The following page, http://www.erasmatazz.com/library/c839b0d2d6b6417787b1/the-l..., has the following boneheaded mistake, which is all the more frustrating for being phrased in such a patronizing way:

> You probably don’t know this, but when two factors are BOTH required for a process, you multiply them together. If either one can compensate for the other, then you add them together. So our formula boils down to just this:

> Rate of photosynthesis = some constant * rate of water uptake * amount of sunlight on the leaf

Nope. You don't get ten times as many moles of glucose per mole of water just because you have ten times as much sunlight (because it's sunny instead of cloudy), or ten times as many calories of glucose per joule of sunlight just because ten times as much water is available.

Let's use the variables R for the rate of photosynthesis, k for the constant, Q for the volumetric flow rate of water, and E for the amount of sunlight. Crawford is saying R = kQE, if the only process consuming the water is photosynthesis (incorporating the water into carbohydrate molecules). This is wrong.

The correct formula under these assumptions is R = kₑE ∧ kₕQₚ, where kₑ and kₕ are two new constants, Qₚ is the maximum possible flow rate under the conditions, and ∧ is the pairwise minimum function: a ∧ b = a if a < b, otherwise b. This correctly expresses Crawford's model in the previous paragraph, "If one of these two is in short supply, that limits the amount of photosynthesis that can take place." If you don't have enough water, more sunlight won't increase the photosynthetic rate, and if you don't have enough sunlight, more water won't either, and in fact won't be sucked up from the roots in the first place.

As I understand the situation, though, this mental model is still incorrect. Typically, most of the water taken up by the roots of a leafy plant (as opposed to a succulent) is lost to evaporation, not incorporated into glucose. This keeps its leaves from overheating, but doesn't add to the amount of glucose. The evaporation rate is tightly controlled by temperature and irradiance by opening and closing the leaf's stomata, which also permit the transport of the gases involved in photosynthesis. If there isn't enough water available, the leaves wilt, die, and dry out.

https://en.wikipedia.org/wiki/Stoma#CO2_gain_and_water_loss

But, under favorable conditions, the sunlight is the limiting factor, so the photosynthesis rate is only proportional to sunlight. The water flow rate also increases with sunlight because sunlight heats up the leaves, but sunlight isn't the only thing that heats up the leaves; hot air can also heat them up. Often, though, the leaves are cooler than the surrounding air, so wind gives the leaves free cooling they don't have to pay for with precious water; they can close their stomata somewhat. So water flow varies over a wide range almost independent of photosynthesis rate.

However, leaves can't acquire CO₂ without opening their stomata to some degree, so under water-limited conditions at high temperatures, C3 and C4 plants switch to a strategy employing PEPCase to permit efficient photosynthesis with less water loss.

Also, in vascular plants, there's a round-trip flow of water: some of the water that comes up from the root (often in the inner bark, never in the cambium, which Crawford misspells "cambian") flows back down from the leaves to the root, carrying sugar with it to provide energy to sustain the life of the non-photosynthetic parts of the plant, as well as the mycorrhiza that interpenetrate the roots of almost all land plants.

But that's just the way I understand things. It might be wrong and is certainly at least incomplete.

I wish I could think that in my own notes (Dercuano etc.) I've avoided such overconfident blunders, or at least phrasing them so patronizingly and then completely failing to uncover my errors. Actually, though, I've probably made far more such arrogant, overconfident blunders than I have any idea of. So I can see how it can happen.