How the maps are made

The data: Sentinel-2, cloud-cleaned

What: The basis is Sentinel-2 (Level 2A, i.e. atmospherically corrected surface reflectance) via the Copernicus Data Space Ecosystem. The satellite pair has been flying since 2015 and 2017 respectively; since 2018 it has covered every place in central Europe roughly every five days. Instead of single scenes we use the median of all usable acquisitions per time window; clouds, shadows and snow are removed beforehand via the scene classification (SCL) that ships with the data. How many acquisitions were left per pixel is counted and published.

Why: The median is insensitive to single outliers (haze, residual clouds) and needs no hand-picking of "pretty" scenes — the result is reproducible rather than curated.

Limits: In cloudy windows the number of observations drops; that is why the observation density (min/median/max per cell) is stated in the methods section. NDVI measures green biomass, not causes: felling, mowing, construction and drought stress look the same from a distance.

The grid: metric, 20 metres, honestly bounded

What: The analysis runs in a metric coordinate system — the UTM zone of the area on the WGS 84 datum, in Germany WGS 84 / UTM 32N (EPSG:32632). The analysis grid is 20 metres; every cell exactly 400 m². Sentinel-2 is natively delivered in precisely this system — the grid follows the data, with no reprojection and no resampling losses. (For those who continue in the official German ETRS89: the offset between the two datums is currently below one metre and irrelevant on this grid.)

Why: Only in a metric system are areas and distances directly measurable. (Runs before August 2026 used an approximate geographic grid; wherever old figures are quoted, that is stated — the difference is around one percent.)

Limits: The cell is the smallest mappable unit. An object smaller than a cell — a single tree crown of ~79 m² — fills only a fifth of it and dilutes its signal below the noise. The field book makes no claims below that limit; the minimum size is stated at every map.

The trend: Theil–Sen and Mann–Kendall

What: Change across years is estimated per pixel with the Theil–Sen slope — the median of the slopes of all pairs of years (Sen 1968; Theil 1950) — and tested for significance with the Mann–Kendall test (Mann 1945; Kendall 1975). Both are explained hands-on in Helsel et al., Statistical Methods in Water Resources (USGS 2020), chapter 12 — freely accessible.

Why: An ordinary least-squares line can be tipped noticeably by a single outlier year — a drought summer, say. The median of pairwise slopes is almost untouched by that; it is the standard in the vegetation-trend literature. The series start in 2018: since then both satellites have been flying, the yearly composites are equally dense, and every additional summer gives the test real power — with six years, p < 0.05 demands near-perfect monotony (13 of 15 concordant year pairs), with eight years 18 of 28 suffice. Earlier runs over 2020–2025 are labelled as first calculations and archived.

Limits: Even eight summers are a short, possibly autocorrelated series — a real trend can slip through, and a one-off collapse followed by a permanently low level meets the same slope threshold as a steady decline; the slope alone does not separate event from trend. That is why the evidence threshold (next section) additionally carries the burden of proof, and both are reported: the test and its result, even when it reads "not significant".

The evidence threshold: four cells, and why

What: Only what (1) crosses a justified threshold and (2) consists of at least four connected cells counts as a find. Single cells above the threshold appear at most as pale hint dots — labelled "hints below the evidence threshold" — and never enter any figure.

Why, three times over: Chance: Every threshold sits a finite number of standard deviations above the noise; among tens of thousands of cells, some quiet ones will slip past it. Only the demand for four connected cells pushes the expected chance clusters practically to zero — chance scatters, real change is contiguous. Registration: According to ESA's quality reports, acquisitions from different years typically sit a few metres offset from one another; at hard edges that creates apparent change in border pixels — a four-cell block cannot be pure offset. Dilution: Objects below cell size dilute their signal beneath the noise anyway; the apparent sensitivity of single pixels is an illusion.

Limits: The price is the minimum area (at 20 m: 0.16 hectares). Anything smaller this analysis cannot substantiate — that is stated at every map, and that is what the site visit is for.

Comparisons: core against ring, signs instead of gut feeling

What: Where an area is compared against its surroundings, we use a core–ring design (the area inside, a reference ring of the same landscape outside) and simple, distribution-free tests: the sign test across the years and, where needed, permutation tests.

Why: The ring controls for everything that hits core and surroundings alike — weather, season, sensor. Distribution-free tests need no assumptions that short series cannot support.

Limits: Even a clean comparison only shows that, never why. And a non-significant result is reported exactly like a significant one.

The cross-check: aerial imagery with three dates

What: Finds are checked one by one against the official orthophoto (in Lower Saxony: DOP20, 20 cm). Every aerial image carries three separate dates: survey flight (when it was flown), edition (which product release), retrieval (when we fetched it).

Why: The three dates are three different truths — a survey flown before leaf-out, for instance, cannot show a loss of crowns. Whoever mixes them up checks against the wrong picture.

Limits: Orthophotos are snapshots years apart; between the survey flight and today remains a gap that only the site visit closes.

Colours and legibility

Diverging colour ramps only around a true zero; colour is never the only distinguishing mark (finds additionally carry circles, thresholds are spelled out in the legend); new ramps are checked for colour-vision deficiency. Figures taken from images also appear as a table in the text, and every figure carries a narrative alternative text.

Licences, verbatim

Every map names its sources with the wording that is binding for each — Sentinel data with the English original "Contains modified Copernicus Sentinel data [year]", state aerial imagery for example as "Geobasisdaten: © LGLN (year) — DOP20, CC BY 4.0, excerpt, data modified", map data as "© OpenStreetMap contributors". Only data whose licence permits this use is used at all; sources with a non-commercial clause are ruled out on principle.

Anyone may recheck

Every analysis comes with a map passport in the episode's methods section: the data basis with its three dates, grid and coordinate system, thresholds with reasoning, the method, the exact script call, the data file holding every figure that carries weight, and the observation density. Scripts and data files live versioned in the public repository github.com/retteten/fieldbook-code — the code under the MIT licence, the derived data under CC BY 4.0 with the source notices of each origin. Whoever calculates differently and arrives elsewhere should be able to see where the paths part — that is exactly what Das Feldbuch is for.

Further learning

For anyone who wants to go deeper without buying a textbook: the SOGA courses of FU Berlin teach statistics and geodata analysis freely on the web (in English, with R and Python versions) — from distributions to time-series and spatial analysis. The properties of Sentinel-2 (orbits, bands, resolutions, product levels) are documented by ESA in the SentiWiki; the interfaces our scripts use to fetch the data are described in the Copernicus Data Space Ecosystem documentation.