A new model o analyze he empe a u e
e ec on he mic oalgae pe o mance a la ge
scale aceway eac o s
E. Rod íguez-Mi anda,†F.G. Acién,‡J.L. Guzmán,∗,¶M. Be enguel,,¶and A.
Visioli,†
†Depa men o Mechanical and Indus ial Enginee ing, Uni e si y o B escia, 25123, I aly
‡Dep. de Ingenie ía, Uni e sidad de Alme ía, CIESOL, 04120 Alme ía, Spain
¶Dep. de In o má ica, Uni e sidad de Alme ía, CIESOL ceiA3, 04120 Alme ía, Spain
E-mail: [email p o ec ed]
1
Abs ac
In his pape a simpli ied empe a u e model o aceway eac o s is de eloped, allowing
o de e mine he empe a u e o he mic oalgae cul u e as a unc ion o eac o design and
en i onmen al condi ions. The model conside s he majo phenomena aking place in aceway
eac o s, especially hea abso p ion by adia ion and hea losses by e apo a ion among o he s.
The cha ac e is ic pa ame e s o he model ha e been calib a ed using gene ic algo i hms, nex
being alida ed wi h a long se o mo e han 50 days co e ing di e en wea he condi ions. I
is wo h o highligh he use o he de eloped model as a ool o analyze he in luence o he
empe a u e on he pe o mance o mic oalgae cul u es a la ge scale. As example, he annual
a ia ion o he pe o mance o up o i e di e en mic oalgae s ains has been de e mined
by compu ing he empe a u e index, hus he no malized alue o pe o mance o wha e e
mic oalgae a he eal empe a u e wi h espec o ha achie able a op imal empe a u e can
be es ablished. Resul s con i m ha only s ains ole an o wide anges o empe a u e can
be e icien ly p oduced all he yea a ound in la ge scale ou doo aceway eac o s wi hou
addi ional empe a u e con ol sys ems.
Keywo ds: Bio echnology, Mic oalgae, Tempe a u e model, Raceway eac o , Ene gy Bal-
ance.
2
In oduc ion
Nowadays, he implemen a ion o mic oalgae eac o s o biomass p oduc ion is expanding due
o he ad an ages and p oduc s ha can be ob ained om hei exploi a ion. F om mic oalgae
biomass, high- alue p oduc s can be ob ained o be used in he chemical indus y1o o ani-
mal ood p oduc ion, such as ish- ood.2Ano he in e es ing ype o applica ion o mic oalgae
biomass, which is cu en ly unde in es iga ion, is he bio uel p oduc ion.3–6 On he o he hand,
he use o was ewa e as a cul u e medium is allowing he de elopmen o new combined applica-
ions such as he simul aneous ea men and pu i ica ion o wa e plus he p oduc ion o biomass
in a single p ocess.7This solu ion is becoming popula because i allows educing ope a ing cos s
and enhancing he use o mic oalgae o low alue applica ions, such as bio e ilize s o bioene gy.
The de elopmen o his ype o applica ions is ca ied ou in aceway eac o s, which a e he mos
ex ended ype o eac o s because hey a e less expensi e and easy o ope a e han ubula -closed
pho obio eac o s.
In addi ion o nu ien supply, he mos ele an a iables in luencing he mic oalgae p oduc ion
p ocesses a e empe a u e, sola adia ion, pH, and dissol ed oxygen.8,9 Tempe a u e and sola
adia ion a e mainly a unc ion o he loca ion whe e he eac o is ins alled and he season o
he yea . The a iables o be con olled a e pH and dissol ed oxygen, in o de o main ain hem
a speci ic ope a ing le els despi e changes in dis u bances, such as sola adia ion.10 Fo ha
eason, de ailed models o he pH and dissol ed oxygen e olu ion in aceway pho obio eac o s
can be ound in li e a u e.11,12 No ice ha he cul u e empe a u e could also be con olled by
using solu ions based on hea exchange s o ex e nal boile s, bu his op ion is omi ed because
i inc eases on he ope a ion cos s. Howe e , i is impo an o ha e dynamical models o he
cul u e empe a u e e olu ion in pho obio ec o s ha can be used as eac o design ools o o
s ain selec ion based on he eac o loca ion.
