Theoretical and Applied Climatology
https://doi.org/10.1007/s00704-019-02973-y
ORIGINAL PAPER
Air temperature in Barcelona metropolitan region from MODIS
satellite and GIS data
C. Serra 1 & X. Lana 1 & M. D. Martínez 1 & J. Roca 2 & B. Arellano 2 & R. Biere 2 & M. Moix 2 & A. Burgueño 3
Received: 28 September 2018 / Accepted: 7 August 2019
# Springer-Verlag GmbH Austria, part of Springer Nature 2019
Abstract
The metropolitan region of Barcelona (BMR) is one of the most densely populated areas in the Mediterranean countries. The
estimation of air temperature at a short scale from satellite measurements would contribute to a better understanding of the varied
and complex spatial distribution of temperatures in BMR. This estimation would be a first step to study several patterns of the
thermometric regime affecting population life quality and health. Taking advantage of MODIS data, air temperature measurements at 48 thermometric stations along the year 2015, together with their geographic and topographic data, multiple regression
analyses have permitted to obtain fine spatial distributions (pixels of 1 km2) of minimum, mean and maximum daily air
temperatures. Previous to the multiple regression, Pearson coefficients and principal component analysis offer a first overview
of the relevance of the variables on the empiric temperatures. The most relevant variables on the multiple regression process at
annual and seasonal scale are land surface temperatures, latitude, longitude and calendar day. At a monthly scale, altitude
(maximum temperature) and continentality (cold months for minimum and hot months for maximum temperatures) are also
relevant. The best fits between empiric temperatures and those derived from the multiple regression processes have square
regression coefficients within the range (0.92–0.96) for the annual case, (0.70–0.92) at seasonal scale and (0.52–0.87) at monthly
scale. The root mean square error varies from 1.5 to 2.0 °C (annual case), from 1.3 to 2.0 °C (seasonal scale) and from 1.2 to
2.1 °C (monthly scale). In agreement with these regression coefficients and mean square errors, the obtained spatial distribution
of temperatures is of notable quality. As an outstanding application, the detection of several urban heat islands on different
conurbations within BMR along the Mediterranean coast becomes possible.
1 Introduction
The estimation of the land surface temperature (LST) from the
thermal infrared radiation (TIR) emitted by the Earth became
possible a few years after the arrival of remote sensing from
the space. Rao (1972) was the first to apply TIR to estimate
temperature patterns for the cities along the USA mid-Atlantic
coast from data collected by the Improved TIROS Operational
Satellite (Gallo et al. 1995). TIR measurement from the space
* X. Lana
francisco.javier.lana@upc.edu
1
Department of Physics, Technical University of Catalonia,
Barcelona, Spain
2
Department of Architectural Technology, Technical University of
Catalonia, Barcelona, Spain
3
Department of Applied Physics–Meteorology, University of
Barcelona, Barcelona, Spain
permits to know the LST assigned to a pixel (Dash et al. 2001,
2002), without considering the multiple parts contained in this
pixel, as vegetation, sunlit and shadowed soils, irregular urban
surfaces or soil moisture, with different albedo and emissivity
values (Tomlinson et al. 2011; Benali et al. 2012). In fact, TIR
is derived from the top of atmosphere radiances, from which
LST is obtained after applying corrections due to atmospheric
attenuation, angular effects and emissivity values at the heterogeneous surface. Water vapour and aerosols are the main
agents causing variable attenuation in the TIR signal. This
reduces the LST availability to only under cloud-free conditions, to avoid a systematic bias toward colder-than-true
values (Williamson et al. 2013). In this sense, the integration
of synergistic information from satellite optical-IR and passive
microwave remote sensing has been proved recently to permit
consistent and reasonable temperature estimations with
cloudy skies (Jang et al. 2014).
The right estimation of the temperature of the air at ≈ 2-m
height above ground (Ta) from LST is possible but complex.
The vertical lapse rate to be applied is function of the surface
C. Serra et al.
energy balance, which varies in function of the nature of the
surface and of the instant of the day, as also of advection,
adiabatic processes, turbulence and latent heat fluxes, all of
them affected by cloud cover, water vapour content and vegetation (Benali et al. 2012). During the night, the estimation of
Ta becomes simpler because the earth surface behaves almost
as homogeneous surface (Didari et al. 2017).
This Ta estimated from satellite measurements would solve
the weather stations scarcity in wider regions, where the
geospatial interpolation methods, as kriging or splines, cannot
provide accurate estimations, as happens, for instance, in
mountainous terrain (Lin et al. 2016) or undeveloped countries. In this way, Ta estimation becomes of crucial importance
to solve spatial gaps for a wide range of applications, in such a
way that it is accepted that TIR produces better Ta estimations
than those obtained by interpolating ground-station temperatures (Mendelsohn et al. 2007).
In the first years of remote sensing, this strategy based on
TIR permitted to obtain extended and automatic LST for large
regions, but with a limited spatial resolution, as in the case of
Meteosat satellite (e.g. Cresswell et al. 1999). Since the year
2000, the MODerate resolution Imaging Spectroradiometer
(MODIS) sensor in Terra and Aqua polar satellites (http://
modis.gsfc.nasa.gov/) have reduced the spatial resolution for
LST to 1 km per pixel. In this way, two images per satellite per
day are generated (Terra satellite passes daily over the equator
close to 10:30 UTC and 22:30 UTC; Aqua at 13:30 UTC and
01:30 UTC), using both the 10.78–11.28 μm and 11.77–12.
27 μm spectral bands, together with split-window algorithms
(Wan et al. 2002). These MODIS products have been submitted to consistent validation (Coll et al. 2005; Wang et al.
2008). In addition to climatological applications, other biological and physical processes on the land and the ocean may be
derived using 36 electromagnetic spectral bands from visible
to TIR available from MODIS (Zhang et al. 2003; Wan et al.
2004; Wang et al. 2009) or also mapping the global distribution of urban land (Schneider et al. 2009).
Given the practical impossibility of Ta direct determination
from MODIS Terra LST, different estimation methods have
been applied (Zaksek and Schroedter-Homscheidt 2009). The
simplest one consists in supposing a linear relation between Ta
and LST by distinguishing different land cover types, as Shen
and Leptoukh (2011) have applied to Central and Eastern
Eurasia, or without this distinction for smaller regions (Fu
et al. 2011; Sohrabinia et al. 2015). The consideration of the
called temperature-vegetation index (TVX), proposed by
Nemani and Running (1989), by applying the normalised difference vegetation index (NDVI) and ignoring its seasonal,
ecosystem type and soil moisture variability, has permitted
the inclusion of the vegetation cover as a relevant factor
(Prihodko and Goward 1997; Vancutsem et al. 2010;
Cristóbal et al. 2008; Nieto et al. 2011; Wenbin et al. 2013;
Shah et al. 2013; Bustos and Meza 2015). Modifications have
been also added, as the differential TVX method (Sun et al.
2014). Certainly, the vegetation cover is determinant by its
transpiration cooling and latent heat fluxes, as also through
their low albedo and roughness which aides efficient sensible
heat dissipation (Benali et al. 2012). Alternatively, the multiple linear regression applies different variables in addition to
LST and NVDI to estimate Ta, as latitude, distance from coast,
altitude and solar radiation (Cristóbal et al. 2008) or albedo
and solar radiation (Xu et al. 2014). Nevertheless, after having
considered different predictors, Lin et al. (2012) have proved
that just the altitude and LST permit to obtain Ta for East
Africa. Zhang et al. (2011) also apply the solar declination
variable along the year and LST to derive Ta in China.
Kloog et al. (2017) derive daily Ta estimations from LST,
NVDI, elevation and the grid cell percentage of urbanicity
for France. But, in general, for extended regions, spatialtemporal variables as Julian day of the year, latitude, longitude, height above sea level, slope, curvature and distance to
the coast use to be considered (Recondo et al. 2013; Peón et al.
