Rod íguez-Lado e al.
460
Sci. Ag ic. (Pi acicaba, B az.), .64, n.5, p.460-467, Sep embe /Oc obe 2007
MODELLING AIR TEMPERATURE FOR THE STATE OF
SÃO PAULO, BRAZIL
Luis Rod íguez-Lado1*; Ge d Spa o ek2; Pablo Vidal-To ado2; Du al Dou ado-Ne o3; Felipe
Macías-Vázquez1
1USC/Ins i u o de In es igaciones Tecnológicas - Lab. de Tecnología Ambien al - Campus Su - San iago de
Compos ela - 15782 - Spain.
2USP/ESALQ - Dep o. de Ciência do Solo, C.P. 09 - 13418-900 - Pi acicaba, SP - B asil.
3USP/ESALQ - Dep o. de P odução Vege al.
*Co esponding au ho <[email p o ec ed]>
ABSTRACT: Spa ial modelling o ai empe a u e (maximum, mean and minimum) o he S a e o São
Paulo (B azil) was calcula ed by mul iple eg ession analysis and o dina y k iging. Clima ic da a (mean
alues o i e o mo e yea s) we e ob ained om 256 me eo ological s a ions dis ibu ed uni o mly
o e he S a e. The co ela ion be ween he clima ic dependen a iables, wi h la i ude and al i ude as
independen a iables was signi ican and could explain mos o he spa ial a iabili y. The coe icien s
o de e mina ion (P < 0.05) a ied in he ange o 0.924 and 0.953, showing ha mul iple eg ession
analysis is an accu a e me hod o he modelling o ai empe a u e o he S a e o São Paulo. Finally,
hese eg ession equa ions we e used oge he wi h he k iged maps o he esidual e o s o build 15
digi al maps o ai empe a u e using a 0.5 km2 Digi al Ele a ion Model in a Geog aphic In o ma ion
Sys em.
Key wo ds: DEM, GIS, mul iple eg ession analysis, k iging, clima e modelling
MODELAGEM DA TEMPERATURA DO AR PARA O
ESTADO DE SÃO PAULO, BRASIL
RESUMO: Fo am u ilizadas écnicas de análise de eg essão linea múl ipla e k igagem o diná ia pa a
a modelagem espacial das empe a u as máximas, mínimas, médias do Es ado de São Paulo (B asil). Os
dados climá icos o am ob idos de 256 es ações clima ológicas dis ibuídas na o alidade do Es ado.
O pe íodo mínimo das sé ies climá icas u ilizadas oi de cinco anos. Os esul ados das análises de
eg essão ap esen a am uma boa co elação en e as a iá eis dependen es analisadas ( empe a u as
médias, máximas e mínimas) com a la i ude, e a al i ude como a iá eis independen es. Os coe icien es
de de e minação (P < 0,05) a iam en e 0,924 e 0,953 indicando que a eg essão múl ipla é um mé odo
p eciso de es ima i a da empe a u a do a no Es ado de São Paulo. As equações de eg essão ob idas
o am u ilizadas, em conjun o com mapas dos esíduos in e polados po k igagem, pa a a elabo ação
de 15 mapas de empe a u a do a sob e um modelo de ele ação digi al de 0,5 km2 de esolução espacial
com a ajuda de geop ocessamen o.
Pala as-cha e: DEM, SIG, eg essão linea múl ipla, k igagem, modelagem climá ica
INTRODUCTION
Knowledge o he spa ial dis ibu ion o cli-
ma ic da a is an essen ial ool o he managemen o
na u al esou ces and he p edic ion o clima ic da a
is e y use ul in a wide numbe o scien i ic disci-
plines (e.g.: ag onomy, geog aphy, and ecology).
Mo eo e , he impac o ossil uel bu ning and
de o es a ion on clima ic change aised he
awa eness o he de elopmen o adequa e and eli-
able p edic ion models o ai empe a u e a ound he
wo ld.
