Physical Heliacal Visibility Phase 1 Direct-Geometry Checkpoint

Date: 2026-07-29

Status: controlled near-horizon direct-transmission geometry gate passed; Phase 1 remains in progress

Scope

This checkpoint establishes a source-traced and independently recomputed error bound for libRadtran 2.0.6 deterministic pseudo-spherical direct transmission near the horizon.

It answers three bounded questions:

1. Which spherical direct-beam law does the selected libRadtran output actually apply at the surface?
2. Can Moira reconstruct that law independently from the bound layer optical depths and vertical grid?
3. Does a proposed lower-atmosphere refinement keep the resulting layer-discretization error below the declared 0.1% controlled-geometry tolerance over the admitted altitude domain?

This is research and validation evidence. It does not add engine calculations, runtime tables, package dependencies, public contracts, or an admitted physical heliacal model.

Source Trace

The external generator remains libRadtran 2.0.6, pinned by:

source archive bytes:
154147176

source archive SHA-256:
64930cc40b6e4a37aa220520974d330fc1563796f466a649b2238131f2d69840

uvspec SHA-256:
d4e94259296a65f7700a0911f0dc7fc14aacde89985befac0266fe0a18531b7a

The libRadtran manual defines the pseudo-spherical direct beam by replacing the plane-parallel optical path with the spherical Chapman integral. The source trace then fixes how that law reaches the selected surface flux output:

• doc/radiative_transfer_theory.tex, equations eq2.24 and pseudoBeer, defines the continuous spherical Chapman path;
• libsrc_c/cdisort.c computes a Chapman optical depth at the midpoint of each layer and stores CH(layer) = vertical_optical_depth_to_midpoint / Chapman_optical_depth_to_midpoint; and
• c_fluxes() evaluates the surface direct output as the full surface vertical optical depth divided by that bottom-layer midpoint CH.

The governing cdisort.c source receipt is:

bytes:
400115

SHA-256:
952c11494efa72ebc53adf2a5e2ab34a9af5a0f241983e38a101f54a5dc03b93

This distinction is material. For a coarse surface layer, the selected libRadtran surface output is not the exact sum of all constant-extinction shell segments from an observer exactly at the surface. It is the full surface vertical optical depth scaled by the Chapman factor reconstructed at the bottom-layer midpoint.

Controlled Design

The versioned probe uses a pure-absorption exponential atmosphere at 550 nm:

• vertical optical depth: 0.1;
• scale heights: 0.25, 0.5, 1.0, 1.5, 8.0, and 20.0 km;
• diagnostic true altitudes: 0, 0.05, and 0.1 degrees;
• admitted true altitudes: 0.25, 0.5, 1, 2, 5, 10, 20, and 45 degrees;
• vertical control: 90 degrees;
• refraction: disabled;
• solver: double-precision DISORT;
• geometry: pseudo-spherical; and
• streams: 16.

Two vertical grids are compared:

Grid	Levels	Role
afglus_source_levels_v1	50	Coarse source-grid control
near_horizon_piecewise_refined_v1	290	Candidate for later named-atmosphere validation

The refined candidate uses 25 m layers from 0-2 km, 50 m from 2-5 km, 100 m from 5-10 km, 250 m from 10-25 km, 1 km from 25-50 km, and 5 km from 50-120 km.

The build contains 144 nonrepeat cases and one fixed-input repeat, for 145 uvspec runs.

Independent Oracles

The builder and validator do not share a numerical quadrature implementation:

• builder: adaptive Simpson integration over a squared-altitude transform;
• validator: adaptive Gauss-Kronrod 15 integration over the same physical continuous atmosphere;
• builder layer reconstruction: direct summation with math.fsum; and
• validator layer reconstruction: separately written compensated summation.

Every case records:

• the selected libRadtran direct transmission and slant optical depth;
• the source-traced bottom-layer-midpoint Chapman reconstruction;
• an exact same-layer shell sum from a surface observer;
• the independently integrated continuous exponential atmosphere; and
• the plane-parallel comparison where defined.

