Apply spline to the mass conserving temperature

[lhy11009]

In this PR, I applied a spline to the mass-conserving temperature. Previously, there was a high-order discontinuity at the coldest part of the slab. This additional treatment would generate a continuous profile by the spline operation.

To show the effect, below is the visualization of a slab temperature (from the new test mass_conserving_slab_temperature_spline.wb).
The line features show 2 profiles across the slab.

One free variable is the number of points on the spline.
To maintain the minimum temperature in the slab, one point is always pinned on the coldest point of the slab.
In addition to that, an equal number of points are chosen on both sides (default is 5).
A profile at 500 km depth (the deeper one in the first plot) is chosen to show the temperature profile from different numbers of spline points.

n = 2 there is a strong smoothing effect on the slab's internal temperature.

n = 5, the spline only affects the center of the slab as designated.
As other parts of the profile are already continuous, the spline would follow the analytic profile.

n = 10, there is little effect on the temperature profile.

[lhy11009]

@MFraters I see there are file differences not from the modification I committed in "File Changed". I only modified the source/world_builder/features/subducting_plate_models/temperature/mass_conserving.cc and the include/world_builder/features/subducting_plate_models/temperature/mass_conserving.h

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.31%. Comparing base (91c6b19) to head (b0d99ad).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #659      +/-   ##
==========================================
+ Coverage   98.28%   98.31%   +0.03%     
==========================================
  Files         107      107              
  Lines        7341     7358      +17     
==========================================
+ Hits         7215     7234      +19     
+ Misses        126      124       -2     

Files	Coverage Δ
...ucting_plate_models/temperature/mass_conserving.cc	99.57% <100.00%> (+0.49%)	⬆️

... and 1 file with indirect coverage changes

---

Continue to review full report in Codecov by Sentry.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update 91c6b19...b0d99ad. Read the comment docs.

[github-actions]

Benchmark	Main	Feature	Difference (99.9% CI)
Slab interpolation simple none	1.022 ± 0.009 (s=463)	1.023 ± 0.007 (s=420)	-0.1% .. +0.3%
Slab interpolation curved simple none	1.018 ± 0.007 (s=470)	1.021 ± 0.005 (s=416)	+0.2% .. +0.4%
Spherical slab interpolation simple none	1.171 ± 0.006 (s=408)	1.168 ± 0.006 (s=364)	-0.4% .. -0.2%
Slab interpolation simple curved CMS	1.058 ± 0.004 (s=416)	1.056 ± 0.003 (s=438)	-0.3% .. -0.1%
Spherical slab interpolation simple CMS	1.561 ± 0.012 (s=282)	1.560 ± 0.013 (s=297)	-0.3% .. +0.2%
Spherical fault interpolation simple none	1.178 ± 0.006 (s=390)	1.178 ± 0.008 (s=376)	-0.2% .. +0.1%
Cartesian min max surface	2.318 ± 0.020 (s=189)	2.302 ± 0.036 (s=203)	-1.1% .. -0.3%
Spherical min max surface	7.235 ± 0.027 (s=61)	7.215 ± 0.031 (s=66)	-0.5% .. -0.0%

[MFraters]

Thanks for this pull request! I think it would be good for @mibillen to take a first look at it, given that she is more familiar with the mass conserving temperature model

@MFraters I see there are file differences not from the modification I committed in "File Changed". I only modified the source/world_builder/features/subducting_plate_models/temperature/mass_conserving.cc and the include/world_builder/features/subducting_plate_models/temperature/mass_conserving.h

I assume you also added the test files? As for the doc/world_builder_declarations files, for now don't worry about them. You can remove them from you commits for now if you want. They will be mostly cleaned up in #652, althoug, because you are adding an option, these files will change in the end.

[mibillen]

Just a few comments to clarify and then this can be merged. This is a very clean straightforward change to the code and the extra "cost" to calculate the spline is minimal due to the way you implemented this with the get_temperatures_analytic function.

[MFraters]

This is cool functionality, thanks for implementing this! This looks good to me, so when you addressed Magali's comments and rebased the code, I think it is good to merge.

[lhy11009]

I have addressed Magali's comments and rebased them.

[MFraters]

This doesn't look correct. Can you run ctest -R generate_declarations_and_schema and check in the new result?

[lhy11009]

I fixed this. But this is from the conflict I get from rebase. I am not sure why this happens:

Auto-merging doc/world_builder_declarations.schema.json
CONFLICT (content): Merge conflict in doc/world_builder_declarations.schema.json
Auto-merging doc/world_builder_declarations_closed.md
CONFLICT (content): Merge conflict in doc/world_builder_declarations_closed.md
Auto-merging doc/world_builder_declarations_open.md
CONFLICT (content): Merge conflict in doc/world_builder_declarations_open.md

[MFraters]

also, do not forget to add a changlog entry, either here or in a follow up pull request.

[lhy11009]

Fix the conflicts and add change log.

[MFraters]

Thanks!