CALC-051

UK geomagnetic latitude from the IGRF-14 dip angle, against the NOAA storm scale

Feeds CLM-0155. Answers QST-001.

Why it was needed. The riometer climatologies in the corpus (CLM-0154, about 66N magnetic) and the severe-event measurement it holds (Robinson et al. 2004, EISCAT, about 65-67N magnetic) both come from well poleward of the UK. Whether they are relevant to a UK rectenna site depends on where the UK sits in magnetic, not geographic, latitude - and that had never been stated.

Inputs.

Working, transcribed.

lambda_m = arctan( tan(70.08 deg) / 2 ) = 54.1 deg N

Against the NOAA G-scale boundaries:
  G3 boundary  50 N   ->  54.1 - 50 = 4.1 deg
  G2 boundary  55 N   ->  54.1 - 55 = 0.9 deg

Result: the UK's geomagnetic latitude is approximately 54.1 degrees North, about 4 degrees inside the G3 (Kp=7) aurora-visibility zone and within about 1 degree of the G2 (Kp=6) boundary.

Conclusion. The UK sits borderline on the G2 boundary, which is the key geographic input for asking whether the high-latitude absorption datasets in the corpus transfer to a UK site. Both of them sit about 11 to 13 degrees poleward of it, which is a large gap in a quantity that varies steeply with latitude.

Where this fails. NOAA's aurora-visibility boundary describes lower-energy (order 1-10 keV) optical-aurora-producing precipitation, not the higher-energy (>15 keV) precipitation that causes D-region radio absorption. Using it as a proxy for the absorption-zone boundary is a defensible approximation, not a measurement. No riometer or absorption dataset at 50-55 degrees magnetic latitude was found to confirm this directly.

SEPARATE FINDING - A DIRECTION WORD, NOT AN ARITHMETIC ERROR. NOT FIXED HERE. The claim reads "only about 1 degree poleward of the G2 (Kp=6) boundary (55N)". 54.1 is lower than 55, so 54.1N is about 0.9 degrees equatorward of the 55N boundary, not poleward. The magnitude is right, the conclusion ("borderline") is right, and the plain field is right - it says "right on the edge of where a moderate (G2) storm's aurora would be seen", which does not commit to a side. Only the direction word in the claim field is wrong. This is the dominant defect class for this register: <!-- PAGE-COPY: shared terminology, the defect-class name the method pages also use --> a correct number labelled as something it is not <!-- /PAGE-COPY --> , and it is the kind that survives arithmetic checking because there is no arithmetic to check. The claim already carries VER-930 PARTIAL 2026-09-05; whether this is what the verifier caught is not recorded, and should be established before the wording is touched. Direction words in this record are written the way the arithmetic gives them.

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