Photosynthetic Rate Calculator

Photosynthetic rate expresses net carbon assimilation per unit leaf area per unit time, conventionally in micromol CO2 per square meter per second. The model used here multiplies a maximum capacity Pmax by three dimensionless limitation terms. The light and CO2 terms take a rectangular hyperbola form because carboxylation by RuBisCO behaves as a saturable enzyme-substrate reaction: doubling the substrate near zero nearly doubles the rate, but near saturation adds almost nothing. The half-saturation constants used are 200 micromol photons per m2 per s for light and 300 ppm for CO2. The temperature term is a Gaussian centered on an optimum of 25 degrees C with a width of 10 degrees C, and dark respiration is subtracted with a Q10 near 2, meaning it roughly doubles for every 10 degrees C rise. Typical measured values put well-lit C3 crops such as wheat, rice and soybean at 10 to 25 micromol CO2 per m2 per s, C4 species such as maize and sugarcane at 30 to 50, and deep-shade understory species below 10. Light compensation points run about 10 to 40 for shade-adapted leaves and 20 to 100 for sun leaves, while light saturation for C3 foliage usually falls between 800 and 1500 micromol photons per m2 per s. The main limitations of this formulation are that it is empirical rather than biochemical: it holds Pmax fixed at 20, so it will understate C4 crops and overstate shade species, and it does not represent stomatal conductance, photorespiration, leaf nitrogen content, or acclimation to a new growing environment over days to weeks.

The idea that photosynthesis is governed by whichever environmental input is in shortest supply was set out by the Cambridge plant physiologist F. F. Blackman in 1905 as the principle of limiting factors, and it remains the conceptual skeleton of multiplicative models like this one. Otto Warburg and Erwin Negelein measured quantum yields of photosynthesis in the early 1920s, establishing that a fixed number of light quanta is required per molecule of CO2 fixed. The biochemistry of the carbon reduction pathway was mapped at Berkeley in the late 1940s and 1950s by Melvin Calvin, Andrew Benson and James Bassham using carbon-14 tracers and paper chromatography, work for which Calvin received the Nobel Prize in Chemistry in 1961. The hyperbolic response form itself was borrowed from the enzyme kinetics that Leonor Michaelis and Maud Menten formalized in 1913. Routine measurement became possible once infrared gas analyzers were adapted to leaf chambers during the 1950s and 1960s, and battery-powered portable systems from the 1980s moved the technique out of the laboratory and into field canopies. In 1980 Graham Farquhar, Susanne von Caemmerer and Joseph Berry published a biochemically explicit model of C3 photosynthesis that partitions the rate between RuBisCO limitation and electron transport limitation, and that framework has since become the research standard. Simpler multiplicative approximations of the kind calculated here survive because they are fast, require few parameters, and are adequate for crop growth models and greenhouse climate controllers.