Thursday, September 6, 2018

Primary Production

How fast could plants in a transparent box starve themselves of CO2?

In the spring, we sprout lots of little tomato and squash plants in a plastic tray. Maybe 60 sprouts in a 2 square foot tray. Initially, we keep the tray indoors, but when the sprouts are a little bigger, we leave it outside so they get more sunlight. Sometimes we put a transparent plastic lid over them to make a little greenhouse to keep them warm on cold days. The lid makes a weak seal around the tray, and I wondered if could be starving the plants of CO2.

As a first order of magnitude check, we would expect CO2 consumption to be a modest fraction (maybe 1/3?) of the total existing mass of the plants over the course of maybe a week because the CO2 is being consumed to create plant material. It seems reasonable that sprouts should grow by 1/3rd every week. The plants in one mini-greenhouse box probably have a mass of (1g x 60) = 60g. So very roughly we would expect CO2 consumption to be somewhere around 20g per week, or about 2g per day.

Ok, lets get more precise. What volume of CO2 is consumed (and O2 released) by a certain mass of plants per day?

If we can assume the box is producing at an average rate somewhere between tundra and grassland (the sprouting tray looks like a little fell field, but it is probably growing faster than one), we can say its mean NPP is about 300 g/(m^2*yr). If our box is 0.2m^2, one day should net about 0.2g in primary production (300g * 0.2m^2 / 365days).

I'm going to use glucose as a carbohydrate representative substance for all of primary production. In photosynthesis, every 6mol of CO2 (44g/mol) yields 1mol of sugar C6H12O6 (180g/mol). So 0.2g (0.001mol) in primary production of sugar requires about 0.3g (0.006mol) of CO2.

Ok, so the plants in the box consume about 0.3g of CO2 per day. Pretty close to our initial estimate of 2g per day, as far as rough estimates go.

Now, how much CO2 is in the box?

Partial pressure of CO2 in dry air at sea level (760torr) is about 0.3torr. So 0.04%. PV=nRT, so for every 100 mol of air, 0.04 mol of CO2. Volume of air in the box is about 20L, so at 1kg/m^3 or 1g/L, we have 20g of air. Air molar mass is 29g/mol (mostly N2), so we have about 1 mol of air in the box, and maybe 0.0006mol of CO2. Which at 44g/mol is 0.026g.

Ok, so there is only about 0.03 grams of CO2 in the box.

Wow, it looks like the CO2 in the box gets used up pretty quickly. Maybe in about 1 hour.

What are the uncertainties in my estimates?
- area or volume of air in the box - probably correct within a factor of 1.5
- mass of plants in the box - probably correct within a factor of 3
- NPP assumption - desert is 90, grassland is 600 g/(m^2*yr) - so probably correct within a factor of 2 or 3.
- Assumption of glucose as a representative substance for all of primary production - the actual substance that gets made in the Calvin cycle is glyceraldehyde 3-phosphate (G3P). G3P is then transformed into sugars like glucose, which in turn are consumed to build the plant itself.

With these uncertainties, my worst case error is factor of 11 (3x1.5x2.5), so worst case bounds are from 5min to 11hours. The root sum of squares (RSS) error is a factor of 4, so the bounds are more likely from 15min to 4hours.

Make sure greenhouses get adequate ventilation!

Some supporting evidence:
“Many greenhouse growers have starved their plants for carbon dioxide in the attempt to conserve heat by limiting or eliminating air exchange in the greenhouse. Up to two full air exchanges an hour have been recommended for greenhouses to keep the plants and the equipment functioning properly.”

It's annoyingly difficult to search for anything related to greenhouses and CO2 and starving because climate skeptic articles overwhelmingly dominate the results.

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