unsworth was used to calculate the total flux of radiation at the earth's surface on the 15th day of each month and these fluxes are plotted as a fraction of the extraterrestrial radiation in Figs. 2, 3 and 4. The mean transmissivity of a clean cloudless atmosphere is relatively more constant through the year in the tropics than in temperate latitudes because there is little seasonal change in the mean depth of atmosphere traversed by the solar beam. At all three stations the transmissivity is close to

Air

" _, > > Aerosol

0-4 E J M M J S N

I.0? ( Air Air

0-8 ------. . _. ... . .. ..--.*---* - _____,- ' Aerosol -- ~~ Aerosol -X

0-6 - lu Cloud

04S~f 1 1~ Liilll J M M J S N J M M J S N

FIGS. 2-4. Annual variation of atmospheric transmission factor 6a ( ), mean monthly maxima as fraction- of extraterrestrial flux (---), and calculated transmission factor for

cloudless dust-free atmosphere (- .

FIG. 2. Sumaru, Nigeria. FIG. 3 Kinshasa, Congo. FIG. 4. Muguga, Kenya.




0-8. It is slightly smaller at Kinshasa where the precipitable water reaches a maximum of about 4 cm in October and slightly larger at Muguga where the amount of water vapour absorbing radiation is restricted by the altitude of the site-2000 m.

The average transmissivity of the real atmosphere sa was determined by dividing the monthly mean insolation measured at each station by the corresponding extraterrestrial radiation. Figs. 2-4 show that s follows a different pattern at each site determined by the seasonal distribution of cloud and aerosol. The annual average of Sa ranges from about 0-48 at Kinshasa where cloud is prevalent through the year to about 0 58 at Samaru where the winter months are almost cloudless.

The differences between the amounts of radiation transmitted by a cloudless, dust- free atmosphere and by a real atmosphere represent the energy absorbed and scattered back into space by cloud droplets and aerosol. The large fraction of radiation scattered forwards by particulates and by isolated cumulus is included in the total flux measured at the surface. The dashed line in each figure represents a tentative effort to distinguish between the effects of aerosol and cloud. It is the maximum radiation received per day in each month of the year averaged over 5 years. In any given month, the maximum radiation will usually be recorded on a day with little or no cloud but this will not necessarily be a day when the attenuation by aerosol is representative of the whole month. It is reassuring that at Muguga (Fig. 2) and at Kinshasa (Fig. 3), the minimum loss of radiation assigned to aerosol interception occurs during the wettest months of the year when the atmosphere is likely to be cleanest and the maximum loss occurs during the inter- vening dry months (e.g. May to September). The average annual loss of radiation at- tributable to aerosol is very small at Muguga, about 0.05 of the extraterrestrial flux, consistent with the altitude of the station. At Kinshasa, the average is about 0.1 of the extraterrestrial flux, comparable with the loss at smoke-free sites in Britain (Monteith 1966).

At Samaru, the partition between cloud and aerosol shown in Fig. 4 is inconsistent with the local climate. During the winter months of November to February, the station is almost free from cloud but is exposed to dust and sand swept south by the Harmattan wind. The loss of about 0l15 of the extraterrestrial flux during these months should be ascribed mainly to aerosol rather than to cloud.

Wendland & Bryson (1970) drew attention to the prevalence of smoke and soil particles carried up from the surface during dry seasons in the tropics and Figs. 2-4 indicate that aerosol and cloud may be equally important in determining the seasonal and geographical distribution of radiation at the surface.

Spectralfactor es The process of photosynthesis in green leaves needs radiant energy in the waveband

from 0 4 to 0 7 Itm, often referred to as 'photosynthetically active radiation', PAR, or simply 'light'. At the earth's surface, the fraction of radiation received within this waveband depends on the extent to which the solar spectrum is modified by absorption and scattering and can be calculated for a given solar elevation as a function of the water vapour and dust content of the atmosphere. Calculations by Moon (1940) showed that the ratio of PAR to total radiation in the direct solar beam was between 44 and 45% when the sun was more than 300 above the horizon and a figure of 45% has often been used by biologists to calculate the receipt of PAR from the flux of total radiation recorded with a solarimeter. This estimate ignores the contribution of diffuse radiation which is scattered by gas molecules in the atmosphere and which contains a much higher propor-



J. L. MONTEITH 751

tion of PAR than the direct beam. On clear days, the diffuse component is visible as light from the blue sky but even when the sky is overcast, the surface of the earth receives this blue light by transmission through the cloud layer. When the solar elevation exceeds 400, the estimated ratio of PAR to total radiation in the diffuse component is about 60%. Combining the direct and diffuse components in appropriate proportions, the ratio of PAR to total radiation is then close to 0 50 (Monteith 1970).

From a series of measurements at Cambridge, England, Szeicz (1970) found that the annual mean ratio was about 0 49, increasing from a minimum of 0O48 in the spring to a maximum of 0 51 in the winter. There was a tendency for the ratio to be smaller on very clear days (047) than on very cloudy days (0-51) probably because cloud water droplets absorb a small fraction of solar energy in the infra-red spectrum. No long-term measurements of spectral composition have been reported for the tropics but Fig. 5 shows measurements made at Samaru, Nigeria in October, 1966, using the Rothamsted band- pass solarimeter described by Szeicz (1967). An average of 050 is probably appropriate in the tropics as well as in temperate latitudes.