Clima ic da a a e usually measu ed in local
me eo ological s a ions. Clima ic maps, co e ing ex-
ensi e a eas depend on he es ima ion o da a a
non moni o ed loca ions based on egis e ed alues
a neighbou ing si es. In e pola ion echniques
a e used o con e he disc e e da a in o con inuous
da a. Se e al in e pola ion me hods a e used
o clima ic maps. Examples o me hods a e adi-
ional hand-in e pola ed isople hs (Bu ough
& McDonnell, 1998), and compu a ional echniques
in ol ing spa ial Thiessen polygon in e pola o s, in-
e se dis ance weigh ing, cubic splining, end su -
ace analysis, hin pla e splines (Hu chinson, 1991;
Lennon & Tu ne , 1995; Sa elie e al., 1998;
Felicísimo-Pé ez e al., 2001), K iging (Dingman e
al., 1988; Bigg, 1991; Philips e al., 1992) o co-
Modeling ai empe a u e 461
Sci. Ag ic. (Pi acicaba, B az.), .64, n.5, p.460-467, Sep embe /Oc obe 2007
K iging (Goo ae s, 2000) a e equen ly used. Mul-
iple eg ession analysis is ano he me hod widely used
o compu e he dis ibu ion o clima ic a iables om
disc e e da a (Collins & Bols ad, 1996; Goodale e al.,
1998; Ninye ola, 2000; Ninye ola e al., 2000; Lennon
& Tu ne , 1995; Vale iano & Picini, 2000; Sil a e al.,
2006).
The objec i e o his s udy we e i) o calcu-
la e spa ial models o bo h mon hly and annual ai em-
pe a u es (mean, minimum and maximum) o he
S a e o São Paulo (B azil) using mul iple eg ession
analysis and o dina y k iging; ii) o use hese models
o de i e digi al as e maps o ai empe a u e o he
s udy a ea.
CASE STUDY
The S a e o São Paulo is loca ed in he sou h-
e n hemisphe e (19-25º S, 44-53ºW) in B azil, wi h
an a ea o 248,816 km2. The S a e is di ided in o i e
geomo phologic uni s (Figu e 1). The Wes e n Pla-
eau cons i u es he main uni (60% o he a ea).
Sedimen a y deposi s o m his pla eau and i s mo -
phology is domina ed by la o undula ed landscapes
o low hills wi h slopes be ween 0-20% (Cachei o-
Pose e al., 2002), and al i udes anging be ween 250-
650 m a.s.l. The Basal ic Cues as sp ead om SW
o NE in he middle o he S a e o ming a ange o
apps wi h al e na ing laye s o basal ic ocks and
eolian sands ones wi h al i udes be ween 500-900 m
a.s.l. The Pe iphe ical Dep ession, si ua ed in he cen-
al po ion o he S a e, cons i u es a zone opo-
g aphically lowe be ween he Basal ic Cues as and
he A lan ic Region, wi h sedimen s, including shales,
sil s ones, sands ones and occasional basal ic
in usions. The A lan ic Region is he mos ele a ed
a ea o med by a pla eau and wo moun ainous
egions (Se a do Ma and Se a da Man iquei a)
wi h s eep slopes be ween 0-20% in he pla eau and
om 10-40% in he moun ains. I is o med mainly
by igneous and me amo phic ocks, wi h al i udes
anging be ween 650-800 m a.s.l. in he pla eau and
up o 2703 m a.s.l. in he moun ain anges. These
moun ainous chains ac as opog aphic ba ie s o
oceanic on s, he e o e an impo an annual ain all
g adien is ound be ween bo h sides o he anges.
The Coas al Region is a la a ea along he coas al
line na owing on he di ec ion SW-NE, whe e he
anges o he “Se a do Ma ” come close o he sea-
coas .
The p edominan clima ic ype in São Paulo
is he opical mois wi h d y win e (Aw) bu
he mois wi h mild win e clima es wi h d y win e
and ho (Cwa) and humid and ho (C a) acco ding
o Köppen’s classi ica ion a e also equen . Mean
empe a u es a e smoo h, anging om 4.7-23ºC
in win e and up o 29ºC in summe . Mean annual
p ecipi a ion anges om 1,350 o 1,550 mm.
Rainy season occu s du ing Oc obe -Ma ch, coincid-
ing wi h he highe empe a u e alues (aus al sum-
me ). The d y season s a s in Ap il and ends in Oc-
obe .
A o al o 256 s a ions eco ding ai empe a-
u e we e u ilized in hese analyses (CIIAGRO da a-
Figu e 1 - Hipsome y o he S a e o São Paulo and loca ion o he 256 me eo ological s a ions used o empe a u e modelling (black
poin s).
Rod íguez-Lado e al.
