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    Although photosynthesis incorporates little water into carbohydrates, it consumes much. The moist site of photosynthesis within the leaf must receive the raw material tex2html_wrap_inline2319. Concomitantly, water escapes or transpires through the same pores or stomata admitting the tex2html_wrap_inline2319. Measured in the units of precipitation, transpiration  from a crop can consume 7 mm/day.gif In California during a season, evapotranspiration --evaporation from the soil plus transpiration  by the crop-totaled about 700 mm (Stewart et al., 1977[SHPtex2html_wrap287777] 207). The magnitude of the 700 mm is grasped better if stated in weight of water/ha: 7,000 tons. How low a ceiling does the global sum of fresh water place over crop production for ten billion people?

Speaking teleologically, I can say that Evolution has noticed transpiration  and has taken measures to reduce consumption of water. Its measures are cells that guard the stomatal entrances to the leaf. Generally, the guards narrow the entrances when abundant tex2html_wrap_inline2319, deficient water. or darkness signal that transpiration can be slowed while scarcely slowing photosynthesis. Sinclair, Tanner, and Bennett argue that biomass accumulation  is ``inextricably linked to transpiration",  and Cowan goes so far as to propose that plants dynamically adjust their stomata to maintain an optimal balance between photosynthesis and transpiration  (Cowan, 1977[Cow77]; Sinclair et al., 1984[STB84]). The point is that although transpired water is not incorporated into carbohydrate, consumption of water inevitably accompanies photosynthesis. Thinking about physical limits hemming in food production,  I cannot escape considering water supply as well as solar energy and tex2html_wrap_inline2319.

If transpiration  must accompany photosynthesis and if stomata have balanced the two processes, they should change in step. The correlation between the two is furthered because radiation, wholly solar for photosynthesis and largely solar for transpiration, energizes both. So a connection between transpiration and photosynthesis should permit a rough calculation of yield from evaporation. Over a generation ago, deWit (1958[deW58]) tested the connection, using observations from early in the twentieth century. Figure 6.3.1 shows that the dry weight of a shoot increases with transpiration.  The shoot is all of the plant above ground and may be thought of as biomass. The harvest index, or ratio of grain to biomass, is about half.gif Because the soil was covered to prevent evaporation from the soil surface, the loss of water can accurately be called transpiration.  Although the observed plants grew in containers, making the dimensions of photosynthesis and transpiration grams/container or `can', the ratio of biomass or shoot to transpiration has the general dimensions of g biomass/kg water.

figure6.3.1 Figure 6.3.1. The production of dry weight of a shoot, as a function of transpiration. The three species of crop were grown in containers in the Great Plains and India (adapted from deWit, 1958).[deW58] 

On Figure 6.3.1 I have written the slopes 3.6, 2.2, and 1.2 g/kg of three lines fitted to the point of `no transpiration,  no yield' and the observations of the three species in the two dry climates. In the moister climate of the Netherlands, deWit (1958[deW58]) estimated oats, 2.6; peas, 3.4; and beets, 6.1 g biomass/kg evapotranspiration.

``At first approximation [the g biomass/kg water were] independent of weather, nutrient level of the soil and availability of water, provided the nutrient level is not `too low' and the availability of water not `too high'." Mutual shading of plants had little effect.

Extending his analysis from crops in containers to those in fields, deWit found the g biomass/kg water supply much the same in several crops. If the annual water supply exceeded the threshold of 100 mm and biomass was twice the grain yield, wheat produced 1 g biomass/kg water supply in fields in semiarid climates of America and India, an amount similar to its production in containers.

Similarly, in Oaxaca, Mexico each kg of water supply above a threshold produced approximately one-half g of maize grain and 1 g of maize biomass. Whether the maize was grown by dry farming on high alluvium or on piedmont, by canal irrigation or by water table irrigation, the relation between water supply and yield remained the same. Kirby used the relation between yield and water supply and then that between water supply and population as an integral part of her anthropological estimation of the ancient Oaxacan population (Kirby, 1973,[Kir73] 53-65).

Leaving water supply, Figure 6.3.2 returns to evapotranspiration, increasing the slopes to about 2 g grain/kg water evaporated. Contributing to the greater slope, maize and sorghum varieties were recent ones grown in experiments to show the effect of irrigation by minimizing other limitations to yield. In step with the higher yields and lesser quantities of water evaporated than supplied, the slopes reach 1.8 and 1.5 g corn and sorghum grain/kg evapotranspiration, which correspond to 3 to 4 g biomass/kg evapotranspiration, respectively (Stewart et al., 1977[SHPtex2html_wrap287777]: Stewart et al., 1983[SMD83]).

figure6.3.2 Figure 6.3.2. Relations in the field of the yields of grain to water supply in California maize and in Texas sorghum. The slopes of 1.5 and 1.8 grain/kg are 3 to 4 g biomass/kg water, respectively. Engineers and agronomists employ dimensions of kg grain/tex2html_wrap_inline2381 water, which give the same values numerically as the g/kg used here (Stewart et al., 1977; Stewart et al., 1983).[SHPtex2html_wrap287777][SMD83] 

A threshold evapotranspiration before the crop produces any grain distinguishes Figure 6.3.2, representing crops in the field, from Figure 6.3.1, representing biomass and transpiration.  The threshold evapotranspiration for any grain or harvest should not surprise when we remember the evaporation from the soil and the sensitivity of flowering to drought. Later I shall discuss the effect of threshold evapotranspiration on water use efficiency.gif

I summarize this wealth of knowledge about diverse places and crops: photosynthesizing 1 to 6 g of biomass consumes 1,000 g of water.

Use of the 1 to 6 g/kg to calculate the limit of water for feeding ten billion people requires global quantities. Annually, tex2html_wrap_inline2383 of water evaporates from land. At the same time, the biota on land takes in tex2html_wrap_inline2385 tons of carbon. A tex2html_wrap_inline2381 of water is a ton, biomass is largely carbohydrate, and carbohydrate is 40% carbon. So the global production of biomass per evaporation is (tex2html_wrap_inline2385 t carbon/0.40 carbon per biomass)/(tex2html_wrap_inline2391 t water), or about 4 g/kg, within the range of 1 to 6 g/kg in containers and fields as shown in the figures.gif

After assuring ourselves that the order of the ratio of biomass production  to evaporation is reasonable, how shall I use it to determine the ceiling that water puts over feeding ten billion people? If the global average of 410 mm evaporates and the ratio of biomass to evaporation is 4 g/kg, cropland should produce 16 t biomass, or 8 t of cereal/ha and 100 billion t of cereal from the earth's 13 billion ha of land. Because a ton of cereal will support four people for a year, I reach the conclusion that the water evaporating from all the world's land could sustain 400 billion people, fully 40 times the ten billion envisioned.gif

Recall that deWit came to ``The staggering conclusion ... that 1,000 billion people could live from the earth if photosynthesis is the limiting factor!" My conclusion that 400 billion could live from the food produced with the evaporation from land is equally staggering.

next up previous contents index
Next: Fertilizer Up: Do GlobalPhysical Limits Previous: Carbon dioxide

Yasuko Kitajima
Thu Jun 19 16:20:56 PDT 1997