A Methodology for Comparing the Surface Urban Heat Island in Selected Urban Agglomerations Around the World from Sentinel-3 SLSTR Data

: Retrieval of land surface temperature (LST) from satellite data allows to estimate the surface urban heat island (SUHI) as the di ﬀ erence between the LST obtained in the urban area and the LST of its surroundings. However, this deﬁnition depends on the selection of the urban and surroundings references, which translates into greater di ﬃ culty in comparing SUHI values in di ﬀ erent urban agglomerations across the world. In order to avoid this problem, a methodology is proposed that allows reliable quantiﬁcation of the SUHI. The urban reference is obtained from the European Space Agency Climate Change Initiative Land Cover and three surroundings references are considered; that is, the urban adjacent (Su), the future adjacent (Sf), and the peri-urban (Sp), which are obtained from mathematical expressions that depend exclusively on the urban area. In addition, two formulations of SUHI are considered: SUHI MAX and SUHI MEAN , which evaluate the maximum and average SUHI of the urban area for each of the three surrounding references. this methodology has been applied to 71 urban agglomerations around the world using LST data obtained from the sea and land surface temperature radiometer (SLSTR) on board Sentinel-3A. The results show average values of SUHI MEAN of (1.8 ± 0.9) ◦ C, (2.6 ± 1.3) ◦ C, and (3.1 ± 1.7) ◦ C for Su, Sf, and Sp, respectively, and an average di ﬀ erence between SUHI MAX and SUHI MEAN of (3.1 ± 1.1) ◦ C. To complete the study, two additional indices have been considered: the Urban Thermal Field Variation Index (UFTVI) and the Discomfort Index (DI), which proved to be essential for understanding the SUHI phenomenon and its consequences on the quality of life of the inhabitants.


Introduction
By 2050, the world's population is estimated to increase to nine billion, 70% of whom will live in urban areas [1]. The rapid increase of these areas without adequate prior planning is an increasingly worrying problem that seriously threatens the environment and the health and well-being of the population [2].
One of the most problematic consequences of rapid urbanization is the increase of the urban heat island (UHI) [3,4], which is defined as the difference between the air temperature (AT) within the urban area and the AT of its surroundings [5]. Generally, the temperature in urban areas is higher than in rural areas, especially at night [5]. This phenomenon, which will be reinforced by the effects of climate change, not only affects people psychologically and physiologically, but also controls daily behaviours and economic activities [6] and can lead to a drastic increase in morbidity and mortality [7], increased