55 0

50 - 0

II I I I 08.00 12.00 16.00

Locol time

FIG. 5. Diurnal variation of radiation in waveband 0 35-07 Apm as fraction of total solar radiation; Samaru, Nigeria, 18 October 1966.

Chlorophyll absorbs very strongly in the blue and red regions of the spectrum so that the light reflected and transmitted by leaves is predominantly green. Integrating over the whole spectrum from 0 4 to 0 7 gum, the fraction of PAR absorbed by leaves is usually between 80 and 90Y/, the precise figure depending on factors such as the amount of chlorophyll per unit area of lamina. An average figure of 0 85 will be adopted here.

The fraction of whole-spectrum radiation absorbed by green leaves is therefore about 0 50 x 0-85 = 0-425 and this quantity will be denoted by the symbol es.

Photochemical efficiency 6q When PAR is absorbed by cells containing chloroplasts, the efficiency of photosyn-

thesis can be defined as the ratio of energy stored in the formation of carbohydrates to the absorbed radiant energy. Most of the absorbed energy is used in biochemical cycles involving many intermediate compounds which act as carriers of energy. In very weak light when the rate of photosynthesis is limited only by the supply of light quanta and not by the supply of carbon dioxide molecules to chloroplasts, about 20% of the absorbed energy is stored in the final products of the photochemical system and the remaining 80%, after being used to form intermediates, is either rejected in the form of heat or is used in the formation of higher compounds such as proteins and fats. More precise, but not




necessarily more accurate figures can be derived by assuming that the formation of one molecule of carbohydrate needs one molecule of CO2 and the energy of 10 light quanta (Hill 1973). Taking account of the spectral composition of sunlight, it can be shown that the average energy content of one quantum of PAR is 3-6 x 10- 19 J. The amount of heat stored in one molecule (CH2 0) is 7-7 x 10-19 J. The maximum efficiency eq of a 10- quantum process in sunlight is therefore

Sq = 10 x (3-6 x l0- 19) = 0-215.

Compounds such as protein and fat which are formed from carbohydrate contribute only a small proportion to the weight of most plant tissue but because they are relatively rich in energy it is necessary to take them into account when the efficiency of photosynthesis is estimated from the amount of dry matter produced by a leaf or a plant. Because the chemical composition of dry matter is seldom reported in productivity studies, Westlake (1963) suggested that a representative figure of 16-7 kJ g- (4 kcal/g) should be adopted. Although this may be an average for herbaceous species, a larger value of about 20 kJ g- 1 is appropriate for woody plants (Lieth 1968). Values in the range 18-20 kJ g'- were reported for grasses by Hadley & Kieckhefer (1963) and by Wiegert & Evans (1964).

Adopting a figure of 16-7 kJ g to conform with calculations by other workers, 1 kJ of solar radiation is equivalent to (0-425 x 0 215)/16&7 = 54 mg of dry matter. It follows that if P is the rate of dry matter production in g m-2 h - 1 and I is solar irradiance for the whole spectrum in kW m-2 (i.e. kJ s- m-2)

P= 54x10-3x3600I= 19-4 L

Recalling the assumptions that were needed to derive the numerical factor in this equation, P = 20 I is an acceptable approximation.

Diffusion efficiency Ed

(i) Single leaves. The maximum photosynthetic efficiency derived in the last section was a theoretical limit achieved in principle only when the irradiance and the gross rate of photosynthesis are very small. In this state, the average concentration of CO2 molecules available to chloroplasts is constant at a value determined by the concentration of CO2 in the air surrounding the leaf and by the respiration rate. When the irradiance is increased from near zero to a larger value, the intercellular concentration of CO2 must decrease because of the finite rate at which the molecules are transported to the chloroplasts by diffusion from the external air and from respiring mitochondria. This decrease in the availability of intercellular CO2 is responsible for the characteristic shape of the photosynthesis-light curve shown schematically in Fig. 6. As the irradiance tends to zero, the gross rate of photosynthesis per unit incident radiation tends to a constant value shown in the figure as a limiting slope l/b and already derived in terms of carbohydrate as 20 g h-' kW- '. As the irradiance increases, the photosynthesis rate falls further and further below the maximum rate of 1 /b and approaches a limiting value shown as 1/a when the intercellular concentration of CO2 approaches zero. In this state, usually referred to as 'light saturation', the rate of photosynthesis is proportional to the concentration of CO2 in the external atmosphere. Values of 1/a determined for crop plants, exposed to air at 300 vpm of C02, range from about 2 g CH2O m-2 h- 1 for cotton, tobacco and sugar beet to about 8 g m-2 h- 1 for species such as maize and sugar cane which form a distinct group



J. L. MONTEITH 753

of photosynthetically efficient plants (D'Costa & Milburn 1973). By introducing the appropriate numerical factor, it can be shown that the total resistance to the diffusion of carbon dioxide from the external air to the chloroplasts is 14a s cm-' where 1/a is in g CH20 m-2 h-' so the values quoted for a are equivalent to resistances ranging from about 7 s cm-' for the least efficient group of species to about 2 s cm-' for the most efficient. As the minimum stomatal resistances reported for a wide range of species are about 1-2 s cm-', these figures suggest that stomatal control of photosynthesis is likely to be more important in plants such as maize and sugar cane than in less efficient species.