2014; Good 2015; Thanh et al. 2016; Yang et al. 2017). A
relation with the variables applied by different authors can be
found in Janatian et al. (2017). Also, the use of spatiotemporal regression-kriging and incorporation of time-series
of remote sensing images have been proved to permit significantly more accurate maps of temperature than if plain spatial
techniques were used (Hengl et al. 2012). At the planetary
scale, the new dataset of spatially interpolated monthly climate data for global land areas at a very high spatial resolution
(approximately 1 km2) has considered LST observations to
cover areas with a low station density (Fick and Hijmans
2017). This effort improves the first LST map at the planetary
scale from MODIS measures (Kilibarda et al. 2014).
Besides different valuable applications of the estimation
of Ta from LST, this study should be the base of future
detailed analyses of the urban heat island (UHI) of
Barcelona considering its entire Metropolitan Region
(BMR). Unless otherwise indicated, UHI intensity is derived as the difference in spatially averaged surface temperatures between urban and non-urbanised surroundings, as a
measure of the excess of warmth of the urban atmosphere
(Voogt and Oke 2003). UHI phenomenon has been usually
analysed from air temperature measurements of a short
number of gauges across the city, sometimes with emplacements submitted to criticism, as gardens or roofs, and others
outside the city influence (Stewart 2011). This humble
departing state (Landsberg 1981), due to the scarcity of
points with measurements, has led to a first spatial and temporal characterisation of the phenomenon (Arnfield 2003).
Later on, thermometers installed in automobile have permitted to extend the analysis for selected transects across the
city (Caselles et al. 1991; Moreno-Garcia 1994) to derive a
thinner description of the anomalous urban thermal behaviour in relation to the rural proximity of the city. Urban
Air temperature in Barcelona metropolitan region from MODIS satellite and GIS data
networks of stations together with different rural temperature observatories around the city have been also undertaken permitting detailed descriptions (Giannaros and Melas
2012; Yang et al. 2013). The multiplicity of urban internal
configurations, due to the diversity of geometry,
morphology and size of the cities, together with local or
regional air dynamics, as the mesoscale sea breeze in the
case of littoral cities, makes the urban climate a difficult
objective to be rightly modelled. This shortcoming is
notably solved by considering Ta series derived from
satellite remote sensing. Voogt and Oke (2003) have
reviewed the research done with thermal remote sensing
before MODIS application. They conclude that the complexity of the urban surface should be analysed through
couple canopy radiative transfer models with both sensor
view models and surface energy balance models to
simulate air temperature in and above the urban canopy
layer. With this purpose, Miao et al. (2009) have applied
MODIS observations with dynamical models to simulate
urban weather features for comparison with observations
in Beijing. Nevertheless, most of the studies analyse the
spatial UHI taking advantage of the high spatial resolution
provided by MODIS but without considering air dynamics
for single cities (Cheval et al. 2009; Cheval and Dumitrescu
2009; Fabrizi et al. 2011; Tomlinson et al. 2012; Ma et al.
2016), as also for sets of cities (Jin et al. 2005; Hung et al.
2006; Yasuoka 2006; Pongrácz et al. 2006, 2010; Imhoff
et al. 2010), for selected episodes, months or a few years.
2 Database
2.1 Study area
The metropolitan region of Barcelona, BMR, with an extension of 3242.2 km2 and a population density of 1566.2 inhabitants/km 2 , according to IdesCat-2017 (Institut Català
d’Estadística), is a crowded area close to the Mediterranean
Sea. Particularly, Barcelona city, with a population of 1.6 million inhabitants, covers an area close to 100 km2 with a population density close to 16,000 inhabitants/km2. The orography of the analysed region is characterised by the Littoral and
Pre-Littoral chains, with moderate altitudes up to 1700 m
a.s.l., both parallel to the Mediterranean coast. Between both
chains are placed the Vallès valley and Penedès Basin. The
most extended urban area (Barcelona city) is constrained
among the Mediterranean shoreline, the Littoral chain and
Llobregat and Besós rivers. The main orographic features of
the region and the distribution of altitude in meters are shown
in Fig. 1a,b. Details of the spatial distribution of CORINE land
cover classes (http://land.copernicus.eu/pan-european/corineland-cover/clc-2012), at level 3 for the year 2012, are shown
in Fig. 1c and Table 1.
2.2 Meteorological station data
Observed daily minimum, Tmin; mean, Tmean and maximum, Tmax temperatures are the dependent variables of
this study. These come from 48 meteorological stations,
37 of them belonging to the Servei Meteoròlogic de
Catalunya (www.meteocat.cat) and 11 to the Agencia
Estatal de Meteorología, (www.aemet.es) for the year
2015. Data are obtained in both cases from automatic
weather stations, and their quality is guaranteed by
periodic instrumental controls of the two governmental
institutions. Additionally, the 48 thermometric records
are free of perturbations, such as sharp changes or
artificial trends, in agreement with the results of the
Buishand (1982) and Pettitt (1979) tests, as proposed by
Wijngaard et al. (2003). Given that these possible perturbations cannot be detected analysing only 1 year, the two
mentioned tests have been applied to longer records including the year 2015, and the results have been also
compared with previous analysis of the thermometric regime in a wider area of Catalonia (Martínez et al. 2010).
Figure 1 d shows the spatial distribution of the stations,
where five of them are outside but very close to the studied region. The stations are well spread over BMR except
in the north, where they are scarce. Table 2 gives the main
geographical and topographic variables of the thermometric station emplacements. Figure 2 a and b show the histograms of altitudes for the 1 km2 pixels covering all the
BMA and for the set of meteorological stations respectively. Altitudes of the available thermometric stations
are mostly emplaced below 600 m a.s.l.
2.3 Satellite data
The daily MOD11A1 LST measured by MODIS Terra, including daytime 10:30 UTC surface temperature, LSTd, and
night time 22:30 UTC, LSTn, with 1 km2 spatial resolution,
has been used in this study. The normalised difference vegetation index, NDVI, is obtained from the 16-day MOD13Q1
product (with a resolution of 250 m):
NDVI ¼
NIR−RED
NIR þ RED
ð1Þ
where NIR is the near-infrared reflectance band-2 (841–
876 nm) and RED, the reflectance of the red band-1 (620–
670 nm). The normalised difference build-up index, NDBI, is
calculated as:
NDBI ¼
MIR−NIR
MIR þ NIR
ð2Þ
where MIR is the surface reflectance band-6 (1628–
1652 nm) from MOD09A1 product of 8-day average (with
C. Serra et al.
b
a
SIN
BA
T
TO
R
AL
AL
AI
N
41.8
EY
LL
VA
CH
Barcelona
AI
N
AN
NE
A
R
ER
IT
ED
M
41.6
Altitude
-9999 (m)
-0
A
SE
R
VE
RI
LI
OR
ÈS
LL
VA
T
GA
RE
OB
LL
S
DÈ
NE
PE
E
TT
IVER
ÒS R
BES
PR
I
-L
CH
0 - 100
100 - 200
200 - 300
300 - 400
400 - 500
500 - 600
600 - 700
700 - 800
800 - 900
900 - 1000
1000 - 1300
1300 - 1700
41.4
41.2
1.6
c
1.8
2.0
2.2
2.4
2.6
d
45
11
27
26
10
25
30
12
2
34
35
18
21
15
14
28
39
375
38
6
46
3
47
31
23
8
48
42
17
29
7
32
41
9
44
43
33
24
40
13
19
22
20 1
4
16
36
Fig. 1 Spatial distribution of main orographic features (a), altitude above sea level (b), CORINE land cover classes (c) and the thermometric stations (d)
a resolution of 500 m). Figure 2 c and d show the histograms of NDVI and NDBI for emplacements of temperature stations. A half of these coefficients are within the
0.3–0.5 interval, corresponding to emplacements with
low vegetation cover. For the whole set of 1 km2 pixels,
the modal value of NDVI is shifted toward 0.6. In consequence, rural areas are slightly predominant in comparison
with urban domains. With respect to NDBI, it is worth
mentioning that most of the station emplacements have
coefficients ranging from − 0.2 to 0.1. For the whole domain, the mode of NDBI is − 0.1, suggesting a slight predominance of nonurban areas.
