High-quality, consistent data measured at the same place over climate-scale time periods are extremely difficult to obtain. For this reason, we use reanalysis data in order to create the data set on heat index.

Reanalysis data are not an equivalent to observation data and should be used carefully . Nonetheless, for our purpose, reanalysis data seem to be the most appropriate choice. A priority is to produce spatially and temporally continuous data of a consistent quality for the entire globe over a long period of time. In addition, as many high-quality observations should be incorporated into the data as possible, without introducing anomalous signals into the data, for example through changes in observation techniques and shifts in observation locations.

The ERA-Interim reanalysis by ECMWF is well suited for this task. It uses the same data assimilation system and dynamic modeling core over a long period of time – from 1979 extended up until the present. The model used to produce the reanalysis, the ECMWF's Integrated Forecast System (IFS), uses three fully coupled components for atmosphere, land surface and ocean waves. This improves accuracy especially for areas surrounded mostly by ocean. Because the model was used to produce a reanalysis, which did not have to be published in a time critical fashion, observations from all over the globe could be assimilated, even if they were only available after a normal forecast model's cutoff time. These observations can be quality-controlled before being assimilated into the model. Using a model rather than, for example, a simpler interpolation approach makes it possible for the model to propagate information obtained through observations through variable domains, space and time . All of these criteria made ERA-Interim an intuitive choice as a basis for our study .

The ERA-Interim reanalysis used four assimilation cycles per day, at 00:00, 06:00, 12:00 and 18:00 UTC. The original data were produced on a reduced Gaussian grid with approximately uniform spacing for surface fields of 79 km .

We use data from the entire available time period of 1979–2013. The data were downloaded after interpolation from the Gaussian onto a regular 0.75∘ × 0.75∘ latitude–longitude grid to ease processing in various GISs. Two variables were downloaded: air temperature and dew point temperature, both at 2 m height above ground.

Heat index has been computed using a variety of algorithms in different studies. We chose the currently operational method used by the (), which was developed by () based on work by (), because it is used widely in the operational production of weather warnings in real-life situations and demonstrates the best agreement among heat index algorithms with the original equations . All calculation was done using GRASS GIS .

The chosen algorithm uses relative humidity and temperature in ∘F at 2 m above ground as input. While temperature is given in the ERA-Interim reanalysis data, relative humidity had to be calculated. Of the many possible ways to compute relative humidity from dew point temperature see, for example,, we decided to follow the methodology of the National Weather Service for the sake of consistency with the method of computing heat index. It is computed as follows: RH=112-0.1T+Td112+0.9T8, with RH as relative humidity, T as temperature in ∘C and Td as dew point temperature in ∘C.

Heat index was computed using an algorithm beginning with a simple approximation: HI=T+61.0+((T-68.0)⋅1.2)+(RH⋅0.094)2, where HI is heat index in ∘F, T the temperature in ∘F and RH the relative humidity.

If HI is < 80 ∘F, this approximation is kept as the final result. Otherwise, it must be computed with a more precise regression: HI=-42.379+2.04901523⋅T+10.14333127⋅RH-0.22475541⋅T⋅RH-0.00683783⋅T2-0.05481717⋅RH2+0.00122874⋅T2⋅RH+0.00085282⋅T⋅RH2-0.00000199⋅T2⋅RH2+adjustment, with the adjustment conditionally given by adjustment=13-RH4⋅17-|T-95|17if RH<0.13 and 80<T<112RH-8510⋅87-T5if RH>0.85 and 80<T<870else.

It should be noted that the heat index, which was created for the purpose of measuring physiological stress due to high heat loads, is not adapted for measuring stress due to coldness. Also, above a certain level the heat index is oversaturated, so that no additional information can be gained from it. For this reason, we rounded extreme heat index values into the range of 40–140 ∘F in our visualizations. This corresponds with the lower bounds of the heat index equation and the rough upper bounds of danger levels derived from heat index . The published raw data, however, are not rounded, so that users can decide whether or not they wish to reduce its value range .

The primary reason that heat index is so relevant in the context of climate change is its direct and indirect effects on human health and the anthropogenic systems connected to it. Thus, we expect that our data on the heat index can and will be used in many further studies, in which they will be connected to other data.

The heat index is calculated for each grid point and for each point in time for which the ERA-Interim reanalysis is available. However, using the calculated heat index in further studies usually implies that data on a daily or even monthly or yearly basis are necessary. Therefore, we aggregated the heat index to daily levels. For each day, the four assimilations were combined in order to produce gridded daily minima, means and maxima. We consider this a good approximation of the nighttime heat index, which represents the daily minimum in most cases; the actual local mean heat index over the course of the day; and the daily midday heat index, which is the maximum in most cases. In addition to producing these daily aggregates, the daily metrics were aggregated to monthly and yearly temporal levels.

In addition to the temporal aggregate, the combination with other data will also make a spatial aggregation necessary in many studies. Other data are often given on a regional or national level. Therefore, we also examine the heat index on the level of countries. For studying the effect on humans and human activities, the heat index in populated areas is especially relevant, as dangerous heat exposure in areas where no people are affected is at most tangentially connected to human well-being.

