environments

Article Spatial and Temporal Variability Patterns of the Urban Heat Island in São Paulo

Fernanda Batista Silva 1,*, Karla Maria Longo 1,2 and Felipe Marques de Andrade 1

1 Center for Weather Forecasting and Climate Studies (CPTEC), National Institute for Space Research (INPE), São José dos Campos, SP 12227-010, Brazil; [email protected] (K.M.L.); [email protected] (F.M.A.) 2 Universities Space Research Association/Goddard Earth Sciences Technology and Research (USRA/GESTAR), NASA Goddard Space Flight Center, Greenbelt, MD 29771, USA * Correspondence: [email protected]; Tel.: +55-12-3208-6639

Academic Editor: Yu-Pin Lin Received: 18 January 2017; Accepted: 22 March 2017; Published: 29 March 2017

Abstract: The spatial and temporal variability patterns of the urban heat island (UHI) in the metropolitan area of Sao Paulo (MASP) were investigated using hourly temperature observations for a 10-year period from January 2002 to December 2011. The empirical orthogonal function (EOF) and cluster analysis (CA) techniques for multivariate analysis were used to determine the dominant modes of UHI variability and to identify the homogeneity between the temperature observations in the MASP. The EOF method was used to obtain the spatial patterns (T-mode EOF) and to define temporal variability (S-mode EOF). In the T-mode, three main modes of variability were recognized. The first EOF explained 66.7% of the total variance in the air temperature, the second explained 24.0%, and the third explained 7.8%. The first and third EOFs were associated with wind movement in the MASP. The second EOF was considered the most important mode and was found to be related to the level of urbanization in the MASP, the release of heat stored in the urban canopy and the release of heat by anthropogenic sources, thus representing the UHI pattern in the MASP. In the S-mode, two modes of variability were found. The first EOF explained 49.4% of the total variance in the data, and the second explained 30.9%. In the S-mode, the first EOF represented the spatial pattern of the UHI and was similar to the second EOF in the T-mode. CA resulted in the identification of six homogeneous groups corresponding to the EOF patterns observed. The standard UHI according to the scale and annual seasons for the period from 2002 to 2010 presented maximum values between 14:00 and 16:00 local time (LT) and minimum values between 07:00 and 09:00 LT. Seasonal analysis revealed that spring had the highest maximum and minimum UHI values relative to the other seasons.

Keywords: urban heat island; air temperature; São Paulo; multivariate statistical techniques; empirical orthogonal function; cluster analysis

1. Introduction Urbanization produces significant changes in the radiative, thermal, and aerodynamic properties of surfaces by forming heat domes over cities, termed urban heat islands (UHIs) [1–4]. The spatial distribution of UHIs is typically marked by a strong horizontal temperature gradient at the urban–rural boundary and a gradual temperature decrease from the center to the edge of the city, and these gradients are strongly affected by local circulation and weather conditions; thus, they are defined by diurnal and seasonal variations [5–7]. The major contributing factors to the development and scale of the spatial patterns of UHIs include the scarcity of vegetation; the extensive use of waterproof, high thermal-capacity and/or albedo materials in construction and paving, thereby reducing evaporation; the typical three-dimensional

Environments 2017, 4, 27; doi:10.3390/environments4020027 www.mdpi.com/journal/environments Environments 2017, 4, 27 2 of 26 geometry of the urban surface (canyon-type configuration), which traps energy; the size of the population; the release of anthropogenic heat through vehicle traffic, industrial processes, human and animal metabolism and energy consumption; and a high concentration of energy-absorbing pollutants (gases and aerosols) in the urban atmosphere. Furthermore, the spatial patterns of UHIs can be strongly influenced by surface characteristics, such as green areas, water bodies and local topographies [1,2,8–19]. The most widely recognized method of studying the spatial and temporal variability patterns of UHIs is by applying statistical techniques to observational meteorological databases [20–24]. This approach can analyze differences between urban and rural areas by comparing the intensity of the day and night UHI periods and by identifying variations at seasonal, interannual and decadal scales [25,26]. The metropolitan area of São Paulo (MASP) in southeast Brazil is among the top ten most highly populated cities and is one of the largest urban areas in the world. Previous attempts to determine the UHI patterns of the MASP have revealed that feedback occurs between the UHI and sea breezes [27–29]. According to Freitas et al. [29], the MASP’s UHI induces the formation of an active convergence zone in the city and accelerates the movement of the sea breeze front radially towards the urban center. The mixture of dry and warm urban air, with relatively damp and cold maritime air, favors convective instability and the development of intense convective cells, transporting a significant amount of humidity from the surface to upper levels, and only when the heat island dissipates, the sea breeze progresses beyond the city. The net effect is the retention of the sea breeze over the metropolitan area for up to two hours [29]. The UHI predominates during daytime, with the maximum and minimum intensities in the afternoon and morning, respectively [30]. However, during November, December, and January the minimum UHI intensity occurs at night. July and September exhibit the highest intensity, and June and November the lowest [30]. To the best of our knowledge, previous studies of the UHI of the MASP are all based on studies of climatological time series [31] and analyses of the effects of urbanization and morphology on temperature patterns [30,32,33]. Recent studies have also included remote sensing [34] and atmospheric modelling [29,35]. Other approaches have investigated the UHI according to its effects on comfort and human health; for example, areas with a more intense UHI (land surface temperature >32 ◦C) have a higher incidence of the disease dengue fever than other urban areas [36]. Nonetheless, the spatial and temporal patterns of urban temperatures and UHIs are not well understood for the largest metropolitan area of South America. The main goal of this study was to determine the spatial and temporal structures of the UHI of the MASP. Specifically, we chose to investigate the diurnal, seasonal and interannual patterns, with a focus on the dominant modes of variability in air temperature anomaly data, to determine the characteristic similarities and differences in the MASP. Multivariate statistical analyses were performed using observational data. The study area, datasets and a review of the statistical analysis methods are described in Section2, the results are presented and discussed in Section3, and a summary and conclusions are provided in Section4.

2. Materials and Methods

2.1. Study Area and Datasets São Paulo city, in the southeast Brazil, is one of the most populated and largest urban conglomerates in South America (Figure1a). The MASP consists of 39 cities (Figure1b), and it is the largest hub of national wealth and the sixth largest city in the world. The MASP occupies a land area of 944 km2 and has a population of approximately 20 million (IBGE/2011). Environments 2017, 4, 27 3 of 26 Environments 2017, 4, 27 3 of 26 Environments 2017, 4, 27 3 of 26

FigureFigure 1. (a )1. Geographical (a) Geographical location location of the of metropolitanthe metropolitan area area of S ãofo PauloSão Paulo (MASP) (MASP) in Brazil; in Brazil; (b) magnified (b) viewsmagnifiedFigure of the 1. MASP. views(a) Geographical of the MASP. location of the metropolitan area of São Paulo (MASP) in Brazil; (b) magnified views of the MASP. The MASP has a topography dominated by hills ranging from 650 to 1200 m above the sea level The MASP has a topography dominated by hills ranging from 650 to 1200 m above the sea (asl); Thethe MantiqueiraMASP has a andtopography Serra do dominated Mar Mountain by hills chains ranging standing from out650 into the1200 northern m above and the southern sea level level (asl); the Mantiqueira and Serra do Mar Mountain chains standing out in the northern and limits(asl); theof Mantiqueirathe region, andrespectively, Serra do Marand Mountainthe Jaragu cháains Peak standing standing out outin the at northernthe west and end southern of the southernMantiqueiralimits limits of the ofMountains region, the region, respectively, (Figure respectively, 2). Sãoand Paulo the and Jaragucity the is Jaragu áapproximately Peaká Peakstanding standing 55 outkm fromat outthe the atwest theAtlantic westend Ocean.of end the of the MantiqueiraTheMantiqueira topography, Mountains Mountains the proximity (Figure (Figure2 to). 2). Sthe Sãoã oocean, PauloPaulo and city th is ise intenseapproximately approximately urbanization 55 55km significantly km from from the theAtlantic influence Atlantic Ocean. the Ocean. The topography,patternThe topography, of atmospheric the the proximity proximity circulation to to the theand ocean, ocean, create and andpeculiar thethe intense weather urbanization urbanization conditions insignificantly the significantly MASP. influence influence the the patternpattern of atmospheric of atmospheric circulation circulation and and create create peculiar peculiar weather conditions conditions in inthe the MASP. MASP.

Figure 2. Three-dimensional view of the MASP, including the Mantiqueira and Serra do Mar Mountains and part of the Paulista Coast. The altitude of Mantiqueira and Serra do Mar Mountains FigureFigure 2. Three-dimensional 2. Three-dimensional view view of the of MASP, the MASP, including including the Mantiqueira the Mantiqueira and Serra and doSerra Mar do Mountains Mar nearMountains to MASP and partrange of betweenthe Paulista 900 Coast. and 1200The almtitude and of400 Mantiqueira and 700 m and above Serra the do Marsea levelMountains (asl), and part of the Paulista Coast. The altitude of Mantiqueira and Serra do Mar Mountains near to MASP respectively;near to MASP while range the MASPbetween alti 900tudes and are 1200between m an700d and400 800and m 700asl. m above the sea level (asl), range between 900 and 1200 m and 400 and 700 m above the sea level (asl), respectively; while the respectively; while the MASP altitudes are between 700 and 800 m asl. MASP altitudes are between 700 and 800 m asl. Environments 2017, 4, 27 4 of 26 Environments 2017, 4, 27 4 of 26

TheThe MASP experiencedexperienced aa growth growth rate rate of of 56% 56% in in the the 30-year 30-year period period from from 1980 1980 to 2010. to 2010. There There were werenearly nearly 12 million 12 million inhabitants inhabitants in 1980, in whereas1980, whereas in 2010 in the 2010 population the population jumped jumped to almost to 21almost million 21 millioninhabitants inhabitants (IBGE, (IBGE, 2010). 2010). The population The population growth growth triggered triggered urban urban expansion expansion at an at accelerated an accelerated rate. rate.From From 1962 1962 to 2002, to 2002, theurban the urban area area increased increased from from 874 km8742 kmto 22092 to 2209 km2 km. Figure2. Figure3 shows 3 shows a map a map of the of thecurrent current land land use distribution use distribution in the MASP,in the highlightingMASP, highlighting the extensive the urbanextensive area urban and the area predominant and the predominanttypes of land types cover. of land cover. TheThe large large urban urban spot spot in in the the MASP MASP (Figure (Figure 33)) duedue to a rapid growth and unplanned urbanization producedproduced several several alterations alterations of of the the natural natural landsc landscape,ape, which which changed changed the the surface surface energy energy fluxes fluxes and and triggeredtriggered dynamic dynamic and and thermodynamic thermodynamic atmospheri atmosphericc changes, changes, including including the the temperature temperature pattern. pattern. TheThe urbanization urbanization has has promoted promoted a a heterogeneous heterogeneous distri distributionbution of of surface surface temp temperatureseratures in in the the MASP, MASP, withwith a a warmer region region in in the nucleus and and colder outer outer regions, regions, which which has has led led to to the the generation generation of of variousvarious microclimatesmicroclimates withinwithin this this area. area. The The map map of apparent of apparent surface surface temperature temperature in Figure in4 ,Figure obtained 4, obtainedby digital by processing digital processing techniques te ofchniques the high of gain the thermalhigh gain band thermal (TM6+) band of the(TM6+) images of capturedthe images by capturedthe LANDSAT-7 by the LANDSAT-7 satellite sensor satellite on 3sensor September on 3 Se 1999,ptember illustrates 1999, illustrates the spatial the distribution spatial distribution of these ofmicroclimates. these microclimates. This map This reflects map the reflects quantitative the quan spatialtitative distribution spatial ofdistribution the apparent of temperature, the apparent as temperature,it captures the as emissivity it captures of the the emissivity surface and of the presents surface sensitivity and presents to thermal sensitiv contrasts.ity to thermal The processedcontrasts. Theimage processed shows the image areas shows with thethe highestareas with apparent the highes temperaturet apparent of thetemperature surface (in of red), the insurface contrast (in tored), the incooler contrast areas to represented the cooler inareas blue. represented Temperatures in blue. range Temperatures from about 24 range◦C to from 32 ◦C. about Detailed 24 °C information to 32 °C. Detailedis available information at [37], last is accessedavailable 3at March [37], last 2017. accessed 3 March 2017.