Biological mic oalgae models can help o es ima e and maximize c op p oduc i i y,13 as well
as cha ac e is ic pa ame e s ha can be used in con ol sys ems o maximize biomass p oduc-
ion.8,10,14 Howe e , al hough he e exis some s udies combining he mic oalgae p oduc i i y and
3
cul u e empe a u e,15,16 mos exis ing biological models do no ake he cul u e empe a u e in o
accoun , wha is a limi ing ac o in he analysis o he mic oalgae p oduc i i y esul s.17–20 Béche
e al. p esen ed a uni e sal empe a u e model o open eac o s,21 which makes use o dimension-
less pa ame e s o hea ans e and e apo a ion phenomena. The e apo a ion phenomenon is a
complex p ocess and di icul o es ima e. In22 a compa ison o di e en e apo a ion models is
p esen ed. On he o he hand, in,23 a dynamic model o he cul i a ion o mic oalgae is de el-
oped whe e an empi ical empe a u e model based on he mal ene gy balances sugges ed in24 is
included. These s udies demons a ed he impo ance o empe a u e on mic oalgae g ow h and
he complexi y o accu a ely es ima ing i s alue. The combina ion o a empe a u e model wi h
he cu en mic oalgae g ow h models would allow a g ea e accu acy in he ep esen a ion o he
mic oalgae beha iou . Thanks o his combina ion, be e con ol a chi ec u es o biomass p o-
duc ion and associa ed applica ions could be de eloped.
In his a icle, a new simple empe a u e model is p esen ed, based on a e iew o he empi ical
ela ionships de ined by Béche e al. and Slege s e al. in,21,24 and adap ed o a aceway eac o .
The cul u e empe a u e is calcula ed om a he mal balance in he eac o , aking in o accoun
all a ailable en i onmen al a iables. This model allows he es ima ion o he empe a u e o he
cul u e in he eac o o ce ain en i onmen al condi ions. In his way, he model could es ima e
pa ame e s o in e es , such as he ime o ha es o an icipa e isk empe a u es ha can nega-
i ely a ec he c op. In addi ion, he model may be used o analyse he empe a u e impac on
biomass p oduc ion o di e en loca ions. In his way, design ools could be de eloped o s udy
he iabili y o he mic oalgae p oduc ion zones o de e mine he mos sui able cul i a ion s ains.
Mo eo e , he empe a u e model can be used o imp o e exis ing mic oalgae es ima ion models
o biomass g ow h models, such as hose p esen ed in11 and.25 Also, he empe a u e model can be
used when he e is a lack o empe a u e measu emen s in he eac o , being used as a empe a u e
es ima o .
The a icle is di ided in he ollowing way. Sec ion 2 p esen s he eac o ha was used o
collec he eal da a and o alida e he models. In Sec ion 3, he componen s o he he mal
4
(a) Real aceway eac o . (b) Reac o scheme.
Figu e 1: Raceway eac o and s uc u e scheme.
balance and he empe a u e model a e de ailed. Sec ion 4 p esen s he esul s ob ained using he
empe a u e model, along wi h an analysis o how empe a u e in luences i e mic oalgae s ains by
using he empe a u e model and he g ow h a e model. Finally, Sec ion 5 s a es he conclusions.
Ma e ial and me hods
This sec ion p esen s de ailed in o ma ion abou he eac o , as well as he mic oalgae cul i a ed
s ain and he measu emen s.
Raceway eac o
The mic oalgae aceway eac o used o he es (Figu e 1a) is loca ed a he IFAPA cen e, nex
o he Uni e si y o Alme ía (Alme ía, Spain). The eac o has a o al su ace o 80 m2, composed
o wo 80 mleng h channels connec ed by a 1 mwide U-shaped bends. Mixing is pe o med by
a paddlewheel o aluminum blades wi h a diame e o 1.5 m, d i en by an elec ic mo o (W12
35 kW, 1500 pm, Eba ba, Ba celona, Spain), wi h gea educ ion (WEB Ibé ica S.A., Ba celona,
Spain). The paddlewheel speed is con olled wi h a equency in e e (CFW 08 WEB Ibé ica,
S.A., Ba celona, Spain) a a cons an eloci y o 0.2 m/s. Ca bona ion is pe o med in a sump
loca ed 1.8 mdowns eam o he paddlewheel, which dimensions a e 1.0 mdep h, 0.65 mleng h
and 1.0 mwid h. In his sump, CO2gas o ai can be injec ed h ough h ee pla e memb ane
5

di use s a he bo om o he sump (AFD 270, EcoTec, Spain). The aceway channels a e made o
low densi y polye hylene o 3 mm hickness while he cu es and sump a e made o high densi y
polye hylene o 3 mm hickness.