Light

0.

C) I Dark E

_ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ resp. Light C ~~~~~~~resp.

FIG. 6. Carbon dioxide exchange of isolated leaf as function of irradiance: EA represents measurement of net uptake with initial slope b- 1 and asymptote a 1; OE is dark respira-

tion; ED is hypothetical light respiration.

Two limits have now been established for rates of photosynthesis by single leaves: P 1/b in very weak light and P = 1/a in very strong light. Analysis of laboratory measurements by Gaastra (1963) and others confirms that these rates can be combined in a simple interpolation formula which allows the rate of photosynthesis to be expressed as a function of irradiance (up to 400 W m-2 PAR) and of carbon dioxide concentration (up to 300 vpm). The formula is

P = (a+b/I)-l (1)

satisfying the conditions that P-+I/b as I-+O and that PF- 1/a as I-+ oc (Monteith 1965a). When P and 1/a are expressed in g CH20 m-2 h-' and Iis in kW m-2, b = 0 05.

(ii) Plant communities. Eqn 1 has been used in a number of equivalent forms to estimate the total photosynthesis of all the leaves assembled in the canopy of a uniform stand of vegetation. Some recent models of canopy photosynthesis include so many parameters that they cannot be used without the help of a computer but they are rigorous enough to predict changes of photosynthesis rate that might occur in response to small changes in the area or disposition of the foliage. In the present context, a relatively simple model (Monteith 1965b) can be used to derive the diffusion efficiency of a stand by expressing the predicted rate of photosynthesis when the diffusion resistance of leaves is finite as a fraction of the rate when the resistance is zero.

The first step in this model is to calculate the area of leaves exposed to direct sunlight. Assuming that a layer of leaves containing unit leaf area index intercepts a fraction (1 -s) of the radiation incident on the layer, it can be shown that in a stand with a total leaf area index L the area index of leaves exposed to direct sunlight is

AO = (I -sL)I(1 -s).




The average irradiance of these leaves is (1 -s)I where I is the irradiance of a horizontal leaf. Assuming that all these leaves have the same photosynthesis light curve and that the carbon dioxide concentration is uniform through the canopy, the total photosynthesis by sunlit leaves is then

PO = AO(a+b/(l-s)I)-'. (2)

A fraction X of the radiation intercepted by a leaf is assumed to be transmitted and is available for photosynthesis by lower leaves; but radiation transmitted by two or more leaves is neglected. Making an arbitrary assumption about the distribution of transmitted radiation, it can be shown that the leaf area index of leaves exposed to light transmitted through one higher leaf is

Al = {1-sL-(1-s)LsL-1}I(1-s)

and the photosynthesis of these leaves is

P1 = A 1 (a + b/IT(-s)I.) (3) The second step in the model is the integration of eqns 2 and 3 over the hours of day-

light h assuming that the irradiance changes sinusoidally and reaches a maximum value of I* at noon, i.e.

I= I* sin (-) h

where t is time after sunrise in the same units as h. The integral is a transcendental function containing the six parameters I and h specifying the radiation climate, X and s specifying the relevant optical and geometrical properties of the canopy, and a and b describing the slope of the photosynthesis light curve.

The diffusion efficiency for a canopy Ed can now be defined as the photosynthesis calculated from eqns 2 and 3 when a is assigned an appropriate finite value divided by the photosynthesis when a is zero, i.e.

= _S[Ao{(l-s)a+b/I} '+A1{(l-s)a+b/'I}-'] dt (4) 8d -(1 +Ta) fh (Ilb) dt

In the limit when the leaf area index is very large so that the canopy intercepts all the light falling on it, sL and 5L-1 tend to zero so that A0 and A1 tend to (1 -s'1. The denominator of eqn 4 can be written (1 + T) Tib where T is the amount of visible solar radiation received in 1 day. If T is expressed in MJ m- 2, T = 0-07 and 1/b = 20 g h- 1 kW- 1 the denominator is (20 Tx 1-07 x 103)/3600 or 6 T g m-2, representing the gross daily production of carbohydrate when a = 0.

Fig. 7 shows Ed plotted as a function of T for three sets of values of a and s selected from the literature because they are relevant to later calculations. Line I (a = 0O 125; s = 0 55) is appropriate for maize and sugar cane; line II (a = 0-25; s = 0 65) for rice, wheat and barley; and line III (a = 0-125; s = 0 55) for dicotyledons such as tobacco, cotton and groundnuts. The relation between Ed and daily radiation is much more sensitive to the value chosen for a than to the value of s.