2.4 GIS data and calendar day
Besides Satellite variables LSTd, LSTn, NDVI and NDBI,
other six geographical and topographic variables are considered. These are latitude (lat), longitude (lon), distance
to coast or continentality (con), altitude (alt), orientation
(ori) and slope (slp) of the terrain for every meteorological station and pixel. The first three are derived from
ArcGIS software (Geographic Information Systems,
GIS). Altitude, orientation and slope are obtained from
the Ground Digital Model (MDT—Institut Cartogràfic I
Geològic de Catalunya, ICGC) with a 15 × 15 m2 resolution. Table 3 summarises the minimum, mean and maximum of LSTd and LSTn, NDVI and NDBI, together with
geographic and topographic variables. Furthermore, the
calendar day, cd, has been transformed into a new calendar day, cd*, according to:
cd* ¼ cos
2πðcd−cdmax Þ
365
ð3Þ
to obtain the linearity respect to the air temperature (Janatian
et al. 2017). cdmax is the calendar day for which the mean
temperature along the year is the highest. Figure 3 a and b
show the relationship between Tmean and cd or cd* respectively. cdmax for the year 2015 is equal to 200 (July 19th). Figure 3
b shows more signs of linearity between the air temperature
and the transformed calendar day, cd*.
Figure 4 a shows the dependence of Tmax on the orientation.
This dependence is unclear and a linear relationship should be
discarded. Trying to solve this lack of linearity, the orientation
is given as sine and cosine compounds. Figure 4 b shows the
case for Tmax against sine compound, where a small linear
increasing tendency is observed. Conversely, the cosine compound does not show signs of linear tendency.
3 Methodology
The estimation of surface air temperatures is based on the
relationships between variables obtained from satellite
(LSTd, LSTn, NDVI and NDBI), geographic and topographic
data (latitude, longitude, altitude above sea level, orientation,
Air temperature in Barcelona metropolitan region from MODIS satellite and GIS data
Table 1
Types of land cover (percentage and areas) on BMR
Land cover
2
Area (km )
(%)
Coniferous forest
Broad-leaved forest
866.91
493.41
26.7
15.2
Discontinuous urban fabric
333.53
10.3
Vineyards
Sclerophyllous vegetation
293.50
291.79
9.0
9.0
Non-irrigated arable land
173.43
5.3
Industrial or commercial units
Continuous urban fabric
166.17
132.75
5.1
4.1
Permanently irrigated land
95.16
2.9
Occupied by agriculture
Transitional woodland-shrub
68.76
68.26
2.1
2.1
Pastures
43.71
1.3
Complex cultivation patterns
Green urban areas
36.72
26.34
1.1
0.8
Mixed forest
22.44
0.7
Fruit trees and berry plantations
19.66
0.6
Sport and leisure facilities
19.48
0.6
Road and rail networks
Mineral extraction sites
18.54
14.05
0.6
0.4
9.34
9.33
8.35
7.44
5.66
5.12
4.22
3.45
3.37
3244.72
0.3
0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.1
100
Construction sites
Airports
Moors and heathland
Port areas
Olive groves
Beaches, dunes, sands
Salt marshes
Sparsely vegetated areas
Watercourses
Total
slope and distance to coast), the modified calendar day (cd*)
and empiric data (Tmin, Tmean and Tmax) recorded at the thermometric stations.
The first step consists of computing the Pearson correlation coefficient for all possible pairs of data, including
empiric data. In this way, possible relationships between
assumed independent variables can be detected.
Additionally, the dependence of empiric data on the set
of independent variables can be determined. The rotated
principal component analysis (RPCA) (Jolliffe 1986;
Richman 1986; Preisendorfer 1988) is the second step.
In this way, more detailed characteristics of relationships
between independent variables can be established; particularly, the ratio of data variance explained by every rotated principal component, RPC, and the contribution (factor
loading) of every independent variable in the RPCs. These
strategies, Pearson correlation and PCA, have been also
applied by Thanh et al. (2016).
The third step consists of a multiple regression process with
software from Statistic package for Social Sciences, IBMSPSS, with an assumed linear relationship between empiric
data and independent variables. The multiple regression goodness of fit is quantified by the square regression coefficient,
R2, including all the significant independent variables according to P values and α = 0.05 (Harrell 2001) and by residuals
between empirical, emp, and estimated, est, temperatures
computed from the root mean square error, RMSE, and the
mean average error, MAE. These errors are computed as:
n
o1=2
RMSE ¼ N −1 ∑Ni¼1 ðempi −est i Þ2
MAE ¼ N −1 ∑Ni¼1 jempi −est i j
ð4aÞ
ð4bÞ
The multiple regression process is repeated adding step by
step a new independent variable. In this way, the relevance of
every variable on the multiple regression process is contrasted
by observing the changes in R2 and RMSE. In addition to the
coefficients of the multiple regression equations, the beta
weights (standardised coefficients) are also computed to determine the relevance of every independent variable on the
multiple regression equation.
As a summary, in comparison with other similar researches
based on satellite and thermometric stations data, it should be
mentioned that in this paper, first, cross-correlation and principal component analysis (PCA) permits the detection of possible redundant variables in the multiple regression process.
Second, new geographic variables (orientation and slope) are
tested. Third, both thermometric satellite data (LSTd and
LSTn) are used in the multilinear regression, whatever minimum, Tmin; mean, Tmean and maximum, Tmax, daily temperatures are deduced from the multiple linear regression. It should
be also remembered that only variables with absolute values
of beta weight exceeding 0.01 have been finally considered
for the multiple regression equations.
4 Results and discussion
4.1 Correlation coefficients and PCA
The Pearson correlation and the RPCA, based on the principal
component analysis, PCA, have permitted to detect the degree
of dependence between empiric data (Tmin, Tmean and Tmax)
and the rest of parameters (geographic and topographic variables and data from a satellite). Table 4 shows the Pearson
correlation coefficients among all variables. The high correlations, ranging from 0.86 to 0.97, between Tmin, Tmean and Tmax
with daytime and nighttime LST and also with cd* are outstanding. The correlation of the empiric temperatures with the
other parameters is always inside ± 0.23.
