Nat Hazards (2016) 83:885–907 DOI 10.1007/s11069-016-2353-6 ORIGINAL PAPER
Urban heat islands in Hong Kong: statistical modeling and trend detection Weiwen Wang1 • Wen Zhou2 Yong Xu3
•
Edward Yan Yung Ng1,3,4
•
Received: 11 November 2015 / Accepted: 6 May 2016 / Published online: 18 May 2016 Ó Springer Science+Business Media Dordrecht 2016
Abstract Urban heat islands (UHIs), usually defined as temperature differences between urban areas and their surrounding rural areas, are one of the most significant anthropogenic modifications to the Earth’s climate. This study applies the extreme value theory to model and detect trends in extreme UHI events in Hong Kong, which have rarely been documented. Extreme UHI events are defined as UHIs with intensity higher than a specific threshold, 4.8 for summer and 7.8 °C for winter. Statistical modeling based on extreme value theory is found to permit realistic modeling of these extreme events. Trends of extreme UHI intensity, frequency, and duration are introduced through changes in parameters of generalized Pareto, Poisson, and geometric distributions, respectively. During the 27-year study period, none of the quantities in winter analyzed in this study increased significantly. The annual mean summertime daily maximum UHI intensities, which are samples from a Gaussian distribution, show an increasing but nonsignificant linear trend. However, the intensity of extreme UHI events in summer is increasing significantly, which implies that the risk of mortality and heat-related diseases due to heat stress at night (when the daily maximum UHI occurs) in summer is also increasing. The warming climate has threatened and will continue to threaten inhabitants of this subtropical high-density city. Strategies for adaptation to and mitigation of climate change, such as adding greenery and planning a city with good natural ventilation, are needed.
& Wen Zhou
[email protected] 1
School of Architecture, The Chinese University of Hong Kong, Hong Kong SAR, China
2
Guy Carpenter Asia-Pacific Climate Impact Centre, School of Energy and Environment, City University of Hong Kong, Hong Kong SAR, China
3
Institute of Future Cities, The Chinese University of Hong Kong, Hong Kong SAR, China
4
Institute of Environment, Energy and Sustainability, The Chinese University of Hong Kong, Hong Kong SAR, China
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Keywords Urban heat island Extreme value theory Peaks-over-threshold model Generalized Pareto distribution Parametric trend
1 Introduction Urban heat islands (UHIs) are urban areas that tend to have higher temperatures than surrounding rural areas, and they are one of the most significant anthropogenic modifications to the Earth’s climate (Oke 1982; Zhao et al. 2014; Zhou et al. 2015). With the ever-increasing urban population, more and more people are vulnerable to problems caused by urbanization (Memon et al. 2008). According to the World Health Organization, the urban population in 2014 accounted for 54 % of the total global population, up from 34 % in 1960, and continues to grow. Meanwhile, the Intergovernmental Panel on Climate Change (IPCC) has reported that climate warming is unequivocal, and the frequency of heat waves has increased in large parts of Europe, Asia, and Australia (IPCC 2013). Urban areas are especially vulnerable to heat waves due to the existence of UHIs and synergistic interactions between UHIs and heat waves (Li and Bou-Zeid 2013; Li et al. 2015). Hong Kong is a high-density city in the subtropics with a hot and humid climate. The UHI effect in Hong Kong has been investigated extensively. Some studies _ENREF_6_ENREF_6 have characterized the spatial pattern of the UHI in Hong Kong using land surface temperatures retrieved from remote sensing data (Fung et al. 2009; Liu and Zhang 2011), and others have evaluated the reliability of UHI intensity as an indicator of urban heating (Memon et al. 2009). Strategies of urban planning for adaptation to and mitigation of UHIs are of interest to the government and researchers in Hong Kong as well (Giridharan et al. 2007; Ng 2009; Ng et al. 2012). But studies of UHIs under the background of secular climate change in Hong Kong have not yet been undertaken, possibly in part because of the lack of long-term observations in rural areas. In previous studies of hazards related to urbanization, long-term trends in meteorological disasters such as heat waves, rainstorms, and haze have been addressed (Chan and Zhou 2005; Shi and Cui 2011; Yan et al. 2011; Wei et al. 2011; Habeeb et al. 2015; Liu et al. 2014, 2015; Qian 2015; Xia et al. 2015). Changes in heat-related mortality in metropolitan areas have been detected as well (Hondula and Davis 2014; Kim et al. 2015; Sheridan et al. 2008). However, as an environmental hazard, UHIs have rarely been directly investigated in terms of their extremes. The objective of this study is to define extreme UHI events, model their behavior, and detect their temporal trends in Hong Kong based on extreme value theory. There is a long tradition of using extreme value theory in meteorological and environmental applications. In the modern theory, the peaks-over-threshold model is used to describe all exceedances above a high threshold rather than just looking at the block maxima (e.g., the annual maximum daily precipitation amount). The theory has been extended to encompass temporal trends. The most common approach for dealing with nonstationarity is to allow for parametric changes with time in the distribution (GarciaAristizabal et al. 2014; Smith 1989). The approach jointly models the occurrence of an event (an exceedance of a high threshold) and its severity (the magnitude of the excess over a high threshold). The exceedances are assumed to occur according to a Poisson distribution, while the excesses above the threshold are assumed to follow a generalized Pareto (GP) distribution (Coles 2001). More recently, approaches to modeling the duration of
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extreme events such as heat waves and cold waves, rather than discarding these clusters, have been advocated (Furrer et al. 2010; Parey and Hoang 2015). Based on the most recent developments in extreme value analysis, an appropriate peaks-over-threshold model of extreme UHI events in Hong Kong for both summer and winter will be set up in this paper.
