Urban climate effects on extreme temperatures in Madison, Wisconsin, USA

Madison, Wisconsin is a city of 233 000 in the north-central United States with an urban agglomeration population of 402 000 (US Census Bureau 2012). It has a humid-continental climate (Köppen: Dfa), 1981–2010 mean annual precipitation of 876 mm, and mean temperatures of −7 °C in January and 22 °C in July (NCDC 2014). Madison is surrounded by lakes and a rural landscape of agriculture, forests, wetlands, and grasslands (figure 1).

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In March 2012, 135 HOBO^® U23 Pro v2 temperature/relative humidity sensors in solar shields (Onset Computing 2010) were installed on streetlight and utility poles across the study area (figure 1). Sensor accuracy is 0.21 °C from 0 to 50 °C for dry bulb temperature and 2.5% from 10 to 90% for humidity (Onset Computing), though errors nearly twice as large have been reported for sensors within shields in field conditions (Nakamura and Mahrt 2005). Additional locations were added in 2012 and 2013 for a total of 150 sensors. The sensors were installed at 3.5 m height to minimize risk of disturbance. This differs from standard meteorological heights of 1.5–2 m, and the possible impacts of this are discussed in our results. Sensors were positioned on the north side of poles except in six cases to avoid the road right-of-way. Instantaneous measurements were recorded every 15 min.

AT reflects the interacting effects of temperature and humidity on physiological heat stress and is commonly used to measure heat exposure in epidemiological studies (Basu 2009). We calculated AT as: AT = −1.3 + 0.92 T + 2.2e (Steadman 1984), where T is dry bulb temperature (°C) and e is vapor pressure (kPa), calculated after Buck (1981). Although our study focuses on temperature and humidity, it is important to remember that other micro-climatic factors, such as wind and sun exposure, also affect heat stress (Steadman 1984) and are also sensitive to urban development (Landsberg 1981).

Our study describes the summer of 2012 and winter of 2013–14, when 133 and 148 sensors were active, respectively. The summer of 2012 was Madison's third hottest since 1869 when records began, with temperatures at the Dane County airport (MSN) reaching 32.2 °C (90 °F) on 39 days compared to the 1981–2010 average of nine days (NCDC 2014). In late June and early July, Madison experienced a severe heat wave with seven consecutive days over 35 °C, three consecutive days reaching 38.9 °C, and five consecutive days with record high temperatures (NCDC 2014).

The winter of 2013–14 was Madison's coldest in 35 years, with 40 days below −17.8 °C (0 °F) compared to the 1981–2010 average of 17 days (NCDC 2014).

UHI intensity (ΔT) is classically defined as the temperature difference between a city and its rural surroundings (Stewart and Oke 2012). However, the degree of urban development varies continuously across landscapes, as will the magnitude of UHI effects. Defining sites as simply urban or rural forces a continuum into a category, oversimplifying both cities and their UHIs. Recently, Stewart and Oke (2012) proposed a wider range of urban and rural land cover categories in order to better describe measurement sites, contextualize UHI intensity, and compare among studies. We offer an alternative definition of ΔT that does not rely on categories, but rather on continuous empirical relationships between temperature and the density of the built environment.

Figure 2 illustrates this definition using simulated data from 20 hypothetical measurement sites. Among these 20 sites, there is a positive relationship between temperature and percent impervious surface coverage (IMP), with a slope of 0.05. For this paper, we define ΔT as the fitted temperature difference between areas with 0% IMP (i.e., rural) and 100% IMP (i.e., dense urban). In figure 2, ΔT is therefore 5 °C. Urban–rural AT differences (ΔAT) are defined in the same way. This definition puts UHI intensity explicitly in terms of urban development and avoids qualitative urban and rural land cover categories. Other measures of urban physical density, such as height–width ratio or sky view factor (Unger 2004), could be used instead of IMP, but for our study area, IMP consistently provided better model fits than sky view or height–width ratio.

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We calculated ΔT on each day of our study period using linear regression models. The response variables were either daily T_MAX, T_MIN, AT_MAX, or AT_MIN at each sensor. The explanatory covariates were average IMP around each sensor (with water masked out), lake proximity, and topographic relief, which all influence temperatures in our study area (Schatz and Kucharik 2014).

Average IMP within circular buffers ranging in radius from 100 to 2000 m (in increments of 100 m) were tested to see which produced the best model fits across the entire study period. Of all radii tested, 600 m provided the best average fit of the temperature and AT data. It was more important to have a consistent set of covariates across the entire study period, enabling direct comparisons of daily ΔT/ATs, than to fit optimal models for each individual day. For lake proximity, we tested various linear and exponential relationships between lake proximity and temperature. The best fitting relationship across the entire study period was e^−8d, where d is kilometers from the nearest lake shore. Topographic relief was the difference between local elevation and average elevation within a 0.8 km radius on a three meter resolution elevation model.