SUHI Selection of the Urban and Surrounding References
The main objective of this work is to present a methodology that allows the analysis and comparison of SUHI in urban agglomerations around the world. For this purpose, night-time LST obtained from satellite data has been used [12] to estimate SUHI MAX and SUHI MEAN , which are defined as the thermal differences between the maximum and average LST of the urban area and the LST of its surroundings, respectively, according to SUHI MAX = LST URB−MAX − LST SUR (1) where LST URB−MAX is the maximum LST of the urban area (hottest pixel), LST URB-MEAN is the average temperature of the pixels that define the urban area, and LST SUR is the average temperature of the pixels that compose the surrounding area. The main problem in estimating SUHI MAX and SUHI MEAN is the difficulty in identifying urban and surrounding references. There is no clear definition in the literature of how to select these areas [32], which makes it extremely difficult to compare SUHI between different urban agglomerations. To address this problem, we propose the following approach: (a) Urban: To define the urban reference, a land cover map with explicit representation of urban areas is the most operational solution. In our case, among the large number of free land cover products available today, we use the global land cover map produced by the European Space Agency (ESA) Climate Change Remote Sens. 2020, 12, 2052 3 of 29 Initiative (CCI) [33] (for more information, visit the website https://maps.elie.ucl.ac.be/CCI/viewer/), where the urban reference is obtained from those classified as "urban areas". From this class, a polygon is generated that is identified with the area of the urban agglomeration selected (A).
(b) Surroundings: As for the surrounding, three different reference areas were defined, the urban adjacent (S U ), the future urban adjacent (S f ), and the peri-urban (S P ). The width (W U , W f , and W P ) of the buffer for each surrounding is calculated as follows: where Awu is the sum of A and Su areas (see Figure 1). Similar expressions for Wu and Wp can be found in [34] and [35], respectively, while W f is introduced in this paper assuming future expansion of the urban area to include the urban adjacent surrounding Su. With this approach, the extent of the surrounding areas is clearly defined and depends only on A (the area of the urban agglomeration).
As an example, Figure 2 shows the application of the methodology to the Paris urban agglomeration.
Remote Sens. 2020, 12, 2052 3 of 31 a) Urban: To define the urban reference, a land cover map with explicit representation of urban areas is the most operational solution. In our case, among the large number of free land cover products available today, we use the global land cover map produced by the European Space Agency (ESA) Climate Change Initiative (CCI) [33] (for more information, visit the website https://maps.elie.ucl.ac.be/CCI/viewer/), where the urban reference is obtained from those classified as "urban areas". From this class, a polygon is generated that is identified with the area of the urban agglomeration selected (A). b) Surroundings: As for the surrounding, three different reference areas were defined, the urban adjacent (SU), the future urban adjacent (Sf), and the peri-urban (SP). The width (WU, Wf, and WP) of the buffer for each surrounding is calculated as follows: where Awu is the sum of A and Su areas (see Figure 1). Similar expressions for Wu and Wp can be found in [34] and [35], respectively, while Wf is introduced in this paper assuming future expansion of the urban area to include the urban adjacent surrounding Su. With this approach, the extent of the surrounding areas is clearly defined and depends only on A (the area of the urban agglomeration). As an example, Figure 2 shows the application of the methodology to the Paris urban agglomeration.

UTFVI and DI Indices
To complement the analysis of SUHI, two additional indices were considered. That is, the Urban Thermal Field Variance Index (UTFVI) [18,31] and the Discomfort Index (DI) [36]. The UTFVI is the most widely used index for the ecological evaluation of urban environment owing to its direct relation to LST and considers the thermal impact of the different sub-areas (district level) in the urban agglomeration area (A), according to UFTVI = 1 -(LSTURB-MEAN /LSTURB-PIXEL) (6) where LSTURB-PIXEL is the LST in K, obtained from satellite data, of a given pixel of A and LSTURB-MEAN is the average LST of the whole urban area (A). Note that SUHIMAX and SUHIMEAN describe the SUHI between the whole urban area and the surroundings, while UFTVI is used for evaluating the effect for each pixel located within the urban area with respect to the whole urban area. UTFVI is divided into six levels by six specific ecological evaluation indices. The thresholds at the six UFTVI levels are shown in Table 1, from no SUHI (excellent) if LSTURB-PIXEL < LSTURB-MEAN to strongest (worst) with UFTVI > 0.02, a situation that occurs when the value of LSTURB-PIXEL is several degrees higher than LSTURB-MEAN, for example, 302 K and 295 K, respectively.

UTFVI and DI Indices
To complement the analysis of SUHI, two additional indices were considered. That is, the Urban Thermal Field Variance Index (UTFVI) [18,31] and the Discomfort Index (DI) [36]. The UTFVI is the most widely used index for the ecological evaluation of urban environment owing to its direct relation to LST and considers the thermal impact of the different sub-areas (district level) in the urban agglomeration area (A), according to where LST URB-PIXEL is the LST in K, obtained from satellite data, of a given pixel of A and LST URB-MEAN is the average LST of the whole urban area (A). Note that SUHI MAX and SUHI MEAN describe the SUHI between the whole urban area and the surroundings, while UFTVI is used for evaluating the effect for each pixel located within the urban area with respect to the whole urban area. UTFVI is divided into six levels by six specific ecological evaluation indices. The thresholds at the six UFTVI levels are shown in Table 1, from no SUHI (excellent) if LST URB-PIXEL < LST URB-MEAN to strongest (worst) with UFTVI > 0.02, a situation that occurs when the value of LST URB-PIXEL is several degrees higher than LST URB-MEAN , for example, 302 K and 295 K, respectively. It is well known that one of the consequences of SUHI is the influence on human health. The Discomfort Index (DI), also known as the Thom's discomfort index [37], is a measure of the reaction of the human body to a combination of heat and humidity. DI can be estimated according to Sobrino et al. [5] at night-time from satellite measurements according to where LST is the land surface temperature in •C, obtained from satellite data, for a given pixel of A and RH is the relative humidity in %. RH can be obtained from in situ or satellite data. Our objective is to propose an operational methodology and, for this purpose, RH is obtained from the atmospheric infrared sounder (AIRS), L3 surface relative humidity product on board NASA's AQUA satellite [38]. DI is divided into ten categories, which are shown in Table 2.