2 Data and methodology 2.1 Observations and definition of UHIs in Hong Kong The Hong Kong Observatory Headquarters (HKO) is a representative urban weather station and a common choice of UHI studies in Hong Kong (Fung et al. 2009; Memon et al. 2009). In this study, we chose HKO as the urban site and three other weather stations, Ta Kwu Ling (TKL), Tsak Yue Wu (TYW), and Waglan Island (WGL), as rural sites to quantify UHI intensities in Hong Kong. The locations of these weather stations are shown in Fig. 1 (black dots). The Urban Climatic Analysis Map of Hong Kong in Fig. 1 visualizes the UHI intensities in Hong Kong using 8 classes (8 degrees) of physiological equivalent temperature (technical reports are available from http://www.pland.gov.hk/pland_en/p_ study/prog_s/ucmapweb/). General information from these sites is listed in Table 1. Though TKL first started operating in 1985, air temperature observations were not available before the summer of 1988. Therefore, hourly observations of air temperature in summer (June–August) during 1989–2015 and in winter (December–February) during
Fig. 1 Locations of Hong Kong Observatory Headquarters (HKO), Ta Kwu Ling (TKL), Tsak Yue Wu (TYW), and Waglan Island (WGL), shown as black dots on the Urban Climatic Analysis Map of Hong Kong, which visualizes the UHI intensities of Hong Kong using 8° of physiological equivalent temperature
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Table 1 General information from meteorological stations for Hong Kong UHI analysis in this study Information
Hong Kong Observatory Headquarters
Ta Kwu Ling
Tsak Yue Wu
Waglan Island
Abbreviated name
HKO
TKL
TYW
WGL
WMO code
45005
45032
–
45045
Longitude (E)
114°100 2700 0
00
114°090 2400 0
00
114°190 2400 0
00
114°180 1200
Latitude (N)
22°18 07
22°31 43
22°24 11
22°100 5600
Elevation above mean sea level (m)
32
15
5
56
Date of first operation
2 Mar 1883
14 Oct 1985
1 Oct 1995
1 Dec 1952
1988/1989–2014/2015 from HKO and TKL are used in this study. Hourly temperature records from WGL are available and utilized 1 year later and from TYW 7 years later (summer during 1996–2015 and winter during 1995/1996–2014/2015). A UHI is defined as the temperature difference between HKO and a rural counterpart, while extreme UHI events are defined as UHIs with intensities higher than a specific high threshold. In addition, hourly relative humidity and daily maximum temperature records from HKO as well as daily rainfall records from both HKO and TKL are further used to elucidate possible causes of changes and impacts of extreme UHIs in Hong Kong.
2.2 Satellite images for land cover changes Located on the southeast coast of China, facing the South China Sea, Hong Kong is affected by clouds most of the time, from early January to late September. To show the land cover change in Hong Kong and adjacent Shenzhen, we collected 8 clear Landsat images for 2 time periods, including 4 Landsat images from the year 1994 (October 1, October 24, October 24, and November 2) and 4 images from the years 2013–2015 (October 5, 2013, December 31, 2013, August 8, 2015, and October 18, 2015). All Landsat data can be downloaded from the US Geological Survey Web site: http://glovis.usgs.gov. Herein, all Landsat images are atmospherically corrected into surface reflectance using the Landsat Ecosystem Disturbance Adaptive Processing System (Masek et al. 2006). After this atmospheric correction, two sets of Landsat data from two periods are geometrically corrected and seamlessly joined into two large images to cover Hong Kong and nearby regions of Shenzhen.
2.3 Atmospheric reanalysis and anomaly composite Reanalysis data during 2005–2014, including the daily mean air temperature at 2 m, mean sea level pressure, and geopotential height, are taken from the National Centers for Environmental Prediction-National Center for Atmospheric Research (NCEP-NCAR) reanalysis (Kalnay et al. 1996). Daily anomalies derived from a smoothed mean daily annual cycle are used to examine the atmospheric characteristics associated with extreme UHIs. These daily anomalies are averaged in corresponding extreme UHI days, and the Student’s t test is used to test their significance.
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2.4 Extreme value theory In the present study, the peaks-over-threshold method is utilized to model the intensity, frequency, and duration of extreme UHI events. Specifically, the intensity above the threshold of UHI is modeled by a GP distribution, the annual frequency is modeled by a Poisson distribution, and the duration is modeled by a geometric distribution (Furrer et al. 2010). A GP distribution is given by 1 x u n xu ; x [ u; 1 þ n [0 ð1Þ F ðx; n; ru ; uÞ ¼ 1 1 þ n ru ru where n stands for the shape parameter, and ru [ 0 denotes the scale parameter depending on the selected threshold u. The Poisson distribution is given by PðkÞ ¼
kk ek ; k!
k ¼ 0; 1; 2; . . .
