## Materials and Methods
### Data and Study Areas
#### 2.1.2 Historical Maps  
Herein, we combine the remote-sensing-derived built-up areas from the GHSL (1975-2014) with urban extents extracted from a range of historical maps dated to the period between 1890 and 1960. These maps are assumed to be the earliest available detailed topographic maps created by systematic land surveying and topographic map production, and thus will allow us to maximize the observation period for each study area. As the GHSL is a globally available product, we chose six study areas in four different countries where digital historical maps were available. Two study areas are located in the United States (i.e., Boston and Atlanta metropolitan areas) and cover different map scales, time periods, and map designs (i.e., 3-color print in Boston (approx. 1900, scale 1:62,500) and 5-color print in Atlanta (approx. 1960, scale 1:24,000)). These historical maps were acquired from the United States Geological Survey (USGS) historical topographic map collection (HTMC), which is a digital archive of >190,000 scanned and georeferenced topographic maps created between 1884 and 2006 [19]. The HTMC is available via the Amazon Web Services (AWS) S3 cloud data storage infrastructure [81]. The USGS-HTMC maps used herein consist of a composite of individual map sheets (see Section 2.2.1) (Figure 1a-d). We also chose two study areas in the United Kingdom (i.e., Greater Birmingham and London, see Figure 2e-g), for which the National Library of Scotland provides georeferenced, seamless composites of historical Ordnance Survey topographic maps [82; 83]. These maps are typically 3-color maps and exhibit different map designs than the USGS HTMC maps. For example, they depict urban settlements as blocks (Figure 1f), whereas USGS-HTMC maps use individual building outlines (Figure 1d), or red-colored urban areas in maps created after 1950 (Figure 1c). Like in the US, the Ordnance Survey maps were produced at different scales: the Birmingham maps (approx. 1900) are of scale 1:10,560 (\"six-inch to the mile\"), whereas the London map (1896) is at a scale of 1:63,360 (\"one-inch to the mile\"). We obtained the Birmingham map through an automated download and mosaicking procedure (see Section \"Data Availability Statement\"), and the London map through manual download, mosaicking, and georeferencing. Figure 1: Input data for the study areas in the US and in the UK: (**a**) GHSL-based built-up area in 2014 and 1975 in Atlanta metro area (US), and (**b**) in the Boston metro area (US); (**c**) 1:24,000 historical map composite for the Atlanta metro area from approximately 1960, and (**d**) historical map composite for the Boston metro area at scale 1:62,500 from approximately 1900; (**e**) GHSL-based built-up area in 2014 in the greater Birmingham area (UK), (**f**) historical Ordnance Survey topographic map composite from approximately 1900 (approximate scale: 1:10,000), with an enlargement of a part of the Birmingham downtown area, and (**g**) historical Ordnance Survey topographic map composite from 1896 for the London area (UK; approximate scale: 1:63,000), overlaid on the GHSL 2014 built-up areas (grey). Finally, we use a historical topographic map covering the region southeast of the city of Sao Paulo (Brazil), at scale 1:100,000 from 1906 (Figure 2a,b), and a map covering the Lahore-Amritsar region (Pakistan/India) at scale 1:254,440 from 1943 (Figure 2c,d). Both the Sao Paulo and Lahore-Amritsar maps are individual map sheets rather than composites, and needed to be georeferenced manually, using a contemporary OpenStreetMap basemap in ESRI ArcMap 10.8. We chose these study areas based on the availability of historical maps, and in order to cover a wide range of different map ages, map styles, map scales, and historical (colonial) settings, covering both traditionally \"data-rich\" (UK, US) and \"data-poor\" environments (Brazil, India-Pakistan), by browsing the historical map search engine available at [25].