462
Sci. Ag ic. (Pi acicaba, B az.), .64, n.5, p.460-467, Sep embe /Oc obe 2007
base). The empe a u e da a a ailable om he
CIIAGRO da abase had eco ds anging om 5 o 15
yea s. Acco ding o he Wo ld Me eo ological O ga-
niza ion (WMO, 1967), o ensu e he op imal clima e
modelling, da a se ies should ex end o a leas 30
yea s long. Such long ime se ies a e o en una ail-
able. Howe e good esul s ha e also been ob ained
using sho e ime se ies (Wo ling e al., 2000;
Ma quinez e al., 2003).
Mul iple eg ession analysis was used, com-
bined wi h o dina y k iging, o ai empe a u e mod-
elling. The mean alues o he clima ic a iables we e
conside ed as dependen a iables in he mul iple e-
g ession analysis. As possible independen a iables
nominal al i ude (ALT), la i ude (LAT) and longi ude
(LON) o he me eo ological s a ions we e consid-
e ed.
The adjus ed eg ession model inally gi es an
exp ession in he o m:
y = E0 + b1(X1) + b2(X2) +…+ bn(Xn) + ε (1)
whe e y is he es ima ed alue o he dependen a i-
able, E0 is he in e cep , bn a e mul iple eg ession co-
e icien s, Xn he signi ican independen a iables and
ε is he esidual e o o he es ima ion.
Fo each model, he mul iple coe icien o de-
e mina ion (R2) was compu ed, he mul iple eg es-
sion coe icien s building he model equa ion and he
le el o signi icance o each independen a iable a e
also shown. Reg ession analyses we e made using he
s epwise me hod wi h inclusion o a iables. Only in-
dependen a iables wi h a le el o signi icance g ea e
han 95% we e accep ed o build up he model.
These eg ession equa ions we e con e ed
o ai empe a u e maps using map algeb a wi h
a Geog aphic In o ma ion Sys em (A cGIS 8.3),
p ocessing he independen a iables as map
laye s in as e o ma . Al i ude as e laye , in
me e s, was ob ained om a 0.5 km2 Digi al Ele a-
ion Model (DEM) o he S a e (GTOPO30, 1996).
La i ude and longi ude as e laye s, in decimal de-
g ees, we e compu ed using he cen al cell coo -
dina es om he same DEM. A each s a ion he
alue o ε ha exp esses he di e ence be ween he
empi ical and he modelled alues o empe a u e
was also calcula ed. The mul iple eg ession esul s
we e imp o ed by analyzing he a iog am unc ions
o he esidual e o s. The a iog am unc ion
desc ibes he a e age dissimila i y be ween he
esidual e o s in ela ion o hei spa ial dis ance
(Goo ae s, 1997). Sample a iog ams could be i -
ed o sphe ical models (Figu e 2) ha inally we e
used o ob ain maps o he esidual e o s by o di-
na y k iging. These maps we e added o he eg es-
sion maps o diminish he e o s o he eg ession
model.
RESULTS AND DISCUSSION
Fo each mul iple eg ession analysis (Table
1), he signi icance alue o longi ude was highe
han 0.05, indica ing ha his a iable does no con-
ibu e o he p edic ion o he alues o ai empe a-
u e in he s udied a ea. The accu acy o he eg es-
sion models was g ea e han 90% in all cases, as
shown in he alues o he coe icien s o de e mi-
s neici eocnoisse ge elpi luMRde sujda
2
naemTylh noM y aunaJ 74600.0-=TLA 761.0=TAL 809.13= pec e nI 359.0
y au beF56600.0-=TLA441.0=TAL936.13= pec e nI359.0
hc aM 06600.0-=TLA 442.0=TAL 113.33= pec e nI 449.0
li pA13600.0-=TLA554.0=TAL177.53= pec e nI639.0
yaM 31600.0-=TLA 355.0=TAL 835.53= pec e nI 149.0
enuJ51600.0-=TLA876.0=TAL250.73= pec e nI429.0
yluJ 30600.0-=TLA 207.0=TAL 283.73= pec e nI 729.0
suguA94600.0-=TLA778.0=TAL173.34= pec e nI039.0
ebme peS 90600.0-=TLA 189.0=TAL 479.64= pec e nI 929.0
ebo cO81600.0-=TLA828.0=TAL786.44= pec e nI049.0
ebme oN 84600.0-=TLA 535.0=TAL 959.83= pec e nI 249.0
ebmeceD26600.0-=TLA853.0=TAL516.53= pec e nI149.0
nimTlaunnA 31600.0-=TLA 517.0=TAL 717.73= pec e nI 729.0
xamTlaunnA56600.0-=TLA441.0=TAL936.13= pec e nI359.0
naemTlaunnA 53600.0-=TLA 445.0=TAL 486.73= pec e nI 649.0
Table 1 - Resul s o he mul iple eg ession analyses o ai empe a u e.