ð2Þ
where k is the number of events in a given year. A geometric distribution that can model the length (duration) of an extreme event is given by PðkÞ ¼ ð1 hÞk1 h;
k ¼ 1; 2; . . .
ð3Þ
with the reciprocal of the parameter h being the mean. The extreme value analysis is based on the assumption that extreme events occur independently. However, extreme events can occur in succession in the case of persistent weather conditions. After the threshold is calibrated in this study, the geometric distribution is applied to check the probability of continuity. If the continuous probability of extreme UHIs is high, the use of geometric distribution can cluster extreme UHI days occurring successively into a single extreme event. Otherwise, the duration cluster can be discarded, and a Poisson–GP model will be sufficient. The independence assumption is therefore fulfilled. Parameter estimation in the model is done using maximum likelihood methods. Taking the GP distribution as an example, suppose that the values y1 ; y2 ; . . .; yk are the k excesses of a threshold u. For n 6¼ 0 the log-likelihood is derived from Eq. (1) as k 1 X nyi : ð4Þ log 1 þ lðru ; nÞ ¼ k log ru 1 þ n i¼1 ru Return levels can be estimated and allow better interpretation of the extreme value model than individual parameters. Suppose that a GP distribution with parameters ru and n is a suitable model for exceedances of a threshold u by a variable X. That is, for x [ u; it follows that 1 x u n ; ð5Þ PrfX [ xg ¼ fu 1 þ n ru where fu ¼ PrfX [ ug. Hence, the level xm that is exceeded on average once every m observations is the solution of
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1 xm u n 1 fu 1 þ n ¼ : ru m
ð6Þ
i ru h ðmfu Þn 1 ; n
ð7Þ
Rearranging, xm ¼ u þ
provided that m is sufficiently large to ensure that xm [ u. By construction, xm is the mobservation return level. Standard errors or confidence intervals for xm can be derived by the delta method. The uncertainty in the estimate of fu should be included in the calculation, but life is made simpler by ignoring the uncertainty in fu ; which is usually small relative to that of other parameters. From Eq. (7), ru ¼
ðxm uÞn ðmfu Þn 1
;
n 6¼ 0
ð8Þ
with fixed xm , substitution into Eq. (4) leads to a one-parameter likelihood that can be maximized with respect to n. As a function of xm, this is the profile log-likelihood for the m-observation return level. The model is further extended to allow for estimating trends in extreme characteristics of UHI intensity, frequency, and duration. One can consider parameters to be fixed within a given year but allow shifts from 1 year to another. That is, for each year x in the record period, ru = ru(x) for the GP scale parameter, k = k(x) for the Poisson parameter, and h = h(x) for the geometric parameter (Wang et al. 2015c). Since changes in the shape parameter of the GP distribution are rarely observed and difficult to model, this parameter is kept fixed. Trends are introduced through covariate effects in the GP scale parameter, with a generalized linear model framework in the Poisson and geometric fittings.
3 Environmental and climatic changes Before investigating the extreme events, the environmental changes and climatological characteristics of UHIs in Hong Kong will first be described. The Landsat images in Fig. 2 demonstrate the land cover change in Hong Kong and adjacent areas of Shenzhen from 1994 (Fig. 2a) to recent years (2013–2015, Fig. 2b). Large developments occurred in New Territories (northern Hong Kong), where TKL is located, and in nearby Shenzhen. On the Kowloon Peninsula, where HKO is located, a major change is that the reclaimed areas on the east and west margins of the peninsula in Fig. 2a are mostly built up in Fig. 2b. Vegetative cover reductions (in red) inside the peninsula are evident as well. Very limited changes are found in Sai Kung (eastern Hong Kong), where TYW is located. This suggests that TYW may be a better rural site than TKL. This is further demonstrated by Fig. 3, which shows that UHI intensities are stronger when computed by records at TYW than at TKL. However, the present study pays more attention to the long-term trend of UHI, so TKL is a better choice because it has longer-term observations than TYW (Table 1). According to Siu and Hart (2013), TYW was deemed the most appropriate representative rural site in Hong Kong, but TKL can still serve as another rural reference site. WGL, which has often been chosen as a representative rural site in early studies (Stanhill and
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Fig. 2 Landsat images of land cover over Hong Kong and adjacent Shenzhen in a 1994 and b 2013–2015. Color bar cannot be shown for these full-color maps. Roughly, red indicates vegetation, blue indicates water, gray denotes buildings, and white denotes flat artificial covers
Kalma 1995; Yim and Ollier 2009), is actually not a good choice (Fig. 3), mainly because it is a marine station (Fig. 1). In the diurnal cycle, UHI intensities in Hong Kong are positive during the night but may be negative during the daytime. Generally, possible causes of positive UHI intensities
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Fig. 3 Diurnal cycle for temperature at four weather stations of Hong Kong in a summer and b winter, and diurnal cycle of UHI intensities calculated by three pairs of weather stations (taking HKO as the urban site) in c summer and d winter. Local standard time is used. The shadings represent one standard deviation
