Supporting evidence for the EGU 2026 talk “LifeWatch ERIC as Catalyst and Connector” (EGU26-11348, ESSI2.6, 3–8 May 2026, Vienna).
The argument, in four steps¶
Global biodiversity analyses must combine GBIF occurrences, ERA5 climate, Copernicus land cover, and Destination Earth model output onto a single common grid before any statistical or machine-learned model can use them. The grid choice is not a visualisation question — it is a scientific-correctness question, especially for climate-driven range-shift attribution, restoration outcome monitoring, and Habitats Directive zonal reporting, where small systematic biases compound across millions of cells × decades into real attribution errors.
The argument the eight notebooks make:
Equal-area is necessary. Regular latitude-longitude grids systematically over-count biodiversity at low latitudes and under-count it at high latitudes, by up to a factor of 23× at 5° resolution — purely because lat-lon cells shrink poleward. Mathematical property of the cells, not a sampling effect (notebooks 01–02).
Any of six equal-area choices passes the count test. Notebook 07 compares HEALPix, H3, rHEALPix, ISEA3H, Mollweide, and the EEA reference grid (LAEA Europe / EPSG:3035) on the same 20,100-record GBIF Quercus suber dataset. All six agree on the apparent density pattern. For biodiversity counts in isolation, the choice between them is not a count-correctness question.
DGGS family preserves cell shape across latitudes; projection family does not. Notebooks 03–04 show that Behrmann (cylindrical equal-area) at 65°N produces 3×3 ML kernels with aspect ratio 5.0 — vertical strips that span multiple biomes north-south. Mollweide and EEA distort more gently but distort. The DGGS family — HEALPix, H3, rHEALPix, ISEA3H — all preserve compact (~aspect-1) cells everywhere. For ML pipelines stacking features into a single cube, this is what makes a CNN’s receptive field mean the same geographic operator everywhere on Earth.
HEALPix is the right common DGGS for the integration of biodiversity with Copernicus EO and Destination Earth climate models (notebooks 06, 08). The case is not that HEALPix is uniquely best for biodiversity counts — step 2 establishes that any of the six equal-area choices works. The case is that biodiversity science is increasingly integrated with high-resolution EO and climate models, and on that integrated surface HEALPix has specific advantages the alternatives do not:
Geometric deep learning on the sphere (DeepSphere, spherical CNNs, equivariant networks) is built on HEALPix; H3 / ISEA3H / rHEALPix have nothing comparable.
Scattering networks for global EO and biodiversity feature extraction —
foscat(the FIESTA stack) operates on HEALPix natively.Sphere-harmonic transforms (
healpy.map2alm/alm2map) are native to HEALPix; absent on the other DGGS.NESTED bit-shift hierarchical refinement (
parent = pix >> 2,children = pix << 2 | k) makes zoom-in / zoom-out O(1) per cell — critical for tile-based Copernicus Zarr × biodiversity ML pipelines.Iso-latitude pixelization makes zonal climate-zone analyses essentially free.
A credible ellipsoidally-correct path — via rHEALPix (already pip-installable) or “Ellipsoidal HEALPix” via the authalic-sphere mapping (the ESA GRID4EARTH approach) — addresses the systematic ~0.7% area bias at boreal latitudes that HEALPix-on-sphere otherwise compounds across decades of integrated Copernicus × biodiversity data.
The honest conclusion: for biodiversity counts at coarse resolution in isolation, any equal-area DGGS works and the choice is largely about ecosystem (EEA grid is the European regulatory standard; H3 has GIS-industry momentum; ISEA3H has Eco-ISEA3H paper alignment). For biodiversity integrated with Copernicus EO and climate models on a single common DGGS — the GRID4EARTH future — HEALPix is the right substrate, not because it is “best for biodiversity” but because the climate-model and spherical-ML sides already live on it, and integration cost dominates.
What this Jupyter Book contains¶
Eight notebooks, each one a single, focused piece of evidence:
Synthetic proof — 1,000,000 uniform random points on the sphere binned on a 5° lat-lon grid versus HEALPix. The lat-lon panel develops a fake equator-pole gradient; HEALPix is uniform. The artefact is mathematical, not statistical.
