*2.2. Diagnostic Equation to Compute Minimum Temperatures in Cities*

Urban heat islands and urban temperatures can be estimated looking at the combined effects of weather conditions and urban morphological characteristics. From these factors, a daily maximum urban heat island (UHImax) can be estimated using a diagnostic equation created by Theeuwes et al. (2017), henceforth referred as T17 [20] (Equation (1)).

$$\begin{array}{l}\text{turban morphism} \\ \text{UHI}\_{\text{max}} = \left(2 - \text{SVF} - \text{f}\_{\text{veg}}\right) \sqrt[4]{\frac{\text{S}^{\text{J}} \text{DTR}^{3}}{\text{U}}} . \end{array} \tag{1}$$

This equation was validated using observational data from 14 cities across northwestern Europe that vary in size. The equation appears to be robust. The UHImax expresses the maximum temperature difference between urban and rural environments on a given day in Equation (1). SVF denotes the sky-view factor and fveg denotes the vegetation fraction of the urban area. S↓ denotes the mean downward shortwave radiation (K·ms−1), DTR denotes the diurnal temperature range (K), and U denotes the mean wind speed (m·s<sup>−</sup>1) measured at a rural station nearby the city. The average measurement period for each of the meteorological parameters can be found in T17 [20]. The heat maps are computed on grid cells with a resolution of 100 m. The SVF and vegetation fraction were determined using a source area of 500 by 500 m around the grid cell, which was designated to a 100 m resolution. The SVF originates from a 5-m-resolution dataset [29], derived from a digital elevation model based on airborne lidar measurements from aircraft measurements made in 2008 [30]. Upscaling from a 5-m to a 500-m resolution was performed by taking the median of street level SVF data points. The vegetation fraction dataset originates from a normalized difference vegetation index map (NDVI) [31].

The spatial contrast of the UHImax across the city is a good measure to estimate which parts of the city suffer more from heat stress. Nevertheless, when climate change is incorporated, the UHImax is not an adequate measure of heat stress anymore, since climate change is heating up the world regardless of whether an area is classified as rural or urban. Therefore, it is useful to make an evaluation based on the absolute values of urban temperatures, such as minimum temperatures (Tncity), which can be computed as follows:

$$\text{Tn}\_{\text{city}} = \text{Tn}\_{\text{runal}} + \text{UHI}\_{\text{max}} \times 0.46. \tag{2}$$

When minimum temperatures are observed at the rural reference station, the UHI is typically substantially smaller than the UHImax. On a typical cloudless day, the minimum rural temperature increases by 46% of the UHImax [3]. This fraction of the UHImax is also known as the UHITMIN. The WMO station in Rotterdam acts as a rural reference station (provides Tnrural in Equation (2)) (Figure 1A). Measurements from other nearby WMO stations were discarded, because they were located too close to the sea (Hoek van Holland) or were recently relocated (Voorschoten). In order to compute climatologies, we used the data from 15 summer half-years (1 April–30 September) covering the years 2002 to 2016 from the WMO station Rotterdam. Finally, we present heat maps showing the average number of nights per year that exceed the minimum temperature of 20 ◦C. This metric is consistent with ongoing climate adaption policies in the Netherlands [32]. These nights are often referred to as tropical nights. The heat maps were generated with the QGIS software [33].