Fig. 4 Seasonal variation of a normalized nocturnal (7 p.m. to 7 a.m. local time) UHI intensity (solid line) in Hong Kong and relative humidity observed at HKO (dashed line), b monthly total rainfall amount (mm) observed at HKO during 1989–2014
include increased absorption of solar radiation and anthropogenic heat generation, increased thermal storage, decreased evapotranspiration, and reduced urban winds in the urban areas (Memon et al. 2008; Oke 1987). But due to canyon shading around the urban site, it may be cooler than the rural site during the daytime (Oke 1982). The case in Hong Kong is more complicated. Daytime negative UHI intensity may be caused by the combined effects of its coastal nature and high-rise and compact urban morphology. On the one
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hand, HKO is closer to the sea than TKL and TYW, which makes it cooler in the daytime. Compared to HKO, the lower daytime temperature and phase difference in diurnal cycles of WGL also lend support to this factor. On the other hand, a recent field model study suggested that the cooler urban daytime phenomenon can be observed only in a high-rise compact model, but not in a low-rise sparse model (Wang et al. 2015a). Seasonality of UHI can be identified in Fig. 3 as well. In general, UHI intensity is higher in winter than in summer, and the difference can be more than 2 °C. Remarkable seasonal variation is evident in all tropical and subtropical cities reviewed by Roth (2007), and the largest UHI intensities are usually measured during the dry season. Figure 4 indicates that this is also the case in Hong Kong: UHI intensities are highly related to humidity and rainfall, weaker in wet seasons and stronger in dry seasons. This seasonality of UHI can probably be explained by surface moisture differences between urban and rural areas. As urban geometry and thermal admittance are primarily contributors of nocturnal UHI, with little vegetative cover, urban cooling potentials do not change much throughout
Fig. 5 Annual summer mean of a daily maximum UHI intensity, daily minimum of hourly temperature at b HKO, and c TKL. Annual winter mean of d daily maximum UHI intensity, daily minimum of hourly temperature at e HKO, and f TKL. Red (blue) dashed lines represent increasing (decreasing) trend
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the year, while some physical properties of the rural surface, such as albedo and thermal admittance, are subject to considerable seasonal change (Roth 2007). The Kolmogorov–Smirnov test (Lilliefors 1967; Massey 1951) is adopted to determine whether the UHI values are samples from a Gaussian distribution. The test shows that the annual means of daily maximum UHI intensities (calculated separately for summer and winter) follow a normal distribution. Therefore, we can use a least squares linear regression to characterize the temporal trend of this quantity. For summertime, UHI intensities in Hong Kong increase with a trend of 0.014 °C per year, but the increase is nonsignificant at the 0.05 significance level (Fig. 5a). The next question is whether the nonsignificance of this increasing trend is due to urban expansion, which may cause, for example, both urban and rural areas to warm up, but the rural areas can warm even faster than the urban areas. Because the daily maximum UHI intensities generally occur at night, particularly in the early morning before sunrise (Fig. 3), the daily minimum of hourly temperature is used to characterize temporal trends of temperature at both the urban and rural sites. It is found that minimum temperature at the urban site increases nonsignificantly with a positive trend of 0.011 °C per year (Fig. 5b), while the rural site shows a slight and nonsignificant decreasing trend (Fig. 5c). Corresponding quantities in winter are shown in Fig. 5d–f. Minimum temperature at HKO is decreasing with a slope of -0.019 °C per year, while at TKL it is decreasing with a larger slope of -0.026 °C per year. But the UHI intensity is increasing with a slope of 0.009 °C per year. None of these three trends in winter is significant at the 0.05 significance level. The above-detected trends lend support to the choice of TKL as a representative rural site: The urban expansion in northern Hong Kong and adjacent Shenzhen (Fig. 2) has not resulted in, at least, faster warming of TKL than HKO.
4 Extreme values and nonlinear parametric trends 4.1 Threshold choice As extreme value theory has not yet been applied to UHI study, the threshold has to be chosen very carefully. We have to balance choosing a sufficiently high threshold, so that the GP distribution of Eq. (1) is essentially satisfied, with choosing a sufficiently low threshold, so that we have enough excesses to estimate the GP parameters. We first adopt the criterion proposed by Coles (2001) for choosing the threshold: two graphical tools, the mean residual life plot and the parameter stability plot. In practice, the scale parameter needs to be adjusted to remove the dependence on the threshold. If a GP distribution is a valid model for excesses of a threshold u0, then excesses of a higher threshold u should also follow a GP distribution. The shape parameters of the two distributions are identical. However, for the GP scale parameter ru for a threshold u [ u0 , it follows that ru ¼ ru0 þ nðu u0 Þ;
ð9Þ
so that the scale parameter changes with u unless n ¼ 0. This difficulty can be remedied by adjusting the GP scale parameter as r ¼ ru nu;
ð10Þ
which is constant with respect to u by Eq. (9). Consequently, estimates of both r* and n should be constant above u0, if u0 is a valid threshold for following the GP distribution.
