Fix possible divide-by-zero error in MoL code

[Thomas Bendall (tommbendall)]

PR Summary

Sci/Tech Reviewer: James Kent (@jameskent-metoffice)
Code Reviewer: Benjamin Went (@MetBenjaminWent)

A calculation in the Koren limiter for the MoL scheme involves the calculation r = y / x, which has been written as:

r = (y + SMALL_R_TRAN) / (x + SMALL_R_TRAN)

to avoid a potential divide-by-zero error. However, this can still lead to a divide-by-zero error in the case that x = -SMALL_R_TRAN. This PR fixes that by changing the calculation to:

r = y / (MAX(ABS(x), SMALL_R_TRAN)*SIGN(1.0_r_tran, x))

This cannot be zero in the denominator, and is generally equal to y / x since ABS(x)*sign(1.0, x) = x.

The other improvement is that now r = 0 if y = 0.

Results

Plots showing the change to the lfric_atm MoL test can be found in this PDF:
results_mol_division_fix_lfric_atm.pdf

Code Quality Checklist

• 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
• All automated checks in the CI pipeline have completed successfully

Testing

• I have tested this change locally, using the LFRic Apps rose-stem suite
• If any tests fail (rose-stem or CI) the reason is understood and acceptable (e.g. kgo changes)
• I have added tests to cover new functionality as appropriate (e.g. system tests, unit tests, etc.)
• Any new tests have been assigned an appropriate amount of compute resource and have been allocated to an appropriate testing group (i.e. the developer tests are for jobs which use a small amount of compute resource and complete in a matter of minutes)

trac.log

Test Suite Results - lfric_apps - mol_division_fix/run2

Suite Information

Item	Value
Suite Name	mol_division_fix/run2
Suite User	thomas.bendall
Workflow Start	2026-03-17T14:16:22
Groups Run	all

Dependency	Reference	Main Like
casim	MetOffice/casim@2026.03.2	True
jules	MetOffice/jules@2026.03.2	True
lfric_apps	tommbendall/lfric_apps@TBendall/mol_division_fix	False
lfric_core	MetOffice/lfric_core@2026.03.2	True
moci	MetOffice/moci@2026.03.2	True
SimSys_Scripts	MetOffice/SimSys_Scripts@2026.03.2	True
socrates	MetOffice/socrates@2026.03.2	True
socrates-spectral	MetOffice/socrates-spectral@2026.03.2	True
ukca	MetOffice/ukca@2026.03.2	True

Task Information

✅ succeeded tasks - 1511

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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 of Generative AI tool name (e.g., Met Office Github Copilot Enterprise, Github Copilot Personal, ChatGPT GPT-4, etc) and I have followed the 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

• All dependencies have been resolved
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• Tests are adequate and have passed
• Documentation is complete and accurate
• Security considerations have been addressed
• Performance impact is acceptable

[James Kent (jameskent-metoffice)]

This is a very small change to fix a possible divide by zero in the Koren kernels. The method chosen is sensible. There are kgo changes in tests that run with MoL and Koren, but all the plots look good and I am happy they are correct. Approved for science review.

[iboutle]

Benjamin Went (@MetBenjaminWent) this PR it appears is blocking #326, and I think any KGO changing PR is likely to encounter the issues that this PR fixes - therefore it would be good if we could prioritise getting this on to help other PRs along.