24 · Spatial II: rasters

Thursday, Nov 19, 2026

Materials for this session are not published yet. They appear here before class.

Objectives

By the end of this session you can:

  • Load, crop and align rasters with terra, and combine them with raster algebra.
  • Compute zonal statistics over polygons with exactextractr.
  • Choose between area and population weights, and predict which way the choice moves a county average.
  • Turn daily gridded weather into a county-by-day table.
  • Convert u/v wind components into speed and direction, and flag the areas downwind of a fire.

What we cover

  • Published work built on rasters, grids of equal-size cells covering the ground, each holding one value such as temperature. Deschênes & Greenstone (AER, 2007) averaged 4-kilometre temperature and rainfall cells over each county’s farmland and related year-to-year swings in weather to farm profits, with degree days taken from weather stations. Dell, Jones & Olken (AEJ: Macro, 2012) averaged a global half-degree grid to countries, weighting cells by population or by land area, to estimate how hot years affect growth. Deryugina et al. (AER, 2019) used shifts in daily county wind direction, computed from gridded wind components, to estimate how fine particles affect elderly mortality and medical costs.
  • A raster is a matrix with coordinates attached. Resolution is the ground width of one cell; extent is the rectangle the grid covers. Raster algebra, arithmetic cell by cell across grids, needs matching resolution, extent, origin and map coordinate system, so first resample one grid onto the other’s cells or project it.
  • A zonal statistic summarises the cells inside each polygon, such as a county’s mean temperature; exactextractr weights each cell by its coverage fraction, the share inside the polygon. Area weights count a cell by its share of the county’s land, population weights by the people in it. The two differ most in large, thinly populated places.
  • Application: daily gridded weather to one row per county and day. Gridded weather products fill a grid with estimates from stations and satellites; a reanalysis rebuilds past weather by running old observations through a forecasting model. Hand-compute one county’s average and compare it with the table.
  • Application: the areas downwind of a fire, where the wind carries its smoke. Wind arrives as east-west (u) and north-south (v) components. Weather data reports where it comes from, clockwise from north; atan2(v, u) gives where it blows toward, counterclockwise from east. Convert first, then compare the flag with smoke imagery or monitor data.
  • The fast method: store the cell-to-county weights once as a sparse matrix (mostly zeros, so only the nonzero entries are kept), and each day’s county averages take one matrix multiply. Time it against the canned function with system.time() and verify the two agree.
  • Gridded products disagree. Several cover the same place with different answers, so name yours and the reason in the methods section.