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Figure 6 shows the mean residual life plot and the parameter stability plot of daily maximum UHIs fitted to the GP distribution against different threshold values in summer, while Fig. 7 shows the plots in winter. The mean residual plots should be linear, and the parameter estimates should be stable (constant) above the threshold at which the GP model becomes valid. In practice, the mean excess values and parameter estimates are computed from a relatively small quantity of data, so the plots will look only approximately linear or constant even when the GP distribution becomes valid. Confidence intervals are included to account for the effects of estimation uncertainty in this evaluation. In the summer case, for instance, in the mean residual life plot (Fig. 6a), we look for approximate linearity while keeping between the confidence bounds. Hence, a threshold above around 5.6 °C is not appropriate because the confidence bounds increase dramatically. And it is obvious in Fig. 6b and c that there are not enough data above a threshold of 5.6 °C. Meanwhile, by taking a threshold below 4.4 °C, the variances in Fig. 6b and c are too small, which means the number of observations is too large and the asymptotic approximation of Eq. (1) will be violated. Therefore, it can be roughly estimated from Fig. 6 that the threshold for summer extreme UHIs should be around 4.4–5.6 °C. Thresholds should be around 7.2–8.6 °C, when similar judgments are imposed on Fig. 7. However, the two graphical tools are helpful only in seeing a range where the threshold should occur, and this still requires a good deal of subjective judgment. Therefore, we propose a further step for threshold selection by taking the Poisson distribution for the frequency of extreme values into consideration. P values representing the goodness-of-fit of the Poisson distribution in modeling extreme UHI events against different threshold choices are given in Fig. 8. For summer, the extreme UHIs are samples from a Poisson distribution only when the chosen threshold is not lower than 4.8 °C, and the p value is highest when the threshold is 4.8 °C. For winter, the Poisson distribution can be satisfied
Fig. 6 a Mean residual life plot (dashed lines: confidence intervals) and b modified parameter ru and c shape parameter n estimates (error bars: confidence intervals) against threshold values for Hong Kong daily maximum UHI in summer
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Fig. 7 Same as Fig. 6 but for winter
Fig. 8 P values represent the goodness-of-fit of the Poisson distribution in modeling extreme UHI events against threshold choices for Hong Kong in a summer and b winter
with many threshold choices higher than 6.8 °C, and the p value is highest when the threshold is 7.8 °C. Therefore, we choose 4.8 °C as the threshold of extreme UHIs for summer and 7.8 °C for winter. These two UHI intensities are in the 97.5th percentile for summer and the 92.5th percentile for winter.
4.2 Stationary modeling Once the thresholds are chosen, extreme UHI events can be calculated and the stationary peaks-over-threshold model applied. Table 2 lists the selected thresholds and fitting
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parameters (standard errors in parentheses) of extreme UHI events in Hong Kong. The stationary modeling results are shown in Figs. 9 and 10. The positive shape parameter in summer and negative parameter in winter demonstrate that extreme UHIs in the two seasons have different statistical behaviors. The fact that the longest duration of extreme UHIs in the study period is only 3 days motivates us to discard modeling this cluster in summer. The thresholds for defining extreme UHIs in each season are calibrated based on extreme value theory, and we concluded that the 97.5th percentile for summer and the 92.5th percentile for winter are the best choices. To verify that the difference in the duration of extreme UHIs between the two seasons is not simply due to a sampling problem (i.e., discrepancy of percentile), we also calculate summer extreme UHIs using the 92.5th percentile as a threshold and model their duration with a geometric distribution (figure not shown). It is found that the probability of 1-day duration is more than 70 %, while the probability of 2-day duration is less than 20 %, and the probability of 3-day duration is only 5.5 %. This is substantially lower than the case of winter in Fig. 10d, which shows that the probability of 1-day duration is below 40 %, and the cumulative probability of 2- to 5-day duration is up to 55 %. A possible reason is that the weather in summer is controlled mainly by relatively shortterm atmospheric convections and conditions (Wang et al. 2014, 2016), while in winter it is controlled by longer-term atmospheric circulations (Cheung et al. 2013, 2015; Zhou et al. 2009). To verify this possibility, we conduct composite analysis of atmospheric anomalies corresponding to extreme UHIs in summer and winter, respectively (Fig. 11). It is obvious that extreme