In he eac o , he e a e i e pH p obes, i e dissol ed oxygen p obes, and 5 empe a u e p obes.
Figu e 1b shows a scheme o he sys em, whe e each ed poin consis s o a senso se ha includes
pH, dissol ed oxygen, and empe a u e p obes. Poin s one, wo and h ee con ain p obes om
C ison, while poin s ou and i e con ain p obes om Hamil on.
The measu emen s o he clima ic condi ions a e ob ained om a me eo ological s a ion, while
he empe a u e o he soil and he dep h o he cul u e a e measu ed wi h senso s inco po a ed in
he aceway eac o i sel . Table 1 shows he model o he senso s o he measu able a iables,
which ep esen he inpu s o he empe a u e model. The sampling pe iod o he measu emen s
is one second.
Table 1: Measu ing senso s
Measu e Model
Wind speed Anemome e Thies Clima 4.3400.30.000
Global sola i adiance Py anome e Kipp & Zonen CM 6B
Ambien empe a u e and humidi y Senso Del a Ohm HD 9008TRR
Cul u e and soil empe a u e T ansduce PT100 wi h signal condi ione
Cul u e dep h Ul asound senso Wenglo UMD402U035
Mic oalgae s ain
The mic oalgae s ain used in he eac o belongs o Scenedesmus alme iensis (CCAP 276/24)
species. A de ailed s udy abou i s cha ac e is ic pa ame e s and condi ions ela ed o pH, dissol ed
oxygen and empe a u e can be ound in.26 The pH alue anges om 3 up o 10, bu he ne
pho osyn hesis a e is close o he maximal alue om 5.7 o 8. Rega ding he empe a u e, he
alue anges om 12 o 46 ◦C, bu he op imum ange is a ound 30 ◦C. The cul u e medium used
in he g ow h o he mic oalgae has been eshwa e and Mann & Mye s medium p epa ed using
e ilize s (0.14 g·L−1K(PO4)2, 0.18 g·L−1Mg(SO4)2, 0.9 g·L−1NaNO3, 0.02 mL ·L−1Welg o,
6
and 0.02 g·L−1Kalen ol).27
The mal balance and empe a u e model
The he mal balance desc ibed in his pape is based on i s p inciples and empi ical equa ions
de ined o he ans e o ene gy due o sola i adiance, long wa e adia ion, e apo a ion, con-
ec ion, and conduc ion.
Based on he models desc ibed in,21,24 he ene gy balances ha a ec he cul u e ha e been
analysed and es ablished, and a new he mal balance has been de eloped o es ima e he cul u e
empe a u e in he eac o om measu able a iables. The sola i adiance inpu comes om da a
measu ed by he global (di ec + di use) adia ion senso men ioned abo e. Long-wa e adia ion
losses a e calcula ed by he S e an-Bol zmann Law (28). The e a e di e en me hodologies in he
li e a u e o ob ain he e apo a ion low21.In his case, he ene gy balance by e apo a ion is calcu-
la ed om he e apo a ion a e ob ained om an expe imen al e apo a ion exchange coe icien .
Con ec ion is exp essed by New on’s Law o cooling, and inally, conduc ion is exp essed as he
hea ans e be ween he mass o he cul u e in he eac o and he polye hylene laye ha insula es
he eac o om he g ound. As a esul o he in oduced ene gy balances, he he mal balance is
exp essed by he ollowing equa ion (Qiin W):
Qaccumula ed =Qi adiance +Q adia ion +Qe apo a ion +Qcon ec ion +Qconduc ion (1)
whe e Qaccumula ed is he hea accumula ed in he eac o , Qi adiance ep esen s he low o hea
om sunligh , Q adia ion is he long-wa e adia ion hea low, Qe apo a ion accoun s o he hea
low p oduced by he e apo a ion p ocess, Qcon ec ion is he hea low caused by con ec ion and
Qconduc ion ep esen s he hea low be ween he eac o and he polye hylene laye unde i h ough
a conduc ion p ocess.
