A.P. de Leon F. de Ca alho e al. (Eds.): Dis ib. Compu ing & A i . In ell., AISC 79, pp. 157–164.
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A Suppo Vec o Reg ession App oach o
P edic Ca bon Dioxide Exchange
Juan F. De Paz, Belén Pé ez, Angélica González, Emilio Co chado,
and Juan M. Co chado1
Abs ac . In his s udy, a new moni o ing sys em o ca bon dioxide exchange is
p esen ed. The mission o he in elligen en i onmen p esen ed in his wo k, is o
globally moni o he in e ac ion be ween he ocean’s su ace and he a mosphe e,
acili a ing he wo k o oceanog aphe s. This pape p oposes a hyb id in elligen
sys em in eg a es case-based easoning (CBR) and suppo ec o eg ession
(SVR) cha ac e ised o hei e iciency o da a p ocessing and knowledge ex ac-
ion. Resul s ha e demons a ed ha he sys em accu a ely p edic s he e olu ion
o he ca bon dioxide exchange.
Keywo ds: Ca bon dioxide, Suppo Vec o Reg ession, Case-based Reasoning.
1 In oduc ion
One o he ac o s o g ea es conce n in climac ic beha iou is he quan i y o
ca bon dioxide (CO2) p esen in he a mosphe e. Ca bon dioxide is one o he
g eenhouse gases ha helps o make he ea h’s empe a u e habi able, so long i
main ains ce ain le els [6]. T adi ionally, i has been conside ed ha he main
sys em egula ing ca bon dioxide in he a mosphe e is he pho osyn hesis and
espi a ion o plan s. Howe e , hanks o ele-de ec ion echniques i has been
shown ha he ocean plays a highly impo an ole in he egula ion o ca bon
quan i ies, he ull signi icance o which s ill needs o be de e mined [7]. Cu en
echnology allows us o ob ain da a and make calcula ions ha we e unimaginable
some ime ago. This da a gi es us an insigh in o ca bon dioxide’s o iginal sou ce,
i ’s dec ease and he causes o his dec ease [1], which allow p edic ions on i ’s
beha iou in he u u e.
This pape p oposes a hyb id in elligen sys em ha in eg a es case-based ea-
soning (CBR) and suppo ec o eg ession (SVR) cha ac e ised o hei e i-
ciency o da a p ocessing and knowledge ex ac ion. CBR is a ype o easoning
Juan F. De Paz, Belén Pé ez, Angélica González, Emilio Co chado, and Juan M. Co chado
Depa amen o In o má ica y Au omá ica
Uni e sidad de Salamanca
Plaza de la Me ced s/n, 37008, Salamanca, Spain
Uni e si y o Salamanca, Spain
e-mail: { co ds,lancho,angelica,esco chado,co chado}@usal.es
158 J.F. De Paz e al.
ha uses pas expe iences o esol e new p oblems, and is e y app op ia e o use
in scena ios whe e adap a ion and lea ning abili ies a e necessa y. In o de o
acqui e in elligen beha iou s, i is necessa y o p o ide he sys ems wi h lea ning
capabili ies. One o he possibili ies is lea ning om pas expe iences, which can
acili a e cogni i e knowledge. CBR sys ems a e aimed a p o iding lea ning and
adap a ion capaci ies [3, 8, 9, 10]. The use o pas expe iences allows hese sys-
ems o esol e new p oblems [8, 11]. SVR is a a ia ion o suppo ec o ma-
chines, able o p o ide eg ession models o non-linea da ase s. The combina ion
o CBR and SVR p o ides an added alue o he p edic ion o he CO2 exchange.
This p oposal is a s ep in his di ec ion and he i s s ep owa d he de elopmen
o p edic i e models based on non-linea da a. The model p esen ed wi hin his
wo k p o ides g ea capaci ies o lea ning and adap a ion o he cha ac e is ics o
he p oblem in conside a ion by using no el algo i hms in each o he s ages o he
CBR cycle ha can be easily con igu ed and combined. I also p o ides esul s
ha no ably imp o e hose p o ided by he exis ing me hods o CO2 analysis.
Sec ion 2 p esen s he p oblem ha mo i a es his esea ch. Then, in Sec ion 3
he ela ed wo k is p esen ed. Sec ion 4 desc ibes he app oach p oposed in his
esea ch. Finally, in sec ion 5 some p elimina y esul s and he conclusions will be
p esen ed.