UHIs in summer have a very weak relationship with large-scale anomalies, which may imply that local, and hence short-term, atmospheric conditions are more important in summer. Correspondingly, extreme UHIs in winter are linked with large-scale temperature and circulation anomalies. Precipitation deficiency in the southeast coastal regions of China is found (Fig. 11b). Associated with this dry condition, there are dipolelike patterns in the near-surface temperature and mean sea level pressure (Fig. 11d, f): warm episodes in the Eurasian continent but localized cold anomalies in the southern region. Negative geopotential height anomalies are found east of eastern China at the midlevel’s of the troposphere (Fig. 11h), corresponding to the positive mean sea level pressure anomalies to their southwest (Fig. 11f). Abnormal sinking motions in the southeast coastal regions are clearly seen from vertical velocity anomalies (figure not shown), which is responsible for the regional dry condition. Having chosen the threshold of 4.8 °C for summertime, for the period of 1989–2015 with 2484 daily maximum UHIs, we get 63 excesses. The number of extreme UHI events accounts for about 2.5 % of the total daily observations. The scale (ru) and shape (n) Table 2 Thresholds and fitting parameters (standard errors in parentheses) of extreme UHIs in Hong Kong Parameters
Summer
Winter
Threshold (u)
4.8 °C
7.8 °C
GP scale (ru)
0.74 (0.143)
1.85 (0.158) -0.48 (0.055)
GP shape (n)
0.03 (0.137)
Poisson (k)
2.33 (0.540)
2.96 (0.614)
Geometric (h)
–
0.43 (0.055)
The GP, Poisson, and geometric models are used to fit intensity, frequency, and duration of extreme events, respectively
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Fig. 9 a Quantile plot and b return level plot for GP distribution fitted to daily maximum UHI intensities in Hong Kong summers. c Frequency of extreme UHI events in Hong Kong summers fitted to the Poisson distribution. The threshold is 4.8 °C
Fig. 10 a Quantile plot and b return level plot for GP distribution fitted to daily maximum UHI intensities in Hong Kong winters. c Frequency and d duration of extreme UHI events in Hong Kong winters fitted to the Poisson and geometric distributions, respectively. The threshold is 7.8 °C
parameters in summer are 0.74 and 0.03, respectively. Diagnostic plots for the GP model are generated, allowing the threshold selection to be revisited to see whether the asymptotic basis of the model is violated. The probability plot is not shown, as the (empirical) circles are sufficiently close to linearity. The quantile plot and the return level plot for summer are given in Fig. 9a and b, respectively. The circles in Fig. 9a are located close to the unit diagonal, which lends support to the fitted GP model. There are two exceptions that
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Fig. 11 Composite anomalies of a, b precipitation (mm); c, d near-surface temperature (°C); e, f mean sea level pressure (Pascal); and g, h 500-hPa geopotential height (m) for extreme UHIs in Hong Kong in summers (left panels) and winters (right panels) during 2005–2014. Shading indicates regions of anomalies that are significant at the 0.05 level in the Student’s t test; warm (cool) colors denote positive (negative) significant anomalies. The black dot denotes the location of Hong Kong
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are not located very close to the unit diagonal, the extreme cases in 2009 and 2013, with UHI intensities of over 8 °C (the two circles with highest empirical UHI intensity in Fig. 9a). However, the confidence intervals in the return level plot (Fig. 9b) suggest that the model departures are not large after allowance for sampling. That is, nearly all of the observed records (circles in Fig. 9b) are located between the 95 % confidence intervals (dashed lines in Fig. 9b). Figure 9c suggests that the Poisson model can permit a realistic modeling of extreme UHI frequency in summer. A frequency of one or two events per summer happens most often, while the maximum occurrence can be up to seven in one summer. A Poisson parameter (k) of 2.33 (Table 2) means the average occurrence of extreme UHIs is 2.33 times per summer. For wintertime, having chosen the threshold 7.8 °C for the 27 winters of 1988/1989–2014/2015, with a total of 2436 daily maximum UHIs, we get 80 extreme UHI spells. The scale (ru) and shape (n) parameters in winter are 1.85 and -0.48, respectively. Figure 10 suggests that the stationary peaks-over-threshold model can permit a realistic modeling of extreme UHIs in winter. The goodness-of-fit in the quantile plot (Fig. 10a) is convincing, and the circles are located inside the confidence intervals on the return level plot (Fig. 10b). Figure 10c and d lends support to the fitted Poisson and geometric distributions, respectively. A Poisson parameter of 2.96 (Table 2) is also the mean frequency of extreme UHIs in winter, while a geometric parameter of 0.43 suggests that the mean duration of extreme UHI events is 2.32 days (the reciprocal of the geometric parameter).
