# Can you quantify the energy of spring?

April 16, 2014 12:04 PM Subscribe

It's spring and the plants and trees which have been bare for months are bursting into life. I've been thinking it must take a lot of energy for a tree to go from having no leaves at all to being covered in too many to count in a relatively short period of time. But how much energy exactly?

I would be really interested to see how this compares to human energy production or consumption. I appreciate that this probably varies a great deal across different plants and conditions.

Educated guesses, energy values for a single tree to go from bare to fully covered in leaves or power per unit area averages all welcome!

I would be really interested to see how this compares to human energy production or consumption. I appreciate that this probably varies a great deal across different plants and conditions.

Educated guesses, energy values for a single tree to go from bare to fully covered in leaves or power per unit area averages all welcome!

There are a few ways to do this (from the non-biologist's perspective, anyway).

There are ways to calculate Leaf Area Index, or the total (one-sided) leaf area for a given area of ground. According to that article, it was about 1.8 m^2 m^-2 for a particular oak grove in California (in other words, 1.8 square meters of leaves per square meter of land). You can also to a leaf mass density similarly (from that study, about 150 grams per square meter). The study also culled a sample of trees and directly measured their leaf masses.

So, knowing how much leaf you have, you can get some good first-order estimates about energy consumption. Analytically, you can start with the basic chemical reactions that take place - conversion of carbon dioxide and water to glucose and then glucose to cellulose and other larger molecules - and perform an energy balance on the equations using standard heats of formation for each chemical (these are tabulated). You can make some educated guesses about how much cellulose, water, and other materials are in a leaf and then simply multiply by how much leaf you have (around 5 kg per tree, according to that link). If I were particularly anal, I'd also figure out the potential energy change required to transport water up the tree to the leaves, but my guess is that it's probably a minor fraction of the total energy required.

Experimentally, you could take leaves and do a calorimetry experiment to see how much energy is released. You'd want to do this on dry leaves, since photosynthesis doesn't generate the stored water in the leaves.

Or, from a thermodynamics perspective, you can make some intelligent guesses about energy conversion. "Ideal" sunlight is about 1 kW of energy per square meter. You know the total leaf area from our study, and can also apply some reduction factors due to overlapping leaves and other inefficiencies. So you'll get a value of the amount of energy the tree actually "absorbs" from the sun per unit area of leaf, and you can figure out how much energy the tree takes in per day. By making a couple of measurements (or guesses) about the amount of leaf area the tree has as it's filling out (and still knowing the energy per leaf area value you figured out before), you can plot a chart of leaf growth over time and integrate that to find the total energy consumed to make a season's worth of leaves.

Performing these calculations is left as an exercise for the reader.

posted by backseatpilot at 12:46 PM on April 16, 2014

There are ways to calculate Leaf Area Index, or the total (one-sided) leaf area for a given area of ground. According to that article, it was about 1.8 m^2 m^-2 for a particular oak grove in California (in other words, 1.8 square meters of leaves per square meter of land). You can also to a leaf mass density similarly (from that study, about 150 grams per square meter). The study also culled a sample of trees and directly measured their leaf masses.

So, knowing how much leaf you have, you can get some good first-order estimates about energy consumption. Analytically, you can start with the basic chemical reactions that take place - conversion of carbon dioxide and water to glucose and then glucose to cellulose and other larger molecules - and perform an energy balance on the equations using standard heats of formation for each chemical (these are tabulated). You can make some educated guesses about how much cellulose, water, and other materials are in a leaf and then simply multiply by how much leaf you have (around 5 kg per tree, according to that link). If I were particularly anal, I'd also figure out the potential energy change required to transport water up the tree to the leaves, but my guess is that it's probably a minor fraction of the total energy required.

Experimentally, you could take leaves and do a calorimetry experiment to see how much energy is released. You'd want to do this on dry leaves, since photosynthesis doesn't generate the stored water in the leaves.

Or, from a thermodynamics perspective, you can make some intelligent guesses about energy conversion. "Ideal" sunlight is about 1 kW of energy per square meter. You know the total leaf area from our study, and can also apply some reduction factors due to overlapping leaves and other inefficiencies. So you'll get a value of the amount of energy the tree actually "absorbs" from the sun per unit area of leaf, and you can figure out how much energy the tree takes in per day. By making a couple of measurements (or guesses) about the amount of leaf area the tree has as it's filling out (and still knowing the energy per leaf area value you figured out before), you can plot a chart of leaf growth over time and integrate that to find the total energy consumed to make a season's worth of leaves.

Performing these calculations is left as an exercise for the reader.

posted by backseatpilot at 12:46 PM on April 16, 2014

In Al Gore's environmental movie (what the heck was that called? I forget) he showed a graph of atmospheric CO2 levels over time. The overall slope of the graph was upward but the line had a sawtooth character which he pointed out reflected the CO2 that left the atmosphere as the more heavily wooded northern hemisphere (I think) leafed out for summer each year.

I think if I were setting up this calculation I'd start here... Figure out the volume of CO2 that is absorbed in the initial growth of plants in the spring, do the stoichiometric calculation to figure out how much energy is required to convert to cellulose.

I recognize that in spring, that initial burst you're speaking of, is fueled not directly by photosynthesis but must be by stored energy (since the leaves aren't out yet and acting as fuel cells). But if the question can be made a little more broad like "how much energy does it take to put on all that initial plant growth", that's probably a decent way to get in the ball park.

posted by Sublimity at 12:57 PM on April 16, 2014

I think if I were setting up this calculation I'd start here... Figure out the volume of CO2 that is absorbed in the initial growth of plants in the spring, do the stoichiometric calculation to figure out how much energy is required to convert to cellulose.

I recognize that in spring, that initial burst you're speaking of, is fueled not directly by photosynthesis but must be by stored energy (since the leaves aren't out yet and acting as fuel cells). But if the question can be made a little more broad like "how much energy does it take to put on all that initial plant growth", that's probably a decent way to get in the ball park.

posted by Sublimity at 12:57 PM on April 16, 2014

*I recognize that in spring, that initial burst you're speaking of, is fueled not directly by photosynthesis but must be by stored energy (since the leaves aren't out yet and acting as fuel cells). But if the question can be made a little more broad like "how much energy does it take to put on all that initial plant growth", that's probably a decent way to get in the ball park.*

a great deal of it is powered by last years leaves. In the fall, as the leaves change color, the tree is 'sucking' the nutrients/energy out of the leaf before discarding the leaf and storing that as sugar(s) in the sap of the plant. Perrenial bulbs/shrubs also do that same thing by storing carbohydrates in the roots. So the calculation you sugges ins't bad, as the woody matter is discarded (the cellulose structure fo the leaves) but this is only a fraction of the actual energy represented by the leafing out in the spring.

posted by bartonlong at 1:56 PM on April 16, 2014

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Info about the number and weight of leaves on a tree is definitely googleable and it's a direct conversion from calories to watt-hours, keeping in mind that a 'calorie' in nutrient terms is 1000 engineering calories. Of course, building the leaf consumes some calories beyond what ends up in the leaf, and the woody structures are a wildcard.

There's also the question of simply transporting all that water upwards, which might be significant for a big tree.

Just some thoughts - good luck!

posted by ftm at 12:21 PM on April 16, 2014