Update 90º phase to match IHO convention

[bkeepers]

Extracting this commit from #238 to review and discuss separately.

The 7th doodson number was negated in original neaps implementation to be consistent with the Schureman/NOAA equations, and that was preserved when adopting the IHO constituent definitions in #208. The problem with this change is that it actually makes the NOAA benchmarks worse. 😭

To quote Claude from Why the IHO List Has Duplicate Constituent Definitions:

The critical rule: whichever convention was used in analysis must be used in prediction. Consistency matters more than which specific formulation you pick.

I'm finally starting to understand why xtide embeds pre-computed equilibrium args and node factors in the TCD.

[bkeepers]

Claude Prompt: This branch changes how the D7 number is used in the tide prediction algorithm. Perform a deep review of this change. Review for correctness. Compare the noaa benchmarks before and after this change, and analize the impact.

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What the commit changes

Two coupled modifications to the tide prediction algorithm:

1. D₇ sign convention (definition.ts:105): Changed from 5 - xdo[6] (negated) to xdo[6] - 5 (uniform offset), treating D₇ the same as D₂–D₆.

2. Julian Day offset for T (astronomy/index.ts:172): Added +0.5 to JD before extracting the fractional day, shifting T from noon-epoch (Schureman convention) to midnight-epoch (claimed IHO convention).

Mathematical analysis of correctness

The two changes interact. For any constituent with species number d₁ and seventh XDO digit D₇:

• The T shift contributes d₁ × 180° to V₀ (since 0.5 day = 180°)
• The D₇ sign flip contributes 2(D₇ − 5) × 90° to V₀

The net change is (d₁ + D₇ − 5) × 180°. This is 0° mod 360° only when (d₁ + D₇ − 5) is even. I checked all 307 XDO-based constituents in the database:

• 286 constituents: net change = 0° (the two changes cancel perfectly)
• 21 constituents: net change = 180° (the two changes do NOT cancel)

The 21 affected constituents include: S1, M3, S3, MS1, MP1, M1C, SK1, SP1, MO1, MQ1, MPS2, MSP2, 2MS3, MS3, 3MS5, 2MS5, MSK5, M7, MA9, NK1, Sta. Most are minor, but M3 (third harmonic of M2) can be significant at some stations.

Which convention is correct?

This is the crux. Two internally-consistent conventions exist:

	Old code (main)	New code (iho-phase)
T epoch	Noon (Schureman)	Midnight (IHO)
D₇	5 - xdo[6] (negated)	xdo[6] - 5 (uniform)
For 286/307 constituents	Same result	Same result
For 21/307 constituents	Different by 180°	Different by 180°

The argument for the new code is that the IHO XDO system should uniformly apply offset-by-5 to all of D₂–D₇, and T should be from lower transit (midnight). The argument for the old code is that it produces better predictions against NOAA data.

Benchmark impact (3,368 NOAA stations, 3-day window)

Metric	main	iho-phase	Change
Height MAE p50	0.0069 m	0.0120 m	+74% worse
Height MAE p90	0.0168 m	0.0261 m	+55% worse
Height MAE p95	0.0217 m	0.0287 m	+32% worse
Timing p95 med|dt|	6.29 min	8.62 min	+37% worse
Height bias (mean)	0.00124 m	0.00029 m	Better bias
Timing bias (mean)	-0.856 min	-0.497 min	Better bias
Missed events	286	305	+7%
Extra events	445	491	+10%

Per-station breakdown: 2,109 stations degraded, 453 improved, 805 unchanged. 590 stations had MAE increase >1 cm, vs only 2 improved >1 cm.

Interpretation

The iho-phase branch shows better bias (closer to zero mean error in both height and timing) but significantly worse MAE (more scatter). This pattern is consistent with a systematic 180° V₀ error in the 21 affected constituents — it shifts their contribution in a way that happens to reduce systematic bias while introducing random-looking errors.

The old code's convention — even though it appears inconsistent (negating D₇ while not negating D₂–D₆) — aligns more closely with how NOAA computes its published harmonic constants and predictions. NOAA uses Schureman-convention harmonics where T is measured from noon. The published phase values (κ) in the harmonic constants are referenced to this convention. Changing the V₀ computation convention without also adjusting the published phase values creates a systematic error.

Key concern: the tolerance widening

The test at packages/neaps/test/index.test.ts:222 widened the NOAA matching tolerance from 5 minutes to 8 minutes. Combined with the benchmark results showing p95 timing going from 6.3 to 8.6 minutes, this is masking a real accuracy regression.

Recommendation

The change should not be merged as-is. While the commit's reasoning about IHO convention consistency is plausible, the empirical evidence is clear: it makes predictions measurably worse against NOAA ground truth across 3,368 stations. The old "inconsistent" convention was actually correct for use with NOAA-published harmonic constants, because those constants were fitted using the Schureman convention (T from noon, negated D₇).

If you want to adopt the IHO convention in the future, the harmonic phase values (κ) from station data would need to be adjusted by 180° for the 21 affected constituents to compensate — otherwise you're mixing conventions.