4.3 Changes in extreme UHI events It is usually more convenient to interpret the extreme value model in terms of quantiles or return levels, rather than in terms of individual parameter values (Coles 2001). Furthermore, return levels estimated by the threshold excess model can be helpful for social applications, such as risk assessment. This can be done by the return levels estimated by the GP model fitted to daily maximum UHI data. As in Figs. 9b and 10b, the 95 % confidence intervals of these estimations are shown by blue dashed lines and the observations are shown by black circles. For quantitative description, it is more convenient to give return levels on an annual scale, that is, the N-year return level is the level expected to be exceeded once every N years (Wang et al. 2015b). The return levels (with 95 % confidence intervals) of extreme UHIs in Hong Kong corresponding to some typical return periods, e.g., approximately 5, 10, 50, and 100 years, are listed in Table 3. As mentioned above, the positive shape parameter of the GP model in summer implies an unbounded tail, while a negative shape parameter of the GP model in winter implies a bounded tail. Corresponding to this characteristic, the gradient of return levels in summer is obviously larger than that in winter, when Fig. 9b is compared with 10b. Table 3 Mean return levels (95 % confidence intervals in parentheses) estimated using a threshold excess model fitted to daily maximum UHI data in Hong Kong Return period (years)
Return level in summer (°C)
Return level in winter (°C)
5.4
6.7 (6.1, 7.2)
11.0 (10.7,11.2)
10.9
7.2 (6.4, 8.0)
11.2 (10.9, 11.5)
54.5
8.6 (6.8, 10.4)
11.5 (11.2, 11.9)
108.7
9.2 (6.7, 11.6)
11.6 (11.2, 12.0)
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The last step is to estimate parametric trends of extreme UHIs from the peaks-overthreshold model through the generalized linear model framework (for Poisson and geometric distributions) and covariate effects (for the GP distribution), as introduced. The results are shown in Figs. 12 and 13 for summer and winter, respectively. The stems represent the observed year-to-year variations of extreme UHI intensity (Figs. 12a, 13a), frequency (Figs. 12b, 13b), and duration (Fig. 13c) in Hong Kong. Parametric trends of extreme UHIs are obtained when nonstationarity is introduced into the model. The red lines in Figs. 12 and 13 show the parametric trends of extreme UHI quantities. In summer, the trend is 0.042 and 0.011 for intensity and frequency per year, respectively (Table 4). P values of the log-likelihood test estimated in the peaks-over-threshold model suggest that the trend of intensity is significant at the 0.05 level (p value \0.05), while the trend of frequency is nonsignificant (p value [0.05). It is found that there is no trend of extreme UHI intensity in winter (Fig. 13a). The increasing trend of extreme UHI frequency in Fig. 13b and the decreasing trend of extreme UHI duration in Fig. 13c are nonsignificant (Table 4). Under the background of remarkable urban expansion (Fig. 2), the reasons why most extreme UHIs are not increasing significantly, except for summertime extreme UHI intensity, are of interest. As can been seen from Figs. 4 and 11b, UHI intensity is highly related to precipitation or air humidity. Therefore, trends of seasonal total rainfall at the urban and rural sites, and their differences (urban minus rural) as well, are detected in Fig. 14. It shows that summer rainfall decreases slightly at HKO, increases slightly at TKL, and therefore results in a decreasing trend in their differences. However, none of these trends is significant. In winter, on the other hand, all three quantities are decreasing. With a significant negative trend at HKO, the differences between HKO and TKL decrease
Fig. 12 Trends (red lines) of a intensity and b frequency of extreme UHI events in Hong Kong summers during 1989–2015 estimated by the GP and Poisson distributions, respectively. The stems represent observed values
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Fig. 13 Trends (red lines) of a intensity, b frequency, and c duration of extreme UHI events in Hong Kong winters during 1988–2014 estimated by the GP, Poisson, and geometric distributions, respectively. The stems represent observed values
Table 4 Nonstationary parametric trends (p values in parentheses) in a Poisson–GP model for extreme UHIs in summer and winter in Hong Kong Parameters
Summer
Winter
GP scale (ru)
0.042 (0.030)
0.0 (1.0)
Poisson (k)
0.011 (0.491)
0.011 (0.437)
Geometric (h)
–
-0.002 (0.897)
significantly as well. According to Roth (2007), when rural surfaces are either wet or saturated, thermal admittance will be increased; hence, the daily surface temperature range will be relatively small and rural cooling will decrease with a corresponding reduction in UHI intensity. We can therefore deduce that a significant decreasing trend in precipitation
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Fig. 14 Total annual summer rainfall at a HKO, b TKL, and c their differences. Total annual winter rainfall at d HKO, e TKL, and f their differences. Red (blue) dashed lines represent increasing (decreasing) trend. Colored slope value indicates the trend is significant at the 0.05 level
differences between the urban and rural sites has contributed adversely to the trend of extreme UHIs in wintertime in Hong Kong.
5 Discussion and conclusions The present study applies extreme value theory to model and detect trends in extreme UHI events in Hong Kong. A UHI is defined as the temperature difference between an urban site, HKO, and a rural site, TKL, which are suggested to be appropriate locations for studying UHIs in Hong Kong (Siu and Hart 2013). Figure 5 demonstrates that during the 27-year study period, the selected rural site is at least not warming faster than the urban site. Another conclusion that can be drawn from Fig. 5 is that an increasing trend of mean UHI intensity exists, but it is statistically nonsignificant. The peaks-over-threshold model is then introduced to study extreme UHIs in Hong Kong.
