*4.2. Applicability and Limitations of the UHI Diagnostic Equation*

Spatial variation in UHImax and night-time minimum temperatures within cities were investigated several times using multi-year observation data in cities. Montavez et al. [46] found that the urbanization of Granada in Spain resulted in increased night-time minimum temperatures predominantly in the city center. Eliasson [47] concluded that urban–park temperature differences were on the same order of magnitude as urban–rural temperature differences, which corresponds to large parks in The Hague. Heusinkveld et al. [23] found that spatial differences in vegetation cover are paramount in determining the spatial variation in UHI, and the correlation coefficients were best for an upwind fetch area of 700 m. In the current study, the wind direction was not taken into account, and therefore, a smaller area of 500 by 500 m was an appropriate choice. When considering SVF, an aerial mean is used to relate the SVF to UHI to incorporate advection effects on air temperature, which was performed in studies such as those by Goh et al. [48] and Unger [49]. Similar to our study, Unger [49] extracted the SVF on a scale of 500 by 500 m.

The verification of two years of crowdsourced city temperature data reveals that the diagnostic method used in this study does not indicate substantial biases in minimum temperatures in urban areas. This supports the use of the current diagnostic equation. Although the diagnostic equation is a physically meaningful equation with conservation of fundamental dimensions, not all potentially important contributing factors were taken into account. One can think of contributing factors such as anthropogenic heat, albedo, thermal admittance, which is related to the heat storage of buildings, distance to open water from a city's edge, and a vertical temperature gradient, as a measure for stability at the rural reference station. The latter two appeared to have less significance [20]. Caution is advised when applying the method to places that have large anthropogenic heat production like industrial areas or highly densely populated areas. Industrial areas were not sampled in the validation of T17 [20]. Anthropogenic heat can be included into the equation by adding it to the incoming solar radiation, or it can be added as a separate variable. When added to the incoming solar radiation, it has no substantial influence, apart from the cautioned areas with large anthropogenic heat production. Since the proximity to open water is not considered in the equation, the urban areas close to the sea have larger uncertainties for our study area. Open water is difficult to implement in a time-invariant UHImax equation, because the effect is strongly dependent on the season [50]. For albedo and thermal admittance, it is a challenge to retrieve reliable area-wide data on building properties. Albedo data can be straightforwardly retrieved from satellite observations, although a top view would over-represent roof albedo, which is less decisive on the street level than wall and street albedo [51].

A conversion factor of 0.46 was used to estimate the UHITMIN from the UHImax (see Equation (2)). The ratio between UHImax and UHITMIN (conversion factor) is probably not fixed for all the percentiles, as demonstrated in a crowdsourced data study conducted in the Netherlands [14], and for city weather stations in Rotterdam [23]. The last study reported UHImax to UHITMIN ratios in the range of 0.63–0.87 for the 95th percentile. However, it might be a safe choice to have a conservative conversion factor, since the rural reference station Rotterdam is affected by UHI mainly due to advection from Rotterdam and the airport itself [23]. Spatially, the conversion factor may change between areas with dominant narrow or wide street canyons [52].
