Darcy's Law in Predicting Tree's Inevitable End

As you and I both know we sapiens have been very consistent at messing up the planet’s climate; days are now hotter than they’re supposed to be

... and this almost certainly means its bad for the ecosystem, and in this case, the plants,

but how big is the boo boo gonna be?

With the help of Darcy’s Law, we can determine one crucial physical property in plants: Conductance (a.k.a. G); simply put, it is the measure of the rate of water transfer through a plant, and therefore the rate of transpiration (but not to be confused with flowrate!);

As always, this is analogous to its electrical counterpart (much like how the entire law is),

where for an electrical conductor:

where A is Area, l is length, and σ is the electrical conductivity.

The lower the conductance, the lower the rate of transpiration, and that’s a bad thing for someone trying to achieve their homeostatic state!

In this case, the following equation can be used (think of xylem as the conductor for tree sap instead)[1] :

where As is conducting area (cm2), Al is leaf area (m2), ks is specific conductivity (ms−1), h is height (m),  is water viscosity (Pa s), (Ψs−Ψl) is the soil-to-leaf water potential difference, and D is vapour pressure deficit (kPa).

Woah there, what are these?

This is a derivation of Darcy’s Law for ecohydrology, in case you want to see how this directly relates to Darcy's law, see here; if that’s too many jargons, here's the gist:

Climate change tells us that the value of D (essentially the measure of water vapour air can hold before reaching saturation) will increase in the future when it gets warmer, thus more water is wasted into the surrounding/atmosphere; while other variables in the equation are mostly dependant on the plant species.

This means conductance, G, will decrease! Note that this happens at different rates depending on the inherent variables our plant species holds.

For example, G decreases when h increases, which means that the taller you are, the lower your conductivity, that means you’re less efficient at getting water to parts higher up where you need them, ergo you terminate your lifecycle sooner*… if you’re a tree, that is.

In this case we can predict the lifecycle of a certain plantation/forest to some extent by looking at the specific variables, and we can then use this information to prolong a forest’s lifespan:

think: many tall trees → earlier preparation for replantation

and by then you’d know what species you should replant instead.

This shows how human intervention is sometimes necessary for the protection of the planet, otherwise not even G-sus would be able to save the plants!

Reference:

[1]N. McDowell & C. Allen. (2015). "Darcy's law predicts widespread forest mortality under climate warming". Nature Climate Change [Online]. vol. 5, no. 7, pp. 669-672. Available: https://www.nature.com/articles/nclimate2641

*No tall trees/people were harmed in the process of this writing.

Beam me to Dam-Nation!