Modeling ai empe a u e 463
Sci. Ag ic. (Pi acicaba, B az.), .64, n.5, p.460-467, Sep embe /Oc obe 2007
Figu e 2 - Empi ical ( ed do ed line) and adjus ed (blue line) a iog am unc ions o he esiduals om he eg ession models. The
numbe o pai s a each lag dis ance, and he s anda d de ia ion (black do ed line) a e also indica ed.
Dis ance uni s co espond o km /10
Rod íguez-Lado e al.
464
Sci. Ag ic. (Pi acicaba, B az.), .64, n.5, p.460-467, Sep embe /Oc obe 2007
na ion. All he mon hs ha e simila p edic o s. The
lowe i s we e ob ained o mean empe a u es in
June, July and Augus (aus al win e ), wi h R2 al-
ues anging om 0.924 o 0.930. This is expec ed
because mean alues in mon hs wi h ex eme em-
pe a u es a e mo e di icul o p edic han in hose
wi h mean o modal alues. Conside ing annual da a,
he lowe i was ob ained o he minimum ai em-
pe a u e.
Reg ession coe icien s o al i ude always
ha e nega i e alues. As expec ed, ai empe a u e
is nega i ely co ela ed o inc eases o al i ude.
Fo la i ude, eg ession coe icien s a e posi i e.
In his case inc eases in la i ude mean dec eases in
inal empe a u e alues since la i udes in he
S a e o São Paulo we e ea ed as nega i e alues
(Sou he n hemisphe e). The equa ions cons uc ed
wi h each eg ession coe icien and in e cep ion
alues we e used o de i e 15 equa ions p edic ing
he spa ial dis ibu ion o ai empe a u e by means
o map algeb a using a Geog aphic In o ma ion Sys-
em.
The spa ial s uc u e o he esidual alues by
o dina y k iging was also analyzed. The shapes o he
empi ical semi a iog ams show ha he esiduals
p esen a pa e n o spa ial dependency (Figu e 2).
Sphe ical models o desc ibe he empi ical a iog am
unc ions o he esiduals showed he bes goodness
o i acco ding o he minimum weigh ed leas squa es
c i e ia.
Nugge s ange be ween 0.05-0.1 and
a iog ams s abilize a app oxima ely 100 km. These
esidual alues accoun o he local a ia ions o em-
pe a u e no adjus ed by he eg ession models. The
eg ession model accu acy can be inc eased by
adding he maps o he k iged esiduals (Figu e 3) o
hose ob ained wi h he eg ession equa ions. We
obse e ha esiduals ake he alues o ± 0.5ºC
in he main pa o he S a e, so ha a good i be-
ween he model and he empi ical da a was ob ained.
The esul s o annual empe a u es a e shown in Fig-
u es 4 o 6. Mon hly empe a u e esul s a e in Fig-
u e 7.
Table 2 shows he mean minimum, mean
maximum and mean empe a u e esul s o
as e laye s in mon hly and annual basis. The
ex eme mon hs a e June (5.41ºC) and Feb ua y
(28.39ºC). Despi e minimum empe a u es in
May, June and July a e lowe han 5ºC i has o be
no ed ha mean empe a u es a e much highe ,
a ound 18ºC, conside ing he whole s udy
a ea. These low alues o empe a u e a e loca ed
in high al i ude a eas in he NE o he coas al moun-
ains.
Finally a linea eg ession analysis o isola e he
in luence o al i ude and la i ude on he in e pola ed al-
ues o empe a u e was made. In Figu e 8 he sca e plo
o he annual mean empe a u es o e al i ude, and he
leas squa e linea eg ession model a e ep esen ed.
The e is a good co ela ion be ween al i ude and em-
pe a u e (R2 = 0.762). A end o a decline in empe a-
u e wi h inc eases in al i ude is obse ed. In his
sca e plo h ee g oups o poin s a e dis inguished.