Criteria for Urban Agglomerations Selection
In order to apply the methodology developed, 71 urban agglomerations were selected around the world: 7 in Africa, 19 in America, 24 in Asia, 18 in Europe, and 3 in Oceania (more information on the characteristics of the selected agglomerations can be found in Appendix A). The criteria used for selection (see Figure 3a-c) were as follows (a) urban agglomeration areas, which cover the globe as extensively and widely as possible at different latitudes and longitudes, in different climatic zones and with different population and density of habitants, giving priority to those that are experiencing a large increase in population [39,40] or are considered particularly vulnerable to climate change [41]; (b) urban areas at different altitudes (e.g., from Perth at 0 m above sea level to Lhasa at 3650 m); (c) coastal and inland agglomerations (e.g., Rio de Janeiro, Moscow); (d) urban agglomerations with high levels of NO 2 [42] and night-time light pollution (e.g., Shanghai, New York); (e) urban agglomerations with an area greater than 50 km 2 in order to have a number of pixels representative at the spatial resolution of the satellite.

Satellite Data
So far, the most used satellites for SUHI estimation have been TERRA, AQUA, and Landsat [11], with few studies using data from the ESA's Sentinel 3 satellites owing to the short period of operation. In this paper, SUHI is analysed using the LST product obtained from the SLSTR sensor onboard Sentinel-3A (Level-2 LST) [29] during the period June 2018 to May 2019. Night images were selected following Sobrino et al. [5], when the SUHI effect is most notable. For each urban agglomeration, the month with

Satellite Data
So far, the most used satellites for SUHI estimation have been TERRA, AQUA, and Landsat [11], with few studies using data from the ESA's Sentinel 3 satellites owing to the short period of operation. In this paper, SUHI is analysed using the LST product obtained from the SLSTR sensor onboard Sentinel-3A (Level-2 LST) [29] during the period June 2018 to May 2019. Night images were selected following Sobrino et al. [5], when the SUHI effect is most notable. For each urban agglomeration, the month with the warmest temperature records was searched, and for that month, a warm and clear night.
Level-2 LST products have been validated against in situ observations from twelve "gold standard" stations spread thoughout the Earth that are installed with well-calibrated instrumentation: seven from the Surface Radiation Budget Network (SURFRAD) in Bondville, Illinois; Desert Rock, Nevada; Fort Peck, Montana; Goodwin Creek, Mississippi; Penn State University, Pennsylvania; Sioux Fall, South Dakota; Table Mountain, and Colorado; two from the Atmospheric Radiation Measurement (ARM) network in Southern Great Plains, Oklahoma; Barrow, and Alaska; and three from the U.S. Clima Reference Network (USCRN) in Williams, Arizona; Des Moines, Iowa; Manhatten, and Kansas. The average absolute accuracy is within the 1 K requirement (better than 1 K) [43].