C. Serra et al.
Table 2 GIS characteristics of the stations: longitude (Lon), latitude (Lat), altitude above sea level (Alt), distance to shoreline (Con), orientation of the
slope (Ori) and topographic slope (Slp). Ori equal to − 1.0 indicates flat terrains (slope equal to 0.0)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
Station
Lon (°)
Lat (°)
Alt (m)
Con (m)
Ori (°)
Slp (%)
Barcelona—Airport
Pontons
Vilafranca del Penedès
Sitges—Vallcarca
Barcelona—CMT
Barcelona—Drassanes
Sabadell—Aeródromo
Vilassar de Dalt
Arenys de Mar
Santa Susana
Fontmartina
els Hostalets de Pierola
Vacarisses
Vallirana
Barcelona Observatori Fabra
el Vendrell
Font-rubí
Sant Martí Sarroca
PN del Garraf—el Rascler
Viladecans
el Montmell
Sant Pere de Ribes—Garraf
Cabrils
Dosrius—Montnegre Corredor
Rellinars
Sant Llorenç Savall
Tagamanent—PN del Montseny
la Granada
Vilanova del Vallès
Montserrat—Sant Dimes
la Bisbal del Penedès
Canaletes
Malgrat de Mar
Badalona Museu
Sant Sadurní d’Anoia
Cunit
Barcelona Zoo
Barcelona—el Raval
Barcelona Z. Universitària
Caldes de Montbui
la Llacuna
Castellbisbal
Sabadell—Parc Agrari
Parets del Vallès
Puig Sesolles
el Prat de Llobregat
Canyelles
Sant Cugat CAR
2.070000
1.519167
1.676944
1.852500
2.200000
2.173889
2.103056
2.362500
2.540000
2.696944
2.431111
1.808131
1.914997
1.935642
2.123885
1.521214
1.623863
1.630325
1.907752
2.037870
1.487694
1.804796
2.377015
2.445317
1.917178
2.026470
2.302911
1.728574
2.300134
1.837509
1.467169
1.693370
2.756574
2.247574
1.794292
1.633462
2.188469
2.167751
2.105397
2.168358
1.535278
1.975463
2.069524
2.226185
2.437738
2.080219
1.721949
2.079558
41.292778
41.416944
41.330278
41.243889
41.390556
41.375000
41.523611
41.505000
41.587500
41.650833
41.760000
41.531094
41.592518
41.381968
41.418432
41.215534
41.432921
41.374910
41.288317
41.299278
41.341706
41.278610
41.517731
41.619917
41.632863
41.681290
41.747610
41.366193
41.544401
41.595390
41.271511
41.485181
41.647064
41.452149
41.433861
41.201869
41.389433
41.383899
41.379197
41.612653
41.479475
41.478924
41.565680
41.567346
41.773622
41.340456
41.288007
41.483110
4
632
177
58
6
5
146
56
74
40
936
316
343
252
411
59
415
257
573
3
545
161
81
460
421
528
1030
240
126
916
185
325
2
42
164
17
7
33
79
176
589
147
258
123
1668
8
148
158
1802.41
25,990.09
13,508.15
925.42
185.5
357.9
14,686.96
1586.01
1406.52
2814.06
22,575.42
31,647.54
31,910.67
13,153.66
6527.97
3946.43
25,729.52
19,374.48
3446.25
3275.54
18,210.02
4823.22
2228.08
8362.11
34,368.7
31,792.68
26,303.64
16,069.11
7461.61
37,477.48
11,123.03
29,463.36
198.76
620.04
21,985.71
990.45
914.09
1324.86
5269.22
18,811
32,688.25
20,531.47
19,910.4
12,099.08
23,695.86
5401.52
7951.78
14,117.55
− 1.00
241.39
243.43
206.57
225.00
− 1.00
− 1.00
150.95
71.57
158.20
182.86
150.52
90.00
160.35
230.31
26.57
161.57
90.00
237.53
− 1.00
153.43
199.80
− 1.00
209.74
315.00
155.56
221.82
78.69
270.00
0.00
180.00
101.31
45.00
135.00
65.56
203.20
135.00
0.00
191.31
45.00
165.96
71.57
135.00
180.00
233.13
− 1.00
21.80
258.69
0.00
20.88
3.73
7.45
1.18
0.00
0.00
8.58
5.27
8.98
33.37
22.02
11.67
24.78
50.89
3.73
7.91
3.33
10.87
0.00
3.73
22.14
0.00
13.44
9.43
10.07
21.25
4.25
11.67
75.00
8.33
4.25
1.18
2.36
20.14
6.35
1.18
1.67
4.25
3.54
6.87
15.81
3.54
6.67
8.33
0.00
8.98
12.75
NDVI and NDBI are strongly correlated (− 0.79) as expected. There is also some correlation between these indices and
the geographical variables latitude, longitude, altitude and
slope, with values for NDVI between 0.26 and 0.52 and for
NDBI between − 0.48 and − 0.36. It is important to mention
that the correlations between the NDVI and NDBI indices
with temperatures are low, with absolute values around 0.20.
Latitude shows its highest correlation with longitude (0.62)
and also with altitude (0.55), continentality (0.50), NDVI
(0.48) and NDBI (− 0.48). Altitude has the highest correlation
with continentality (0.60) and with latitude and NDVI index
(0.52). The orientation has low correlations with all the other
variables, although the highest ones correspond to those of the
NDVI and NDBI indices. Finally, the slope, with low correlations in general, presents the highest ones with NDVI,
NDBI, continentality and altitude.
Figure 5 shows some examples of the possible linear relationship between Tmin, Tmean or Tmax and some of the independent variables. The variables with the clearest linear relationship are, as expected, LSTd and LSTn according to the
Air temperature in Barcelona metropolitan region from MODIS satellite and GIS data
a
b
12
600
11
10
9
Number of stations
Number of areas 1kmx1km
500
400
300
200
8
7
6
5
4
3
100
2
1
0
0
0
200
400
600
800
1000
Altitude (m)
1200
1400
1600
1800
0
400
600
800
1000
Altitude (m)
1200
1400
1600
1800
d
0.4
0.4
0.3
0.3
Relative frequency
Relative frequency
c
200
0.2
0.1
0.2
0.1
0
0
0
0.1
0.2
0.3
0.4
0.5
NDVI
0.6
0.7
0.8
0.9
1
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
NDBI
0.1 0.2 0.3 0.4 0.5
Fig. 2 Histograms of altitude for all the pixels (a) and meteorological stations (b). Histograms of NDVI (c) and NDBI (d) only for meteorological
stations
high correlation value obtained between these variables and
the temperatures.
The first four RPC selected with the eigenvalue exceeding
1.0 criterion have a similar percentage of explained variance
(from 23.4 to 14.6%). Whereas they explain 77.2% of data
variance, the remaining eight RPC are associated with the
22.8% of data variance. Consequently, the revision of the results offered by the PCA is centred on these four first RPCs.
Tables 5b and 6b show the RPC factor loadings and the explained variance by the components, for the set of thermometric stations. The first component, RPC1, is strongly related to
LSTd and LSTn and cd*, explaining 23.4% of data variance.
The second component, RPC2, is mainly correlated with
continentality and altitude, and also related to slope, latitude
and NDVI. This component explains 22.6% of data variance.
RPC3 is highly correlated with longitude and latitude, and
slightly negative with NDBI. The third component explains
16.6% of data variance. Finally, RPC4 is notably correlated
with the sine of the orientation, moderately with the cosine of
the orientation and with NDVI and NDBI. This last component explains the variance of 14.6%. It is worth mentioning
that NDVI and NDBI have middle weights on the second,
third and fourth components, this fact suggesting that these
two variables will probably have a lesser role in the multiple
regression equations than expected. Given that PCA is applied
to 12 variables for the 48 thermometric stations, this relatively
low number of samples in comparison with the high number
of 1 km2 pixels could mask the relevance of some variables on
the spatial distribution of Tmin, Tmean and Tmax. In order to
detect these possible differences, RPCA has been also applied
C. Serra et al.
Table 3 Mean, minimum and maximum of recorded diurnal (LSTd)
and nocturnal (LSTn) temperatures, normalised difference vegetation index (NDVI) and normalised difference built-up index (NDBI), latitude
Pixels
Mean
LSTd (°C)
LSTn (°C)
NDBI
(Lat), longitude (Lon), distance to shoreline (Con), altitude (Alt), orientation (Ori) and slope (Slp) for all 1 × 1 km pixels and for the 48 stations
NDVI
Lat (°)
Lon (°)
Con (m)
Alt (m)
Ori (°)
Slope (%)
23.00
11.09
− 0.09
0.52
41.52
2.09
15.565.01
294.53
165.86
23.40
− 13.93
48.13
− 8.39
30.65
− 0.57
1.00
− 0.20
0.98
41.19
41.81
1.47
2.78
1.92
41.103.86
0.00
1646.00
0.00
359.26
0.00
163.91
Mean
Min
23.54
− 3.35
11.47
− 5.67
− 0.04
− 0.75
0.41
0.10
41.46
41.20
2.01
1.47
13.313.41
185.50
279.17
2.00
148.30
0.00
10.66
0.00
Max
45.31
27.19
0.44
0.85
41.77
2.76
37.477.50
1668.00
360.00
75.00
Min
Max
Station
to pixels with 1 km2 resolution. Tables 5b and 6b summarise
the RPC factor loadings and the explained variance by the
components, for the 4042 pixels of 1 km2. By comparing with
results of Tables 5a and 6a, the first RPC is quite similar for
both cases. The second RPC for Table 5a is equivalent to the
third RPC for Table 5b, almost disappearing the contribution
of the slope, NDVI and latitude. The third component
(Table 5a), linked to latitude, longitude and NDBI, corresponds to the fourth RPC (Table 5b). The fourth RPC
(Table 5a), with the contribution of NDVI, NDBI and orientation, is substituted by the fifth RPC (Table 5b), basically
sinus of the orientation. Finally, the 2nd RPC (Table 5b) is
constituted by NDBI, NDVI and slope. Conversely to
Table 5a, where NDVI and NDBI are linked with moderate
weights to more than one component, for Table 5b, these
parameters are clearly related only to the second RPC. As a
summary, the degrees of independence of the multiple regression variables are quite similar considering data from the set of
thermometric stations or from a denser network of 1 km2
pixels. Only some discrepancies are detected comparing factor
loadings corresponding to NDVI and NDBI for both spatial
resolutions.
