## 2 Materials and Methods
### Heat Waves  
HW refers to a period of hot weather that may be accompanied by high humidity. They occur due to stationary or slow moving pressure systems and therefore are large-scale phenomena. They have different expressions locally due to other factors such as small-scale surface features (i.e., elevation, surface type, and surface slope orientation). The properties of materials present in cities may also amplify the expression of HW, which is known as the urban heat island effect. The simulated data used in this study is obtained from RCM models, which consider the physical properties of different land-use lower boundary surfaces (i.e., urban, forest, rural, and many others). However, these models do not specifically consider the urban canopy of cities, and therefore, temperature-simulated data may not fully represent the local intensification of HW due to the heat island effect. Nevertheless, since temperatures and HW are compared between climates, this problem is minimized, particularly if the Urban Heat Island (UHI) does not change between climates. There is no universal accepted definition of HW. HW may be defined using different criteria. Most studies consider that HWs are defined relative to the climate of a particular region, and therefore, the same atmospheric conditions may represent a HW in different locations or not. In a special report of the IPCC [48], a HW was defined as \"a period of abnormally hot weather\". Most meteorology institutes use the World Meteorological Organization (WMO) definition of HW as: \"A marked unusual hot weather (maximum, minimum and daily average temperatures) over a region persisting at least two consecutive days during the hot period of the year based on local climatological conditions, with thermal conditions recorded above given thresholds.\" [49; 50]. Different definitions of HW may be devised depending on the need to focus on a particular sector of application that requires specific thresholds to take actions. Most HW indices consider an absolute or relative temperature threshold value above which the maximum daily temperature must occur for more than a certain number of consecutive days. The Task Team on the Definition of Extreme Weather and Climate Events (TT-DEWCE), established by the WMO Commission for Climatology, presents a detailed discussion and suggests guidelines on the definition and indices of a HW [49]. Most studies consider only Tmax when assessing HWs. Some studies also consider Tmin in the definition of HW [7; 51]. This is relevant, since night time temperatures (i.e., Tmin) may represent some thermal relief during a HW [52; 53]. [PERSON] et al. [17] and [PERSON] et al. [54] present a thoroughly review on the HW definitions and metrics used in HW research. The choice of the HW definition depends on the objective of the study. Here, we want to supply useful information for society to adapt to climate change in a particular locality. It is not the objective of the present study to evaluate impacts for the thermoregulation of the human body neither to compare HWs changes across distinct locals or regions. Therefore, the main objective of the methodology presented here is to be used locally at other places, without having to change the HW definition. The HW definition is applied equally to the present climate and to future projections considering the present characteristics of HW for the present climate. Here, we define a HW partially following [PERSON] et al. [4] that is relevant for the objectives of this study. This HW definition was recently applied in [21; 23]. HW is defined as a period of at least three consecutive days where the Tmax is above a certain threshold value (Tmax_c) in each day. This climatological threshold is calculated for each day of the year and is equal to the 90 th percentile of Tmax of all days on a 31-day window centered on that day. For example, to obtain Tmax_c for each of the 365 days, all 31 days of the 20 years (i.e., 620 days) are considered.