The maximum gross photosynthesis for a crop with known coefficients a and b can now be estimated either directly from measured values of solar radiation or from an appropriate fraction of the solar constant. In the first case, the daily total of visible solar radiation T MJ m-2 is obtained from a solarimeter record and the diffusion efficiency is



J. L. MONTEITH 755

Cci Cm-2 day-' 200 400 600

0.8 I I I

0-2_

I 0 20 30 MJ m-2 day-'

FIG. 7. Diffusion efficiency Ed of crop canopies intercepting radiation completely. For crop types I, II, III see text.

estimated from eqn 4 or from the appropriate curve in Fig. 7. The required rate of photosynthesis is then 6 Ed T g CH20 m-2 day- 1.

Interception efficiency Si The interception efficiency Si of a stand can be defined as the ratio of the actual rate of

gross photosynthesis to the maximum rate estimated for a stand of identical plants with enough leaves to intercept all the incident light. Field measurements of photosynthesis using chambers containing whole plants show that the photosynthesis of maize and cotton is proportional to the intercepted radiation (Hesketh & Baker 1967). It has also been found that the rate at which soybeans and maize produce dry matter in the vegetative phase of growth is proportional to the fraction of intercepted light (Shibles & Weber 1966; Williams, Loomis & Lepley 1965). These measurements suggest that Si can be identified with the fraction of incident light intercepted by a stand, a quantity readily obtained by direct measurement or by inference from the leaf area index.

The photosynthesis rate of a crop canopy cannot be strictly proportional to the fraction of intercepted radiation unless all the leaves are working at the same photochemical efficiency. This implies either (i) all the leaves are working on the linear portion of the photosynthesis/light curve; or (ii) all the leaves are exposed to the same radiant flux and respond to light in the same way. Condition (i) is satisfied in weak light, i.e. on dull days and at sunrise and sunset on bright days. Condition (ii) is satisfied when photosynthesis by shaded leaves can be neglected in comparison with photosynthesis by sunlit leaves (or portion of leaves) with the same light response curve. Proportionality observed between photosynthesis and intercepted radiation can be ascribed to the operation of condition (i) (but not (ii)) in cloudy weather and condition (ii) (but not (i)) in cloudless weather. Proportionality will be preserved over any period during which the relative proportions of sunny and cloudy weather are relatively constant from day to day and week to week.

A linear relation between photosynthesis and intercepted radiation is consistent with the model described in the last section. The fraction of radiation transmitted by unit leaf layer is s+ (1 -s)r so the fraction intercepted by a leaf area index of L is

1-{s+(1s-)T}L = 1 _L _[LsLl(1 S)T].

When the radiation flux is very weak (condition i) b/I is much larger than (1 -s)a and it can be shown from eqns 2 and 3 that




e = I-s'_[Ls'-1(1-S)T1(1 + T)]

a quantity almost identical to the fraction of intercepted radiation when X = 007 because the terms in square brackets will usually be much smaller than 1 - sL. Condition (ii) is consistent with the model for leaves transmitting a negligible fraction of PAR. Then putting X = 0, it can be shown that the fraction of transmitted radiation and 8, are both equal to (1 - L). When X = 0 07, rates of photosynthesis predicted by the model increase almost linearly with the fraction of intercepted radiation except when s is very large (e.g. 0 80) and a is small (e.g. 0X120). Thus to a good approximation valid for most crops and climates, the ratio of actual photosynthesis by a stand to the maximum rate achieved at full light interception can be calculated as

Si = 1-[s+(I-s)rT]L.

Fig. 8 shows Si plotted as a function of s and L when X = 0 07. 1.0-

0.8

0-6-

0-4-

022_ ~ ~ ~ ~ ~~~I I I 2 4 6 8

LAI

FIG. 8. Interception efficiency ej as function of leaf area index LAI and the geometrical factor s (beside curve).

Respiration factor s, In previous sections it was tacitly assumed that the gross uptake of carbon dioxide by

a leaf can be measured as a function of the irradiance and of the external carbon dioxide concentration. In practice, the exchange of carbon dioxide usually measured in the laboratory is a net exchange, the difference between gross photosynthesis and respiration rates. If respiration proceeded at the same rate in the light and in the dark, the true rate of gross photosynthesis could be readily determined by adding the dark respiration rate to the net photosynthesis rate in the light. This classical method of estimating gross rates of uptake is open to criticism because an important component of the respiratory system in leaf cells is coupled to the photosynthesis system. This component produces carbon dioxide at a rate that increases with the photosynthesis rate and therefore with the irradiance. True rates of gross photosynthesis are very difficult to estimate because unknown amounts of carbon dioxide and oxygen may cycle between the sites of assimilation and respiration within cells.

Fortunately, it is not essential to distinguish between light and dark respiration in productivity studies provided the net rate of photosynthesis is estimated by a consistent convention shown in Fig. 6. At an arbitrary irradiance, the net or apparent rate of carbon dioxide uptake is AB. Respiration at the same irradiance is BD decreasing to OE in the dark (whether BD should be regarded as light plus dark or simply as light respiration is still being argued by physiologists: the point is irrelevant here, however important it may



J. L. MONTEITH 757

be biochemically). The true gross photosynthesis is AD, but the classical method of estimating gross photosynthesis yields the smaller value AB + BD = AC. The net rate of photosynthesis from which the net rate of dry matter production can be calculated is determined either by subtracting the true rate of respiration in the light BD from the true rate of gross photosynthesis AD or by subtracting the dark respiration rate OE from the gross photosynthesis in the light estimated as AC. The gross photosynthesis referred to in previous sections corresponds to AC. Note that the asymptote 1/a is measured from the axis EC and not from OB.