Fig. 3 Evolution of Tmean with
the calendar day, cd (a) and the
transformed calendar day, cd* (b)
4.2 Multiple regression
4.2.1 Annual case
The first multiple regression is applied to the annual case,
including all days along the year 2015 accomplishing two
conditions: first, only not cloudy days can be selected, given
that LSTn, LSTd, NDVI and NDBI cannot be accurately computed for cloudy days; second, days with missing Tmin, Tmean
or Tmax are not chosen for the multiple regression procedure.
The set of days accomplishing both conditions are designed as
complete data days and the same dataset with the same constraints are used at seasonal and monthly scale. Table 7 gives
the different models obtained in every stepwise regression,
being added one more variable until all the significant variables are used. This table also gives the R2 coefficients and
RMSE. The goodness of fit improves step by step, but with
minor differences. For Tmin, Tmean and Tmax in the first step
with a single variable, values of R2 from 0.860 to 0.935 and
RMSE from 1.8 to 2.7 °C are obtained. When all significant
variables are involved, R2 coefficients of 0.920, 0.955 and
0.918 and RMSE of 1.9 °C, 1.5 °C and 2.0 °C are reached.
Air temperature in Barcelona metropolitan region from MODIS satellite and GIS data
Fig. 4 Dependence of Tmax on
orientation, Ori (a) and sinus
compound, ORIsin (b)
Table 8 gives the standardised (beta weight) and nonstandardised multiple regression coefficients for the last
models of every dependent variable. In the case of Tmin, the
variable with the highest beta weight is LSTn, while LSTd
does not appear in the multiple regression equation because
it is not significant. Latitude, longitude and calendar day also
have prominent standardised coefficients. For Tmean, the most
important variables are LSTn and LSTd, with the rest of the
variables having small or non-significant coefficients. Finally,
in the case of Tmax, the variables LSTd and LSTn have the
highest beta weights and are also quite similar. Latitude, longitude and altitude also play a significant role in Tmax. It
should be noted that NDVI and NDBI indices have small or
non-significant coefficients.
Orientation and slope are the variables that present the lowest beta weight coefficients for the three temperatures, possibly because a much denser network of stations would be necessary to represent all the variety of slopes and orientations.
Figure 6 shows the bar histogram of the beta coefficients of
the last model, including all the significant variables. It is
outstanding the positive values for LSTn and, not so relevant,
the positive values of LSTd. Among the negative values, the
beta weight corresponding to latitude for Tmin is the most
relevant.
The relationships between the temperatures obtained from
the multiple regression equations and the observed Tmin, Tmean
and Tmax are plotted in Fig. 7. While R2 for Tmean is 0.96, for
Tmin and Tmax is 0.92. The RMSE (MAE) ranges from 1.5
Table 4 Pearson correlation coefficients for empiric temperature data, satellite data, geographic and topographic variables and transformed calendar
day. The not significant coefficients (α = 0.05) are codified as ns
Tmax
Tmean
Tmin
LSTd
LSTn
NDBI
NDVI
Lat
Lon
Con
Alt
orisin
oricos
Slp
cd*
Tmax
Tmean
Tmin
LSTd
LSTn
1000
0.961
0.881
0.928
0.913
0.961
1000
0.968
0.930
0.967
0.881
0.968
1000
0.864
0.953
0.928
0.930
0.864
1000
0.907
0.913
0.967
0.953
0.907
1000
0.214
0.194
0.163
0.247
0.139
− 0.210
− 0.221
− 0.205
− 0.262
− 0.181
− 0.127
− 0.139
− 0.146
− 0.143
− 0.102
− 0.064
ns
0.070
− 0.043
0.087
− 0.071
− 0.162
− 0.227
− 0.113
− 0.203
− 0.229
− 0.200
− 0.157
− 0.204
− 0.166
0.100
0.042
− 0.018
0.066
ns
0.036
0.036
0.036
0.060
0.039
− 0.112
− 0.079
− 0.035
− 0.145
− 0.060
0.868
0.897
0.874
0.855
0.902
NDBI
NDVI
lat
lon
con
alt
orisin
oricos
slp
cd*
0.214
− 0.210
− 0.127
− 0.064
− 0.071
− 0.229
0.100
0.036
− 0.112
0.868
0.194
− 0.221
− 0.139
ns
− 0.162
− 0.200
0.042
0.036
− 0.079
0.897
0.163
− 0.205
− 0.146
0.070
− 0.227
− 0.157
− 0.018
0.036
− 0.035
0.874
0.247
− 0.262
− 0.143
− 0.043
− 0.113
− 0.204
0.066
0.060
− 0.145
0.855
0.139
− 0.181
− 0.102
0.087
− 0.203
− 0.166
ns
ns
− 0.060
0.902
1000
− 0.792
− 0.482
− 0.463
− 0.066
− 0.379
0.269
0.257
− 0.357
0.136
− 0.792
1000
0.481
0.255
0.281
0.524
− 0.300
− 0.291
0.445
− 0.103
− 0.482
0.481
1000
0.624
0.502
0.551
0.037
− 0.028
0.242
ns
− 0.463
0.255
0.624
1000
− 0.331
0.034
− 0.110
ns
− 0.011
ns
− 0.066
0.281
0.502
− 0.331
1000
0.599
0.182
0.037
0.369
ns
− 0.379
0.524
0.551
0.034
0.599
1000
− 0.281
− 0.177
0.435
ns
0.269
− 0.300
0.037
− 0.110
0.182
− 0.281
1000
0.210
− 0.187
ns
0.257
− 0.291
− 0.028
ns
0.037
− 0.177
0.210
1000
ns
ns
− 0.357
0.445
0.242
− 0.011
0.369
0.435
− 0.187
ns
1000
ns
0.136
− 0.103
ns
ns
ns
ns
ns
ns
ns
1000
C. Serra et al.
Fig. 5 Dependence of Tmax and
Tmin on some of the variables of
the multiple regression process
Air temperature in Barcelona metropolitan region from MODIS satellite and GIS data
Table 5 Rotated principal
components
(a) RPC (stations)
1
(b) RPC (pixels)
2
3
4
1
2
3
4
5
LSTdia
0.962
− 0.103
− 0.070
0.088
0.957
− 0.194
− 0.036
− 0.036
0.001
LSTnit
NDBI
NDVI
0.964
0.137
− 0.136
− 0.131
− 0.343
0.552
0.031
− 0.558
0.388
− 0.022
0.546
− 0.544
0.969
0.156
− 0.153
− 0.025
− 0.851
0.878
− 0.102
− 0.033
0.160
0.014
− 0.306
0.245
0.000
0.055
− 0.046
Lat
− 0.036
0.531
0.784
0.127
0.018
0.232
− 0.300
0.899
− 0.022
Lon
Con
0.032
− 0.067
− 0.228
0.897
0.933
− 0.083
− 0.098
0.283
− 0.020
− 0.047
0.248
0.045
0.439
0.946
0.819
− 0.016
0.002
0.025
Alt
Slp
− 0.067
− 0.030
− 0.012
0.009
0.817
0.664
− 0.099
0.012
0.152
0.000
0.073
− 0.065
− 0.224
− 0.255
0.777
0.570
− 0.035
0.015
0.010
0.022
0.457
0.789
0.073
0.224
0.769
0.170
− 0.069
− 0.167
0.061
− 0.058
− 0.096
− 0.291
− 0.016
0.035
0.932
− 0.378
0.978
0.046
− 0.019
0.009
0.977
− 0.028
0.043
− 0.002
− 0.004
orisin
oricos
cd*
(a) 48 thermometric stations
(b) 4042 pixels of 1 km × 1 km
(1.2) °C for Tmean to 2.0 (1.6) °C for Tmax. The histogram for
Tmean residuals is also shown in this figure. Fifty-one per cent
of differences between estimated and observed temperatures
are lower or equal to 1.0 °C.
4.2.2 Seasonal and monthly cases
Table 9 shows the R2, RMSE and the number of samples, N,
with complete data for seasonal multiple regressions and for
the different temperatures. The highest correlations correspond to Tmean for spring and autumn, possibly due to the
moderate range of the temperatures in these seasons. The lowest R2 corresponds to the winter Tmin. The RMSE values do
not exceed 2.0 °C, which corresponds to Tmax in summer.