Daily ΔT/AT models were well behaved for normality, constant variance, and independence of predictors, but significant spatial autocorrelation occurred in 21% of daily models, for which we used spatial regression (Anselin 2002). The spatial models used inverse distance weighted neighbor matrices with maximum neighbor distances of 10 km in either spatial error or spatial lag models, which were selected using Lagrange multiplier tests (Anselin 1988). Using this same method, we explored diurnal UHI patterns during the July 2012 heat wave by calculating ΔT and ΔAT every 30 min.

This analysis addressed two questions. First, did extremely hot or cold days have stronger UHIs? Second, were these relationships due to the extreme temperatures themselves, or to the weather conditions coinciding with extreme temperatures?

To answer the first question, we used linear mixed-effects models to test the relationship between temperature and UHI intensity. To test for extreme heat effects, we used data from the 50 consecutive days of the year with the highest average temperature across our study period (15 June–3 August for 2012–2014; n = 150 days) and fit models between daily ΔT and T_MAX and between daily ΔAT and AT_MAX. To test for extreme cold effects, we used data from the 50 days of the year with the lowest average temperature across our study period (23 December to 13 February for 2012–2014; n = 100 days) and fit models between daily ΔT and either minimum temperature or wind chill temperature (WCT). The WCT incorporates the perceived temperature effect of moving air increasing the rate of heat loss from the skin surface, and was calculated as

$$\begin{eqnarray*}{\rm{WCT}} & = & 13.12+0.6215\;T-11.37\;{V}^{0.16}\\ & & +0.3965\;T{V}^{0.16},\end{eqnarray*}$$

where T is temperature (°C) and V is wind speed (km hr⁻¹; Osczevski and Bluestein 2005). In all mixed models described in this section, year was included as a fixed effect, and a first order autoregressive correlation structure accounted for serial autocorrelation.

To answer the second question, we used a series of two linear mixed-effects models (Pinheiro et al 2014) on the extreme heat or cold data. The first model controlled for weather effects, with daily ΔT or ΔAT as the response variable. Covariates were daily average wind speed, percent sun, and either soil moisture (warm weather model) or snow depth (cold weather model), which are the primary meteorological determinants of UHI intensity in our study area (Schatz and Kucharik 2014) and elsewhere (Oke 1982, Runnalls and Oke 2000, Malevich and Klink 2011, Smoliak et al 2015). The second model used the residuals from the first model as the response variable, with daily T_MAX or T_MIN as the explanatory covariate. This series of models allowed us to test whether extreme temperatures had independent effects on UHI intensity beyond their correlation with key weather conditions.

For the weather covariates, temperature, wind speed, and snow depth came from MSN (NCDC 2014). Percent sun was calculated as measured insolation (300–1100 nm; S-LIB-M003 pyranometer, Onset Computing) averaged over three sites in our study area as a percent of potential insolation, which was calculated after Allen et al (1998). Soil moisture was measured at 10 cm depth (EC-5 sensor, Decagon) and also was averaged over three sites in our study area (figure 1).

The intensity and duration of extreme temperatures were visualized on a 400 × 400 m resolution grid using regression kriging, which uses information about the land surface to inform data interpolation (Hengl et al 2007). For covariates, IMP, lake proximity, and topographic relief were used (each as described in section 2.2). Lake effect and topography were averaged within each 400 m grid cell; IMP was averaged over a 600 m radius of each grid centroid (with water masked out). Spherical or exponential variogram fits were selected using Akaike Information Criterion. In winter 2013–14, lakes were frozen (Wisconsin State Climatology Office 2015) and there was no significant effect of lake proximity on temperatures, so lake effects were not included.

Madison's most densely built urban areas are primarily concentrated in the isthmus located between the region's two largest lakes, near the center of out study region (figure 1). In summer 2012, these densely built urban areas experienced mean July T_MAX up to 1.8 °C higher; mean July T_MIN up to 5.3 °C higher; and up to twice as many hours ⩾32.2 °C (90 °F) than rural areas (figures 3(a)–(c). The physical density of the built environment, represented by IMP, was the primary spatial driver of these differences (table 1, figures 4(a)–(c)). The lakes tended to decrease adjacent temperatures, though these effects were mostly restricted to shoreline locations, as reflected by the rapid exponential decay of lake influence with distance from shore (section 2.2). Local topography was only statistically significant with respect to minimum temperatures (table 1), presumably due to cold air drainage to low lying areas.