FigureFigure 3. PresentPresent land land use use of of the the MASP. MASP. The The color color sca scalele indicates indicates the the urban urban area area (red), (red), and and the the predominantpredominant types of land covers MASP [38]. [38].

TheThe analyzed analyzed database database includes includes ten ten years years of of hourly hourly air air temperature observations observations from from nine nine near-surfacenear-surface weather weather stations stations in in the the MASP MASP from from 2002 2002 to to 2011, 2011, with with approximately approximately 87,600 87,600 data data points points perper station, station, hourly hourly distributed. distributed. In In total, total, the the MASP MASP dataset dataset consists consists of of 788,4 788,40000 data data points, points, in in which which approximatelyapproximately 244,304 244,304 (31%) (31%) are are missing data. The The missing missing data data is is however randomly distributed withinwithin the the hours, hours, days, days, and and years. years. Therefore, Therefore, no statis notical statistical method method was used was to fill used the gaps to fill in the the gapsdataset in becausethe dataset these because failures these were failuresnot significant were not relative significant to the relativeoverall size to the of the overall dataset, size or of compromise the dataset, its or generalcompromise pattern. its Figure general 5 pattern.depicts the Figure locations5 depicts of the the MASP locations stations of the distributed MASP stations within distributed the 39 cities within that composethe 39 cities the that MASP compose (Figure the 5a), MASP and (Figureaccording5a), to and the according land-use to classification the land-use (Figure classification 5b). The (Figure weather5b). stationsThe weather available stations include available conventional include aerodrome conventional stations aerodrome (METAR stations code), (METAR automatic code), stations automatic under thestations responsibility under the of responsibility the Environmental of the EnvironmentalProtection Agency Protection of the State Agency of São ofthe Paulo State (CETESB) of São Paulo and one(CETESB) automatic and station one automatic operated stationby the University operated by of theSão UniversityPaulo (USP). of The São spat Pauloial (USP).distribution The spatialof the meteorological stations with 10-year data available is not homogenous and does not cover the entire MASP. Therefore, we reduced the study to a smaller region with observational representativeness.

Environments 2017, 4, 27 5 of 26

Environmentsdistribution 2017 of, the4, 27 meteorological stations with 10-year data available is not homogenous and5 does of 26 not cover the entire MASP. Therefore, we reduced the study to a smaller region with observational Inrepresentativeness. Figure 5a, the dark In Figure grey5 a,area the illustrates dark grey areathe area illustrates under the analysis area under in this analysis study. in Except this study. for ParelheirosExcept for Parelheiros (number 9) (numberand Guarulhos 9) and Guarulhos(number 6), (number which are 6), in which the transition are in the region transition of urban region area of andurban shrublands, area and shrublands, most stations most are stationswithin the are urban within area. the urban area. In addition,addition, we we analyzed analyzed the the correlation correlation coefficients coefficients of the seaof the surface sea temperaturesurface temperature (SST) anomalies (SST) anomaliesbetween the between Equatorial the Equatorial Pacific and Pacific southern and Atlantic southern Oceans Atlantic and Oceans the mean and temperature the mean temperature anomalies anomaliesobserved inobserved the MASP in to the investigate MASP to whether investigate teleconnections whether teleconnections affect the temporal affect variability the temporal of the variabilityurban temperature of the urban and temperatur to determinee and the to related determine intensification the related orintensification attenuation ofor theattenuation UHI. The of SSTthe UHI.data wasThe fromSST thedata ERA-Interim was from Europeanthe ERA-Interim Centre forEuropean Medium-Range Centre for Weather Medium-Range Forecasts (ECMWF) Weather Forecastsreanalysis (ECMWF) data, with reanalysis 1.5◦ × 1.5 data,◦ horizontal with 1.5° resolution× 1.5° horizontal [39]. Theresolution monthly [39]. average The monthly SST grid average data SSTcorresponds grid data to corresponds the same 10-year to the periodsame 10-year of the meteorologicalperiod of the meteorological data (2002 to 2011). data (2002 to 2011).

Figure 4. Map ofof thetheapparent apparent surface surface temperature temperature in in MASP MASP on on 3 September 3 September 1999, 1999, 09:57 09:57 local local time time (LT) (LT)inferred inferred by the by satellite the satellite Landsat-7 Landsat-7 [37]. [37].

Environments 2017, 4, 27 6 of 26 Environments 2017, 4, 27 6 of 26

FigureFigure 5. (a 5.) Map(a) Map of of the the MASP MASP with with the following following weather weather station station locations: locations: (1) Ibirapuera (1) Ibirapuera Park; (2) Park; Congonhas Airport; (3) Taboão da Serra; (4) Pinheiros; (5) Mirante de Santana; (6) Guarulhos Airport; (2) Congonhas Airport; (3) Taboão da Serra; (4) Pinheiros; (5) Mirante de Santana; (6) Guarulhos (7) São Caetano do Sul; (8) Água Funda; and (9) Parelheiros. The dark grey area highlights the new Airport; (7) São Caetano do Sul; (8) Água Funda; and (9) Parelheiros. The dark grey area highlights delimitation of the maps, which demarcates the effective area used in this study; (b) MASP station the new delimitation of the maps, which demarcates the effective area used in this study; (b) MASP locations shown over a land-use satellite image. The same color scale depicted in Figure 3 is valid stationhere locations [38]. shown over a land-use satellite image. The same color scale depicted in Figure3 is valid here [38]. 2.2. Statistical Analysis 2.2. Statistical Analysis 2.2.1. EOF Analysis 2.2.1. EOFWe Analysis applied the Empirical Orthogonal Function (EOF) analysis, also known as principal Wecomponent applied theanalysis Empirical (PCA), Orthogonal to investigate Function the spatial (EOF) and analysis, temporal also variabilities known as in principal the UHI component of the MASP. The EOF technique is one of the most widely used multivariate statistical techniques for analysis (PCA), to investigate the spatial and temporal variabilities in the UHI of the MASP. The EOF atmospheric science analyses [40,41], and it became popular after Lorenz [42]. technique is one of the most widely used multivariate statistical techniques for atmospheric science In this study, we employed the EOF technique to analyze the hourly mean temperature data analysesover [ 40a 10-year,41], and period it became from January popular 2002 after to LorenzDecember [42 2011.]. We subtracted the temperature at each Instation this study,by the we spatially employed averaged the EOF temperature technique in to the analyze MASP, the therefore, hourly mean linear temperature combinations data of over a 10-yeartemperature period fromanomalies January ( =− 2002 to) December were used2011. to calculate We subtracted the Principal the temperatureComponents (PC’s). at each The station by theEOF spatially could be averaged either based temperature on analysis in of the the MASP, correlation therefore, matrix linear or the combinations covariance matrix. of temperature In this anomaliesstudy, (weT0 =usedT − theT )correlationwere used matr toix calculate obtained the from Principal the standardized Components (n × K (PC’s).) anomalies The matrix EOFcould [Z], be eitherwhere based K onis the analysis number of of the variables correlation under matrixanalysis or (temperature the covariance anomalies) matrix. and In n thisis the study, number we ofused the correlationobservations matrix from each obtained weather from station the [43]. standardized (n × K) anomalies matrix [Z], where K is the Depending on which parameters are selected, the EOF variables can be specified with different number of variables under analysis (temperature anomalies) and n is the number of observations from modes of decomposition. To obtain the spatial anomaly pattern, the T-mode EOF is used, and to each weather station [43]. define the temporal trend and variability of the grid points, the S-mode EOF is used [44–50]. In this Dependingstudy, we analyzed on which both parameters the T-mode are and selected, S-mode EO theFs EOF to identify variables the cancharacteristics be specified of the with spatial different modesand of temporal decomposition. pattern and To obtain the temper the spatialature anomaly anomaly fields, pattern, respectively. the T-mode EOF is used, and to define the temporalDetailed trend information and variability about of EOF the analysis grid points, and ab theout S-mode the T mode EOF and is usedS mode [44 are–50 in]. Appendix In this study, A. we analyzed both the T-mode and S-mode EOFs to identify the characteristics of the spatial and temporal pattern2.2.2. and Cluster the temperature Analysis anomaly fields, respectively. DetailedIn addition information to the EOF, about we EOF also analysis applied the and cl aboutuster analysis the T mode (CA). andEOF S and mode CA areare inuseful Appendix tools A. for verifying how samples are related by determining the level of similarity with specific variables. 2.2.2.CA Cluster is used Analysis to identify and classify objects/individuals based on their characteristics and to obtain Insimilar addition groups. to theThis EOF, analysis we uses also predetermined applied the cluster selection analysis criteria (CA).to classify EOF objects and CAaccording are useful to the tools similarities of elements to those within other groups [51,52]. for verifying how samples are related by determining the level of similarity with specific variables. In this study, regions of homogeneity were identified by arranging the temperature data in a CA is(m used × n)to matrix, identify where and m classify corresponds objects/individuals to the nine stations based and onn corresponds their characteristics to the mean and hourly to obtain similar groups. This analysis uses predetermined selection criteria to classify objects according to the similarities of elements to those within other groups [51,52]. In this study, regions of homogeneity were identified by arranging the temperature data in a (m × n) matrix, where m corresponds to the nine stations and n corresponds to the mean hourly Environments 2017, 4, 27 7 of 26 temperature anomalies. Thus, CA was performed to provide a statistical description of the standard air temperature of each region to determine the temperature variability and weather patterns or local control factors in the MASP. DetailedEnvironments information 2017, 4, 27 about cluster analysis is in AppendixB. 7 of 26

