## 2 Materials and Methods
### The Urban Heat Island and Heat Waves  
HWs in the present study are defined using the maximum daily temperature that occurs during the daytime, typically a few hours after noon. The UHI effect is mainly a night time warming effect. This is generally acknowledged by some studies that also refer to the cooling effects, which are also called an 'inverse' UHI, that the UHI may represent during the day (i.e., UHI \(<\) 0 \({}^{\circ}\)C) [58; 59; 60]. This is particularly true for summer, which is the season considered here to study HWs.  
The interaction between HWs and the UHI is complex and may depend on the city and the particular HW [61; 62; 63; 64]. To clarify this issue, we performed a set of simulations with the WRF model for the city of Lisbon and for one of the strongest HWs that occurred in the Europe, namely the 2003 HW. The simulations were performed for a very high horizontal resolution of 333 m to more realistically justify the use of an Urban Canopy Model (UCM). The following simulations were performed:  
1. Without urban canopy parametrization (i.e., no_UCM).
2. Using a single-layer urban canopy model (SLUCM) (i.e., UCM1).
3. Using a multi-layer urban canopy model (BEP) (i.e., UCM2).  
The UHI intensity is calculated as the averaged urban temperature minus the averaged rural temperature. Figure 2 shows the UHI intensity, averaged for all urban grid points, for this extreme HW for Lisbon for no_UCM, UCM1 and UCM2. One may conclude that:  
1. The UHI in the Lisbon metropolitan area is essentially a nocturnal phenomenon with its intensity reaching between 1.5 and 2.0 \({}^{\circ}\)C during the night. However, in certain areas of Lisbon, the UHI intensity at night could reach values greater than 5 \({}^{\circ}\)C (not shown).
2. During the day, urban near-surface urban air temperatures could be up to 0.5 \({}^{\circ}\)C lower than its rural surroundings.
3. The intensity of the UHI is slightly stronger when the UCM is not used. This means that the gross features of the UHI intensity of Lisbon are mainly determined by the three urban surface types already specified in the land-use data of WRF and not by using an UCM coupled to WRF. In fact, the UCM acts to reduce the temperature and accumulated heat when compared to not using the UCM.  
The evaluation of spatial details of the interaction between HWs and the UHI at very high horizontal resolutions (a few hundred meters) in cities may be accomplished using UCMs coupled to regional models and by performing simulations for specific events of only a few days. It is not the purpose of this study to analyze the fine details of the UHI expression during a HW, for example to identify areas within the city where the UHI effect is stronger.  
Therefore, we do not anticipate significant differences in the temperature and HW-derived metrics mentioned in Section 2.5 between using or not an UCM coupled to the WRF model. We reinforce that this study is concerned with statistical (i.e., climate) changes of HW metrics between climates. In addition, it would be unfeasible, due to computing resource limitations, to perform climate simulations at high enough horizontal resolutions (of the order of a few hundred meters) to simulate all HWs identified in each 20-year climate simulations used in this study with the WRF model coupled to an UCM. In fact, to the authors' knowledge, no one has performed climate simulations with an UCM coupled to a regional model. In fact, many studies have performed WRF-UCM high-resolution simulations for HW events of only a few days.  
Therefore, in this study, we do not use an urban canopy parametrization to obtain the fine detail expression of the UHI.  
Figure 2: The average Urban Heat Island (UHI) intensity for Lisbon during the 2003 heat wave (from 29 July to 2 August 2003) for no_UCM, UCM1, and UCM2 (see text). Heat wave intensity is calculated as the difference between the urban minus rural average Tmax.