Results and Discussion
In this section, values of SUHI, UTFVI, and DI in 71 urban agglomerations around the world are given. It is important to note that whether a given agglomeration has high or low values of SUHI, or can be classified according to the values of UFTVI and Di, should be interpreted as these are the results for the day and time of the selected Sentinel 3A image (more information, including the numerical values of the indices and the Level-2 LST for each agglomeration, can be found in Appendix A).
We also want to point out that the main objective of the present work is to propose an operational methodology that allows a systematic and effective assessment of SUHI, UTFVI, and DI in order to detect warning situations and identify the vulnerabilities of the urban area. This is particularly necessary in the current context of global warming, but even more so if we consider future scenarios, for example, Sobrino et al. [44] shows a linear warming trend of the surface temperature of the planet of 0.18 K per decade. In that sense, the inhabitants of the urban area, especially those who live or develop their activities in urban districts with high UTFVI values, are already intensely suffering the effects of the increase in temperature. MEAN values, respectively, which vary according to the agglomeration and the surrounding area considered. The proposed methodology has the potential to reflect the differences in a quantitative way. For example, the European agglomerations show less dispersion than the American and Asian agglomerations, among which there were those that present greater differences with respect to the selected surrounding.

Figures 4 and 5 show the SUHI MAX and SUHI
In general, the highest differences are for the peri-urban areas (S p ), and the smallest are for the urban adjacent (Su). We only identified three cases (San Diego-Tijuana, Los Angeles, and Taskent) that show a different pattern to the other 68 cities with greater temperature differences in the adjacent urban surroundings (Su) and smaller in Sf and Sp. In the case of San Diego-Tijuana and Los Angeles, the temperature of the most remote areas is higher owing to the proximity of desert and other urban agglomerations that emit heat. Taskent, on the other hand, has an adjacent urban area of crops and irrigated land that cools the surface, while the farthest areas are covered with dry vegetation or bare soil. Other particular cases are agglomerations that show similar SUHI values for Su, Sf, and Sp (e.g., Dammam, Calcutta, Shanghai, or Athens). In most cases, this corresponds to urban areas whose surroundings present similar characteristics to the area close to the urban nucleus. Characteristics that are not very common in the rest of the selected agglomerations. In the case of Lhasa, the values Remote Sens. 2020, 12, 2052 8 of 29 for Sf and Sp are much higher than for Su. This is because the city of Lhasa is built in the valley of the Brahmaputra river, surrounded by the Himalayan mountains that take altitudes immediately higher than those of the city in very short distances, which contributes to the maintenance of higher temperatures in the urban area. In addition, the dams built in the river regulate the temperature of the city holding part of the heat accumulated during the day. In some cases, there is a big difference in LST in the hottest area within the urban area compared with the peri-urban area (Sp). Figure 4 (blue column) shows values above 8 • C in Vancouver, New York, Tokyo, Lhasa, Ürümqi, Las Vegas, Ciudad de Mexico, Rio de Janeiro, Jakarta, Buenos Aires, San José, and Moscow.
surroundings present similar characteristics to the area close to the urban nucleus. Characteristics that are not very common in the rest of the selected agglomerations. In the case of Lhasa, the values for Sf and Sp are much higher than for Su. This is because the city of Lhasa is built in the valley of the Brahmaputra river, surrounded by the Himalayan mountains that take altitudes immediately higher than those of the city in very short distances, which contributes to the maintenance of higher temperatures in the urban area. In addition, the dams built in the river regulate the temperature of the city holding part of the heat accumulated during the day. In some cases, there is a big difference in LST in the hottest area within the urban area compared with the peri-urban area (Sp). Figure 4 (blue column) shows values above 8 °C in Vancouver, New York, Tokyo, Lhasa, Ürümqi, Las Vegas, Ciudad de Mexico, Rio de Janeiro, Jakarta, Buenos Aires, San José, and Moscow.