2.2.3. Urbantemperature Heat Islandanomalies. Intensity Thus, CA was performed to provide a statistical description of the standard air temperature of each region to determine the temperature variability and weather patterns or Welocal calculated control factors the UHI in the intensity MASP. (UHII) in the MASP based on differences in the mean hourly temperatureDetailed between information urban/suburban about cluster (Tu analysis) areas is and in Appendix non-urban/vegetated B. (Tr) areas. This definition has been used in many studies, such as [25,53]: 2.2.3. Urban Heat Island Intensity

We calculated the UHI intensity (UHII)UHII in the= T MAu −SPT rbased on differences in the mean hourly (1) temperature between urban/suburban (Tu) areas and non-urban/vegetated (Tr) areas. This definition Equationhas been (1) used is in a traditionalmany studies, approach such as [25,53]: in which two stations (urban and vegetated) are applied to analyze the UHII. This approach is typically used = − when there are few stations in the study(1) area. However, whenEquation there (1) is is only a traditional one station approach in the in urbanwhich two area stations and many (urban stations and vegetated) in neighboring are applied areas, the UHII isto best analyze defined the UHII. as the This difference approach betweenis typically the used urban when station there are and few a stations representative in the study average area. of the countrysideHowever, stations. when there When is thereonly one are station many in stations the urban within area and both many the stations urban in area neighboring and vegetated areas, area, a representativethe UHII is station best defined for the as the urban difference area shouldbetween be the carefully urban station selected and a becauserepresentative significant average variations of the countryside stations. When there are many stations within both the urban area and vegetated usually occur within an urban area. In this study, we chose the representative stations in the urban area, a representative station for the urban area should be carefully selected because significant and vegetatedvariations areas usually used occur for within the UHII an urban analysis area. afterIn this performing study, we chose the the CA. representative stations in the urban and vegetated areas used for the UHII analysis after performing the CA. 3. Results 3. Results 3.1. MASP Local Climate 3.1. MASP Local Climate For the 10-year period from January 2002 to December 2011, the average temperature of the MASP was 17 ◦C inFor the the coldest 10-year month period andfrom 23 January◦C in the2002 hottest to December month 2011, (Figure the 6average). Summer temperature and spring of the months MASP was 17 °C in the coldest month and 23 °C in the hottest month (Figure 6). Summer and spring presented the highest solar radiation mean values (between 180 W/m2 and 200 W/m2), and winter months presented the highest solar radiation mean values (between 180 W/m2 and 200 W/m2), and 2 monthswinter presented months the presented lowest solarthe lowest radiation solar meanradiation values mean (approximately values (approximately 100 W/m 100 W/m). The2). mean spatial distributionThe mean spatial of thedistribution 10-year of temperature the 10-year te inmperature the MASP in the was MASP substantially was substantially uniform uniform and ranged from 17and to 23ranged◦C. from 17 to 23 °C.

Figure 6.FigureAnnual 6. Annual cycle cycle of temperatureof temperature near near thethe surfac surfacee (blue (blue bars), bars), and andsolar solarradiation radiation (red line) (red line) averaged over the 10-year period from January 2002 to December 2011 in the MASP. averaged over the 10-year period from January 2002 to December 2011 in the MASP. The 10-year mean diurnal temperature cycle in the MASP presented a peak of 25 °C at Theapproximately 10-year mean 14:00 diurnal local time temperature (LT) (Figure cycle7), primarily in the related MASP to presented the solar radiation a peak cycle, of 25 ◦C at approximatelyalthough 14:00also influenced local time by (LT)the high (Figure level7 of), anth primarilyropogenic related heat release. to the With solar the radiation nighttime cycle, cooling, although the temperature dropped to a minimum of 17 °C on average around 06:00 LT. Moreover, the daily also influenced by the high level of anthropogenic heat release. With the nighttime cooling, the cycle fluctuated with an amplitude of approximately 7.6 °C. temperature dropped to a minimum of 17 ◦C on average around 06:00 LT. Moreover, the daily cycle fluctuated with an amplitude of approximately 7.6 ◦C. Environments 2017, 4, 27 8 of 26 Environments 2017, 4, 27 8 of 26 Environments 2017, 4, 27 8 of 26

Figure 7. Diurnal cycle of air temperatures averaged over the period from January 2002 to December FigureFigure 7.7. DiurnalDiurnal cyclecycle ofof airair temperaturestemperatures averagedaveraged overover thethe periodperiod fromfrom JanuaryJanuary 20022002 toto DecemberDecember 2011 in the MASP. 20112011 inin thethe MASP.MASP. The sea breeze prevailing to the south/southeast, which corresponds to the oceanic/continental pathTheThe seathatsea breezeoccursbreeze during prevailingprevailing the daytime, toto the the south/southeast, stronglysouth/southeas influencest, whichwhich the wind correspondscorresponds regime in MASP, totothe the despite oceanic/continental oceanic/continental its 55 km pathpathdistance thatthat occursoccurs from duringduring the coast thethe (Figure daytime,daytime, 8). In stronglystrongly addition, influencesinfl thereuences was theanthe eastern windwind regimeregimecomponent inin MASP, throughout despitedespite most itsits of 5555 kmkm distancedistancethe region, fromfrom thethewhich coastcoast is most (Figure(Figure likely8 8).). related In In addition, addition, to differenti there thereal was surfacewas an an heating eastern eastern and component component the surface throughout throughout characteristics, most most of of thethe region,region,such as whichwhichthe parks, isis mostmost water likelylikely bodies, relatedrelated and more toto differentialdifferenti built-up environments.al surfacesurface heatingheating The wind andand speed the surface in the MASP characteristics, was suchsuchtypically asas thethe parks,parks, low, ranging waterwater bodies,bodies,from 0.5 and andto 2.1 moremore m/s. built-upbuilt-up environments.environments. TheThe windwind speedspeed inin thethe MASPMASP waswas typicallytypically low,low, rangingranging fromfrom 0.5 0.5 to to 2.1 2.1 m/s. m/s.

Figure 8. Mean compass rose (direction and intensity) measurements at stations in the MASP for the period from 2002 to 2011.

Figure 8. 3.2.Figure EOF 8. Analysis MeanMean compasscompass roserose (direction(direction andand intensity)intensity) measurementsmeasurements atat stationsstations inin thethe MASPMASP forfor thethe period from 2002 to 2011. periodThe from T-mode 2002 EOFto 2011. produced three dominant modes of temperature variability in the MASP, with the first, second and third EOFs together explaining approximately 99% of the total variance. 3.2. EOF Analysis 3.2. EOFThe first Analysis mode (or the first PC score) explains 67% of the total variance and has a clear diurnal cycle. The temporal coefficient of the first mode or PC loadings (Figure 9) has the highest correlation TheThe T-modeT-mode EOFEOF producedproduced threethree dominantdominant modesmodes of temperature variability in the MASP, (values greater than 0.8) between 00:00 and 06:00 and 21:00 and 23:00 LT. This result indicates that withwith thethe first,first, secondsecond andand thirdthird EOFsEOFs togethertogether explainingexplaining approximatelyapproximately 99% of the total variance. The firstthe late mode night (or and the early first morning PC score) periods explains are subject 67% of to the a distinct total variance spatial pattern. and has Thus, a clear during diurnal these cycle. The periods,first mode a structural (or the first corresponden PC score)ce explains occurs in 67%the temperature of the total anomvariancealy fields. and hasThe aspatial clear structurediurnal cycle. The temporal coefficient of the first mode or PC loadings (Figure9) has the highest correlation (values The temporal coefficient of the first mode or PC loadings (Figure 9) has the highest correlation greater(values thangreater 0.8) than between 0.8) between 00:00 and 00:00 06:00 and and 06:00 21:00 an andd 21:00 23:00 and LT. 23:00 This LT. result This indicates result indicates that the latethat nightthe late and night early and morning early morning periods are periods subject are to subject a distinct to spatiala distinct pattern. spatial Thus, pattern. during Thus, these during periods, these a structuralperiods, a correspondencestructural corresponden occurs ince the occurs temperature in the temperature anomaly fields. anom Thealy spatialfields. The structure spatial associated structure

Environments 2017, 4, 27 9 of 26

EnvironmentsEnvironments 2017 2017, 4, ,27 4, 27 9 of9 26of 26 with the first PC score (Figure 10a) has a dipole pattern with negative values in the east, north, and associatedassociated with with the the first first PC PC score score (Figure (Figure 10a) 10a) has has a dipolea dipole pattern pattern with with negati negativeve values values in inthe the east, east, northwest MASP regions and positive values in the south MASP region. This pattern is associated with north,north, and and northwest northwest MASP MASP regions regions and and positive positive va valueslues in inthe the south south MASP MASP region. region. This This pattern pattern is is the MASP circulation mechanisms, representing the strong influence of the sea breeze with south and associatedassociated with with the the MASP MASP circulation circulation mechanisms, mechanisms, representing representing the the strong strong influence influence of ofthe the sea sea southeastbreezebreeze windswith with south insouth the and southernand southeast southeast part winds winds of the in MASP,inthe the southe southe whilern rnpart in part the of of norththe the MASP, MASP, part prevailingwhile while in inthe the the north north circulation part part of terrestrialprevailingprevailing breeze the the circulation with circulation east andof ofterrestrial northeastterrestrial breeze breeze winds. with with east east and and northeast northeast winds. winds.

FigureFigureFigure 9. Principal 9. Principal9. Principal components components components (PC) (PC) (PC) loading loading loading time time timeseries series series ofof theofthe the firstfirst first (67%),(67%), (67%), second second (24%) (24%) (24%) and and and third third third (8%) (8%) T-mode empirical orthogonal functions (EOFs) calculated using the hourly mean temperature T-mode(8%) empiricalT-mode empirical orthogonal orthogonal functions functions (EOFs) (EOFs) calculated calculated using using the hourly the hourly mean mean temperature temperature anomaly anomaly data for the MASP from January 2002 to December 2011. dataanomaly for the MASPdata for from the MASP January from 2002 January to December 2002 to December 2011. 2011.

FigureFigureFigure 10. 10.PC 10. PC score PC score score spatial spatial spatial pattern pattern pattern ofof of the the ( (aa ))( afirst first) first (67%); (67%); (67%); (b ()(b bsecond)) secondsecond (24%) (24%) (24%) and and and(c) ( thirdc) ( cthird) third (8%) (8%) T-mode (8%) T-mode T-mode EOFsEOFs calculatedEOFs calculated calculated using using using the the hourlythe hourly hourly meanmean mean temperatur temperature temperature anomalye anomaly anomaly data data of theof of the theMASP MASP MASP from from from January January January 2002 2002 to 2002 to to DecemberDecemberDecember 2011. 2011. 2011. The The thickerThe thicker thicker black black black lineline line represents represents zero zero zero value. value. value. Isolines IsolinesIsolines are are areon on 0.2 on 0.2 intervals. 0.2 intervals. intervals.

