The CHTSmax dataset is based on interpolated grids of weather station observations of monthly maximum 2m air temperature anomalies, combined with a static high resolution (0.05) background Tmax climatology describing average 1981-2010 air temperature conditions at each location. For station-based estimates of air Tmax anomalies, Berkeley Earth and Global Telecommunciation System station data were used. For each month, candidate Berkeley-GTS station data locations were derived by identifying stations with at least seven observations over the 14 years between 2003 and 2016. Additional tests were also developed through statistical and visual analysis of the Berkeley-GTS station data, details of which can be found in Funk et al., 2019. Values were selected that removed obviously bad data but left as much station coverage as possible. For the screened stations, monthly Tmax values were translated into anomalies by subtracting the 2003–16 median from each time series. Additional filtering was used to identify and remove potential erroneous extremes. A spherically correct spatial interpolation toolkit (Spherekit) was used to interpolate the monthly station anomalies using an inverse distance weighted (IDW) technique, with an angular correction to reduce the influence of clustered station observations. Spherekit uses direction cosines to calculate correct geospatial Earth distances. This algorithm is similar to the commonly used Spheremap procedure. For details, please see Funk et al. 2019.