7
Accumula ed hea low
The hea accumula ed in he eac o ep esen s he sum o all ene gy e ms ha a ec he eac o ,
and i is exp essed by he ollowing equa ion:
Qaccumula ed =h·A·Cp·ρ·dTw
d (2)
wi h h(m) he cul u e dep h, A(m2) he su ace o he eac o , Cp(J kg−1◦C−1) he speci ic hea
capaci y o he cul u e, ρ(kg m−3) he densi y o he cul u e and Tw(◦C) he empe a u e o he
cul u e in he eac o .
Hea low due o he e ec o sola i adiance
The hea low due o inciden sola i adiance on he eac o su ace ep esen s he main hea inpu
in o he eac o . I is exp essed by he ollowing equa ion:
Qi adiance =Ig·a·A(3)
whe e Ig(W m−2)is he global (di ec + di use) sola i adiance, a(−)is he abso p i i y, and
A(m2) ep esen s he o al a ea o he eac o .
Radia ion hea losses
The eac o emi s he mal ene gy as long-wa e adia ion. The low o adia ed ene gy be ween he
eac o and he sky is calcula ed using he ollowing equa ion:
Q adia ion =σ·A·e·Tsky4−(Tw+273.15)4(4)
wi h σ(W m−2K−4) he S e an-Bol zmann cons an , e(−) he wa e emissi i y and Tsky (K) he
equi alen empe a u e o he sky, exp essed in (28) wi h he ollowing exp ession:
8
Tsky = (273.15+Tamb)(0.711+0.0056·Tdew ·0.000073·T2
dew +0.13·cos(15· sola ))0.25 (5)
whe e Tamb (◦C)is he ambien empe a u e, Tdew (◦C) he dew poin empe a u e, and sola (−)
ep esen s he numbe o hou s a e midnigh .
E apo a ion hea low
The e apo a ion p ocess ep esen s he main sou ce o hea loss in he eac o and depends on he
shape o he eac o , he e apo a ion a e and he la en hea o apo iza ion, as p esen ed in (29).
The e apo a ion hea low is de e mined as ollows:
Qe apo a ion =A·Ep·ρ·h g (6)
whe e Ep(m s−1)is he e apo a ion a e, ρ(kg m−3)is he densi y o he cul u e and h g (J kg−1)
is he la en hea o apo iza ion, exp essed as ollow:
h g = (2494−2.2·Tw)·1000 (7)
The e apo a ion a e can be calcula ed as an empi ical equa ion which depends on he di e -
ence in apou p essu es be ween he ambien ai and he eac o cul u e mass (29,30), in addi ion
o an e apo a ion exchange coe icien which depends on wind speed Ws:
Ep=RH ·p0
A
100 −p0
A·he ap (8)
whe e RH (%)is he ela i e humidi y, p0
A(Pa)is he apo p essu e o he ai a ambien empe a-
u e and he ap (m s−1Pa−1)is an e apo a ion exchange coe icien , ob ained expe imen ally om
he ollowing equa ion:
9
Figu e 3: Tempe a u e calib a ion esul s. Each indi idual colo plo ep esen s h ee consecu-
i e days o he selec ed mon hs om Augus o Decembe . Dashed lines ep esen eal eac o
empe a u e while solid lines ep esen es ima ed empe a u e. Fo he co ec isualiza ion o he
colo s in he g aphs, e e o he web e sion o he pape .
model and e i y ha i ai h ully ep esen s he dynamics o he sys em, ega dless o he mon h.
Figu e 5 shows he alida ion esul s o he empe a u e model, whe e each mon h is ep esen ed
indi idually ollowing he same han o he calib a ion esul s. The model ollows he dynamics
o he cul u e empe a u e in he eac o , wi h a maximum e o o 3.9 [◦C] and a mean e o o
0.86 [◦C]. Fo he en i e da a se an RMSE alue o 1.03 [◦C] has been ob ained.
As in he calib a ion esul s shown in Figu e 3, he es ima ed empe a u e o he mon hs o
Augus and Sep embe adequa ely esembles he eal empe a u e o he eac o , wi h a mean e o
o 0.5 [◦C]. The esul s o he mon h o Oc obe du ing he day ime pe iod a e e y sa is ac o y,
howe e , du ing he nigh ime he e a e ce ain disc epancies, inc easing he mean e o o 0.95
[◦C]. These e o s, like in he las ep esen ed day o Oc obe , may be due o e o s in he mea-
su emen s o he inpu a iables o isola ed punc ual phenomena ha a ec he empe a u e o he
eac o . On he o he hand, he mon hs o No embe and Decembe ha e a g ea e e o (mean
e o o 1.15 [◦C]) in he es ima ion, al hough he dynamics esembles he eal empe a u e and he
esul s a e sa is ac o y.
