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Constant-territory time series

Source: vignettes/constant_territory.Rmd
constant_territory.Rmd

build_constant_territory_series() estimates a time series of a quantity over a fixed set of boundaries — the polities active in a chosen ref_year — from data that was reported under the changing historical boundaries of each data year.

The problem

Borders move. A 1900 wheat figure for “Austria-Hungary” is not a figure for present-day Austria, so a constant-present-day-territory series cannot be read off the raw data — it has to be estimated. (WHEP’s existing pre-1962 country extension already produces a constant-modern-territory series a different way: it anchors on each modern country’s later value and walks it back along that country’s LUH cropland trajectory. This function is the complementary spatial route — useful once real data for genuinely historical polities, whose borders differ from any modern country, is brought in.)

The method (dasymetric areal interpolation)

For each data year:

  1. Disaggregate — each source polity’s reported value is spread across a regular equal-area grid covering that polity’s own extent for that year, in proportion to a covariate density (gridded cropland for crop output, population for demographic series, livestock density for animals). With covariate = NULL the weight is cell area (plain areal interpolation).
  2. Re-aggregate — the grid is summed into the ref_year target boundaries; a target’s covered value is the grid mass inside it.
  3. Impute the gap — target territory not covered by any source-with-data that year still carries covariate mass, so it is filled at a donor intensity (donor = "regional": the region-wide value per unit covariate). The covariate fraction that had to be imputed is returned as imputed_share — an honest confidence signal (0 = fully observed, 1 = fully extrapolated).

The estimate is only as good as the covariate; supply the same gridded surface used elsewhere in WHEP spatialization for consistency.

Why a covariate, not just area

Production/population is not spread uniformly over a territory. Weighting by cropland (or population) puts the source’s value where the activity actually was, so when a modern boundary cuts the historical source, each side gets its real share — not its area share. covariate = NULL (area) is the fallback when no density surface is available.

How the gap is handled

Because the imputation rides on a spatially complete covariate (e.g. an LUH reconstruction has no holes), a slice of the target that no historical source reported is still estimated: its own covariate mass × a transferred intensity. There is no silent zero. Watch imputed_share — a few percent is solid; a large fraction means the year/territory is mostly modeled and should be treated as such.

Usage 

series <- build_constant_territory_series(
  data     = reported,          # tibble: year, polity_code, value
  ref_year = 2020,              # target boundaries = polities active in 2020
  covariate = cropland_density, # function(centroids_sf, year) -> density; NULL = area
  resolution = 25000            # grid cell size in metres
)
# series: target_polity_code, year, value, covered, imputed, imputed_share, n_sources

Boundaries come from get_polity_geometries() by default; pass polities to use a subset (and to keep the gridded region compact — a continent-spanning target trips the max_cells guard).

Worked example

Reallocating a 1900 Austria-Hungary total of 1000 to present-day boundaries (ref_year = 2020, area weighting) gives, for a few successors:

present-day state covered imputed_share note
Hungary 136 0.00 wholly inside the empire
Austria 123 0.00 wholly inside
Czechia 115 0.02 wholly inside
Slovakia 73 0.00 wholly inside
Romania 159 0.57 only Transylvania was in A-H
Poland 53 0.89 only Galicia/Silesia fringe
Italy 22 0.95 only South Tyrol / Trieste

sum(covered) ≈ 1000 (mass conserved). Read covered as the faithful territorial reallocation; treat a high imputed_share (Romania, Poland, Italy) as “mostly modeled, not observed.”

A present-day-Austria series assembled from differently-bounded sources — empire-wide in 1850/1900, modern Austria from 1925 — yields the territorial slice in the empire years (96.6 in 1850, 123 in 1900, imputed_share 0) and the reported value once the source already is modern Austria.