Allow computation and storage of height at W0

[tommbendall]

PR Summary

Sci/Tech Reviewer: @jameskent-metoffice
Code Reviewer: @MatthewHambley

We can already store the vertical height field at many function spaces, but the W0 function space is missing. This PR adds it in.

Linked to: MetOffice/lfric_apps#165

Code Quality Checklist

(Some checks are automatically carried out via the CI pipeline)

• I have performed a self-review of my own code
• My code follows the project's
  style guidelines
• Comments have been included that aid understanding and enhance the
  readability of the code
• My changes generate no new warnings

Testing

• I have tested this change locally, using the LFRic Core rose-stem suite
• If required (e.g. API changes) I have also run the LFRic Apps test suite
  using this branch
• If any tests fail (rose-stem or CI) the reason is understood and
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trac.log

Test Suite Results - lfric_core - height_w0/run1

Suite Information

Item	Value
Suite Name	height_w0/run1
Suite User	thomas.bendall
Workflow Start	2026-01-20T16:15:30
Groups Run	developer

Dependency	Reference	Main Like
lfric_core	tommbendall/lfric_core@TBendall/HeightW0	False
SimSys_Scripts	MetOffice/SimSys_Scripts@2025.12.1	True

Task Information

✅ succeeded tasks - 372

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Performance Impact

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AI Assistance and Attribution

• Some of the content of this change has been produced with the assistance
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  Simulation Systems AI policy
  (including attribution labels)

Documentation

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Sci/Tech Review

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Please alert the code reviewer via a tag when you have approved the SR

Code Review

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[tommbendall]

This is ready for Science Review, thanks @jameskent-metoffice

[jameskent-metoffice]

This is a very simple change to one file. I have one query which I've commented in sci_geometric_constants_mod. Other than that I am happy that this passes science review.

[tommbendall]

Just commenting to say this is ready for code review @MatthewHambley, as I'm not sure exactly what is being picked up by notifications