Poin s belonging o a ea A co espond o
da a o me eo ological s a ions om he Coas al Re-
gion. The oceanic in luence in his a ea causes annual
mean empe a u es o be lowe han he modelled al-
ues explained by he simple linea co ela ion model o
al i ude o e empe a u e. Fo simila al i ude alues,
he e is a g adien o empe a u e om poin s in zone
C o hose in zone B ha can be explained by hei
la i ude posi ion. The cu poin be ween bo h zones is
loca ed a 22.11ºS. Real empe a u es in his a ea end
o be highe han modelled empe a u es by his simple
eg ession model. The con a y occu s in zone C. This
shows ha , in addi ion o he e ec o al i ude, he e
is a ce ain con ibu ion o la i ude o he spa ial dis-
ibu ion o empe a u e.
Plo ing annual mean empe a u es in ela ion
o la i ude (Figu e 9) a g oup o poin s (zone A) co -
esponding again o he same s a ions o he Coas al
P o ince can be obse ed. On he o he hand, he co-
e icien o de e mina ion is low, showing a poo
weigh o la i udes in ela ion o al i udes when explain-
ing he dis ibu ion o empe a u es. Fo each la i ude
Table 2 - Desc ip i e s a is ics o he mon hly and annual
ai empe a u e laye s (451,534 as e cells).
)Cº(naemT
naeM.D.SniMxaM
y aunaJ 15.42 5.1 48.01 01.82
y au beF66.425.146.0193.82
hc aM 41.42 5.1 61.01 96.72
li pA60.226.127.871.52
yaM 57.81 6.1 37.5 85.12
enuJ94.817.114.564.12
yluJ 43.81 7.1 35.5 14.12
suguA81.029.143.677.32
ebme peS 96.12 9.1 66.8 64.5
ebo cO57.228.145.971.62
ebme oN 63.32 7.1 26.9 94.62
ebmeceD98.326.198.903.72
niMlaunnA 33.81 7.1 13.5 34.12
xaMlaunnA66.425.146.0193.82
naeMlaunnA 89.12 6.1 15.8 79.42
Modeling ai empe a u e 465
Sci. Ag ic. (Pi acicaba, B az.), .64, n.5, p.460-467, Sep embe /Oc obe 2007
he e is a empe a u e g adien due o he e ec o al-
i ude, he cu poin being be ween zones B and C lo-
ca ed a 570 m.
The e o e, he mul iple eg ession models p o-
posed in his s udy imp o es he accu acy o simple
linea eg ession models o empe a u e alues o e al-
i udes.
Al i udes and la i udes o he map as e
laye s o his s udy we e compu ed using he
GTOPO30 DEM, and he low esolu ion o his DEM
can be a cause o ince i ude o he empe a u e
maps. The use o a mo e accu a e DEM o he S a e
would lead o a mo e ealis ic dis ibu ion o ai em-
pe a u es.
Figu e 3 - Maps o he k iged esiduals o empe a u e in he S a e o São Paulo, B azil.
Figu e 4 - Annual mean minimum empe a u e in he S a e o São
Paulo, B azil.
Figu e 5 - Annual mean maximum empe a u e in he S a e o São
Paulo, B azil.
Rod íguez-Lado e al.
466
Sci. Ag ic. (Pi acicaba, B az.), .64, n.5, p.460-467, Sep embe /Oc obe 2007
CONCLUSIONS
Mul iple eg ession analysis is a sui able me hod
o model ai empe a u e in he S a e o São Paulo. The
models c ea ed can p edic ai empe a u e wi h an ac-
cu acy g ea e han 90% in all cases. The spa ial dis-
ibu ion o empe a u e can be explained using only
la i ude and al i ude as independen a iables. Longi-
ude was, in all analyses, a non-signi ican a iable able
o p edic ai empe a u es. The k iging o he esidu-
als allows o ake in o accoun local anomalies in o he
eg ession models and hus o imp o e he inal esul s.
Figu e 6 - Annual mean empe a u e in he S a e o São Paulo,
B azil.
Figu e 7 - Mon hly mean empe a u e in he S a e o São Paulo, B azil.
Modeling ai empe a u e 467
Sci. Ag ic. (Pi acicaba, B az.), .64, n.5, p.460-467, Sep embe /Oc obe 2007
Linking hese eg ession models o a mo e accu a e
DEM would lead o a be e spa ial pa e n o mon hly
and annual ai empe a u es in he S a e o São Paulo.
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Recei ed May 30, 2006
Accep ed June 22, 2007
Figu e 8 - Sca e plo o annual mean empe a u e o e al i ude.
Figu e 9 - Sca e plo o annual mean empe a u es as a unc ion
o la i ude.