2 Ca bon Dioxide Exchange
The oceans con ain app oxima ely 50 imes mo e CO2 in dissol ed o ms han he
a mosphe e, while he land biosphe e including he bio a and soil ca bon con ains
abou 3 imes as much ca bon (in CO2 o m) as he a mosphe e [7]. The CO2
concen a ion in he a mosphe e is go e ned p ima ily by he exchange o CO2
wi h hese wo dynamic ese oi s. Since he beginning o he indus ial e a, abou
2000 billion ons o ca bon ha e been eleased in o he a mosphe e as CO2 om
a ious indus ial sou ces including ossil uel combus ion and cemen p oduc ion.
I is impo an , he e o e, o ully unde s and he na u e o he physical, chemical
and biological p ocesses, which go e n he oceanic sink/sou ce condi ions o
a mosphe ic CO2 [7, 4].
The need o quan i y he ca bon dioxide alence, and he exchange a e be-
ween he oceanic wa e su ace and he a mosphe e, has mo i a ed us o de elop
he dis ibu ed sys em, p esen ed he e, ha inco po a es a CBR model capable o
es ima ing such alues using accumula ed knowledge and upda ed in o ma ion.
The CBR model ecei es da a om sa elli es, oceanog aphic da abases and ocea-
nic and comme cial essels. The case-based easoning sys em inco po a ed is able
o op imize asks such as he in e p e a ion o images using a ious s a egies [5].
The in o ma ion ecei ed is composed o sa elli e images o he ocean’s su ace,
wind di ec ion and s eng h, and o he pa ame e s such as wa e empe a u e, sa-
lini y and luo escence. An imp o emen o he o ecas ing me hods p esen ed in
[0, 1, 2] is inco po a ed in he CBR model p esen ed in his pape .
I is possible o ind di e en sys ems in li e a u e aimed a p edic ing C02 ex-
change a es [15, 16, 1]. These wo ks p opose an app oach based on ob aining
A Suppo Vec o Reg ession App oach o P edic Ca bon Dioxide Exchange 159
eg ession models ha a e gene a ed manually by expe s. The wo ks p esen ed in
[15, 16] ocus on he a ia ion o he exchange o CO2 p oduced du ing he day
and du ing he nigh , while he wo k p esen ed in [1] p io i izes he di e ence o
p essu es ha exis s be ween he ocean su ace and he ai . The eg ession models
p oposed in hese wo ks ha e, in gene al, a high le el o complexi y and some-
imes equi e he inco po a ion o new a iables once he model has been gene a -
ed, which means ecalcula ing he equa ions o he model. In his sense, he es i-
ma ion o he CO2 exchange a e ob ained by means o manual models p esen s
de iciencies when wo king in dynamic en i onmen s, whe e he sys em needs o
au oma ically adap i sel o he changes ha occu in i ’s su oundings and e ol e
o e ime.
3 Suppo Vec o Reg ession
SVR comes om Suppo Vec o Machine (SVM) and is specialized in ob aining
eg ession models by means o a change in he dimensionali y o he da a. SVM is
a supe ised lea ning echnique ha is applied o he classi ica ion and eg ession
o di e en elemen s. SVM acili a es wo king wi h da a ha canno be adjus ed o
linea models [12], ini ially concei ed o ob ain classi ica ions in linea sepa able
p oblems, by means o inding a hype plan able o sepa a e he elemen s o a se .
One o he ad an ages o SVM is ha i also allows sepa a ion o non-linea da a.
To ob ain non-linea sepa a ion, SVM pe o ms a mapping o he ini ial da a in o a
high dimensionali y space, whe e he da a can be linea ly sepa able using speci ic
unc ions. Gi en ha he dimensionali y o he new space can be e y high, mos
o he ime i is no iable o use hype plans o ob ain linea sepa a ion. As a solu-
ion, non-linea unc ions called ke nels a e used. SVR is a a ia ion o SVM o
gene a e eg essions [12, 13, 14]. The aim is o adjus he da a. As in he case o
SVM he e is a mapping o he inpu da a in o a high dimensionali y space. In his
new space he eg ession can be ca ied ou wi hou he ini ial limi a ions. Equa-
ion (1) shows he linea eg ession ob ained by means o gj(x) unc ions ha
ans o m he inpu ec o s om hei ini ial coo dina es o a high dimensionali y
space.
(1)
4 Sys em Desc ip ion
The model p oposed in his pape p esen s a case-based easoning sys ems, which
models he ai -sea CO2 exchange a e. The CBR sys em has wo aims. The i s
one is o gene a e models which a e capable o p edic ing he a mosphe ic/oceanic
in e ac ion in a pa icula a ea o he ocean in ad ance. The second one is o pe -
mi he use o such models.
