Methods

How we calculated it

The global publication table contains 2,147,229 land samples: a regular 0.10° latitude–longitude grid supplemented by 4,368 island representative points. Natural Earth land geometry determines sampling. The degree grid has different physical spacing at different latitudes; it is not an equal-area sample or a survey of residents. The Equal Earth map projection supports the visual comparison but does not turn sample counts into population or land-area percentages.

For each point, the model calculates solar events and converts their UTC instants using the civil offset actually applicable on that date. It uses timezone-boundary-builder polygons and pinned IANA rules, both recorded as 2026e, rather than inferring time zones from longitude. The policy maps Asia/Urumqi to official Asia/Shanghai for the main comparison while retaining the original polygon identifier and ambiguity flags.

Conventional sunrise is the upward crossing of a geometric solar-center altitude of −0.833°. This is a standard approximation incorporating the apparent solar radius and typical horizon refraction, not a measurement of the atmosphere on a particular morning. The engine uses NOAA/Meeus geometry with NREL SPA refinements for sensitive high-latitude cases. UTC padding and local-date assignment handle events near midnight; where multiple sunrises occur on one local date, the later event is used and multiplicity is retained.

Elevation, surrounding terrain, buildings, clouds and actual atmospheric refraction are not modeled. The results describe a conventional sea-level observer and unobstructed horizon. Adding elevation alone would not establish when sunlight reaches a valley or a window. Keeping that conventional definition is appropriate for this geographical illustration, provided we do not describe it as observed local visibility or measured light exposure.

The current maps use the 07:00 cutoff. Earlier 08:00 fields remain in the complete database for continuity; they do not set the cutoff used by the current maps.

What the checks establish

The main event check includes missing-event decisions as well as finite event-time comparisons. Its reference is SPA; because some production refinements also use SPA, independence is incomplete in those branches. The separate Skyfield/JPL DE421 polar check provides an additional reference, but its sample contains model-occurring sunrises rather than a fully independent search for every possible event. The Spanish full-year check confirms daily timing, extrema and the original 08:00 counts; it is not a separate global validation of the 07:00 categories.

For the waking scenarios, 736 separate Skyfield/DE421 comparisons found no threshold-classification disagreements in the checked sample. The largest solar-altitude difference was 0.000487°. The existing automated-test record reports 23 passing tests, and export checks cover the map formats and layouts. These are computational checks, not external peer review, field measurements or an absolute error bound at every global point.

Exact values close to 07:00 deserve particular care. Numerical precision to seconds does not imply that real-world sunrise visibility is known to seconds. A small modeling or environmental difference can change a threshold classification near the boundary.