The respiration factor sr can now be defined as the ratio (P - R) :P = 1- RIP where R is the weight of carbohydrate used for respiration per day calculated by multiplying the mean dark respiration rate (g m-2 h-') by 24; and P is the weight of carbohydrate produced by photosynthesis over the same period calculated by adding the dark respiration rate to the net uptake of photosynthesis hour by hour throughout the day. In any plant community, the ratio of respiration to photosynthesis over the same period depends on many internal and external factors, notably the growth rate of the stand, the fraction of total dry weight represented by leaves and other photosynthetic organs, and the temperature of respiring tissue. Accurate and relevant estimates of 8, are rare because plant physiologists have seldom tried to measure the respiration rate of whole plants and because crop ecologists underestimated the importance of respiration in determining net rates of dry matter production. The traditional figure for 8, is about 0 20-025 but Gaastra (1963) quoted a range from 0 25 to 0 50 consistent with growth-room measurements on barley (Watson & Hayashi 1965) and Hamil grass (Ludlow & Wilson 1968), and with field measurements on lucerne (Thomas & Hill 1949), barley (Monteith 1968), maize and wheat (Lemon 1970). An even higher value of 0 75 was reported for tropical rain forest (Kira et al. 1967) and a similar figure was derived by Muller & Nielsen (1965) for a forest in the humid region of the Ivory Coast.

The proportion of assimilate used for respiration is expected to be larger in tropical than in temperate climates because the temperature coefficient for respiration of green tissue exceeds the coefficient for photosynthesis over the range of temperatures in which plants usually grow. From laboratory measurements on isolated sections of tissue, the Q1o of respiration is close to 2 but Chang (1968) analysed Thomas and Hill's measurements on lucerne to give

Sr = 0 92-0 012 T,

where Tis in 0C, giving a Q10 of about 1-4 at 20? C. McRee (1970) recently showed that the respiration of a stand of white clover in the

vegetative stage of development was a linear function both of the photosynthesis rate P and of the standing dry weight W. At a temperature of 200 C the relation was

R = 0-25 P+0-015 W(g CH2O m-2 day- 1).

Assuming a Q10 of 2 and dividing through by P the relation becomes

Br = 1- {00625+O000375 WIP}2T/1,

and at 250 C, an appropriate daily mean temperature in the tropics, Br is 0 65 -0021 WIP. During the vegetative stage of growth, photosynthesis by a stand of dicotyledenous plants may reach P = 50 g m 2 day- 1 when W = 500 g-2 so that Br = 0 44.

Taking account of the wide range of values quoted in the literature and the relatively




rA

o a o 0~~~~~~~~~ 0~~~~~~~~~

O .o 0

o0

a E a 8 E

~O o o~ o r

W5 0>-ry_

_, _4 U, 2 a)~~~~~~~~~~~~~~~y 0 -

0~~~~~~~~~~~~~~0 C' U, 0

Cd 40 0 d n d

LO00

a.) 10 ~~~~Q"Oa) a)0 Cd'0

# ~ ~ a

NN

U~~~~~~~~~~~~~~~~~~~~U 0 ~~~~~~~~~~~O

* CI a' a'Cj



J. L. MONTEITH 759

high mean temperatures recorded in the tropics, it was decided to adopt an arbitrary mean value of s = 05 and to adjust this value if experience showed that it was incorrect for a particular species or for a particular period of development.

TESTS OF THE ANALYSIS

The efficiency with which a stand of vegetation is expected to store solar energy by photosynthesis can now be derived as a product of the seven factors examined in previous sections. The percentage accuracy of e (g, r) or of the equivalent rate of dry matter production is the sum of the percentage accuracy in the individual factors sg, Ea. . . , etc.

The first factor sg can be calculated to any required degree of accuracy and may therefore be regarded as errorless. When solar radiation records are available, Sa can be calculated from values of insolation and from 6g with an accuracy limited only by the performance of the recording system. For a properly calibrated and well-maintained station, the uncertainty in sa will be about +2%. At sites where it is necessary to estimate sa from records of cloudiness or sunshine hours, the uncertainty in monthly averages of 6a will be of the order of + 10%.

The spectral factor ga iS unlikely to change much, either with climate or with species, and will rarely depart from the norm of 0 425 by more than + 5%. The photochemical efficiency sq = 0-215 was based on a constant spectral composition for sunlight and on an arbitrary choice of 10 quanta per molecule. Uncertainty in this figure can be set at + 20% but if eh is over- or under-estimated, there will usually be a complementary error in estimating Ed. In very bright light, the two errors will be equal and opposite (because photosynthesis rates depend only on a and not on b) and in very dim light the complementary error in Ed will be zero (because photosynthesis rates depend only on b and hence on the figure assumed for quantum need). A figure of + 5% will be assumed for the average error in she

The factor Si is calculated as a function of leaf area index L which can usually be determined to about + 10% with careful sampling. The corresponding error in si will be + 10% when L is small, so that Si is proportional to L, decreasing to zero when L is large and si tends to unity. For the whole life of a crop, the average error in si may be about ?5%.

