Simple Assimilation Models

14.7 Simple Assimilation Models

Two general approaches have been used to derive models relating assimilation to environment. One is more empirical and the other more mechanistic. Both are useful for understanding and predicting

interaction. The simpler model applies mainly to plant communities. (1977) observed that when biomass accumulation by a plant community is plotted as a function of the accumulated solar radiation intercepted by the community, the result was a straight line. Figure 14.4 shows

Plants and Plant Communities

Intercepted Solar Radiation

a crop as a function ot total "cumulative" intercepted radiation

F IG UR E 14.4. Total dry matter produced by

Monteith, 1977).

Monteith's results. The model suggested by Fig. 14.4 is

where

is the fraction of incident solar radiation intercepted by the canopy, and e is the conversion efficiency for the canopy. This conversion efficiency can be expressed in several ways; the radiation can be intercepted or absorbed as well as photosynthetically active or solar radiation, and the canopy assimilation can be expressed as

is the total solar radiation incident on the canopy,

or dry matter. All these possible combinations have been used and the numerical values for each is different from the others. Monteith expressed assimilation as g

and as the total solar radiation in

and reported e values around 1.5 for C3 crop species. More recently the photosynthetically active radiation has been used to estimate canopy assimilation rather than solar radiation because only the visible wavelengths are effective in photosynthesis. Furthermore, both

uptake and light can be expressed meaningfully in molar units so that the light use efficiency is dimensionless, as an efficiency should be. Sometimes the absorbed radiation is used in Eq. (14.13). Since the ab- sorptivity of leaves is so high in the PAR band, there is little difference between absorbed and total PAR, but this is not the case for total solar radiation, since so much of the

is reflected. This is another reason to use PAR rather than solar. When the conversion efficiency is expressed as dry matter divided by intercepted radiation, some factors that have little to do with photosynthesis and light get included; for example, dark

Simple Assimilation Models 237

respiration and the composition of dry matter (fraction of carbohydrates, proteins, or lipids). The most stable conversion efficiencies are likely to

be mol (mol Typical daily conversion efficiencies in these units are 0.01 to 0.03 mol

This is sometimes referred to as canopy light use efficiency. The conversion efficiency ap- proach is used to estimate daily, monthly, or seasonal assimilation. One of the factors that is known to affect conversion efficiency (e) on a daily basis is the fraction of incident radiation that is

(mol

versus solar beam; with

radiation being more efficient. Monteith and others have pointed out that using accumulated dry ter and intercepted radiation amounts to relating two variables that are accumulated sums. Summing any two sets of numbers, even bers, induces a high correlation, similar to that shown in Fig. 14.4. The fact that we get nice straight lines is therefore not necessarily an indica- tion of a causal relationship between the two quantities. It is known from other information, though, that light and photosynthesis are causally re-

lated, so this induced correlation may add, rather than detract from the model since it makes the model very robust. The real question is whether the model is useful for prediction of dry matter production. This depends on how conservative e is. A number of experiments have shown that e is very conservative in situations where water, nutrients, and temperature do

not limit plant growth. Equation (14.13) is therefore useful for predicting maximum productivity. When stresses limit growth, it is often possible to quantify their effect either in terms of a reduction in conversion ef- ficiency, e, or a decrease in interception,

This allows experiments carried out under different conditions of light availability to be compared or normalized.

The Monteith model focuses on light as the limiting substrate for photosynthesis. Another simple model can be derived by considering gas exchange. The net carbon assimilation for a leaf can be computed from:

where is the conductance of the boundary layer and surface (stom- ata) for

concentration (around 350

is the atmospheric

concentration in the intercellular spaces of the leaf. The subscript n on the assimilation rate means the net assimilation rate. Wong, et al. (1979) found that

and

is the

is maintained at a fairly constant value in light. Genotypes vary in the values they maintain, but the main variation is between C3 and C4 species. In C3 species values around 280

are common, while in C4 the values are around 130

Photorespiration therefore maintains a much larger intercellular concentration in C3 leaves. Water vapor diffuses through the same

pores as so any assimilation is accompanied by transpiration. The rate of transpiration can be computed

Eq.

(with the

canceled). Taking the

Plants and Plant Communities

ratio of assimilation to transpiration gives:

Referring to Table 7.4 it can be seen that the ratio of ranges from

0.66 to 0.75 for and convection processes. Since part of the transport is by

and part by convection we use a midrange value of 0.7 for the ratio. From Fig. 14.1 it can be seen that leaf temperature tends to be quite close to air temperature when stomata are open and leaves are in the sun. We could therefore approximate the vapor pressure difference between the leaf and the air by the vapor deficit of the air, D. Our simple photosynthesis model then becomes:

where k = 0.7 - Tanner and Sinclair (1983) extended this model to apply to plant communities and showed that the only difference between the leaf and canopy model was the value of k used.

Relationships like Eq. (14.16) were obtained over a century ago by researchers who correlated biomass production and transpiration of crops. The fact that dry environments (with high vapor deficits) pro- duce less biomass per unit transpiration than humid environments was also observed long before this equation was derived from gas exchange principles. The theory therefore appears to fit the observations.

Like Eq. Eq. (14.16) applies to any leaf or canopy situation if the appropriate values for k and D are known. Equation (14.16) is more useful though if k is conservative and D is large enough so that ignor- ing the temperature difference between the leaves and the air does not cause too much error. Equation (14.16) is therefore not very useful under conditions of low light and high humidity. Fortunately, these are exactly the conditions for which Eq. (14.13) works well. The two equations are therefore somewhat complementary. Equation (14.16) implicitly includes light effects through the effect of radiation on E.

Equation (14.16) is useful for a number of predictions without even doing computations. For example, it predicts that dry matter produc- tion cannot occur unless there is transpiration. The amount of production which will occur per unit of water used is determined by k, which is related to the intercellular

concentration in leaves. Species with C4 metabolism maintain much lower internal

concentration than so they produce more dry matter per unit water than do C3. Improvements

in water use efficiency (dry matter produced per unit of water used) in

a species must come mainly from decreased intercellular concen- tration. This obviously has a limit and dreams of genetically engineering plants that will grow in the desert and produce dry matter without us- ing water are obviously conjured up without much understanding of the physics of photosynthesis.

Biochemical Models for Assimilation 239