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The UHI had similar effects on AT as on dry bulb temperature (figures 4(a)–(c)). However, the slope of AT_MAX versus IMP was lower than the slope of T_MAX versus IMP, indicating that the UHI increased AT less than it increased T. This may relate to urban areas tending to have drier air, causing the UHI to raise AT_MAX less than it raised T_MAX. Calculating urban–rural differences of mean July 2012 maximum dew point confirms this, yielding a ΔDP of −0.5 °C, indicating that urban areas averaged lower dew points.

Our sensors were at 3.5 m height, complicating comparisons with the official NOAA observing station at MSN (figure 1), which is at 2 m. However, comparing observed daily T_MAX at the airport to T_MAX interpolated from our sensors for the same location indicates that at 3.5 m, downtown Madison experienced up to 10 more days ⩾32.2 °C than MSN in 2012 (figure S1). If this 10 day difference held at 2 m as well, downtown Madison experienced approximately 49 days over 32.2 °C compared to the 39 days officially recorded at MSN in 2012. This underscores the impact of urban climates on heat exposure, as well as the potential for rural or semi-rural airport stations to underestimate heat wave severity for nearby urban populations.

During the summer of 2012, Madison also experienced a record setting heat wave. From 1 to 7 July, the densest urban areas, which are near the center of our study region, experienced daily T_MAX from 1.6 to 2.2 °C higher than rural areas, with similar urban effects on AT_MAX (figure 5). Urban effects on nighttime temperatures were particularly striking. Figure 5 shows the growth of each day's UHI during the evening and nighttime hours, prolonging high temperatures and diminishing nocturnal relief from extreme heat. Minimum temperatures in the densest urban areas averaged 4.4 °C higher than rural areas. This is reflected in the number of consecutive nights without temperatures falling below 26.7 °C (80 °F), which is a heat stress threshold used by the National Weather Service (NWS) (Robinson 2001). While most rural areas cooled below 26.7 °C every night, the densest urban areas spent over four days (temperature) and nearly 7 days (AT) without falling below 26.7 °C (figures 6(a) and (b)).

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Madison's UHI also affected exposure to cold temperatures. In winter 2013–14, Madison's most densely built areas experienced a mean January T_MAX up to 1 °C higher and a mean January T_MIN up to 3 °C higher than rural areas (figures 7(a) and (b)). Remarkably, urban areas also experienced up to 40% fewer hours ⩽−17.8 °C (0 °F) than rural areas, a difference of nearly 200 h (figure 7(c)). The physical density of the built environment, represented by IMP, was the primary spatial driver of these patterns (table 1; figures 8(a)–(c)). Lake proximity was not significant in winter, when the lakes were frozen (Wisconsin State Climatology Office 2015), and local topography was only statistically significant with respect to average January T_MIN, presumably due to cold air drainage to low lying areas.

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More densely populated areas tended to experience larger UHI effects. The log of average population density (2010 US Census block group data) within a 1000 m radius of each sensor was linearly related to UHI intensity (figure 9). This was true during both the winter (figures 9(c)–(e)) and summer (figures 9(a), (b) and (f), with minimum temperatures showing the strongest relationships (figures 9(c) and (d)).

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During our warm temperature study period, there was a positive relationship between daily T_MAX and ΔT at T_MAX compared to summer average UHI intensity (figure 10(a)) with a similar relationship between AT_MAX and ΔAT (figure 10(b)). Put simply, the daytime UHI tended to be stronger on hotter summer days, with most days over 32.2 °C experiencing above average UHI intensities (figures 10(a) and (b)). There was a weaker positive relationship between T_MAX and UHI intensity at T_MIN (figure 10(c)), but no significant relationship between AT_MAX and ΔAT at AT_MIN (figure 10(d)). Although these are weak relationships, they nonetheless indicate that UHI effects tended to be slightly stronger on hotter summer days. These relationships appeared to be due to hotter summer days coinciding with weather conditions that favor stronger UHIs. After accounting for the variation in ΔT that was explained by percent sun, wind, and soil moisture, T_MAX no longer had significant effects on UHI intensity. Of these weather factors, only percent sun was significant (p < 0.0001).

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During our cold temperature study period, most of the strongest UHIs occurred at T_MIN ⩽−17.8 °C, while days with a T_MIN over −5 °C experienced no above average UHIs (figures 11(a) and (b)). This created a negative relationship between daily T_MIN and ΔT, such that colder days and particularly nights tended to have stronger UHI effects. Using WCT, however, rendered these relationships non-significant (α = 0.01), presumably because the strong winds that cause low WCTs also tend to weaken UHIs (Oke 1982). As with extreme heat, any significant relationships between T_MIN and ΔT were due to colder days coinciding with weather conditions that favor stronger UHIs. Percent sun and snow depth were each significantly related to both T_MIN and ΔT and accounted for any significant correlations between the two, though increased anthropogenic heating during very cold conditions could also play a role (Sailor 2011).