The second PC score explained 24% of the total variance, with the highest correlation values TheThe second second PC PC score score explained explained 24% 24% of of the the total total variance, variance, with with the the highesthighest correlationcorrelation values from fromfrom 12:00 12:00 to to20:00 20:00 LT LT (Figure (Figure 9). 9). The The spatial spatial st ructurestructure of ofthe the second second PC PC score score had had a patterna pattern of of 12:00 to 20:00 LT (Figure9). The spatial structure of the second PC score had a pattern of negative negativenegative and and positive positive scores scores at atthe the center center an and dedges edges of ofthe the MASP, MASP, respectively respectively (Figure (Figure 10b). 10b). andComparison positiveComparison scores of ofthe atthe spatial the spatial center pattern pattern and of of edgesthe the temperature temperature of the MASP, anomaly anomaly respectively of ofthe the second second (Figure PC PC (Figure 10 (Figureb). Comparison10b) 10b) with with of the spatial pattern of the temperature anomaly of the second PC (Figure 10b) with the map of the apparent surface temperatures of the MASP (Figure4) revealed similarities in spatial behaviors, with the warmest regions coinciding with positive nuclei of the mode. The central region towards the Environments 2017, 4, 27 10 of 26

Environments 2017, 4, 27 10 of 26 northeast–southwest axis had a warmer core (Figure4), and this region coincided with the central area in Figurethe map10b. of The theareas apparent in Figure surface4 tethatmperatures show colder of the core MASP temperatures (Figure 4) revealed match similarities the negative in spatial anomaly valuesbehaviors, of −0.2 towith− 0.6the inwarmest Figure regions 10b. Therefore,coinciding with the secondpositive modenuclei of is the associated mode. The with central urbanization, region representingtowardsthe the releasenortheast–southwest of heat stored axis from had urban a warmer areas core as (Figure well as 4), from and otherthis region anthropogenic coincided with sources beyondthe the central circulation area in Figure process 10b. in The the areas MASP. in Figure The second4 that show mode colder of thecore EOF temperatures is the one match that the better representsnegative the anomaly UHI of thevalues MASP. of −0.2 to −0.6 in Figure 10b. Therefore, the second mode is associated with Theurbanization, third mode representing explains 8%the ofrelease the total of heat variance, stored andfrom the urban PC loadingareas as timewell seriesas from exhibits other the highestanthropogenic correlation sources values beyond from 07:00the circulation to 11:00 proc LTess (Figure in the9 ).MASP. The The third second mode’s mode spatial of the EOF structure is the one that better represents the UHI of the MASP. (Figure 10c) is similar to that of the first mode because it also displays dipole behavior, although it The third mode explains 8% of the total variance, and the PC loading time series exhibits the displayshighest positive correlation values values in the from southwestern, 07:00 to 11:00 southern, LT (Figure and eastern9). The areasthird mode’s of the MASPspatial andstructure negative values(Figure in the 10c) northern is similar and to northwesternthat of the first areasmode ofbecause the MASP it also displays region. dipole The third behavior, EOF although appears it to be associateddisplays with positive the local values circulation in the southwestern, due to terrain sout orhern, urban and effects, eastern andareas is of therefore the MASP related and negative to the first mode.values It can in be the interpreted northern and as a northwestern complementary areas representation of the MASP region. of the windThe third circulation EOF appears mechanisms to be in the MASP.associated with the local circulation due to terrain or urban effects, and is therefore related to the Infirst the mode. S-mode It can EOF, be thereinterpreted were as two a compleme dominantntary modes representation of variability, of the andwind they circulation explained approximatelymechanisms 80% in the of MASP. the total variance. For the S-mode, the spatial pattern (or PC loading) of the variableIn underthe S-mode study EOF, shows there the were correlation two dominant fields determined modes of variability, by the PC and score they time explained series and approximately 80% of the total variance. For the S-mode, the spatial pattern (or PC loading) of the all points in the spatial domain. The PC loading map shows the region(s) where the time series is variable under study shows the correlation fields determined by the PC score time series and all representativepoints in ofthe the spatial temporal domain. behavior The PC ofloading the temperature map shows anomalies.the region(s) Areas where with the lowtime PCseries loadings is do notrepresentative correspond toof thethe temporal behavior behavior of the original of the te observationsmperature anomalies. for that Areas particular with PC.low PC The loadings time series (or PCdo score) not correspond describes to the the principalbehavior of types the original or patterns observations of temporal for that variabilityparticular PC. for The the time temperature series anomaly(or PC [50 ].score) describes the principal types or patterns of temporal variability for the temperature Theanomaly first PC[50]. (or first PC score) explained 49% of the total variance and had a clear diurnal cycle (Figure 11).The The first time PC series(or first highlights PC score) explained the patterns 49% of of variability the total variance of the temperatureand had a clear anomalies diurnal cycle during each period,(Figure with11). The positive time valuesseries highlights between 00:00the patte andrns 11:00 of variability LT and negative of the valuestemperature between anomalies 12:00 and during each period, with positive values between 00:00 and 11:00 LT and negative values between 23:00 LT. The spatial pattern of the first PC loading map (Figure 12a) is similar to that of the second PC 12:00 and 23:00 LT. The spatial pattern of the first PC loading map (Figure 12a) is similar to that of of the T-mode EOF (Figure 10b), with positive values in the center and negative values at the edges of the second PC of the T-mode EOF (Figure 10b), with positive values in the center and negative the MASP.values The at the S-mode edges EOFof the demonstrates MASP. The S-mode that theEOF temperature demonstrates anomaly that the temperature in the center anomaly of the MASPin is positivethe center between of the 00:00 MASP and is positive 11:00 LT between and negative 00:00 and otherwise, 11:00 LT and whereas negative the otherwise, edge areas whereas presented the an invertededge pattern, areas presented representing an theinverted temporal pattern, behavior representing of the MASPthe temporal temperature behavior anomaly. of the Therefore,MASP the firsttemperature PC of the anomaly. S-mode correspondsTherefore, the to first the PC spatial of the patternS-mode corresponds of the UHI into the spatial MASP, pattern and it of is the similar to theUHI second in the PC MASP, of the and T-mode. it is similar to the second PC of the T-mode.

Figure 11. PC score time series of the first (49%) and second (31%) S-mode EOFs calculated using the

hourly mean temperature anomaly data of the MASP from January 2002 to December 2011. Environments 2017, 4, 27 11 of 26

Figure 11. PC score time series of the first (49%) and second (31%) S-mode EOFs calculated using the hourly mean temperature anomaly data of the MASP from January 2002 to December 2011.

The second PC score pattern explains 31% of the total variance in temperature and also features a well-defined diurnal cycle (Figure 11). The temporal behavior of the second PC is similar to the first PC although advanced by 3 h. The dominant feature of the spatial structure of the second PC loading map (Figure 12b) is a positive structure on the west side of the MASP and negative structures elsewhere. Thus, on the western side of the MASP, the temperature anomaly is negative between 07:00 and 15:00 LT and positive otherwise. On the east side of the MASP, the temperature anomaly is positive from 07:00 to 15:00 LT and negative otherwise. This dipole pattern, also observed in the first and third PC of the T-mode EOF (Figure 10a,c), is associated with wind circulation in the MASP. In summary, the second PC of the T-mode approach and the first PC of the S-mode approach represent the spatial pattern of the UHI in the MASP, whereas the first and third PCs of the T-mode approach and the second PC of the S-mode represent the wind circulation pattern in the MASP. According to Salles [47], similar results in both modes implies a simple linear spatial and temporal Environmentsrelationship2017, 4 ,that 27 precludes other effects, such as dispersion, which occurs over time because of the11 of 26 non-linearity of real systems.

FigureFigure 12. PC 12. loading PC loading spatial spatial pattern pattern of the of (a the) first (a) (49%) first (49%) and (b and) second (b) second (31%) S-mode(31%) S-mode EOFs calculatedEOFs usingcalculated the hourly using mean the temperature hourly mean anomaly temperature data anomaly of the MASP data of from the JanuaryMASP from 2002 January to December 2002 to 2011. December 2011. The thicker black line represents zero value. Isolines are on 0.2 intervals. The thicker black line represents zero value. Isolines are on 0.2 intervals. We also performed seasonal analysis of the spatial structures of the EOF for the T-mode EOF Theintending second toPC obtain score the pattern spatial explains patterns 31%of the of temperature the total variance anomaly in temperaturefield and their and sequences also features of a well-definedoccurrence diurnal throughout cycle (Figurethe year. 11 The). The temporal temporal and behavior spatial patterns of the second(Figures PC 13–16) is similar were similar to the firstto PC althoughthe T-mode advanced patterns by 3 h.(Figures The dominant 9 and 10). feature However, of the summer spatial and structure winter ofonly the presented second PC two loading modes map (Figure(Figures 12b) is13 a and positive 14), whereas structure autumn on the and west spring side presented of the MASPthree modes and negative (Figures 15 structures and 16). During elsewhere. summer and winter, the first EOF mode explained 78% and 75% of the variance, and the second Thus, on the western side of the MASP, the temperature anomaly is negative between 07:00 and 15:00 mode explained 17% and 20% of the variance, respectively. During fall and spring, the first EOF LT and positive otherwise. On the east side of the MASP, the temperature anomaly is positive from mode explained 69% and 55% of the total temperature variance, the second explained 23% and 28%, 07:00and to 15:00 the third LT and explained negative 6% otherwise.and 14%, respectively. This dipole Th pattern,is reduction also in observed the number in theof variability first and thirdmodes PC of the T-modeis likely EOF associated (Figure with10a,c), a consolidated is associated config withuration wind circulation of the thermodynamic in the MASP. properties of the Inatmosphere summary, during the second summer PC and of winter the T-mode compared approach with those and of the transition first PC ofseasons the S-mode in the MASP. approach represent the spatial pattern of the UHI in the MASP, whereas the first and third PCs of the T-mode approach and the second PC of the S-mode represent the wind circulation pattern in the MASP. According to Salles [47], similar results in both modes implies a simple linear spatial and temporal relationship that precludes other effects, such as dispersion, which occurs over time because of the non-linearity of real systems. We also performed seasonal analysis of the spatial structures of the EOF for the T-mode EOF intending to obtain the spatial patterns of the temperature anomaly field and their sequences of occurrence throughout the year. The temporal and spatial patterns (Figures 13–16) were similar to the T-mode patterns (Figures9 and 10). However, summer and winter only presented two modes (Figures 13 and 14), whereas autumn and spring presented three modes (Figures 15 and 16). During summer and winter, the first EOF mode explained 78% and 75% of the variance, and the second mode explained 17% and 20% of the variance, respectively. During fall and spring, the first EOF mode explained 69% and 55% of the total temperature variance, the second explained 23% and 28%, and the third explained 6% and 14%, respectively. This reduction in the number of variability modes is likely associated with a consolidated configuration of the thermodynamic properties of the atmosphere during summer and winter compared with those of the transition seasons in the MASP. Environments 2017, 4, 27 12 of 26 Environments 2017, 4, 27 12 of 26

FigureFigure 13. 13. PCPC score score spatial spatial patterns patterns of of the the (a ()a first) first (78%) (78%) and and (b ()b second) second (17%) (17%) T-mode T-mode EOFs EOFs in in summer summer andand the the patterns patterns in inthe the (c) (firstc) first (75%) (75%) and and (d) second (d) second (20%) (20%) T-mode T-mode EOFs EOFs in winter; in winter; these patterns these patterns were calculatedwere calculated using usingthe hourly the hourly meanmean temperature temperature anomaly anomaly data dataof the of theMASP MASP from from January January 2002 2002 to to DecemberDecember 2011. 2011. The The thicker thicker black black line line represents represents zero zero value. value. Isolines Isolines are areon on0.2 0.2intervals. intervals.