The positive-altitude production extraction remains edir / sin(target_true_altitude). The pure-absorption 4 * pi * uavgdir channel is a cross-check only. It remains forbidden as a general production transmission channel because aerosol delta-M scaling changes its semantics.

Acceptance Results

Gate	Frozen tolerance	Maximum observed	Result
Admitted libRadtran vs source-traced midpoint-Chapman slant optical depth	2e-5 absolute	5.353239300731616e-7	Pass
Admitted positive-altitude extraction-channel difference	5e-5 relative	5.973554226944694e-7	Pass
Refined midpoint-Chapman vs continuous atmosphere	0.001 relative	0.0003497406476989963	Pass
Vertical optical-depth control	2e-5 absolute	1.99328181738068e-8	Pass
Fixed-input repeat	Byte-identical	Byte-identical	Pass

Additional diagnostics:

• refined exact-shell versus continuous maximum: 0.0007030175882411937;
• coarse source-grid midpoint-Chapman versus continuous admitted maximum: 0.10138558685013145;
• plane-parallel versus continuous admitted maximum: 9.857026256012775; and
• exact horizon remains diagnostic-only and is not admitted.

The coarse-grid result demonstrates why lower-atmosphere refinement is required. The refined-grid result admits this 290-level construction only as a candidate for the next named-atmosphere and full-spectral probe.

The 0, 0.05, and 0.1 degree cases deliberately have no admission tolerance. At extremely small transmissions, libRadtran's fixed-width text output can amplify rounding when converted back to optical depth. Those cases remain useful diagnostics but cannot weaken or fail the explicitly admitted domain beginning at 0.25 degrees.

Immutable Receipts

Repository specification:

scripts/visibility_reference_lab/phase1_direct_geometry_probe_spec.json
bytes: 7753
SHA-256:
5f2052236632764a67325951a55b8262f21dc51e630149194ff87baf5ff2a316

Builder:

scripts/build_visibility_direct_geometry_probe.py
bytes: 63892
SHA-256:
957f196ed69ab3fa071119f7110f6d4cbbaf4555a45cd394b94ff829e9d3f74e

Independent validator:

scripts/validate_visibility_direct_geometry_probe.py
bytes: 54163
SHA-256:
af0221277c9ac63156c85ec39b7ffad1adc621c3ed477ea30f79cfe75f079878

External artifact manifest:

bytes: 521126
SHA-256:
b69b377bd465b4740ef0dacd802c03d9fb6ee9eaf809a41356d60126dd23cd92

generation fingerprint:
138ee8e4f516aaacd0538f95f188b89aabb68c1ee1e591a0dc13b8d7bdd185b5

bound files: 1305
bound file bytes: 2564019

The compact source-owned receipt is tests/artifacts/visibility_reference_lab/phase1_direct_geometry_checkpoint_2026-07-29.json.

Both earlier Phase 1 checkpoint identities remain byte-for-byte unchanged.

Closed and Open

Closed by this checkpoint:

• the selected libRadtran surface direct-beam implementation trace;
• independent reconstruction of its bottom-layer midpoint Chapman use;
• controlled near-horizon solver/output agreement over the admitted domain;
• controlled continuous-atmosphere error for the 290-level refined candidate;
• deterministic positive-altitude extraction; and
• a fixed-input repeat.

Still open:

• validate the refined grid against the named atmosphere and the complete spectral direct-transmission design;
• freeze the final spectral and atmospheric design axes;
• freeze the adaptive sparse directional-radiance design;
• resolve the deep-twilight solar-only tail;
• generate the admitted spectral products;
• run untouched off-grid holdouts;
• measure storage and interpolation error;
• propagate source, solver, storage, and interpolation error into limiting magnitude and event time; and
• construct and validate the separately versioned visibility data pack.

Phase 2 remains inactive.