A relevant aspect to highlight is that the average difference between SUHIMAX and SUHIMEAN for all cases is (3.1 ± 1.1) ⁰C (see numerical values in Table A2 of Appendix A). This implies that, on average for the agglomerations selected, the inhabitants of the urban zone where the maximum temperature occurs experience up to 3.1 degrees higher LST than the rest of the inhabitants of the urban agglomerations. Note that a difference of zero between SUHIMAX and SUHIMEAN would imply a value of UFTVI lower than 0 (i.e., an excellent ecological evaluation index, see Table 1).   As a complement to Figure 5, Table 3 shows the SUHIMEAN values for the three surrounding areas (Su, Sf, and Sp) ordered according to the following criteria: by continent, for populations above 20 million inhabitants, with an urban area higher than 1000 km 2 , at a minimum distance of 1000 km from the coast, at an altitude higher than 1 km above sea level, by climate classification according to the five Köppen vegetation groups [45] and including the 71 agglomerations.
Taking these last values as reference, the average heat island effect of 1.8 °C for the adjacent surrounding area increases by 0.8 °C for Sf and 1.3 °C for Sp, which means that, considering this average as a representative on a global scale and assuming a linear warming trend of 0.18 K per decade [44], the inhabitants of the urban agglomerations in the world are already suffering the effects of the warming that will be reached by the inhabitants of the adjacent surrounding area in the next century.
It is also noted that Europe is the continent with the highest values of SUHI in the three reference areas, with Africa being the continent with the lowest values. High values are also observed in the seven agglomerations with more than 20 million inhabitants, being 0.3 °C higher than those obtained for agglomerations with surfaces above 1000 km 2 . With regard to the agglomerations situated at a distance of more than 1000 km from the coast, values similar to the world average are obtained, with the elevation producing a slight decrease of 0.3 °C compared with the average in Su. Finally, in terms A relevant aspect to highlight is that the average difference between SUHI MAX and SUHI MEAN for all cases is (3.1 ± 1.1) 0 C (see numerical values in Table A2 of Appendix A). This implies that, on average for the agglomerations selected, the inhabitants of the urban zone where the maximum temperature occurs experience up to 3.1 degrees higher LST than the rest of the inhabitants of the urban agglomerations. Note that a difference of zero between SUHI MAX and SUHI MEAN would imply a value of UFTVI lower than 0 (i.e., an excellent ecological evaluation index, see Table 1).
As a complement to Figure 5, Table 3 shows the SUHI MEAN values for the three surrounding areas (Su, Sf, and Sp) ordered according to the following criteria: by continent, for populations above 20 million inhabitants, with an urban area higher than 1000 km 2 , at a minimum distance of 1000 km from the coast, at an altitude higher than 1 km above sea level, by climate classification according to the five Köppen vegetation groups [45] and including the 71 agglomerations. Taking these last values as reference, the average heat island effect of 1.8 • C for the adjacent surrounding area increases by 0.8 • C for Sf and 1.3 • C for Sp, which means that, considering this average as a representative on a global scale and assuming a linear warming trend of 0.18 K per decade [44], the inhabitants of the urban agglomerations in the world are already suffering the effects of the warming that will be reached by the inhabitants of the adjacent surrounding area in the next century.
It is also noted that Europe is the continent with the highest values of SUHI in the three reference areas, with Africa being the continent with the lowest values. High values are also observed in the seven agglomerations with more than 20 million inhabitants, being 0.3 • C higher than those obtained for agglomerations with surfaces above 1000 km 2 . With regard to the agglomerations situated at a distance of more than 1000 km from the coast, values similar to the world average are obtained, with the elevation producing a slight decrease of 0.3 • C compared with the average in Su. Finally, in terms of climate, the highest values are found in warm temperate and snow climates, and the lowest in the equatorial and arid climates.

UTFVI
UTFVI is a complementary index to SUHI MEAN that allows to detect areas affected by heat accumulation within the urban agglomeration. In Figure 6, we present the maximum values of the UFTVI index for each urban agglomeration. The highest values are obtained for the urban agglomerations of San José and Ürümqi, followed by Mexico City, New York, Los Angeles, Toronto, Jakarta, Kuala Lumpur, and Buenos Aires.
UTFVI is a complementary index to SUHIMEAN that allows to detect areas affected by heat accumulation within the urban agglomeration. In Figure 6, we present the maximum values of the UFTVI index for each urban agglomeration. The highest values are obtained for the urban agglomerations of San José and Ürümqi, followed by Mexico City, New York, Los Angeles, Toronto, Jakarta, Kuala Lumpur, and Buenos Aires.