The standardised beta coefficients for each variable are
given in Table 10, with only significant coefficients. The italic
entries correspond to coefficients greater than 0.10, seeing at a
glance the most important variables in the multiple regression
equations. Tmean is the variable that depends on the minimum
number of variables in any season of the year, especially in
spring and autumn. For example, in autumn, only the LSTn
and LSTd temperatures have notable beta coefficients, and in
spring, the cd* is also important. The NDVI and NDBI indices
Table 6 Total variance and
percentage of variance and
cumulated variance for every
RPC
do not have high coefficients in any of the seasons. Only
NDVI has values slightly higher than 0.10 in winter and summer for Tmax, while NDBI has a negative coefficient in spring
for Tmax. The geographical variables that more contribute to
the multiple regression are latitude, longitude, continentality
and altitude, especially for Tmax and Tmin. Slope and orientation have small or non-significant beta weights.
Table 11 shows R2, RMSE and N for every monthly multiple regression and for each temperature. For monthly cases,
R2 is lower than for seasonal or annual cases, ranging from
0.503 for July (T max ) to 0.867 for November (T mean ).
However, RMSE have lower values than seasonal or annual
cases, especially for Tmean, which ranges from 1.2 to 1.5 °C.
The highest values correspond to April (Tmin) and July (Tmax),
both with 2.1 °C. Figure 8 shows the RMSE for every month
and Fig. 9 the estimated versus observed Tmean for November.
Table 12 summarises the significant variables on the multiple
regression process for every month and the different temperatures. A significant difference in comparison with annual and
seasonal scale is the relevance of LST. Whereas LST is the
most relevant at annual and seasonal scales, some differences
are detected at monthly scale depending on the specific month
and Tmin, Tmean and Tmax. The first multiple regression
RPC (a)
Total
Variance (%)
Cumulated (%)
RPC (b)
Total
Variance (%)
Cumulated (%)
1
2
2811
2712
23,427
22,600
23,427
46,027
1
2
2862
2539
23,849
21,158
23,849
45,006
3
4
1992
1753
16,600
14,606
62,627
77,232
3
4
5
1872
1736
1019
15,599
14,470
8492
60,606
75,076
83,568
(a) 48 thermometric stations. (b) 4042 pixels of 1 km × 1 km
C. Serra et al.
Table 7 Models obtained with
the stepwise regression analysis
for Tmin, Tmean and Tmax at annual
scale
Model Tmin
1
2
3
4
5
6
7
8
9
10
11
Model Tmean
1
2
3
4
5
6
7
8
Model Tmax
1
2
3
4
5
6
7
8
9
10
11
12
R2
RMSE
Variables
0.908
0.910
0.912
0.914
0.916
0.917
0.919
0.920
0.920
0.920
0.920
2075
2047
2027
2004
1981
1968
1947
1937
1932
1930
1928
LSTn
LSTn, lat
LSTn, lat, cd
LSTn, lat, cd, lon
LSTn, lat, cd, lon, slp
LSTn, lat, cd, lon, slp, NDVI
LSTn, lat, cd, lon, slp, NDVI, alt
LSTn, lat, cd, lon, slp, NDVI, alt, orisin
LSTn, lat, cd, lon, slp, NDVI, alt, orisin, con
LSTn, lat, cd, lon, slp, NDVI, alt, orisin, con, NDBI
LSTn, lat, cd, lon, slp, NDVI, alt, orisin, con, NDBI, oricos
.935
.950
.952
.953
.954
.955
.955
.955
1780
1551
1525
1509
1497
1484
1480
1474
LSTn
LSTn, LSTd
LSTn, LSTd, lon
LSTn, LSTd, lon, orisin
LSTn, LSTd, lon, orisin, cd
LSTn, LSTd, lon, orisin, cd, alt
LSTn, LSTd, lon, orisin, cd, alt, slp
LSTn, LSTd, lon, orisin, cd, alt, slp, oricos
.861
.890
.896
.900
.903
.913
.916
.917
.918
.918
.918
.918
2659
2365
2299
2248
2222
2096
2069
2053
2046
2044
2042
2041
LSTd
LSTd, LSTn
LSTd, LSTn, lon
LSTd, LSTn, lon, orisin
LSTd, LSTn, lon, orisin, lat
LSTd, LSTn, lon, orisin, lat, alt
LSTd, LSTn, lon, lat, alt, NDVI
LSTd, LSTn, lon, lat, alt, NDVI, cd
LSTd, LSTn, lon, lat, alt, NDVI, cd, oricos
LSTd, LSTn, lon, lat, alt, NDVI, cd, oricos, orisin
LSTd, LSTn, lon, lat, alt, NDVI, cd, oricos, orisin,con
LSTd, LSTn, lon, lat, alt, NDVI, cd, oricos, orisin,con, slp
Table 8 Standardised and not standardised multiple linear regression
coefficients for the annual case. Discarded variables for the multiple
regression are codified by ns
Constant
LSTd
LSTn
NDBI
NDVI
lat
lon
con
alt
orisin
oricos
slp
cd
Standardised coefficients
Coefficients
Tmin
Tmax
Tmin
Tmean
Tmax
0.414
0.473
ns
0.057
0.123
− 0.149
0.062
− 0.189
0.015
− 0.028
− 0.014
0.091
532.394
ns
0.786
1.818
− 1.481
− 13.089
5.015
5.723E−5
0.002
0.368
− 0.175
0.023
1.398
5.023
0.172
0.660
ns
ns
ns
− 0.703
ns
− 0.001
0.326
− 0.221
0.011
0.914
− 228.921
0.298
0.484
ns
2.812
5.886
− 3.341
3.839E−5
− 0.004
0.178
− 0.315
− 0.007
0.921
ns
0.801
0.027
− 0.031
− 0.286
0.234
0.096
0.083
0.033
− 0.016
0.047
0.144
Tmean
0.245
0.660
ns
ns
ns
− 0.032
ns
− 0.043
0.029
− 0.020
0.022
0.092
variable for Tmin is the latitude for 8 months, the longitude
(1 month) and LSTn only for 3 months. Conversely, for
Tmean, LSTn is the most relevant for 11 months. Only for
August is detected a slightly higher relevance of LSTd in comparison with LSTn. Finally, for Tmax, the first multiple regression variable is the altitude for 5 months, LSTd (5 months) and
LSTn (2 months).
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
Tmin
Tmean
Tmax
Fig. 6 Histogram of the beta coefficients of the last model at an annual
scale for Tmin, Tmean and Tmax
Air temperature in Barcelona metropolitan region from MODIS satellite and GIS data
Fig. 7 Estimated versus observed
Tmin, Tmean and Tmax, and the
histogram for residual Tmean at an
annual scale
4.3 Spatial distribution of Tmin, Tmean and Tmax
Some examples of the spatial distribution of temperatures
on BMR obtained by multiple regression are shown in
Figs. 10, 11, and 12. Figure 10 corresponds to T min ,
Table 9 Square regression coefficient, R2, root mean square error,
RMSE and number of samples, N, at seasonal scale
Season
Variable
R2
RMSE
N
Winter
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
0.696
0.853
0.799
0.857
0.921
0.852
0.765
0.829
0.738
0.808
0.865
0.821
1.95
1.32
1.83
1.96
1.35
1.94
1.73
1.42
1.97
1.83
1.41
1.67
1241
1241
1241
1368
1368
1368
1146
1146
1146
1183
1183
1183
Spring
Summer
Autumn
Tmean and Tmax obtained for November 29. The UHI phenomenon is quite evident for Tmin, being associated with
Barcelona city and a neighbouring area at the south of the
city with the highest temperatures. Yellow, green and blue
areas represent zones of lower temperatures, which correspond to the Littoral and Pre-Littoral chains (yellow and
blue areas respectively) and the Vallès valley (green area).