Environments 2017, 4, 27 13 of 26 Environments 2017, 4, 27 13 of 26

FigureFigure 14.14. PCPC loadingloading timetime seriesseries ofof thethe firstfirst andand secondsecond T-modeT-mode EOFsEOFs duringduring (a(a)) summersummer andand (b(b)) winter, winter, which which were were calculated calculated using using hourly hourly mean mean temperature temperature anomaly anomaly data data of of the the MASP MASP from from JanuaryJanuary 2002 2002 to to December December 2011. 2011.

Environments 2017, 4, 27 14 of 26 Environments 2017, 4, 27 14 of 26

FigureFigure 15.15. PCPC scorescore spatialspatial patternpattern ofof thethe ((aa)) firstfirst (69%);(69%); ((bb)) secondsecond (23%)(23%) andand ((cc)) thirdthird (6%)(6%) T-modeT-mode EOFsEOFs duringduring fallfall andand thethe patternpattern inin thethe ((dd)) firstfirst (55%);(55%); ((ee)) secondsecond (28%)(28%) andand ((ff)) thirdthird (14%)(14%) T-modeT-mode EOFsEOFs duringduring spring; spring; these these patterns patterns were were calculated calculated using using the hourlythe hourly mean mean temperature temperature anomaly anomaly data ofdata the of MASP the MASP from Januaryfrom January 2002 to 2002 December to December 2011. The 2011. thicker The thicker black line black represents line represents zero value. zero Isolines value. areIsolines on 0.2 are intervals. on 0.2 intervals.

AnotherAnother result that stands stands out out in in this this seasonal seasonal an analysisalysis is isthe the total total variance variance representative representative of the of thevariability variability modes modes of ofeach each season. season. During During summe summerr and and winter, winter, two two dominant variabilityvariability modesmodes explainexplain aboutabout 98% 98% of theof totalthe variance,total variance, whereas wher in fall,eas three in variabilityfall, three modes variability explain modes approximately explain 98%approximately of the total 98% variance, of the and total in spring,variance, three and modes in spring, explain three 97% modes of the explain variance. 97% These of the differences variance. betweenThese differences seasons and between the different seasons atmospheric and the diff thermodynamicerent atmospheric patterns thermodynamic that occur at patterns each station that (asoccur described at each above) station may (as be described associated above) with remote may be influences, associated which with can remote increase influences, the total variancewhich can in theincrease transitional the total seasons variance relative in to the the transitional other seasons. seasons The most relative prominent to the remote other influencesseasons. thatThe affectmost theprominent southeastern remote part influences of Brasil are that the affect El Niño-Southern the southeastern Oscillation part of (ENSO), Brasil Madden-Julianare the El Niño-Southern Oscillation (MJO)Oscillation and Pacific-South (ENSO), Madden-Julian American (PSA) Oscillation [54]. (MJO) and Pacific-South American (PSA) [54]. WeWe analyzedanalyzed thethe seasonalseasonal distributiondistribution ofof thethe correlationcorrelation coefficientscoefficients betweenbetween thethe SSTSST anomaliesanomalies andand thethe meanmean temperaturetemperature anomaliesanomalies observedobserved inin thethe MASPMASP forfor thethe 10-year10-year periodperiod (2002–2011)(2002–2011) (Figure(Figure 17 17).). We We found found an an intense intense correlation correlation between between these these two two coefficients coefficients in the in Atlanticthe Atlantic Ocean Ocean area offarea the off coast the ofcoast southeast of southeast Brazil (anomalyBrazil (anomaly marked marked as a square as a on square the Atlantic on the OceanAtlantic near Ocean the MASP near the in FigureMASP 17in), Figure which 17), indicates which that indicates the MASP that the is primarily MASP is affectedprimarily by affected the nearby by the ocean nearby SST. Theocean ENSO SST. remoteThe ENSO influence remote (square influence on the (square Equatorial on the Pacific Equatori Oceanal inPacific Figure Ocean 17) has in no Figure remote 17) influence, has no remote except duringinfluence, fall andexcept spring. during During fall and the transitionspring. During seasons the (Figure transition 17b,d) seasons we detected (Figure a correlation,17b,d) we detected although a weakercorrelation, than thealthough one with weaker South than Atlantic the one Ocean with area, South with Atlantic the Niño Ocean 3.4 area. area, These with results the Niño indicate 3.4 area. that theThese seasonal results factors indicate in that this the area, seasonal such as factors the air in temperature/UHI this area, such as the intensity air temperature/UHI in the MASP, as intensity well as local-levelin the MASP, phenomena, as well as are local-level also remotely phenomena, influenced are also by the remotely ENSO. influenced by the ENSO.

Environments 2017, 4, 27 15 of 26 Environments 2017, 4, 27 15 of 26

Figure 16. PC loading time series of the first first and second T-mode EOFs during ( a) fall and ( b) spring, which were calculated using hourlyhourly mean temperature anomaly data of the MASP from January 2002 to December 2011.2011.

Environments 2017, 4, 27 16 of 26

Figure 17. DistributionDistribution of of the the correlati correlationon coefficients coefficients between between the the sea sea surface temperature (SST) anomaly datadata and and mean mean temperature temperature anomaly anomaly data data in the in MASP the MASP at the 95% at the significance 95% significance level (Student’s level (Student-test): ( asolid) summer; (dashed) (b) isolines fall; (c) winterand the and first (d value) spring. is 0.55 The (− regions0.55). Isolines with positive are on (negative)0.1 intervals. correlation Oceanic areasare solid of (dashed)the South isolines Atlantic and thealong first valuethe southeas is 0.55 (–0.55).tern region Isolines of are Brazil on 0.1 and intervals. Equatorial Oceanic Pacific areas correspondingof the South Atlantic area of along the Niño the southeastern 3.4 are delimited region in of square. Brazil and Equatorial Pacific corresponding area of the Niño 3.4 are delimited in square.