∑
=
+= m
j
jj bxgwwx
1
)(),(
160 J.F. De Paz e al.
Mo eo e , he easoning cycle is one o he ac i i ies ca ied ou by he sys em.
We can see how he easoning cycle o a case-based easoning sys em is included
among he ac i i ies, composed o s ages o e ie al, euse, e ise and e ain.
Also, an addi ional s age ha in oduces expe ’s knowledge is used.
Fig. 1 In e nal s uc u e o CBR-Sys em
Figu e 1 shows he in e nal s uc u e o he p oposed CBR. P oblem desc ip-
ion (ini ial s a e) and solu ion (si ua ion when inal s a e is achie ed) a e
ep esen ed as a se o alues ela ed o he oceanic and a mosphe ic s a us, he
inal s a e is he solu ion achie ed o he p oblem ( he p edic ed lux o CO2),
and he sequences o ac ions a e he s eps ca ied ou in each o he s ages o he
CBR cycle. The s uc u e o a case o he CO2 exchange p oblem can be seen in
Table 1. Table 1 shows he desc ip ion o a case: DATE, LAT, LONG, SST, S,
WS, WD, Fluo_calib a ed, SW pCO2 and Ai pCO2. Flux o CO2 is he alue o
be iden i ied. DATE ep esen s he da e o he case, LAT ep esen s he la i ude
o he loca ion whe e he da a has been ob ained and LONG, he longi ude in de-
cimal deg ees. SST ep esen s he empe a u e o he ocean and S, he salini y. WS
is he wind s eng h and WD is he wind di ec ion. Fluo_calib a ed ep esen s he
luo escence calib a ed wi h chlo ophyll.
4.1 Re ie e
The p edic ion o he CO2 exchange a e is ob ained om he pa ame e s shown
in Table 1. The p edic ion is ca ied ou aking in o conside a ion di e en egions
ε
ε
ξ
*
ξ
*
ξ
x
A Suppo Vec o Reg ession App oach o P edic Ca bon Dioxide Exchange 161
Table 1 Case A ibu es.
Case Field Measu emen
DATE Da e (dd/mm/yyyy)
LAT La i ude (decimal deg ees)
LONG Longi ude (decimal deg ees)
SST Tempe a u e (ºC)
S Salini y (uni less)
WS Wind s eng h (m/s)
WD Wind di ec ion (uni less)
Fluo_calib a ed Fluo escence calib a ed wi h chlo ophyll
SW pCO
2
Su ace pa ial p essu e o CO
2
(mic o A mosphe es)
Ai pCO
2
Ai pa ial p essu e o CO
2
(mic o A mosphe es)
Flux o CO
2
CO
2
exchange lux (Moles/m2)
o he A lan ic Ocean and, in o de o ob ain an e ec i e p edic ion, he sys em
needs o eco e he app op ia ed pas expe iences. Tha is, hose cases ha con-
ain p oblem desc ip ions o simila la i udes and longi udes. In o de o es ablish
his i s il e in he e ie e s age, he oceanic egion aken in o conside a ion o
his s udy was di ided in o g ids o 10º o he la i udes and longi udes. The p e-
dic ions and es ima ions a e p o ided o he comple e g id as a se . Once a egion
has been selec ed, he selec ion o he mos simila case s udy is pe o med ac-
co ding o he cosine dis ance applied o he ollowing se o a iables SST, S,
WS, WD, Fluo_calib a ed, and Ai pCO2. The cosine dis ance is used o a oid
da a no maliza ion and co esponding p oblems wi h he da a uni s.
4.2 Reuse
Once he mos simila cases ha e been e ie ed, he eg ession model is gene -
a ed. As indica ed in Sec ion 4, he echnique ha will be used o c ea e he eg es-
sion model is Suppo Vec o Reg ession (SVR). The inpu ec o x ep esen s a
da ase wi h he s uc u e p esen ed in Table 1. The inpu ec o can be ep e-
sen ed as x=( DATE, LAT, LONG, SST, S, WS, WD, Fluo_calib a ed, SW pCO2
and Ai pCO2). The eg ession is ob ained making use o all he ec o s p o ided
by he mos simila cases e ie ed in he p e ious s age o he CBR cycle, and he
SVR is calcula ed ollowing he algo i hm p esen ed in Sec ion 4. The eg ession
model is used o es ima e he swap o he new case, which is used o gene a e he
p edic ion alue.