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An extreme UHI event is defined as a UHI with an intensity higher than a specific high threshold. Based on a series of tests, we chose a threshold of 4.8 and 7.8 °C for summer and winter, respectively. One interesting result is that a positive shape parameter is obtained when extreme UHIs in summer are fitted to a GP model. This implies that it has an unbounded tail. In winter, on the other hand, a negative GP shape parameter is obtained, implying that it has a bounded tail. The mean residual life plots in Figs. 6a and 7a and the return level plots in Figs. 9b and 10b provide statistical support for this finding. This further implies that summer extreme UHIs are relatively discrete, while winter extreme UHIs have stronger continuity, which is probably due to differences in atmospheric anomalies that are bonded to extreme UHIs in the two seasons (Fig. 11). After appropriate thresholds are chosen, the peaks-over-threshold model shows realistic modeling of extreme UHI events in both summer (Fig. 9) and winter (Fig. 10). In time-dependent trend detection of environmental and meteorological series, ordinary parametric trend estimation (least squares regression) is not recommended mainly because it requires the time series to be normally distributed, which is likely to be violated for extreme events. Therefore, nonparametric trend detection methods, which require only that the data be independent, are widely used (Alexander and Arblaster 2009; Birsan et al. 2014; Deng et al. 2014; Wang et al. 2012). The nonparametric Kendall-Mann test (Kendall 1975; Mann 1945) and Kendall’s tau-based slope estimator (Sen 1968) are most frequently adopted in these studies. However, if the distributional form is known, a parametric method usually has a better test power (Zhai et al. 2005). Zhang et al. (2004) compared the least squares method, the Kendall’s tau-based method, and the generalized extreme value method and concluded that explicit consideration of the extreme value distribution when computing the trend always gives the best performance. Madsen et al. (2014) also suggested that parametric tests seem to be the most powerful for extreme value data when the distributional assumptions are fulfilled. We therefore perform trend detections for extreme UHIs in Hong Kong by introducing parametric changes to fitted peaks-over-threshold models. It can be concluded that during the last 27 years, the only significant increasing trend is in the intensity of extreme UHIs in summer. But this is an unfortunate finding, particularly for Hong Kong.
Fig. 15 Scatter plot of summer daily maximum temperatures at HKO versus daily maximum UHI intensities. The vertical (horizontal) black dashed line denotes the 88th percentile of daily maximum temperature, 33.0 °C (UHI intensity, 3.8 °C). The vertical (horizontal) red dashed line denotes the 97.5th percentile of daily maximum temperature, 33.9 °C (UHI intensity, 4.8 °C)
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As a high-density city in the subtropics, Hong Kong is suffering from the ill effects of UHIs due to land use, urbanization, and human activities. The old and the weak living in their tiny rooms in urban areas will have to face an increasing number of hot nights with no air conditioning (Lam 2006). What we have taken into account is the daily maximum UHI, which usually occurs at nighttime. Meanwhile, extreme UHIs have a high possibility of happening at a time when the background temperature is high, due to the synergistic interactions between UHIs and heat waves, which has been found in other places (Li and Bou-Zeid 2013; Li et al. 2015). For the case in Hong Kong, we demonstrate this possibility simply by a scatter plot of daily maximum temperatures recorded at HKO versus daily maximum UHI intensities (calculated from hourly temperatures) (Fig. 15). A hot day in Hong Kong is commonly defined when the daily maximum temperature at HKO is above 33.0 °C, which is the 88th percentile of the data we utilized here (summer days during 1989–2015). The 88th percentile of summer UHI intensity is 3.8 °C. We can define this as a lower criterion (black dashed lines in Fig. 15), while a higher criterion can be defined by the 97.5th percentile (red dashed lines in Fig. 15). It is found that for the lower criterion, the probability of extreme UHI occurrence is 10.5 % during nonhot days and increases to 32.3 % during hot days. For the higher criterion, the probability of extreme UHI occurrence is 2.4 % during nonhot days and increases to 11.5 % during hot days. By synergy with summertime heat waves, UHIs can foster heat stress, creating a biophysical hazard (Zhou and Shepherd 2009). A significant increasing trend in the intensity of extreme UHI events in summer implies that the risk of mortality and heat-related diseases due to heat stress at night in summer, when the daily maximum UHI occurs, is also increasing significantly. A study in Hong Kong has reported that a 1 °C rise in physiological equivalent temperature may result in a 1.8 % increase in heat stress-related mortality (Goggins et al. 2012). The warming climate has threatened and will continue to threaten inhabitants in this subtropical high-density city. Strategies for mitigating human impacts on the climate system during urban planning, such as adding greenery and planning a city with good natural ventilation, need to be implemented (Guindon and Nirupama 2015; Ng et al. 2011, 2012). Because it is located in a subtropical coastal region, Hong Kong has a hot and humid climate. Though UHIs in winter are stronger and their extreme events last longer than those in summer, extreme UHIs in winter mean that it is warmer in the urban areas than in the surrounding rural areas and this does not locally harm the inhabitants in the city. Furthermore, extreme analysis detected no significant trends in wintertime extreme UHIs (Fig. 13), which may relate to the significant decreasing trend of urban–rural precipitation differences (Fig. 14). Acknowledgments This study was supported by the Research Grants Council of the Hong Kong Special Administrative Region (Project No. 14408214 and 11305715), City University of Hong Kong Campus Sustainability Project (698603), and Institute of Environment, Energy and Sustainability, CUHK (Project ID: 1907002). We thank the Hong Kong Observatory for providing meteorological records. We appreciate the valuable comments and suggestions from the three anonymous reviewers.
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