What the map shows
Each cell is a node of the hindcast of Reis, Guimarães et al. (Ocean Engineering, 2026): 2,589 in the open sea, on a 4° lattice of the globe, a 1° lattice of the Brazilian margin and the report's 13 nodes. The colour is the design wave: the significant wave height (Hs) of the 100- or 1000-year return level, in the family Anderson–Darling decides among six, on the daily, weekly or monthly maxima of 1993 to 2024. A refused cell is hatched: there no family is decided, or its level does not close into an exact interval, and the card says why. The 679 that the hindcast's own sea ice touches at some step are dotted: shown, not certified.
Every cell at its true area
The map uses the Equal Earth projection (Šavrič, Patterson and Jenny, 2018), which keeps areas: each cell takes a share of the map in proportion to its share of the ocean, and a 4° cell near the pole looks no bigger than it is. Drag to move, use the wheel or two fingers to zoom; “Brazilian margin” frames the 1° lattice.
How to read each number
A decided number is an exact interval, rounded outward to the centimetre: the lower end down, the upper end up. The width another 32 years of the same sea could give (95%, the delta method) is statistical, dash-underlined: computed, not decided. A refusal has no mark: ∅ and the reason.
decided
exact arithmetic backs it
computed
float, or a number someone printed; nothing decided it
refused
no mark — the void is drawn
What each number rests on
The arithmetic is exact, and each number rests on premises checked to different rungs; a conclusion is as checked as its weakest premise. Each cell's card repeats this chain with its own figures.
- assumed
The hindcast GLOBMULTI_ERA5_GLOBCUR_01 (Ifremer WAVEWATCH III), a wave model's output; against the Navy's PNBOIA buoys, at 9 nodes of the Brazilian margin (25,215 pairs, 2009–2018), its bias ran −0.65 to +0.22 m and its RMS 0.34 to 2.18 m (certs/janela-pnboia-check.json): over every sea state. Its extremes, which a design wave reads, were never checked.
- assumed
Independent maxima, from a climate that does not change each block's maxima are taken as independent and from one law, and 32 years of one climate stand for 100 or 1000; daily maxima come in storms (each cell's card says how much).
- verified
The fits each family, by maximum likelihood, is a box the Krawczyk operator proves holds the likelihood's one maximum there, the Hessian proved negative definite: decided. The code reproduces closed forms and 50-digit values (instruments/hseva/battery.js).
- assumed
Each family's best maximum that no better maximum lies elsewhere in the family is the search's claim, as it is any optimiser's.
- assumed
The family chosen on the same sample Anderson–Darling chooses among the six on the same maxima they were fitted to; no held-out sample decides between families.
The arithmetic is exact; the weakest premise is assumed: the hindcast, the independence, the search and the choice of family.
The globe
On the globe are the paper's regional claims, decided as boxes, the other views (which family, the criteria, the seventh family, the uncertainty) and, in each cell, the certificate: it can be certified again in your browser, with the record's own code, from the data pinned by sha256.
Sources
Waves: Ifremer WAVEWATCH III GLOBMULTI_ERA5_GLOBCUR_01 (doi), CC BY-SA 4.0. Land: Natural Earth, public domain. The record: certs/hseva-atlas.json. Code (MIT): playground/return-level-atlas.