The combined effect of the vicinity to the Mediterranean
coast and the UHI phenomenon is detected on the Tmean
map, with the highest temperatures along a narrow littoral
fringe. It is also worth mentioning the detection of two
nuclei of high temperatures, spatially coincident with
those observed for Tmin. For Tmax, this effect of the vicinity to the littoral disappears and high temperatures cover a
good part of the metropolitan region. Only at the northern
extreme of BMR (Pre-Littoral chain) small green and blue
areas are detected with lower temperatures.
At seasonal scale, some examples of the spatial distribution of average Tmin for the winter season are shown in
Fig. 11. Figure 12 depicts the monthly average of Tmin for
winter months (January, February and March). In spite of
the spatial distributions, the other three seasons are obtained with a notable degree of accuracy; the winter case
C. Serra et al.
Table 10 Standardised and not standardised multiple linear regression coefficients for the seasonal scale. Discarded variables for the multiple
regression are codified by ns
Winter
Spring
Summer
Autumn
Tmin
Tmean
Tmax
LSTd
0.277
0.457
0.643
− 0.055
0.190
0.349
0.061
0.331
0.534
0.188
0.282
0.476
LSTn
0.641
0.625
0.409
0.712
0.611
0.458
0.497
0.301
0.068
0.709
0.663
0.452
NDBI
NDVI
Lat
ns
− 0.085
− 0.598
ns
ns
ns
0.062
0.121
0.334
ns
− 0.052
− 0.387
− 0.053
ns
ns
− 0.114
ns
0.104
ns
ns
− 0.478
ns
ns
ns
− 0.074
0.120
ns
ns
− 0.077
− 0.623
ns
− 0.057
ns
ns
0.052
0.284
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Lon
0.457
ns
− 0.264
0.320
ns
− 0.221
0.455
ns
ns
0.465
ns
− 0.350
Con
Alt
0.305
0.128
0.115
− 0.119
ns
− 0.412
0.129
0.101
ns
− 0.088
0.167
− 0.206
ns
0.060
ns
− 0.193
0.201
− 0.323
0.256
0.237
ns
ns
ns
− 0.390
Slp
orisin
oricos
cd*
0.077
0.064
− 0.052
0.049
ns
− 0.054
ns
− 0.038
ns
0.063
0.039
ns
ns
0.044
− 0.021
ns
0.065
− 0.048
0.117
0.043
ns
0.061
0.056
− 0.030
ns
0.067
− 0.064
0.085
0.059
ns
0.075
0.036
ns
− 0.036
ns
ns
− 0.131
− 0.138
− 0.181
0.234
0.213
0.176
0.209
0.310
0.297
ns
ns
− 0.040
Month
Variable
R2
RMSE
N
January
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
Tmin
Tmean
Tmax
0.671
0.815
0.726
0.664
0.824
0.774
0.707
0.824
0.788
0.648
0.769
0.692
0.517
0.651
0.604
0.692
0.748
0.605
0.606
0.606
0.503
0.665
0.727
0.666
0.735
0.779
0.746
0.706
0.765
0.797
0.825
0.867
0.822
0.669
0.728
0.721
1.86
1.24
1.72
1.84
1.24
1.72
1.96
1.34
1.92
2.06
1.32
1.68
1.77
1.20
1.76
1.67
1.21
1.90
1.66
1.29
2.05
1.67
1.25
1.60
1.51
1.22
1.40
1.74
1.45
1.40
1.81
1.37
1.70
1.76
1.28
1.22
609
609
609
356
356
356
276
276
276
393
393
393
455
455
455
520
520
520
504
504
504
423
423
423
219
219
219
301
301
301
615
615
615
267
267
267
February
March
April
May
June
July
August
September
October
November
December
for Tmin is introduced here given that the characteristics of
these four maps clearly manifest the UHI phenomenon in
the BMR. The map of average winter Tmin reproduces the
two nuclei of UHI on the downtown of the Barcelona city
and at the south along the coast. If the spatial analysis is
revised at a monthly scale, very similar spatial patterns to
those observed for November 29 (Tmin) are now found for
the cold months of January and February. In the case of
March (a more temperate month), the UHI is not so clear,
but the two nuclei appear again.
3.0
Tmin
Tmean
Tmax
2.5
2.0
RMSE (oC)
Table 11 Square regression coefficient, R2, root mean square error,
RMSE and number of samples, N, at monthly scale
1.5
1.0
0.5
0.0
1
2
3
4
Fig. 8 RMSE for every month
5
6
7
Month
8
9
10
11
12
Air temperature in Barcelona metropolitan region from MODIS satellite and GIS data
20
4.4 Discussion of the results
November
Estimated Tmean (ºC)
16
12
8
4
0
0
4
8
12
Observed Tmean (ºC)
Fig. 9 Estimated versus observed Tmean for November
Table 12 Significant variables in
decreasing order exceeding Beta
equal to 0.20 for the multiple
regression process at monthly
scale of Tmin, Tmean and Tmax
Month
January
February
March
April
May
June
July
August
September
October
November
December
Month
January
February
March
April
May
June
July
August
September
October
November
December
Month
January
February
March
April
May
June
July
August
September
October
November
December
16
20
With respect to the correlations among dependent and independent variables used in the multiple regression, it is noticeable, as expected, the high correlation (0.97) between the three
daily temperatures (minimum, mean and maximum) and the
two LST temperatures and also the calendar day. The correlations are notably small for the rest of independent variables,
sometimes achieving values lower to 0.23. Another relevant
question is that results obtained by PC analysis, taking into
account the thermometric stations or the dense network of
1 km2 pixels, are very similar. Consequently, the relatively
sparse distribution of the 48 thermometric gauges would not
be a shortcoming to obtain a reliable spatial distribution of
temperatures, being then defined a relatively good image of
the thermometric variability on the BMR.
With respect to the multiple linear processes, the square
regression coefficients obtained at annual scale are notably
good, in spite of the RMSE varies within the (1.5–2.0 °C),
results quite similar to those obtained by Cristóbal et al. (2008)
Tmin significant standardised beta coefficients > 0.20
lat(− 0.926), lon (0.754), con(0.524), LSTn(0.486), LSTd (0.358), alt(0.254)
lat(− 0.723), LSTn(0.690), lon(0.456), con(0.425)
LSTn(0.661), LSTd(0.205)
LSTn(0.701), lat(− 0.683), lon(0.531), con(0.626)
lat(− 0.709), lon(0.686), LSTn(0.361), NDBI(0.231)
lat(− 0.564), lon(0.533), LSTn(0.499), NDVI (− 0.242), alt (0.236), cd*(0.231), slp(0.217)
lon(0.628), lat(− 0.582), LSTn(0.467), NDVI(− 0.207)
lat(− 0.600), lon(0.476), LSTn(0.474)
lat(− 0.893), lon(0.835), LSTn(0.439)
LSTn(0.690), lat(− 0.569), lon(0.462)
lat(− 0.770), LSTn(0.600), lon(0.584), con(0.311), alt(0.270)
lat(− 0.598), LSTn(0.531), alt(0.309), NDVI(− 0.238)
Tmean significant standardised beta coefficients > 0.20
LSTn(0.588), LSTd (0.457), con(0.213)
LSTn(0.482), alt(− 0.323),LSTd (0.286)
LSTn(0.650), LSTd(0.393)
LSTn(0.685)
LSTn(0.376),alt(− 0.366), LSTd (0.250), cd*(− 0.202)
LSTn(0.451), LSTd (0.409), NDBI(− 0.219)
LSTn(0.435), alt(− 0.333), cd*(− 0.318), LSTd (0.208)
LSTd(0.358), LSTn (0.282), alt(− 0.273)
LSTn(0.369), alt(− 0.377), LSTd (0.265), NDVI(0.212)
LSTn(0.629), LSTd (0.219)
LSTn(0.645), LSTd (0.223)
LSTn(0.577), LSTd (0.271), slp(0.227)
Tmax significant standardised beta coefficients > 0.20
LSTd(0.530), alt(− 0.532), LSTn (0.398), lat(0.484), lon(− 0.309)
LSTd(0.557), alt(− 0.547), lat (0.357), lon(− 0.322)
LSTd(0.556), LSTn(0.489), con(0.329), alt(− 0.317)
alt(− 0.459), lon(− 0.490), LSTn(0.415), lat(0.360), LSTd(0.260)
alt(− 0.409), LSTd(0.395), con(0.387), cd*(− 0.313)
LSTd(0.510), alt(− 0.422), con (0.330), NDBI(− 0.329)
alt(− 0.403), LSTd(0.399), con(0.390), cd*(− 0.347)
LSTd(0.535), alt(− 0.468), con (0.243)
alt(− 0.604), LSTd(0.456), NDVI(0.364)
LSTn(0.503), LSTd(0.363), lon(− 0.345), alt(− 0.329), lat(0.275)
LSTn(0.434), LSTd(0.430), alt(− 0.410), alt(− 0.329), lon(− 0.359), lat(0.284)
alt(− 0.814), lon(− 0.508), lat(0.481), LStd(0.355)