EnvironmentsEnvironmentsEnvironmentsEnvironmentsEnvironments 2017 2017 ,20172017 20174, 427,,, , 27 4 44,, , 27 2727 1717 of 17 17of2617 of26 ofof 26 2626 Environments 2017, 4, 27 Environments17 of 262017 , 4, 27 17 of 26 3.3.3.3. 3.3.3.3.Cluster3.3. Cluster Cluster ClusterCluster Analysis Analysis Analysis AnalysisAnalysis 3.3. Cluster Analysis 3.3. ClusterTheTheThe TheTheEOF AnalysisEOF EOFEOFEOF methodology methodology methodologymethodologymethodology allowed allowed allowedallowedallowed the the thethethedeterminatio determinatio determinatiodeterminatiodetermination nof nnofn theof ofofthe thethethespatial spatial spatialspatialspatial patterns patterns patternspatternspatterns of of temperatureof ofoftemperature temperaturetemperaturetemperature The EOF methodology allowed the determination of the spatial patterns of temperatureanomaliesanomaliesanomaliesanomaliesanomalies in in the in inthein theMASP, thethe MASP, MASP, MASP,MASP, identifying identifying identifying identifyingidentifying warmer warmer warmer warmerwarmer and and and andandcool cool cool coolercooler coreer ercoreer core core coreareas areas areas areasareas as as well as asaswell well well wellas as the as asasthe thetemporal thethe temporal temporal temporaltemporal evolution evolution evolution evolutionevolution The EOF methodology allowed the determination of the spatial patterns of temperature anomalies anomalies in the MASP, identifying warmer and cooler core areas as well as the temporalof of evolutiontheseof ofofthese thesethesethese spatial spatial spatialspatialspatial patterns patterns patternspatternspatterns throughout throughout throughoutthroughoutthroughout the the thetheday.the day. day.day. day.Ba Based BaBasedBa sedsedonsed on these onon onthese thesethesethese results, results, results,results,results, we we weidentifiedwewe identified identifiedidentifiedidentified homogeneous homogeneous homogeneoushomogeneoushomogeneous in the MASP, identifying warmer and cooler core areas as well as the temporal evolution of these spatial of these spatial patterns throughout the day. Based on these results, we identified homogeneousregionsregionsregionsregionsregions or or groupsor ororgroups groupsgroupsgroups and and and andanddetermined determined determineddetermineddetermined the the thethedegreethe degree degreedegreedegree of of similarityof ofofsimilarity similaritysimilaritysimilarity and and and andanddifferen differen differendifferendifferencesces cescesamongces among amongamongamong individual individual individualindividualindividual patterns throughout the day. Based on these results, we identified homogeneous regions or groups and regions or groups and determined the degree of similarity and differences among observations.individualobservations.observations.observations.observations. Based Based BasedBasedBased on on theseonon onthese thesethesethese results, results, results,results,results, we we wewedefinedwe defined defineddefineddefined groups groups groupsgroupsgroups of of stations of ofofstations stationsstationsstations that that that thatthatare are arearesimilar.are similar. similar.similar.similar. In In the In InInthe thetheCA,the CA, CA, CA,CA, determined the degree of similarity and differences among individual observations. Based on these observations. Based on these results, we defined groups of stations that are similar. theInthe thehomogeneousthethe homogeneous homogeneous homogeneousCA,homogeneous groups groups groups groupsgroups should should should shouldshould correspond correspond correspond correspondcorrespond with with with withwith th the thgroups ethth groupseee groups groupsgroups observed observed observed observedobserved in in the in inthein thespatial thethe spatial spatial spatialspatial regionalization regionalization regionalization regionalizationregionalization results, we defined groups of stations that are similar. In the CA, the homogeneous groups should the homogeneous groups should correspond with the groups observed in the spatial regionalizationofof theof oftheof theEOF thethe EOF EOF EOFEOF analysis. analysis. analysis. analysis.analysis. correspond with the groups observed in the spatial regionalization of the EOF analysis. of the EOF analysis. ThereThereThereThereThere is isno is noisis theory no no notheory theory theorytheory or or definition or orordefinition definition definitiondefinition to to determine to todetermineto determine determinedetermine th the thnode ethth nodeeee node nodenode heights heights heights heightsheights in in a in inCAain CAa aa CA dendrogram.CACA dendrogram. dendrogram. dendrogram.dendrogram. As As the As AsAs the thegoal thethe goal goal goal goal There is no theory or definition to determine the node heights in a CA dendrogram. As the goal is There is no theory or definition to determine the node heights in a CA dendrogram. isAs isto isthetois isgather to togatherto goal gather gathergather stations stations stations stationsstations with with with withwith similar similar similar similarsimilar characteristics, characteristics, characteristics, characteristics,characteristics, we we willwe wewe will will willwillnot not notconsider notnot consider consider considerconsider high-rescaled high-rescaled high-rescaled high-rescaledhigh-rescaled distances distances distances distancesdistances because because because becausebecause to gather stations with similar characteristics, we will not consider high-rescaled distances because is to gather stations with similar characteristics, we will not consider high-rescaled distancestheythey theybecausetheythey form form form formform large large large largelarge groups groups groups groupsgroups with with with withwith high high high highhigh intra-cluster intra-cluster intra-cluster intra-clusterintra-cluster diversity. diversity. diversity. diversity.diversity. Therefore, Therefore, Therefore, Therefore,Therefore, we we weused wewe used used usedused 50% 50% 50% 50% 50%of of the of ofofthe the distancethethe distance distance distancedistance to to to toto they form large groups with high intra-cluster diversity. Therefore, we used 50% of the distance to they form large groups with high intra-cluster diversity. Therefore, we used 50% of thedetermine distancedeterminedeterminedeterminedetermine to the the thenumber thethe number number numbernumber of of groups. of ofgroups.of groups. groups.groups. determine the number of groups. determine the number of groups. TheTheThe ThethresholdThe threshold threshold thresholdthreshold of of six of ofsixof intra-homogeneous six sixsix intra-homogeneous intra-homogeneous intra-homogeneousintra-homogeneous groups groups groups groupsgroups wa was wa wawathes thesss thebest thethe best best bestbestrepresentation representation representation representationrepresentation of of the of oftheof theMASP thethe MASP MASP MASPMASP pattern pattern pattern patternpattern The threshold of six intra-homogeneous groups was the best representation of the MASP pattern The threshold of six intra-homogeneous groups was the best representation of the MASPandandand andwasandpattern was was waswasconsistent consistent consistent consistentconsistent with with with withwith the the resultsthe thethe results results resultsresults we we foundwe wewe found found foundfound with with with withwith the the EOFthe thethe EOF EOF EOF EOFanalysis. analysis. analysis. analysis.analysis. The The The ThesixThe six inner six sixsix inner inner innerinner groups groups groups groupsgroups (Figure (Figure (Figure (Figure(Figure 18a) 18a) 18a) 18a) 18a) and was consistent with the results we found with the EOF analysis. The six inner groups (Figure 18a) and was consistent with the results we found with the EOF analysis. The six inner groups (Figureareare aregroupareare group group18a)groupgroup 1 1(USP, (USP,111 (USP,(USP,(USP, Guarulhos), Guarulhos), Guarulhos),Guarulhos),Guarulhos), group group groupgroupgroup 2 2(Congonhas, (Congonhas,222 (Congonhas,(Congonhas,(Congonhas, Mirante), Mirante), Mirante),Mirante),Mirante), group group groupgroupgroup 3 3(Ibirapuera, (Ibirapuera,333 (Ibirapuera,(Ibirapuera,(Ibirapuera, Taboão Taboão TaboãoTaboãoTaboão Serra), Serra), Serra),Serra),Serra), are group 1 (USP, Guarulhos), group 2 (Congonhas, Mirante), group 3 (Ibirapuera, Taboão Serra), are group 1 (USP, Guarulhos), group 2 (Congonhas, Mirante), group 3 (Ibirapuera, Taboãogroupgroupgroupgroup groupSerra), 4 4(Pinheiros), (Pinheiros),4 44 (Pinheiros), (Pinheiros),(Pinheiros), group group group groupgroup 5 5(São (São5 55 (São (São (SãoCaetano Caetano Caetano CaetanoCaetano do do Sul),do dodo Sul), Sul), Sul),Sul), and and and andandgroup group group groupgroup 6 6(Parelheiros). (Parelheiros).6 66 (Parelheiros). (Parelheiros).(Parelheiros). Figure Figure Figure FigureFigure 18b 18b 18b18billustrates18b illustrates illustrates illustratesillustrates group 4 (Pinheiros), group 5 (São Caetano do Sul), and group 6 (Parelheiros). Figure 18b illustrates group 4 (Pinheiros), group 5 (São Caetano do Sul), and group 6 (Parelheiros). Figure 18bthe theillustrates thedistributionthethe distribution distribution distributiondistribution map map map mapmap of of the of oftheof thestations thethe stations stations stationsstations according according according accordingaccording to to the to totheto thesix thethe six homogeneous six sixsix homogeneous homogeneous homogeneoushomogeneous groups groups groups groupsgroups in in the in inthein MASP,the thethe MASP, MASP, MASP,MASP, and and and andeachand each each eacheach the distribution map of the stations according to the six homogeneous groups in the MASP, and each the distribution map of the stations according to the six homogeneous groups in the MASP,colorcolor andcolorcolorcolor corresponds eachcorresponds corresponds correspondscorresponds to to a to togroup.ato group. a aa group. group.group. The The The ThespatialThe spatial spatial spatialspatial distribution distribution distribution distributiondistribution of of the of oftheof groupsthe thethe groups groups groupsgroups (Figure (Figure (Figure (Figure(Figure 18b) 18b) 18b) 18b) 18b)indicates indicates indicates indicatesindicates that that that thatthatthe the sixthe thethe six six sixsix color corresponds to a group. The spatial distribution of the groups (Figure 18b) indicates that the color corresponds to a group. The spatial distribution of the groups (Figure 18b) indicateshomogeneous thathomogeneoushomogeneoushomogeneoushomogeneous the six groups groups groupsgroupsgroups from from fromfromfrom the the thetheCAthe CA CACAcorrespondCA correspond correspondcorrespondcorrespond to to areas tototoareas areasareasareas with with withwithwith spatial spatial spatialspatialspatial patterns patterns patternspatternspatterns found found foundfoundfound with with withwithwith the the theEOFthethe EOF EOFEOFEOF six homogeneous groups from the CA correspond to areas with spatial patterns found with the EOF homogeneous groups from the CA correspond to areas with spatial patterns found withanalysisanalysis theanalysisanalysisanalysis EOF in in bothin ininboth bothbothboth modes. modes. modes.modes.modes. Overall, Overall, Overall,Overall,Overall, the the thetheCAthe CA CACACAcorro corro corrocorrocorroboratesboratesboratesboratesborates the the thetheEOFthe EOF EOFEOFEOF analysis, analysis, analysis,analysis,analysis, with with withwithwith the the thetheCAthe CA CACACAgroups groups groupsgroupsgroups analysis in both modes. Overall, the CA corroborates the EOF analysis, with the CA groups matching analysis in both modes. Overall, the CA corroborates the EOF analysis, with the matchingCAmatching matchingmatchingmatchinggroups the the thespatial thethe spatial spatial spatialspatial pattern pattern pattern patternpattern of of the of oftheof thesecond thethe second second secondsecond PC PC ofPC PCPC of the of oftheof theT-mode thethe T-mode T-mode T-modeT-mode and and and andandthe the thefirst thethe first first firstfirstPC PC ofPC PCPC of the of oftheof theS-mode. thethe S-mode. S-mode. S-mode.S-mode. the spatial pattern of the second PC of the T-mode and the first PC of the S-mode. matching the spatial pattern of the second PC of the T-mode and the first PC of the S-mode.

FigureFigureFigureFigureFigure 18. 18. 18. ( 18.a 18.( 18.)(a aThe) ) ( ( Thea(Theaa)) ) The resultingTheThe resulting resulting resultingresulting dendrogram dendrogram dendrogram dendrogram dendrogramdendrogram for for fornine for for fornine nine nine ninenineweather weather weatherweather weatherweather stations stations stations stationsstations and and and ( andandb ()b the () (b (btheb)) )distribution the thethe thedistribution distribution distributiondistribution distribution map map map map mapof map of the of oftheof the thethe Figure 18. (a) The resulting dendrogram for nine weather stations and (b) the distribution map of theofstationsstations thestationsstationsstations stations within within withinwithinwithin withinsix six homogeneous sixsix sixhomogeneous six homogeneoushomogeneoushomogeneous homogeneous groups groups groupsgroupsgroups groups in in the ininthein in MASP.thethethe theMASP. MASP.MASP.MASP. MASP. Each Each EachEach Each Eachsymbol symbol symbolsymbolsymbol (or (or colour) (or(or (orcolour) colour)colour) colour) corresponds corresponds correspondscorresponds corresponds to to a totoato aaa stations within six homogeneous groups in the MASP. Each symbol (or colour) corresponds totogroup: agroup: agroup:group: group: (red—group (red—group (red—group(red—group(red—group 1); 1); 1); 1); (yellow—group (yellow—group (yellow—group(yellow—group(yellow—group 2) ;2) ;2) 2) 2);2); ; ; (orange—group (orange—group (orange—group(orange—group(orange—group 3); 3); 3); 3); 3);3); (green—group (green—group (green—group (green—group(green—group(green—group 4); 4); 4);4); 4); 4); (purple—group 5) and (blue—group 6). group: (red—group 1); (yellow—group 2); (orange—group 3); (green—group 4); (purple—group(purple—group (purple—group(purple—group(purple—group 5) 5)and 5) 5)and5) and andand (blue—group (blue—group (blue—group (blue—group (blue—group 6). 6). 6). 6).6). (purple—group 5) and (blue—group 6). AA subjective AAsubjectiveA subjective subjectivesubjective analysisanalysis analysis analysis analysisanalysis ofof of thethe of oftheof land-use theland-use thethe land-use land-use land-useland-use classification classification classification classification classificationclassification map map map (Figuremapmapmap (Figure (Figure (Figure (Figure(Figure5b) 5b) resulted5b) 5b)resulted 5b)5b) resulted resulted resultedresulted in thein in the identificationin inthein theidentification thethe identification identification identificationidentification of A subjective analysis of the land-use classification map (Figure 5b) resulted in the identificationsixofof six groups,of ofofsix groups,sixsixsix groups, groups,groups,groups, which which which we whichwhichwhich classifiedwe we weclassifiedwewe classified classifiedclassifiedclassified as follows: as as follows: as asasfollows: urbanfollows:follows:follows: urban groupurban urbanurbanurban group 1group (S groupgroupgroupão 1 Caetano 1(São 1(São11 (São(São (SãoCaetano Caetano do CaetanoCaetanoCaetano Sul, do purple), do Sul, dododo Sul, Sul,Sul,Sul,purple), urbanpurple), purple),purple),purple), group urban urban urbanurbanurban 2 of six groups, which we classified as follows: urban group 1 (São Caetano do Sul, purple),(Pinheiros,groupgroupgroupgroupgroup urban 2 2(Pinheiros, 2(Pinheiros, green),22 (Pinheiros,(Pinheiros,(Pinheiros, urban green), green), groupgreen),green),green), urban urban 3 urban (Taboaurbanurban group group groupgroup Serragroup 3 3(Taboa and 3(Taboa33 (Taboa(Taboa(Taboa Ibirapuera, Serra Serra SerraSerraSerra and and orange), and andandIbirapuera, Ibirapuera, Ibirapuera,Ibirapuera,Ibirapuera, urban orange), group orange), orange),orange),orange), 5 (Congonhasurban urban urbanurbanurban group group groupgroupgroup and 5 5 555 group 2 (Pinheiros, green), urban group 3 (Taboa Serra and Ibirapuera, orange), urbanMirante, group yellow), 5 urban group 6 (Guarulhos and USP, red) and the vegetated group (Parelheiros, blue).

