How daily satellite pixels become the statistically-ready cell sums everything on this site is computed from.
Every product is summarized onto the same discrete global grid: S2 cells at level 5. The S2 library projects the sphere onto the six faces of a cube and subdivides each face recursively; at level 5 there are 6 × 45 = 6,144 cells worldwide, each about 83,000 km2 (roughly 290 km across). Of those, 5,451 touch ocean in GHRSST MUR and 4,867 in OISST (the products differ at coasts and ice). The cells nest exactly inside their parents, every cell has a compact sortable token for an id, and a region of any shape is just a set of cells — which is why the Explorer treats regionalization as selection, and why the cube-net view there shows the grid's native geometry.
The daily fields are never warped, resampled, or interpolated. Each source pixel is assigned, whole, to the one cell that contains its centre — a dense positional mapping from pixel index to cell id, computed once per grid and stored beside the sums (a grid stamp guards against ever applying a mapping to the wrong grid). A level-5 cell contains on the order of 70,000–100,000 MUR pixels (0.01°) or about 100–170 OISST pixels (0.25°); both sources land in the same cells, at their own native resolution.
The same principle carries to polygons: if your workflow needs to rasterize regions against a native grid, see controlledburn, which computes exact polygon coverage as sparse cell runs without materializing a mask, and its natural partner in Rust, rwarp, for the cases where data genuinely must move between grids.
For each cell, each day, the accumulation keeps four numbers over the contributing ocean pixels: the pixel count n, the summed area weight sumw (each pixel weighted by its spherical area, so high-latitude pixels count for what they cover, not for how many they are), and the weighted sums sumwx and sumwx2 of the value and its square. One Parquet file per date; a failed date writes nothing and is simply re-run.
The algebra that makes the store "statistically ready":
mean = sumwx / sumw
variance = sumwx2 / sumw - mean^2
and the sums are mergeable: the statistics of any union of cells, days, or both come from adding the rows first and taking the ratio once. No averaging of averages, no reweighting step, no loss of exactness. A regional daily series, a monthly cell mean, a 23-year trend input — all are the same operation at different groupings.
This is why the Explorer can compute the series for any hand-picked set of cells instantly in your browser: it holds monthly sumw-weighted means per cell and combines them by the identity above. And it is why "add a region" is a one-line change — a region is a cell list, not a new computation.
The design has deep prior art. NASA ocean colour has stored exactly these accumulations — weighted sums and sums of squares per equal-area bin — since SeaWiFS in 1997, in the L3bin format's integerized sinusoidal rows (a proto-DGGS: each latitude row holds just as many bins as it needs). trend.sst swaps the ragged rows for a hierarchical cell index and HDF for Parquet on object storage, but the statistical contract is the same one that scheme proved decades ago. NASA's own explainer of the scheme was lost in a site migration; a restored copy lives with the hypertidy/L3bin package, which also implements the scheme in R.
| tier | what | where | size |
|---|---|---|---|
| pixels | daily COGs / netCDF, full resolution | source.coop, NOAA | TBs |
| sums | per-date Parquet of (cell, n, sumw, sumwx, sumwx2) | projects.pawsey.org.au/aad-derived/trend-sst | GBs |
| site data | baked series, per-cell metrics, monthly means | docs/data/ on this site | MBs |
Each tier is derived from the one above and can be rebuilt from it; nothing on this site is hand-maintained. Anything you see here can be reproduced against the sums directly — select cells in the Explorer and use Get the data for ready R / SQL / Python snippets, including the bulk-sync route for intensive work. The Mechanics page watches the gap between the tiers (what the bucket holds vs what this site was baked from), and the trailing ~10 days of GHRSST / ~14 of OISST are provisional pending upstream finalization.
Summaries at cell level are exact in a way masked or warped pipelines are not: every source pixel is counted once, with its own area, in its own cell, and the stored sums determine the mean and variance of any cell union to floating-point precision. What is approximated is the region boundary itself — a "Pacific" built from 290 km cells has a 290 km-grained edge. That trade is deliberate: boundary-exact masks are a per-region, per-grid recomputation; cell sums are computed once and answer every region after the fact. For boundary-sensitive work the pixel tier remains upstream, untouched.
Campbell, J.W., Blaisdell, J.M. and Darzi, M. (1995). Level-3 SeaWiFS Data Products: Spatial and Temporal Binning Algorithms. NASA Technical Memorandum 104566, Vol. 32 (SeaWiFS Prelaunch Technical Report Series), NASA Goddard Space Flight Center. PDF — the operational prior art: weighted sums and sums of squares accumulated per equal-area bin, as run for every NASA ocean colour mission since SeaWiFS.
Chan, T.F., Golub, G.H. and LeVeque, R.J. (1983). Algorithms for computing the sample variance: analysis and recommendations. The American Statistician 37(3), 242–247 — the numerical analysis of exactly the merge used here: combining sums and sums of squares across partitions of the data.
Fisher, R.A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society A 222, 309–368 — where "sufficient statistic" gets its name and its meaning: the stored sums carry everything the data had to say about the quantities reported.
This work uses resources of the Pawsey Supercomputing Research Centre, with funding from the Australian Government and the Government of Western Australia: the backfills run on Pawsey systems and the authoritative sums are served from Pawsey object storage.