Real biodiversity data — 20,100 Quercus suber (cork oak) occurrences from GBIF, binned on a 1° lat-lon grid and on HEALPix nside=64. Within the species’ Mediterranean range, lat-lon cell areas vary by ~23%; the same true density therefore appears as 23% more “occurrences per cell” in southern cells than northern, with no ecological content.
Cell-shape anisotropy — for 1° lat-lon, 5° Behrmann (cylindrical equal-area), and HEALPix nside=16, render a representative cell at 0°, 40°N, 70°N and report aspect ratio. HEALPix stays close to 1; lat-lon and Behrmann diverge.
What an ML kernel sees — at 65°N, 15°E (boreal Scandinavia), draw the 3×3 kernel of an ML model on each grid. Behrmann’s kernel covers a 159 × 796 km vertical strip (aspect 5.0); HEALPix’s covers a compact 502 × 562 km neighbourhood (aspect 1.3).
Three-grid comparison — lat-lon vs Behrmann vs HEALPix on the same 1 M uniform points. Behrmann and HEALPix are both uniform; the count bias is a solved problem under any equal-area scheme.
Hierarchical indexing — a single HEALPix NESTED parent cell (nside=8), exactly tiled by 16 children (nside=32) and 256 descendants (nside=128), drawn over Scandinavia. Refinement is a deterministic bit-shift on the cell index — no projection, no interpolation, no resampling.
Comprehensive multi-grid comparison — same Quercus suber GBIF data on eight grids: lat-lon (cautionary), HEALPix nside=64 (sphere), HEALPix-geo nside=64 (WGS84 via authalic-sphere mapping — the GRID4EARTH path), H3 res 3, rHEALPix res 4 (WGS84 cube-projected), Mollweide ~100 km, the EEA reference grid (LAEA Europe / EPSG:3035 — the INSPIRE / Habitats Directive standard), and ISEA3H res 8 (the system the Eco-ISEA3H paper advocates). All seven equal-area choices agree on the apparent density pattern; lat-lon is the only one that distorts. Establishes that equal-area is the load-bearing property — what notebooks 03–06 and 08 then add is the case for HEALPix specifically.
HEALPix-specific advantages and refinements — three HEALPix-family properties that make it the right common DGGS for climate-driven biodiversity science:
Section A — Sphere vs WGS84 ellipsoid. HEALPix is on the sphere; biodiversity occurrences and Copernicus EO products are on WGS84. The mismatch is ~0.7% systematic area error at boreal latitudes — small per-cell, systematic and compounding across millions of 1 km cells × decades of climate-attribution data. Two solutions: rHEALPix (already used in notebook 07) and “Ellipsoidal HEALPix” via authalic-sphere mapping (the ESA GRID4EARTH approach).
Section B — NESTED bit-shift refinement. Parent and children of any HEALPix cell are pure integer arithmetic (
parent = pix >> 2,children = pix << 2 | k). Zoom in / zoom out is O(1) per cell, no projection, no resampling — critical for Copernicus Zarr × biodiversity tile pipelines.Section C — Iso-latitude pixelization. Every HEALPix cell sits on a fixed-colatitude ring; zonal climate-zone analyses are essentially free. H3 hex tessellation breaks this property.
How to use this material¶
The notebooks are designed to be read in order, but each one is self-contained: you can drop into any single notebook and it will run on its own. Notebook 02 downloads ~440 KB of GBIF data on first run (15–20 minutes due to GBIF API throttling); subsequent runs read the cache. All other notebooks are pure synthetic.
To run everything end-to-end, see the README — snakemake --cores 1 all reproduces every figure.
Connection to ESA GRID4EARTH¶
This Jupyter Book is the biodiversity-side version of the case the ESA GRID4EARTH initiative makes for Ellipsoidal HEALPix as a Common DGGS (grid4earth.eu) — bridging spherical climate models (Destination Earth) and ellipsoidal Earth-observation data (Copernicus) on a single ellipsoidally-correct, hierarchical, scalable DGGS. Notebook 08 Section A makes the biodiversity-precision argument for that bridge.
Citation¶
If this material is useful in your own work please cite the repository (DOI on first release) and the foundational references in CITATION.cff — Górski et al. 2005 (HEALPix), Sahr et al. 2003 (DGGS), Hauffe et al. 2023 (DGGS for biodiversity), Kmoch et al. 2022 (DGGS area distortions).