Environments 2017, 4, 27 18 of 26

(Congonhas and Mirante, yellow), urban group 6 (Guarulhos and USP, red) and the vegetated group (Parelheiros,Environments 2017 blue)., 4, 27 18 of 26

3.4.3.4. UHI UHI Intensity Intensity WeWe used the average air temperature in in each each of of the six homogeneous groups groups to to determine determine the the UHIUHI intensity, intensity, being, therefore, a mean UHII. It It should should be be emphasized emphasized that that no no filtering filtering or or removal removal of of thethe influence influence of of synoptic synoptic scale scale was was carried carried out; out; also, also, no no filtering filtering or or removal removal was was carried carried out out for for days days withwith a a prevalence prevalence of of weak weak winds, winds, days days with with significant significant cloudiness, cloudiness, and and even even days days corresponding corresponding to to weekendsweekends and and holidays. holidays. AmongAmong the the six six groups groups identified identified with with the the CA, CA, group group 6 6 (composed (composed of of Parelheiros Parelheiros station station only) only) standsstands outout for for being being located located in the in region the region farthest fart fromhest the from central the area central of MASP area and of was MASP predominantly and was predominantlycharacterized by characterized scarce urbanization by scarce and urbanization more vegetated and more area. vegetated Therefore, area. to estimateTherefore, the to UHII,estimate we thechose UHII, group we 6 chose to represent group the6 to temperature represent the of non-urban/vegetated temperature of non-urban/vegetated areas, and the other areas, groups and (1,the 2, other3, 4 and groups 5) to (1, represent 2, 3, 4 and the 5) urban to represent area. the urban area. WeWe estimated thethe UHIIUHII forfor eacheach one one of of the the urban urban groups groups considering considering the the differences differences between between the theaverage average temperature temperature of each of urbaneach groupurban andgroup Parelheiros and Parelheiros (group 6), (group which were6), which then, respectively,were then, respectively,denominated denominated as case 1 to 5,as after case the 1 to group 5, after number. the group Except number. for case Except 5, we for observed case 5, we a clear observed diurnal a clearcycle diurnal of the UHII, cycle althoughof the UHII, each although case peaks each at case different peaks times at different (Figure times 19). (Figure 19).

FigureFigure 19. 19. AnnualAnnual mean mean diurnal diurnal cycle of cycle the urban of the heat urban island heat(UHI) island intensity (UHI) for the intensity different for cases: the casedifferent 1 cases:(São caseCaetano 1 (S ãodo Caetano Sul—Parelheiros), do Sul—Parelheiros), case 2 case (Pinheiros—Parelheiros), 2 (Pinheiros—Parelheiros), case case 3 3 (Congonhas/Mirante—Parelheiros),(Congonhas/Mirante—Parelheiros), case case 4 4(Ibirapu (Ibirapuera/Taboera/Taboãoã oda da Serra—Parelheiros), Serra—Parelheiros), and and case case 5 5 (Guarulhos/USP—Parelheiros).(Guarulhos/USP—Parelheiros).

ForFor cases cases 1, 1, 2 2 and and 4, 4, the the UHII UHII peaks peaks in in the the afternoo afternoon,n, at at approximately approximately 15:00 15:00 LT LT for for cases cases 1 1 and and 2, 2, andand 17:00 17:00 LT LT for for case case 4. 4. For For case case 3, 3, a apeak peak occurs occurs in in the the morning morning at atapproximately approximately 08:00 08:00 LT LT and and a secondarya secondary peak peak occurs occurs late late in inthe the evening evening at at approximately approximately 22:00 22:00 LT. LT. The The selection selection of of reference reference stationsstations reflects reflects very very distinct distinct pa patternstterns of of the the UHII, UHII, therefore, therefore, specific specific criteria criteria are are recommended recommended for for theirtheir selection. selection. AmongAmong the the UHII UHII cases cases analyzed, analyzed, case case 1 1 is is consistent consistent with with the the pattern pattern found found by by Ferreira Ferreira et et al. al. [30], [30], whowho estimated estimated the the monthly monthly UHI UHI for for 2004. The The dayt daytimeime behaviour behaviour of of the the UHII UHII follows follows the the diurnal diurnal evolutionevolution ofof netnet radiation radiation at at the the surface surface for allfor months all months of the of year, the with year, a 3-hwith delay a 3-h with delay the maximumwith the maximumintensity of intensity net radiation. of net Therefore,radiation. Therefore, we chose casewe chose 1 to assess case 1 the to seasonalassess the variability seasonal variability of the MASP of UHI (Figure 20). Spring had the highest maximum and lowest minimum UHII values compared with Environments 2017, 4, 27 19 of 26

Environments 2017, 4, 27 19 of 26 the MASP UHI (Figure 20). Spring had the highest maximum and lowest minimum UHII values compared with the other seasons, and winter had the lowest UHII values. The maximum UHII occurredthe other seasons,at different and times winter for had each the lowestseason. UHIIIn spring, values. summer The maximum and wint UHIIer, the occurred maximum at different UHII valuestimes for occurred each season. at 15:00 In LT, spring, 13:00 summer LT, and and 16:00 winter, LT, respectively. the maximum In UHII autumn values, there occurred were two at 15:00 peaks, LT, 13:00one at LT, 12:00 and LT 16:00 and LT,another respectively. between In 14:00 autumn, and 15:00 there LT. were This two variation peaks, oneis likely at 12:00 to be LT related and another to the incidentbetween 14:00solar andradiation 15:00 LT.at Thisthe variationsurface, which is likely does to be have related a significant to the incident seasonal solar radiationvariation. at The the shortwavesurface, which radiation does have in São a significant Paulo peaks seasonal during variation. spring, The particularly shortwave radiationin September, in Sã oand Paulo presents peaks minimumduring spring, values particularly during fall inand September, winter [30,55]. and presents minimum values during fall and winter [30,55].

Figure 20.20. SeasonalSeasonal diurnal diurnal cycle cycle of UHIof UHI intensity intensity in the inMASP the MASP for case for 1: case spring 1: (green),spring (green), fall (brown), fall (brown),summer (red)summer and (red) winter and (blue). winter (blue).

4. Conclusions Multivariate analysis of observational temperat temperatureure data demonstrated the spatial and temporal structures of the UHI in the MASP for the periodperiod fromfrom 20022002 toto 2011.2011. In EOF analysis, both S- and T-modes allowed thethe recognitionrecognition ofof dominantdominant modesmodes ofof variabilityvariability ofof thethe UHI.UHI. For the T-mode EOF, we identifiedidentified three main modes of variability in in the the MASP, MASP, and they explained 99% of the total variance. The first first mode explained 67% of the variance, the second mode explained 24%, and the third mode explained 8%. We We associated the first first and third modes of the EOF with the wind movement mechanisms of the MASP related to the sea breeze, whereas the second mode withwith thethe urbanization urbanization and and the the release release of heat of heat from from the urban the urban canopy canopy and anthropogenic and anthropogenic sources, sources,as well as as local well wind as local circulation wind incirculation the MASP. in Thethe spatialMASP. pattern The spatial of the temperaturepattern of the anomaly temperature of the anomalysecond PC of is the similar second to thePC is spatial similar distribution to the spatial of the distribution apparent of surface the apparent temperature surface of thetemperature MASP. of the MASP.For the S-mode EOF, we found only two modes of variability, and they accounted for 49% and 31% ofFor the the total S-mode variance. EOF, Inwe the found S-mode, only thetwo first modes mode of representedvariability, and the spatialthey accounted pattern of for the 49% UHI and in 31%the MASP, of the andtotal itvariance. was similar In the to theS-mode, second the mode first mode of the represented T-mode EOF. the spatial pattern of the UHI in the MASP,In the and analysis it was of similar seasonal to EOFs,the second we observed mode of athe difference T-mode inEOF. the number of variability modes, withIn summer the analysis and winter of seasonal each presenting EOFs, we two observed modes, a anddifference fall and in spring the number each presenting of variability three modes, modes. Thiswith differencesummer and is probably winter associatedeach presenting with the two thermodynamic modes, and fall patterns and spring of the atmosphere,each presenting which three are modes.different This during difference each season, is probably as well associated as due to with remote the influences,thermodynamic such patterns as El Nin ofõ/La the Ninatmosphere,ã events, which canare different influence during seasonal each air season, temperatures as well in as MASP. due to remote influences, such as El Ninõ/La Ninã events,Both which forms can of influence EOF analysis seasonal enabled air temperatures the identification in MASP. of the various warm core temperatures and theirBoth intensities,forms of EOF sizes, analysis locations, enabled and variationsthe identifi throughoutcation of the the various diurnal warm cycle. core We temperatures identified six andhomogeneous their intensities, groups sizes, with thelocations, CA, which and werevariations consistent throughout with the the core diurnal spatial cycle. patterns We we identified found with six

Environments 2017, 4, 27 20 of 26 the EOF analysis. Therefore, by applying multivariate analysis, we determined the main temperature anomaly patterns for the MASP. In analysis of UHII, estimates of the temperature differences between the urban/suburban areas and the non-urban/vegetated areas were calculated. Group 6 (Parelheiros station) was regarded as the non-urban/vegetated group because it is located further from the central area of the MASP, and the other groups (1, 2, 3, 4 and 5) were regarded as the urban/suburban groups. The results of the UHII estimations showed that the maximum and minimum intensities of the UHI occurred at different hours for each case. Therefore, the selected reference stations may have reflected distinct UHII patterns, indicating what criteria should be adopted when selecting stations. Detailed annual and seasonal analyses of the UHI for case 1 (temperature differences between the São Caetano do Sul and Parelheiros stations), demonstrated—in UHII annual analysis—a diurnal pattern with a maximum UHII between 14:00 and 16:00 LT and a minimum UHII between 07:00 and 09:00 LT. The daytime behavior of UHII found in the results agrees with the study of Ferreira et al. [30]; the maximum UHII value in the diurnal pattern occurred in the afternoon at approximately 3 h after the maximum intensity of net radiation. In UHII seasonal analysis, spring had the highest maximum and minimum UHI values. The maximum UHII in spring, particularly in September, is related to the maximum incident solar radiation caused by significant seasonal variations in atmospheric transmissivity and emissivity. In September, additional solar radiation reaches the surface and transmits a greater amount of longwave radiation. The characterization of the air temperature field using multivariate analysis techniques (principal component analysis and cluster analysis) is an approach that is not well explored in urban climate studies. In this study, we demonstrated the robustness of this type of analyses, identifying the spatial and temporal patterns near the surface temperature in the urban area and surroundings of the MASP, which allowed us to assess and quantify the UHI phenomenon. Within the principal components, we recognized the primary physical patterns and mechanisms that act and influence the MASP, such as urbanization, local circulation, and the mutual influence between them that derives from other effects, such as urban breeze circulation. In the cluster analysis, the stations with similar characteristics are distributed in groups. The application of the multivariate analysis techniques highlights a new approach that could be further explored for urban studies to determine the intensity of UHI across regions and similar microclimatic zones. In addition, this study evidenced another aspect not commonly discussed in urban studies. Although the UHI phenomenon is primarily established and dimensioned by the local characteristics of the urban area, the remote and local influences can also play a role in the seasonal behavior of air temperature, and thus in the UHI intensity. Our results highlight the importance of taking into account the remote and local influences in urban studies.