Uncertainty in s (g, i) is therefore + 10 + 5 + 5 + 5 or + 17%, and is a combination of random and systematic errors in the individual components of efficiency. The errors in Ed and gr are more difficult to establish a priori, but the error in e (g, r) can be determined empirically by comparing measured rates of dry matter production in the field, Cm with estimated rates Ce. These estimates are derived from a figure for e (g, i) expected to have an error of + 17%, from an arbitrary figure of sr = 0 50, and from a value of Ed that depends on the accuracy and relevance of laboratory determinations of a and b. Compari- son of Cm and Ce were attempted for the few tropical crops for which determinations of C and of L were available. To include more data, the comparison was extended to recently published measurements on tropical crops grown in Japan for an IBP project (Table 1).

When preliminary calculations showed that estimates of crop growth rate were much more sensitive to differences in a than in s, it was decided (i) to work with three values of a spanning the range derived from photosynthesis curves published in the literature; (ii) to assign one of these values to each crop; and (iii) to associate one appropriate value of s with each value of a as follows.




a s Crops (m2 h g-')

Group I 0-125 0 55 Maize, bulrush millet Group II 0-25 0-65 Sorghum, rice Group III 0 50 0 55 Soybean, groundnuts

Group I contains the tropical grasses which are known to have relatively fast rates of photosynthesis in bright light. Sorghum would be expected to belong to this group but was assigned to Group II when it was found that a crop in Nigeria produced dry matter at a rate 20-25% less than the rates predicted for a Group I crop. Group II contains rice as well as sorghum and would probably be an appropriate group for cereals such as wheat and barley which, in bright light, assimilate carbon dioxide faster than dicotyledons. Group III contains two dicotyledons and is an appropriate group for cotton, cassava, beans and many other tropical plants.

Parameters assumed to be the same for all six species were b (0 05), X (0.07) and 8, (0 50). Mean values of insolation were calculated from daily solar radiation except at Katherine where, in the absence of records, a constant value of 23 MJ day was assumed through the season. The leaf area index was assumed to increase exponentially with time so the mean value of leaf area index L between two harvests was calculated from the standard formula

L = (L2-Lj)/ln(L21L1).

Results of this exercise are presented in Figs. 9-13 where each point represents the relation between Ce and Cm for a period of between 2 and 4 weeks during the vegetative stage of growth. The distribution of points in each figure is determined mainly by differences in leaf area rather than in solar radiation (cf. changes of E with radiation in Fig. 7 and of Si with L in Fig. 8).

For maize and millet (Fig. 9), Ce and Cm agree very well up to 300 g m2 week , a rate rarely exceeded in the field. The estimated rates of sorghum (Fig. 10) tend to be a few per cent larger than measured rates but differences in total dry matter production between the tall indigenous variety Fara-fara and the dwarf hybrid NK 300 can be accoun- ted for purely by differences in leaf area index. Results for four varieties of rice grown at three sites show more scatter than other crops (Fig. 11) and there is a tendency for Ce to underestimate the rate of dry matter production by mature stands. There is less scatter for four varieties of soybean (Fig. 12) grown at two fertiliser levels and at four different sites. Exceptionally good estimates of crop growth were derived for two varieties of groundnuts (Fig. 13) each in two treatments: sprayed with Dithane as a protection against Cercospora leaf spot; and unsprayed. For this crop, differences of leaf area index between varieties and treatments account almost completely for differences in dry matter production during vegetative growth.

The success of these comparisons implies that the error in estimating dry matter production from constant values of sr and a during vegetative growth and from values of s calculated from leaf area index is comparable with the error in conventional measurement of production, about + 10-15% over a period of 1 or 2 weeks. During the reproductive stage of growth, Ce was always greater than Cm, probably because the development of a non-photosynthetic storage organ made Sr larger than 0 5 and because senescence of leaves was responsible for a systematic decrease of 1/a after new leaves stopped ap- pearing.

As an aid to determining Ce for other crops, Fig. 14 shows maximum weekly dry



J. L. MONTEITH 761

300 .

200 -

200~ ~~~ '0

200 0

0 0~~~~~0

I00 200 300 100 200

200 - 0 O/ 100 /A

100 200 100 1OO Cm

FIGS. 9-13. Comparison of dry matter production rates from measurements Cm and estimates Ce. For crop details, see Table 1.

FIG. 9. *, Maize; 0, bulrush millet. FIG. 10. Sorghum: 0 Fara-fara; *, NK 300. FIG. 11. Rice. FIG. 12. Soybeans. FIG. 13. Groundnuts: circles, S 38; triangles, F 439; solid symbols, sprayed; open symbols,

unsprayed.

cal cm-2 day'? 200 400 600

II I /

300 -/ It

0)~ ~ ~ ~~C

0)/

FIG.~// 9E 0 Maze 0-25rshmllt

* 0 0 20 30

MJ m-2 day-' FIG. 14. Estimated dry matter production for crop canopies intercepting radiation com-

pletely.




matter production for each group when e1 = 1. The value of Ce is found by reading off a maximum rate from this figure and multiplying by ei determined from eqn 4 or Fig. 8.