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Madison's UHI substantially increased extreme heat exposure, particularly at night. Heat stress is cumulative, and prolonged heat exposure poses greater risks to public health than isolated hot days (Schwartz 2005, Tan et al 2007, Kalkstein et al 2011). As such, perhaps our most alarming finding was that during the July 2012 heatwave, nearly all rural areas cooled below 26.7 °C every night, but the densest urban areas near the center of our study region spent over four days (temperature) and nearly a full week (AT) without falling below 26.7 °C. This exemplifies the power of urban climates to fundamentally alter the severity of heat waves by prolonging and intensifying hot conditions. The UHI had similar effects on AT as on temperature, though during the daytime, urban effects on AT tended to be smaller than urban effects on dry bulb temperature. This is presumably because evapotranspiration from rural soils and vegetation raised rural humidity relative to the urban landscape, particularly during the daytime when evapotranspiration typically peaks.

At the other end of the temperature spectrum, Madison's UHI reduced exposure to cold temperatures, which can be a significant health risk factor (Mercer 2003). Urban warming during severe cold could save lives and significantly reduce winter heating demand (Kolokotroni et al 2012). In regions susceptible to cold temperatures, it is important to consider these potential cold weather benefits when designing UHI mitigation measures to lower heat risk.

Not only did the UHI increase the severity of extreme heat in Madison, but UHI intensity was greater than the summer average during periods of extreme heat. Several other studies have also reported that UHI intensity is as strong or stronger during heat waves compared to summer background conditions (Harlan et al 2006, Li and Bou-Zeid 2013, Meir et al 2013, Li et al 2015). In Madison, we attributed this to hot summer days coinciding with clearer skies, which favor stronger UHIs (Oke 1982). In Baltimore, Li and Bou-Zeid (2013) attributed the phenomenon to low wind speeds and drier soils during heat waves, which also facilitate stronger UHIs (Oke 1982). In general, heat waves result from stagnant high pressure systems (Loikith and Broccoli 2012) that are associated with clearer skies, calmer winds, and drier soils, all of which favor greater UHI intensity (Oke 1982, Schatz and Kucharik 2014). This suggests that heat wave conditions may generally facilitate stronger UHIs.

Further, Li et al (2015) explored the synergy between heat waves and UHIs using an energy budget approach in Beijing. They found that heat waves increased sensible heat flux relatively more in urban areas and latent heat flux relatively more in rural areas, leading to greater urban–rural temperature divergence on hotter days. Essentially, heat waves tended to magnify existing differences in urban and rural energy budgets, with more energy partitioned to latent heat in rural areas and more to sensible heat in urban areas. These traits of urban and rural energy budgets are typical of cities (Oke 1982), providing further support for the hypothesis that UHIs strengthen during heat waves. Anthropogenic heating from combustion and air conditioning may also increase during heat waves (Stone 2012), further strengthening UHIs. More research is needed to test these hypotheses, but taken together, this represents a growing body of evidence that UHIs tend to strengthen during extreme heat.

Oke (1973) first described the positive relationship between the log of a city's population and its maximum UHI intensity. Our study is the first to show a similar relationship within a single urbanized area, such that the most densely populated parts of our study region tended to experience the strongest UHI effects. This does not imply that large concentrations of people create intense UHIs (but see Sailor 2011), but rather that densely built urban areas tend to have both high population density and intense UHI effects. We suspect that this will hold true in many cities, although population density and the physical density of the built environment certainly can be decoupled. People may not live in commercial or industrial areas, for example, and informal urban settlements can have extremely high population densities (Streatfield and Karar 2008) without the dense, tall buildings associated with strong UHIs. Nonetheless, urban residents tend to spend much of their time in densely built areas, whether to live or to work, where they may encounter not just urban warming, but relatively strong urban warming.

Climate change projections commonly report future changes in the number of days above high temperature thresholds. For example, Madison currently averages 9 days per year ⩾32.2 °C, but this is projected to reach 29–37 days by mid-century and 37–65 days by late century (Kucharik et al 2011), depending on the greenhouse gas emissions scenario (B1, A1B, A2; IPCC 2000). However, these projections do not account for urban climate effects, which is concerning for two reasons. First, cities are where most people will encounter future warming. Second, we observed substantially more time above high temperature thresholds in urban areas compared to rural areas (figures 3, 6, S2), including up to 21 more days ⩾32.2 °C in urban versus rural areas in 2012 (figure S1). This suggests that projections failing to account for UHIs could considerably underestimate the amount of heat for which urban communities need to prepare (Fischer et al 2012, Argüeso et al 2015, Oleson et al 2015), with the largest underestimates in the largest cities with the highest populations and strongest UHIs.