Acknowledgments: The authors would like to thank the National Council of Technological and Scientific Development (CNPq) for the financial support for this research. We also thank the CETESB, INEA, INMET, REDEMET and USP for providing access to their data. Author Contributions: This paper is part of the first author Ph.D. thesis. The second and third authors are the advisor and a climate expert, respectively. Fernanda Batista Silva designed and carried out the research, gathering the data and applying the multivariate analysis. Karla Maria Longo de Freitas contributed with the data analysis and reviewed the work. Felipe Marques de Andrade contributed to the analysis of the relationship of remote and local influences with the local UHI phenomenon. All the authors reviewed and approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A. EOF Analysis The EOF analysis aims to transform correlated original variables (K) to new uncorrelated or orthogonal (M) components/variables. These components are linear functions of the original components. Therefore, for vector × with multiple observations of (K × 1) data, the EOF generates a new vector u of (M × 1), which includes elements that are linear combinations of the elements of vector x and contain most of the information from the original vector. The elements of this new vector Environments 2017, 4, 27 21 of 26 represent the maximum fraction of the variability in the original data and are called the principal components (PCs) [43]. Each PC generated by the EOF represents a portion of the variability in the dataset, and as the variance explained by the PC increases, the importance of PC in the representation of the dataset increases. The first mode or first PC is the linear combination of the original standardized variables, and it represents the fraction or percentage of the maximum variance. The second mode or second PC is the main component, or the linear combination of variables, which does not correlate with the first mode, and represents the largest proportion of the remaining variance. The subsequent principal components include linear combinations with the largest proportion of the remaining variance, and they are uncorrelated with principal components that have lower indices. The EOFs of each PC are mutually uncorrelated. Thus, the major advantage of using the EOF technique is that the classification of the eigenvectors associated with the largest eigenvalues of the correlation matrix allows the maximum variance to be explained [40]. The correlation matrix is written as follows: 1 R = [Z]T[Z] (A1) n − 1

T where [Z] is the transposed matrix of Z. The correlation matrix [R] is obtained by M eigenvalues λm T (λ1 ≥ λ2 ≥ .... ≥ λk), and each of the eigenvalues corresponds to an eigenvector (em):

T em = [e1m, e2m, ..., ekm], m = 1, 2, 3, . . . , M (A2)

Each eigenvector is one of the M components of the new orthogonal basis. The new variables (PCs) are obtained projecting the original data on the new basis given by the eigenvectors of [R]: K u T [Z] = e Z , m = 1, 2, 3, . . . , M (A3) m=em ∑k=1 k,m k Each of the M eigenvectors contains one element pertaining to each of the K variables and can be represented on a map that indicates the locations with the largest contributions to their main component and the simultaneous anomalies that are represented by this major component. The EOF also provides the variance of the total analysis, which is defined by the sum of the variances of the observed variables as follows:

K K V = ∑ Sk,k = ∑ λm (A4) k=1 k=1

The value of the variance accounted for by each component is given by:

λ λ = m · = m · αm K 100% K 100% (A5) ∑k=1 λk ∑k=1 Sk,k

An important question regarding the EOF technique pertains to the number of eigenvalues that must be retained to differentiate between significant information and noise. To select the appropriate number of PCs for the analysis, the Kaiser truncation criterion is applied to retain the λm that meets the criterion: T K λm ≥ ∑ sk,k (A6) K k=1 where sk,k is the sample variance of the kth element and T is a threshold parameter. Kaiser’s criterion [54] uses Equation (6) with a threshold parameter T = 1 [43]. In this criterion, eigenvalues greater than one are considered the most significant. Environments 2017, 4, 27 22 of 26

The EOF rotated by the varimax orthogonal rotation method [56] was used to maximize the variance of the results. This method is a commonly used approach, and it is determined by choosing the elements of the rotation matrix to maximize as follows:

 2 2 n  2   n 2  n ∑i=1 ai,j − ∑i=1 ai,j V∗ = (j = 1, . . . , r) (A7) n2 where n is the number of variables, r is the number of PCs, and bi are the eigenvectors. The rotated EOF has the advantage of producing new compact patterns that can be used for regionalization; thus, it divides the area into a limited number of homogeneous subareas [41]. The main objectives of rotated EOF analysis are to alleviate the strong constraints of the EOF (i.e., orthogonal/uncorrelated variables of PCs), to alleviate the dependence of the EOF pattern on the domain shape, and to obtain simple structures and easy interpretations of obtained patterns. In the T-mode approach, the spatial fields (at a given time) of the variables used in analysis are considered the statistical variables. The domain is now temporal and the statistical observations are the different spatial points included in the instantaneous field [47]. Therefore, the T-mode not only identifies the main spatial patterns of the temperature anomaly field but also the order of occurrence. To analyze the T-mode, a data matrix (n × m) was built, where n corresponds to the spatial field or “snapshot” of the mean hourly temperature anomalies (n = 9, which are weather stations of the MASP) and m corresponds to the statistical observations (m = 24, which are the mean hourly temperature anomalies of the 10 years of observations). In the T-mode, the spatial patterns (PC scores) correspond to the principal types of temperature anomalies that describe the observed spatial variability, whereas the time series (PC loading) represents the correlation between the spatial patterns and each of the hourly mean anomaly fields. In the time series, the time at which a specific pattern occurs and the significance of its contribution to the real field at that time are observed. Therefore, when the time series shows low values (low PC loadings) for a specific time, the spatial pattern does not correspond to the structure of the temperature anomaly field. Thus, values closer to 1 in the time series represent sequences of weather conditions similar to the sequences of obtained patterns [48,49]. In the S-mode, the statistical variables are points in space, and the statistical observations are the observation times at which the variables are measured; thus, this mode can be used to study the behavior of the time series. The aim of the S-mode is to isolate the subsets of the spatial domain that have similar time variations and identify regions of similar behavior in time [50]. Therefore, although the characteristics of the field of study are not identified, the main features of the temporal variability of the field and the areas of influence of these modes are determined. For S-mode analysis, a data matrix (n × m) was built, where n is the number of variables (n = 24, which is the mean hourly temperature anomalies of the 10 years of observations) and m corresponds to the number of observations (m = 9, which is the nine weather stations of the MASP). In the S-mode approach, the time series (PC scores) correspond to the principal patterns of temporal variability for the temperature anomaly, and the spatial patterns (PC loadings) represent the correlation fields determined by the time series and all points in space. The spatial pattern field shows areas where the grid-point time series presents an in-level or anti-phase temporal behavior similar to that of the time series [50] such that low correlation values (low PC loadings) do not correspond to the behavior of the original observations for that particular mode. T-mode and S-mode EOFs describe different aspects of the same real case. However, these two modes are supplementary and equally exclusive because their results cannot be reproduced by the mathematical manipulation of one another. In certain special cases, the S-mode and T-mode EOFs may produce results that are apparently similar, and a relationship might be observed between these “similarities” if there is an intrinsic and large linear spatial and temporal relationship that precludes Environments 2017, 4, 27 23 of 26 any other effects, such as dispersion, which occurs over time because of the non-linearity of real systems [47,50].

Appendix B. Cluster Analysis In Cluster analysis, the degree of similarity and difference between individual observations, x, is used to define the groups and to assign group membership. For a data vector sample x, which is defined by the (n × k) data of matrix [X], a classification scheme will define G groups and assign group memberships at varying levels of aggregation [43]. The CA fundamentally consists of a grouping function (called a distance or similarity measure) and a mathematical grouping criterion [51]. The composition of a cluster is based on the measured distances; thus, it is composed of points separated by small distances relative to the distances between clusters [43]. The similarity measure most commonly used in a CA is the Euclidean distance in the spatial dimension of the data vectors, and this approach was used here. A detailed discussion of various similarity measures can be found in [52]. The Euclidean distance between two vectors xi and xj is defined as follows: 1 " K # 2    2 di,j = xi − xj = ∑ xi,k − xj,k (A8) k=1 After selecting a distance measure to quantify the dissimilarity or similarity between the pair of vectors xi and xj, the next step in CA is to choose a method or grouping criteria. The grouping processes can be divided into hierarchical or non-hierarchical processes, and hierarchical processes are more commonly used. The hierarchical clustering method is characterized by creating a set of groups in a hierarchy, each of which is formed by the integration of one pair from a collection of previously defined groups. The hierarchical method used in this study was Ward’s method [57], which is the most commonly used hierarchical method. In this method, the pair of groups to be merged minimizes the sum of the squared distances between the points and the centroids of their respective groups summed over the resulting groups. Thus, among all possible methods of merging two of the G + 1 groups to make G groups, the merge that minimizes W, is performed [43]:

G ng G ng K 2  2 W = ∑ ∑ kxi − xgk = ∑ ∑ ∑ xi,k − xg,k (A9) g=1 i=1 g=1 i=1 k=1

This hierarchical search method for partitions minimizes the loss of information associated with each cluster [51]. One of the main advantages of the Ward method beyond its effectiveness in forming groups is that it tends to produce groups with the same number of elements. The CA results are presented by a dendrogram or tree diagram, where the successive mergers of individuals into a single group are verified and the results are summarized. One of the difficulties of a CA is choosing how many clusters for analysis because an intermediate phase must be selected as the final solution. Thus, a level of clustering must be selected that minimizes the differences between the members of a given cluster and maximizes the differences between the members of different clusters [43]. There are no set criteria for the selection of clusters, although the process of interruption requires a subjective choice according to the goals of the analysis.

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