*4.1. Thresholds in Urban Planning Strategies*

In this paper, we studied the effects of different urban planning strategies on heat stress for current and future climates in the agglomeration of The Hague. It appears that preserving green spaces was clearly the best urban planning strategy in order to avoid heat stress for The Hague Southwest. The difference between the strategies for the CID was much smaller. An explanation for this difference appears when examining the statistical relationship among the density of residences, the SVF, and the vegetation fraction (Equation (5)). The larger the slope or partial derivative is in Equation (5), the more residences could be built per a certain decrease in SVF or decrease in vegetation fraction. Thus, the effectiveness of the strategy depends on the specific urban conditions. The vast majority of the data points in Figure 4 are positioned above the black line, which means that more residences could be built per percentage point decrease in the SVF than per percentage point decrease in the vegetation fraction. Note that a percentage point decrease in the SVF has the same effect on UHImax as a percentage point decrease in the vegetation fraction (Equation (1)). This means that, for the majority of neighborhoods, a decrease in the SVF due to high-rise buildings causes less heat stress than building low- and mid-rise buildings on green spaces.

$$\text{SVF} = \text{f}\_{\text{veg}} - 7.1.\tag{6}$$

The threshold which determines the favorable strategy can be derived from Equation (5) and is denoted in Equation (6). It is also represented as the dotted black line at the bottom of Figure 4. Note that this relationship is specific for The Hague agglomeration and might alter slightly for other urban areas, even in the similar climates of other countries in northwestern Europe.

This threshold indicates that reducing the SVF by constructing high-rise buildings is a better measure, unless the SVF is considerably low and the vegetation fraction is high. This is relatively rare for the agglomeration of The Hague. The differences in effectiveness between the strategies can be attributed to the cross product in Equation (5), which appeared to be significant. The density of residences can be imagined roughly as a product of urban fraction (inverse of vegetation fraction) and

height of the buildings (more or less correlated with the inverse of SVF). Two intermediate values in this product result in a substantial larger density of residences rather than a low and a high value for equal levels of heat stress.