16

Figu e 4: En i onmen al inpu a iables o alida ion. Each mon h ( om Augus o Decembe )
is ep esen ed by di e en colo s and i is made up o 10 consecu i e days each. Fo he co ec
isualiza ion o he colo s in he g aphs, e e o he web e sion o he pape .
Figu e 5: Tempe a u e alida ion esul s. E e y indi idual colo plo ep esen s en consecu i e
days o he selec ed mon hs om Augus o Decembe . Solid line ep esen s es ima ed empe -
a u e while dashed line ep esen s eal eac o empe a u e. Fo he co ec isualiza ion o he
colo s in he g aphs, e e o he web e sion o he pape .
17
Tempe a u e in luence on mic oalgae ac i i y o di e en s ains
Using he de eloped empe a u e model, an analysis on how empe a u e in luences on mic oalgae
g ow h was ca ied ou o i e mic oalgae s ains. Fo his issue, he empe a u e-e ec on g ow h
model p esen ed by Be na d e al. in16 was used oge he wi h he empe a u e model desc ibed in
his pape .
The mic oalgae speci ic g ow h a e model has been used ex ensi ely in li e a u e16,26 and was
o mula ed by Camacho-Rubio e al. in.34 This model s a es ha he mic oalgae g ow h a e, µ,
is made up o ou ac o s ha depend on pho osyn he ically ac i e adia ion and ligh a ailabili y
inside he cul u e (Ia ), cul u e empe a u e (Tw), he pH, and he dissol ed oxygen (DO) in he
eac o . The g ow h model is desc ibed by he ollowing equa ion:
µ=µ(Ia )·µ(Tw)·µ(pH)·µ(DO)(17)
The speci ic g ow h a e (µ) is mainly a unc ion o ligh a ailabili y inside he eac o summa-
ized by he a e age i adiance inside he cul u e (Ia ) (35). This unc ion is exp essed as ollows:
µ(Ia ) = µmax ·Ia n
Ikn+Ia n(18)
whe e µmax [day−1]is he maximum g ow h a e, Ia [µE m−2s−1]is he ligh a ailabili y inside he
eac o summa ized by he a e age i adiance inside he cul u e, Ik[µE m−2s−1]is he minimum
ligh needed by he mic oalgae o achie e maximum pho osyn hesis and n[−]is a o m pa ame e .
Fo a speci ic geome y, he a e age i adiance (Ia ) is a unc ion o he ligh pa h inside he
cul u e, he biomass concen a ion and he ex inc ion coe icien o he biomass. The speci ic
g ow h a e hype bolically inc eases wi h he a e age i adiance up o achie e he maximum spe-
ci ic g ow h a e µmax o he selec ed s ain. Wha e e he mic oalgae s ains, o any ope a ional
condi ions a ix speci ic g ow h a e is achie ed, being highe o lowe acco ding o he op imal
alue o o he cul u es pa ame e s such as empe a u e, pH and dissol ed oxygen among o he s.
The ac o s o empe a u e, pH and dissol ed oxygen a e no malized alues and he o e line
18
indica es ha he e m a ies be ween 0 and 1, which mul iply he sola adia ion pa ame e . The e-
o e, when hese h ee (Tw,pH and DO) pa ame e s a e op imal and ha e a alue o 1, he speci ic
g ow h a e only depends on sola adia ion and would ha e he maximum possible alue. How-
e e , i any o hese pa ame e s is no op imal, i would ha e a di ec nega i e impac on he g ow h
a e.
The empe a u e index (µ(Tw)) is a pa ame e ha ep esen s he in luence o empe a u e on
mic oalgae g ow h, di ec ly ela ed o biomass g ow h, whe e 1 means he maximum yield due o
an op imal empe a u e o he cul u e. The biomass g ow h pe o mance can be diminished by he
e ec o he empe a u e, he e o e a empe a u e abo e o below he cha ac e is ic limi s o he
mic oalgae would esul in null g ow h. Fo example, a s ain ha does no exceed a empe a u e
index o 0.5 in a loca ion means ha a mos , i is no capable o eaching hal i s maximum g ow h
a e, so i would be limi ed o a g ea ex en due o empe a u e condi ions. Thus, he empe a u e
index can be used independen ly o analyze he in luence o empe a u e on mic oalgae s ains, as
i has a di ec e ec on he speci ic g ow h a e.