The Global Rural-Urban Mapping Project (GRUMP) provides high-quality gridded population data. The data set consists of estimates of human population for the years 1990, 1995 and 2000 on a 30 arc-second grid (meaning a horizontal resolution of approximately 1 km) for the entire globe. GRUMP is based on work originally done for the Gridded Population of the World (GPW) data set , which was produced by resampling census and survey data for administrative units onto a regular grid. The population was temporally interpolated between sampling points to the above-mentioned snapshot years. GRUMP refined the original data by identifying urban areas with the help of administrative data and nighttime satellite data. Population was then redistributed inside administrative areas to the respective urban and rural areas in order to match the proportion of urban–rural population described by data from the United Nations .

Because of the large number of changes in administrative boundaries and population distribution in the years following the dissolution of the Soviet Union in 1991, the authors of GRUMP were often forced to combine heterogeneous data sources into their results . Although this was done with a high degree of care and in-depth knowledge of each individual case, the uncertainties that this produced prompted us to consider the estimates from 1990 to be the best compromise between quality, consistency and the required accuracy for our analyses. Thus, we only use the GRUMP data for 1990 to aggregate our data to the national level.

Furthermore, for the sake of consistency, we aggregated the population data into current political boundaries , rather than adjusting the data to accommodate the modification, addition or dissolution of national borders over time. Therefore, all statements about changes in the climate of given countries in this study should be interpreted as referring to the geographic areas currently officially occupied by the country in question, rather than the possibly dynamic geographic area occupied by the country over the study period.

The following steps were used to aggregate our data to the country level. First, the heat index data for the areas covered by each country were rasterized onto the same coordinate system as the GRUMP data. This made it possible to discretely sum the population inside each country according to the GRUMP estimates. Per-grid-point population weights were produced by calculating the proportion of population within that country that contained the grid point in question, as follows: pweight=ptotalpcount, where pweight is the cell's population weight inside the country, ptotal the country's total population and pcount the population count for the grid point.

The per-country weighted mean heat index was then computed as follows: HIweight=∑pweight⋅HI.

Weighted means were produced for each country with available data and each temporal aggregation level, as outlined in Sect. .

Figure  shows the heat index metrics for the entire globe on a typical day in summer in the Northern Hemisphere. Dangerous heat index levels can be seen both in the daytime maximum, as well as during the night in hot, moist regions near the Equator. The diurnal cycle is especially high for hot and moist regions, high for dry areas in which the temperature fluctuates highly in the course of the diurnal cycle, and low in drier areas with relatively small diurnal temperature cycles.

The change between both reference periods is shown in Fig. . The maximum heat index shows large changes in both directions for single grid points. This is due to the fact that the maximum heat index for each entire reference period stems from single, significant events that are highly specific in both time and space. This causes spatial shifts in the occurrence of extreme heat index events to produce large deviances between reference periods, similar to the double-penalty problem encountered when computing skill scores for high-resolution forecast models . Mean and minimum heat indices increase almost across the globe between both reference periods, with the most notable differences in minimum heat index over continents in the Northern Hemisphere.

An evaluation of the change in monthly mean heat index across the globe for both reference periods, as shown in Fig. , offers a glimpse into the temporal distribution of heat index changes in the course of the year. The monthly means of heat index clearly increase across the globe, most visibly at higher latitudes.

One of the most important applications of our data is the evaluation of danger due to high heat loads. We classified danger due to high heat index according to the criteria outlined in Table .

For each reference period and each of the classification criteria shown above we calculate the probability that the peak heat index of each day exceeds the threshold for extreme danger in each month. Then, we compare the exceedance likelihood between the two reference periods. The results, shown in Fig. , demonstrate that the likelihood of heat index values reaching levels that indicate “extreme danger” has increased worldwide in every month. South America during southern summer and the Gulf of Mexico in northern summer had especially large increases in likelihood of extreme danger. West Africa also had increased likelihood of dangerous heat index levels the year round, as did northern Eurasia for most months. Most parts of Asia, especially northern Asia, showed increases in heat index throughout most of the year. Two notable exceptions are northern Eurasia and Alaska, which both showed decreases in heat index during northern winter.

Another interesting application of the new data set is the classification of countries according to their heat index climatologies. We use the population-weighted heat index minima, means and maxima in each month and apply an iterative k-means cluster identification , implemented in the statistical software R . After each iteration, the sum of squared distance between points in each cluster was examined in order to determine the point at which additional clusters no longer produced useful information p. 251.

The clustering is applied to both reference periods: eight clusters are created. This number of clusters matched both reference periods well – more clusters did not seem to produce any substantial gains, whereas fewer clusters would have meant a larger sum of squared distance between points inside individual clusters.

The clusters were examined using ordination plots based on the methods by (). The clusters created by the data for each reference period are similar, but not identical. The changes between both reference periods are shown more clearly in Fig. . Most changes are in Africa, southern Europe and Asia. A first visual analysis indicates that subtropical heat index climates have expanded away from the Equator and toward the poles. Especially cool, dry or humid areas retain their climatology across both reference periods.