C. Serra et al.
Fig. 10 Example of the spatial
distribution of Tmin, Tmean and
Tmax derived by multiple
regression for November 29,
2015
Temperature (ºC)
Tmin 29/11/2015
-6 to -5
-5 to -4
-4 to -3
-3 to -2
-2 to -1
-1 to 0
0 to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
6 to 7
7 to 8
8 to 10
Temperature (ºC)
Tmean 29/11/2015
2 to 3
3 to 4
4 to 5
5 to 6
6 to 7
7 to 8
8 to 9
9 to 10
10 to 11
11 to 12
Temperature (ºC)
Tmax 29/11/2015
for the whole Catalonia. For the results at seasonal and monthly scales, even though the square regression coefficients are
lesser than those obtained at an annual scale, the RMSE values
are very similar, being not exceeded 2.1 °C. Consequently, the
images of the spatial distribution of temperatures should be of
similar quality at annual, seasonal and monthly scales.
Nevertheless, the highest RMSE values are detected at a
monthly scale (Tmin for April and Tmax for July).
7 to 8
8 to 9
9 to 10
10 to 11
11 to 12
12 to 13
13 to 14
14 to 15
15 to 16
16 to 17
17 to 18
Another noticeable characteristic is the low weight of
NDVI and NDBI on the multiple linear regression, which
has been also detected in other similar analysis around the
world. In spite of both coefficients could be relevant, as
they represent the type of vegetation and building respectively, the LST obtained from satellite data could itself
include a great percentage of the information concerning
NDVI and NDBI.
Air temperature in Barcelona metropolitan region from MODIS satellite and GIS data
Tmin Winter 2015
Fig. 11 Winter season spatial
distribution of average Tmin
derived by multiple regression
Temperature (ºC)
-6 to -5
-5 to -4
-4 to -3
-3 to -2
-2 to -1
-1 to 0
0 to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
6 to 7
7 to 8
8 to 9
9 to 10
From an applied point of view, given that the obtained thermometric maps are submitted to a maximum RMSE of 2 °C, a
dense network of minimum, mean and maximum temperature
data could be possible to analyse thermometric phenomena
(UHI and hot and cold outbreaks) affecting life quality and
health of BMR population. Additionally, data obtained with
smaller pixels, for instance with LANDSAT satellite, would
permit a notable increase in the spatial resolution of temperatures. Unfortunately, the available data from LANDSAT is
nowadays minor than that found from MODIS satellite, and
the accuracy of the results would be then questionable.
5 Conclusions
Previous to the multiple regression process, the Pearson correlation coefficient and the PCA have permitted to detect links
between empiric temperatures recorded at 48 meteorological
stations and satellite data, geographic and topographic data
and transformed calendar days. The PCA has also permitted
to validate if the set of the thermometric stations are appropriate for a good multiple regression process by comparing RPCs
and factor loadings corresponding to 48 stations dataset and
1 km2 pixel network. In spite of the very different spatial data
density for thermometric stations and pixel coverage, a few
discrepancies are found with respect to the factor loadings of
NDVI and NDBI. In this way, a denser network of thermometric data would improve the role of NDVI and NDBI on the
multiple regression. It is also worth mentioning the substitution of the topographic parameter of orientation (Ori) by
cos(Ori) and sin(Ori), being detected a slight improvement
on the relevance of sin(Ori) when it is used instead of Ori in
the multiple regression process.
A revision of the multiple regression analyses results manifests the strong relevance of LSTn for Tmin and Tmean and
LSTd for Tmax at the annual scale, as obtained by Thanh
et al. (2016). A similar pattern is observed at a seasonal scale.
The relevance at a monthly scale of LSTd on Tmin is not significant for February, April, May, June and September.
Additionally, the relevance of LSTn on Tmax is not significant
for September.
With respect to specific results at the annual scale, first of
all, it is noticeable that the best fit between empiric temperatures and those generated by multiple regression is usually
found for Tmean, being obtained the worst for Tmax in terms
of R2 and RMSE. It is also noticeable that cd* only plays a
relatively important role for Tmin and the set of relevant variables are not the same for Tmin, Tmean and Tmax. At monthly
scale, whereas the best fits are effectively obtained since
January to December for Tmean, the worst fit is obtained for
Tmax (June, July) and Tmin (April). At a seasonal scale, the
results are quite different. Whereas the minimum residual for
Tmean is detected in winter and spring, for Tmin it is found in
summer and for Tmax in autumn.
In short, the reasonably good results of the multiple regression process would permit:
–
–
Describing with detail (pixels of 1 km2) the spatial distribution of temperatures, notably improving the spatial data
density on BMR derived from the thermometric network
and without applying interpolations.
Obtaining detailed maps of UHI phenomenon on urban
areas. It has to be remembered that these details of the
UHI intensity could not be obtained from a few thermometric stations. In particular, two clear focus of high UHI
intensity for T min in winter have been detected.
Additionally, the smooth temperatures along the
Mediterranean coast are verified by observing Tmax and
Tmean maps.
A systematic and detailed spatial description of temperatures with the methodology used in this paper could be a
significant improvement in the analysis of cold and hot outbreaks. It should be underlined that these analyses could be
C. Serra et al.
Fig. 12 Monthly spatial
distribution (winter season) of
average Tmin derived by multiple
regression
Tmin January 2015
Temperature (ºC)
-6 to -5
-5 to -4
-4 to -3
-3 to -2
-2 to -1
-1 to 0
0 to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
6 to 7
7 to 8
8 to 10
Tmin February 2015
Temperature (ºC)
-6 to -5
-5 to -4
-4 to -3
-3 to -2
-2 to -1
-1 to 0
0 to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
6 to 7
7 to 8
8 to 10
Tmin March 2015
Temperature (ºC)
-6 to -5
-5 to -4
-4 to -3
-3 to -2
-2 to -1
-1 to 0
0 to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
6 to 7
7 to 8
8 to 9
9 to 11
very useful to study the effects on the life quality and health of
the Barcelona city and metropolitan area inhabitants.
Conversely to a relatively scarce distribution of thermometric
stations used to analyse these outbreaks, the multiple linear
regression method provides a more detailed (1 km × 1 km)
spatial distribution of air temperatures.
Finally, comparing R2 and RMSE for BMR with those
obtained by Cristóbal et al. (2008) for the whole Catalonia,
it is observed that better results have been obtained for BMR.
Whereas for Tmin and Tmax, the best results are achieved for
BMR (R2 equal to 0.92 in front of 0.54–0.57 and RMSE equal
to 1.5–1.6 °C in front of 2.3–1.8 °C), for Tmean, R2 is again
better for BMR (0.96 in front of 0.66). The RMSE for Tmean
obtained for the whole Catalonia (1.3 °C) is slightly better
than that obtained for BMR (1.5 °C). One reason for these
differences could be that BMR area is ten times smaller than
Catalonia, implying a minor variability of temperatures and
geographical characteristics and permitting a better
Air temperature in Barcelona metropolitan region from MODIS satellite and GIS data
description of the spatial distribution of temperatures. A
higher spatial density of thermometric stations could be another factor favouring the BMR results.
Acknowledgements Temperature data were gently provided by the
Agencia Estatal de Meteorología, AEMET, and Servei Meteorològic de
Catalunya, SMC.
Funding information This research has been supported by the Spanish
Government through the project BIA2015-68623-R (Ministerio de
Economía y Competitividad, MINECO and European Regional
Development Fund (ERDF).
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