GPU parallel prefix scan for clear-sky adding method — 6/6 tests pass

[consigcody94]

Summary

The non-scattering (clear-sky) adding method in ADA_Module.f90 (lines 228-246) can be parallelized using a parallel prefix scan with affine tuples, reducing sequential depth from O(N_layers) to O(log N_layers).

The radiance recurrence Rad_UP[k-1] = source_up[k] + trans[k] * Rad_UP[k] is an affine map, and affine map composition is associative — enabling a Hillis-Steele parallel scan on GPU.

Benchmark (RTX 3060, CUDA 13.2)

Configuration	Profiles	Layers	Angles	GPU Time	Max Rel Error	Status
IR sounder	10,000	60	6	0.18 ms	4.1e-07	PASS
IR sounder	50,000	60	6	0.87 ms	4.3e-07	PASS
High-res	10,000	100	6	0.32 ms	4.3e-07	PASS
MW sounder	100,000	60	2	0.59 ms	3.5e-07	PASS
Multi-stream	10,000	60	16	0.44 ms	4.4e-07	PASS
Deep atm	1,000	200	6	0.06 ms	3.1e-07	PASS

Zero NaN, zero Inf across all tests.

Scope & Limitations

What works: The scalar (non-scattering) adding path where layer transmittance and reflectance are diagonal. Each discrete ordinate angle is processed independently.

What is NOT tested: The full scattering path (lines 198-226) which involves nZ×nZ matrix operations with matinv at every layer. The matrix Redheffer star product is theoretically still associative, but the parallel scan with matrix inverses inside the operator is more complex and may have numerical issues. This needs further research.

Hardware limitation: Tested on RTX 3060 12GB only. Production CRTM workloads on WCOSS2 would need A100/H100 validation.

Mathematical Basis

Same technique as applied to rte-rrtmgp (earth-system-radiation/rte-rrtmgp#393):

• Affine tuple operator: (a₂,b₂) ∘ (a₁,b₁) = (a₂·a₁, a₂·b₁+b₂) (Martin & Cundy, ICLR 2018)
• Associativity proven by Grant & Hunt (1969) for RT layer operators

Code

CUDA kernel: https://github.com/consigcody94/parallel-prefix-rt/blob/master/benchmarks/cuda/crtm_scalar_adding.cu

[consigcody94]

Code has been reorganized to: https://github.com/consigcody94/noaa-gpu-kernels/tree/main/radiation/crtm

[consigcody94]

AI Attribution: This work was developed using Claude Code as an AI-assisted development tool. Code generation and benchmark automation were performed by Claude under my direction. I designed the research methodology, selected mathematical approaches, and validated all results on physical hardware (RTX 3060). All commits carry a Co-Authored-By: Claude tag. When results failed validation (e.g., tensor compression on rte-rrtmgp#394), they were publicly retracted.

[BenjaminTJohnson]

Thank you your contribution, I've been on PTO for the past two weeks which is why I haven't responded.

I'll take a look over the next few days and get back to you .

[consigcody94]

@BenjaminTJohnson No rush at all -- welcome back from PTO.

For full transparency: this kernel was developed using Claude Code as an AI-assisted development tool under my direction. I designed the research methodology and validated all results on physical hardware (RTX 3060). All commits carry a Co-Authored-By: Claude tag. The AI attribution comment I posted earlier has the full details.

Happy to answer any questions about the benchmark methodology or discuss what a real integration path into CRTMv3 would look like. The clear-sky scalar path was straightforward to extract and validate, but I understand that the full scattering path with matrix operations would be a much larger effort.

Looking forward to your feedback.