4.3 Re ise
This phase is pe o med in an au oma ic ashion, and akes in o accoun he e o
a e p o ided by he SVM. The e o a e is calcula ed om he p e ious exis ing
da a using he coe icien o a ia ion, in such a way ha i he alue ob ained
is mino han a p e- ixed alue, hen he p edic ion can be conside ed as success-
ul. I is necessa y o ake in o accoun ha once he eal da a a e ob ained, he

162 J.F. De Paz e al.
p edic ed exchange alues a e elimina ed. The es ima ed alues a e only used o
ob ain p edic ion models unde di e en condi ions.
Mo eo e , du ing he e ision s age an equa ion (F) is used o alida e he p o-
posed solu ion p*.
(2)
Whe e: F: is he lux o and k: is he gas ans e eloci y. Then
(3)
5 Resul s and Conclusions
In o de o make e iden he need o ca y ou a sepa a ion o he da a in la i udes
and longi udes, Figu e 2 shows he esul s ob ained a e calcula ing he p edic-
ions using SVR wi h a da ase o 365 cases dis ibu ed in a homogeneous manne
along he No h A lan ic Ocean. The ke nel unc ion used o he expe imen s was
polynomial and he loss unc ion was -insensi i e. The blue lines in Figu e 2
ep esen he eal alue o he da a and he ed lines ep esen he p edic ed alues.
As can be seen in Figu e 2, he e o a e ob ained in his expe imen is e y high
compa ed he e o a e ob ained in Figu e 3. The nume ical alues ep esen he
millions o Tonnes o ca bon dioxide ha ha e been abso bed (nega i e alues) o
gene a ed (posi i e alues) by he ocean du ing each o he h ee mon hs.
To e alua e he p edic ion capaci ies o he sys ems p esen ed in his s udy, di -
e en es s we e pe o med along he No h A lan ic oceanic egion wi h da a
ob ained du ing 2009. In each o he es s, when a case con aining he desc ip ion
o an oceanic a ea was in oduced o he sys em, he mos simila cases in he g id
wi h he same la i ude and longi ude as he new case we e aken in o conside a ion
Fig. 2 P edic ion i p e ious simila cases a e selec ed
)( 22 AIRpCOSWpCOksoF−=
2
CO
3600/)765,2562729,0204,5( ++−= LongLa k
ε
0 100 200 300
-2000 0 2000 4000 6000
cases
swap
_
_swap
SVR
A Suppo Vec o Reg ession App oach o P edic Ca bon Dioxide Exchange 163
Fig. 3 Compa ison be ween he eal alues and he p edic ion alues o he CO2
exchange a e.
o ob ain he p edic ion. Figu e 3 shows he esul s ob ained om he expe imen .
The blue line ep esen s he eal alue and he ed line ep esen s he p edic ed
alue. Mo eo e , Figu e 3 shows he absolu e e o a e ob ained o he p edic ed
alue ( ed line) p o ided by he SVR. The absolu e e o a e ob ained was 31.43,
wi h an e o de ia ion o 39.63. The e o pe cen age ob ained was 2.5%.
The absolu e e o a e ob ained wi h he SVR has been compa ed o he e o
a e p o ided by al e na i e echniques, such as he mul ilaye pe cep on and he
oceanog aphe s' manual models. Figu e 3 shows he absolu e e o a e ob ained
o each o hese p edic ions. The g een line ep esen s he e o in oduced in he
sys em when he p edic ion is ca ied ou using a mul ilaye pe cep on. The mul-
ilaye pe cep on used 27 neu ons in he hidden laye and he inal e o pe cen-
age ob ained was 5.1%. Finally, he e o a e in oduced in he sys em when he
manual models a e conside ed was 6.7%.
This s udy has p esen ed a CBR in elligen sys em o p edic and moni o he
CO2 exchange a e in he No h A lan ic Ocean. I applies a hyb id easoning
sys em speci ically designed o analyze da a om sa elli e images and essels and
p edic po en ial CO2 luxes in o de o p o ide an inno a i e me hod o explo -
ing he CO2 exchange p edic ion p ocess and ex ac knowledge. This knowledge
helps human expe s o unde s and he p edic ion p ocess and o ob ain conclu-
sions abou he ele ance o he si ua ion o he oceanic en i onmen .
Acknowledgemen s. This wo k has been suppo ed by he MICINN TIN 2009-13839-C03-
03 p ojec .
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_
_
_
_
_
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SVR
e o SVR
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