GENERALIZATION AND EXTENSIONS

Primary production Having established and tested a method of predicting crop growth rates which is

consistent with field measurements in the tropics and sub-tropics, differences in the efficiency with which different stands use energy can now be assigned to specific physical or biological factors. Table 2 illustrates this type of comparison for the annual production of dry matter by a Class III crop growing in the tropics and in a temperate climate.

Table 2. Annual production of dry matter Tropical agriculture Temperate

Intensive Subsistence agriculture 8e 0 30 0 30 0-20 8a 0 50 0 50 0 35 8L 0.20 0 05 0-33 es 0-425 0-425 0-425 eq 0-215 0-215 0-215 Ed 0 30 0.15 0 35 8r 0 50 0 50 0 60

e (i, r) 0-27% 0034%4 0-50% e (g, r) 0-041% 0O005% 0 038%4

Ce 11 0 9 10 (kg Mr-2 year 1)

Table 3. Maximum rates of dry matter production Tropical Temperate

(wet season) (summer) Class I Class III Class III

8e 030 035 8a 0 60 0-40 El 0095 095 es 0-425 0-425 eq 0-215 0 215 Ed 0-62 0-32 0-36 8r 0050 0 50 0 60

e (i, r) 2. Rio 1-4% 1-9%o e (g, r) 049%4 0-25% 0-27%

Ce 34 18 19 (g m- 2 day 1)

Differences of latitude and cloudiness are taken into account by Eg and sa respectively. The interception factor is largest for the temperate climate because relatively little radiation is received during the winter months when the leaf area is zero. In the tropics, however, large amounts of radiation are received throughout the year but can be used only when the temperature and rainfall regime allow a canopy to develop. Growth of the subsistence crop is assumed to be limited by a serious shortage of nutrients and water. The main effect of these shortages is to restrict leaf development so ei is set at 005, and assuming that photosynthesis is also checked, Ed is set at 020. A respiration factor of 060 is assumed for a temperate climate to allow for lower mean temperatures. The lower



J. L. MONTEITH 763

part of the table shows: (i) the efficiency of the whole system E (g, r); (ii) the corresponding rate of dry matter production; and (iii) the quantity E(i, r), the efficiency with which solar radiation incident on a crop canopy is converted to dry matter. The figures in the table and others that can be calculated for different periods of growth and systems of management are consistent with the estimates of efficiency which Penman (1968) derived from FAO world records of crop production.

Maximum efficiencies of photosynthesis in a given climate can be calculated on the assumption that ei = 0 95 when the leaf area index is very large and Table 3 compares rates for tropical and temperate climates assuming average rates of insolation. Note that the efficiency E (g, r) for a Class I crop is about twice the value for a Class III crop and that the yield predicted for a Class III crop is about the same in tropical and temperate climates because greater insolation in the tropics is balanced by smaller values of Ed and Sr*

In this analysis, the interception factor ei emerges as a major discriminant of dry matter production accounting, on the one hand, for differences of productivity under different conditions of climate and management and, on the other, for differences between the mean and maximum rates of production within a particular stand.

Secondary production Analysis of crop growth in terms of energy conversion can readily be extended to

include the economic yield of a crop, secondary productivity, and the energy available as human food. The fraction of useful energy removed from a crop can be written Eu and will assume different values depending on whether the material is harvested by man- in which case EU will be almost the same as the crop factor discussed by Holliday (1973)- or grazed by animals. For example, in Queen Elizabeth Park, Uganda, grazing by large herbivores removes about one-third of the vegetation produced annually (C. D. Pigott, personal communication). Assuming that half the energy of this material can be meta- bolized E,,-0 15. At a level of 500 g m2 year-', the annual production of dry matter is equivalent to 0-27 W m-2 or to E (g, r) = 2 x 10-4. (Referring to Table 2, this efficiency can be derived by putting ei = 0-2 in the column for subsistence agriculture.) The power available to herbivores is therefore 0 15 x 0-27 W m-2 and for the Mweya Peninsula with an area of 5 km-2 the power is 200 kW. According to Eltringham (1973) the total metabolism of all the herbivores in this area is 252 x 106 cal h-' which is equivalent to 290 kW in good agreement with the power equivalent of consumed dry matter.

As the metabolism of large animals is nearly proportional to their surface area, it is possible to calculate the total skin surface that a given weight of vegetation can support. The rate of fasting metabolism is about 40-50 W m-2 and allowing for the extra energy used in movement and in digestion, a round figure of 60 W m-2 will be adopted here. Dividing the energy available from dry matter in W m-2 by 60 W m-2 gives a skin area index, the area of herbivore supported by unit area of ground. At Queen Elizabeth Park where the energy supply is 4 x 10-2 W m-2, the skin area index is 4 x 10-2/60 or 7 x 10-4, i.e. 1500 m2 of ground area are needed to produce enough energy for 1 m2 of animal. The same ratio can be derived by dividing 1360 W m-2 by 60 to get a skin area index corresponding to the solar constant; this is 22-7. Multiplying 22-7 by the efficiency E, E (g, r) = 3 x 10-5 gives the figure of 7 x 10-4 appropriate to Queen Elizabeth Park. To estimate the energy available from a crop as human food, it may be assumed that

the economic yield is a fixed fraction of total dry matter production and that a further fraction Ef is retained after losses in harvesting, storage and preparation for the table.