DI
With regard to the DI index, the values are correlated to climate, geographical location, and altitude, so that, in some cases, the accumulation of temperature in urban areas allows a transition

DI
With regard to the DI index, the values are correlated to climate, geographical location, and altitude, so that, in some cases, the accumulation of temperature in urban areas allows a transition from cold to comfortable categories (e.g., Vancouver).   Table A2 of Appendix A) of the Discomfort Index (DIMAX) for the urban agglomeration areas selected in this paper. The colors indicated the DI categories according to Table 2. Figure 8 shows the maximum and average values of the DI versus the LSTURB-MEAN for the selected agglomerations. As can be seen, 89% of the 71 agglomerations have a DIMEAN above 20 °C (hot) and 10% are very hot (see Table 2). As for the DIMAX, 37% of the urban agglomeration are very hot and 9% are torrid.  Table A2 of Appendix A) of the Discomfort Index (DI MAX ) for the urban agglomeration areas selected in this paper. The colors indicated the DI categories according to Table 2. Figure 8 shows the maximum and average values of the DI versus the LST URB-MEAN for the selected agglomerations. As can be seen, 89% of the 71 agglomerations have a DI MEAN above 20 • C (hot) and 10% are very hot (see Table 2). As for the DI MAX , 37% of the urban agglomeration are very hot and 9% are torrid.  Table A2 of Appendix A) of the Discomfort Index (DIMAX) for the urban agglomeration areas selected in this paper. The colors indicated the DI categories according to  Figure 8 shows the maximum and average values of the DI versus the LSTURB-MEAN for the selected agglomerations. As can be seen, 89% of the 71 agglomerations have a DIMEAN above 20 °C (hot) and 10% are very hot (see Table 2). As for the DIMAX, 37% of the urban agglomeration are very hot and 9% are torrid.   Table 4.

Conclusions
Retrieval of land surface temperature (LST) from satellite data allows the estimation of the surface urban heat island (SUHI) as the difference between the LST obtained in the urban area and the LST of its surroundings. However, this definition depends on the selection of the urban and its surrounding.
So far, there is no clear definition in the literature of how to select these reference areas, and thus this makes it extremely difficult to compare the SUHI between different urban agglomerations.
In this work, a methodology was proposed to estimate the SUHI in a precise and simple way in which the urban reference is obtained from the urban area class of the ESA CCI land cover map and three surroundings references are defined: the urban adjacent (S U ), the future adjacent (S F ), and the peri-urban (S P ), which are obtained from mathematical expressions that depend exclusively on the total urban area (A). In addition, two formulations of SUHI are considered: SUHI MAX and SUHI MEAN , which evaluate the maximum and average SUHI of the urban area for each of the three surrounding references.
The proposed methodology was applied to the LST level-2 data product obtained from the SLSTR sensor on board the Sentinel-3A satellite in 71 urban agglomerations worldwide. To complete the study, two additional indices were considered: the Urban Thermal Field Variation Index (UTFVI) and the Discomfort Index (DI), which proved to be complementary to the SUHI phenomenon.
Once the methodology was presented and applied, future work will require a systematic evaluation of SUHI MAX and SUHI MEAN in urban agglomerations around the world in order to analyse the impact of latitude, longitude, morphology of the urban area, season, distance from ocean, as well as the impact of global warming, which will make necessary to take preventive measures against episodes of heat waves that will be increasingly intense and frequent.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Appendix A
Characteristics of the Urban Agglomerations Selected (see Table A1) Table A1. Urban agglomerations selected in the present paper. CITY is the name of the urban agglomeration. LAT and LON are the latitude and longitude. HEIGHT is the average elevation above sea level in meters. CLIMATE indicates the climatic zone according to Köppen-Geiger classification, see Table 1 Figure A1. Land surface temperature images (Sentinel-3A SLSTR Level-2 LST product) of the urban agglomerations selected. The images cover the peri-urban area. The polygon is the urban area obtained from ESA CCI [33].