Approximate soil energy Jacobian

[kmdeck]

Purpose

Add in our first approximation for the energy equation Jacobian, which only includes d\rho e_int/dT.

This does allow us to take much bigger timesteps, more comparable to our target of 15 minutes, except in the cases where the soil is freezing or the canopy is present. If we make the thermal mass of the canopy larger, we can take bigger steps.
-> need to think about how we handle soil freezing in terms of implicit stepping
-> canopy temp probably does need an implicit solver.

To-do

Content

• Alter imp/exp tendencies for soil energy hydrology
• Alter update jacobian for soil energy hydrology
• Increase timesteps in tutorials and some experiments. In cases with a canopy, this involved increasing ac_canopy as well, so those are unchanged
• Add unit test/update unit tests
• Adds a buildkite run showing performance as a function of timestep, similar to what we had in Richards equation. We simulation the exact same system, but in one case with T > T freeze, and in one case with T < Tfreeze. The timestep required is orders of magnitude different.
  No Phase change:
  
  

With Phase change:

Note the differences in x and y axes. The solution at dt = 10, 100 seconds for the phase change one has lots of oscillations and is not good enough, although the relative error is not terrible

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• I have read and checked the items on the review checklist.

[juliasloan25]

This looks great!! Thank you Kat

[kmdeck]

@juliasloan25 thank you for the review! I wont be able to address your comments until next week, but if you have time, let me know if you think these are the main things, or if you see any issues with how we defined J. I think it's all OK because it was just adding terms copying what we do for theta_l, but it would be helpful if you took a close look at that part too.

[dennisYatunin]

These changes all look good!

[dennisYatunin]

Just a note though that this will allocate two surface Fields on every implicit tendency update. It would generally be better to cache these Fields somewhere, or to redefine heat_top_flux_bc and heat_bottom_flux_bc to be Fields of WVectors instead of Fields of scalars.

[kmdeck]

Thanks, Dennis! good catch!