G




Assuming EU = 0 5 and ES = 0 5, the efficiency with which food energy is produced in subsistence agriculture is 0-25 x 0 5 x 10-4 or 1P3 x 10-5 using the factors in Table 2.

On a basis of 60 W m-2, a man with a skin area of 1P7 m2 will metabolize energy at a mean rate of 100 W (2100 cal day-1) consistent with figures of energy intake in the tropics (but 50% smaller than the average intake in developed countries). The solar constant of 1360 W m-2 is equivalent to the energy produced by 13-6 men m-2 or 13 600 men ha-1. In regions supported by subsistence agriculture where a relatively small fraction of food energy is derived from meat and animal products, the number of people per unit area of cultivated land can be predicted by multiplying the personal equivalent of the solar constant by the efficiency ES s,4 E (g, r). For example, given a level of subsistence agriculture with Es = 0 05 the equivalent population is 1P36 x 105 x 1P3 x 10- 5 or 1P8 men ha-1, and since half a hectare is about the limit that one man can farm with traditional tools (Boshoff 1973), subsistence farming at this level must be close to the lower limit at which communities can survive. Generalizing, Fig. 15 shows the predicted relationship

4 I005 0; 10 Tropical S. America

S.E. Asia -r / -Middle America

3_ Middle S. Asia 3 - W. Africa

N. Africa S. Europe

S 2 - E. Africa

W / - S.W Asia o I Middle Africa

5 10 E (Or) X 1 04

FIG. 15. Estimate of population densities in relation to interception efficiency 8g and efficiency of crop production e (g, r).

between population per unit area of cultivated land, the combined efficiency E (g, r) and the interception efficiency ei using the parameters in Table 2 with 8U8f = 0-25. The same figure shows the actual population densities in underdeveloped countries abstracted from United Nations statistics by Revelle (1966). These densities are consistent with a range of values of E (g, r) from 3 to 12 x 10-4 or of ei from 0-03 to 0412.

CONCLUSIONS

(1) The efficiency with which plants store solar energy can be expressed as the product of seven factors which describe the dependence of dry matter production on latitude and season (Eg), on cloudiness and the aerosol content of the atmosphere (Sa), on the spectral composition of radiation (Es) and the quantum need of the photochemical process (sq), on leaf area index and leaf arrangement (8k), on the concentration of CO2 in the canopy and the diffusion resistance of individual leaves (Ed), and on the fraction of assimilates used in respiration (er). The analysis can be extended to estimate animal and human populations from the relation between primary production and rates of metabolism.

(2) Estimates of dry matter production for a range of agricultural crops growing be-



J. L. MONTEITH 765

tween 140 S and 430 N agree well with measurements during the vegetative stage of growth but overestimate production during reproductive growth, either because photosynthesis rates are overestimated or respiration rates are underestimated or both. The agreement for vegetative growth is not necessarily peculiar to one particular model of canopy photosynthesis but is probably common to several models.

(3) The main limitations of the models currently used to predict crop growth from photosynthesis rates are: (i) ignorance about whether the decrease of Ed as a leaf ages is a result mainly of an increase in the resistance to CO2 diffusion within mesophyll tissue or of a decrease in the concentration of carboxylating enzymes; (ii) ignorance about the way in which rates of respiration are related to the contemporary rate of photosynthesis and to the accumulated dry weight of the stand; and (iii) ignorance about ways in which the partitioning of assimilates may be determined by an interaction of environmental factors and endogenous controls. The need to use measurements instead of predictions of leaf area index is a weakness of most models. The ELCROS model developed by de Wit & Brouwer (1970) includes an estimate of the rate at which leaves expand after germination but much more research is needed both in the field and in the growth room to determine how leaf expansion rates depend on environmental factors such as temperature and the availability of water and nutrients in the root zone.

ACKNOWLEDGMENTS

I am very grateful to my colleagues Mr K. Gregson and Dr M. H. Unsworth who wrote computer programs to calculate photosynthesis rates and insolation respectively; to Dr J. Kowal, Institute of Agricultural Research, Samaru and Dr F. J. Wangati, E.A.A.F.R.O., Nairobi, for records of solar radiation; and to Dr J. Elston of Reading University for many stimulating discussions on the subject of this paper.

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* Papers contributed to IBP/UNESCO Meeting on Productivity of Tropical Ecosystems, Makerere University, Uganda, September 1970. Proceedings in preparation.

(Received 5 June 1972)



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Solar Radiation and Productivity in Tropical EcosystemsSOLAR RADIATION AND PRODUCTIVITY IN TROPICAL ECOSYSTEMS* BY J. L. MONTEITH Department of Physiology and Environmental Studies,