Extended Data Fig. 6: Recovering local temperature-energy consumption relationships using aggregate energy consumption data.

An illustration demonstrating how the effect of local temperature on local per capita energy consumption can be recovered from observations of local temperatures and national per capita energy consumption. a: Let a hypothetical, linear response of daily temperature and energy consumption exist at a local (i.e. grid cell) level, depicted by the diagonal grey line. Let E denote baseline daily energy consumption on a 20 °C day. Average per capita energy consumption is observed on day d in countries i (blue circle) and j (pink circle), respectively consisting of 8 and 5 equally populated grid cells experiencing different temperatures. While the temperature is observed in each grid cell, only the national average per capita energy consumption is observed. b: Height of each bar represents unobserved energy consumption on day d within each grid cell. Pink bars are grid cells in country j and blue bars are grid cells in country i. Energy consumption within each grid cell responds to temperature within that grid cell. Averaging temperature and per capita energy consumption across grid cells within each country produces the country-level observations in Panel a. A regression using these observations recovers the grid cell-level response. Note that this illustration depicts a linear energy-temperature response for illustrative purposes, however a nonlinear temperature-energy consumption response can be recovered as well, if nonlinear transformations of temperature are computed at the grid-cell-level before being aggregated to the national level (‘Econometric estimation of energy–temperature responses’ in Methods, Equation 2).