As commen ed abo e, he es o ac o s in equa ion (17) a e no malized ac o s ha a ec s
µ(IPAR). Speci ically, he empe a u e index can be ob ained om he ollowing equa ion, based
on he maximum (Tmax), minimum (Tmin) and op imum (Top ) empe a u e alues o he mic oalgae
s ain, shown in Table 4:
µ(Tw) = (Tw−Tmax)·(Tw−Tmin)2
(Top −Tmin)·((Top −Tmin)·(Tw−Top )−(Top −Tmax)·(Top +Tmin −2·Tw)) (19)
whe e Tw[◦C]is he empe a u e o he cul u e, calcula ed wi h he empe a u e model desc ibed
in equa ion (15).
The analysis has been done wi h ep esen a i e da a o 8 days o each seasonal pe iod o e a
yea a Alme ía, in Spain, cha ac e ized by mode a e empe a u es in summe and empe a e in
win e . The clima e in Alme ía is conside ed a local s eppe clima e, wi h li le ain all. Du ing he
19
cou se o he yea , he empe a u e gene ally a ies om 8 [◦C] o 30 [◦C] and a ely d ops below
6 [◦C] o ises abo e 35 [◦C]. The objec i e has been o e i y he in luence o empe a u e on
mic oalgae cul i a ion o i e di e en species o mic oalgae h oughou an annual pe iod in his
loca ion. These mic oalgae species co espond o Dunaliella e iolec a,Nannochlo opsis ocean-
ica,Chlo ella py enoidosa and Spi ulina pla ensis, being commonly used o biomass p oduc ion
a indus ial scale, in addi ion o Scenedesmus alme iensis, he s ain used in he aceway eac o
s udied. Table 4 ep esen s he cha ac e is ic empe a u e pa ame e s o each mic oalgae s ain,
applied o he empe a u e index model and ob ained om he li e a u e (16,26) and expe imen al
es s in ou esea ch g oup. Despi e he ac ha he mic oalgae used in he eac o is Scenedesmus
alme iensis, he empe a u e model is independen o he ype o s ain used, because i is a model
o es ima e he cul u e empe a u e. The cha ac e is ic empe a u e pa ame e s o each s ain a e
necessa y in he ca dinal model (equa ion 19), which in combina ion wi h he empe a u e model,
allows o analyze i s in luence o any mic oalgae s ain.
Table 4: Mic oalgae cha ac e is ic empe a u es
Mic oalgae s ain Tmin [°C] Top [°C] Tmax [°C]
Scenedesmus alme iensis 12 30 46
Dunaliella e iolec a 5 32.6 38.9
Nannochlo opsis oceanica -0.2 26.7 33
Chlo ella py enoidosa 5.2 38.7 45.8
Spi ulina pla ensis 7.7 37 50.6
Figu e 6 ep esen s he analysis ca ied ou o he i e ypes o mic oalgae du ing 8 days o
each season o he yea . The i s i e g aphs ep esen he empe a u e ac o (16) ha a ec s
he mic oalgae g ow h. The las g aph a he bo om ep esen s he es ima ed empe a u e in he
aceway eac o o he en i e da a se using he empe a u e model. The ideal seasons o cul i a e
he mic oalgae Scenedesmus alme iensis, used in he eac o desc ibed in Sec ion 2, a e he las
hal o sp ing, he summe and he i s hal o au umn. Howe e , du ing win e , he empe a u e
index is p ac ically 0, which deno es ze o g ow h. The Dunaliella e iolec a s ain is esis an o
medium/high empe a u es and wi h a good empe a u e index la e sp ing, summe and ea ly au-
umn, while i s pe o mance can be diminished by he low empe a u es o win e . The mic oalgae
20
Figu e 6: Tempe a u e index analysis du ing seasonal pe iods. The esul s o he da a se o eigh
days a e ep esen ed indi idually and di ided in ou colou s ep esen ing he di e en seasons.
Fi s g aph co esponds o Scenedesmus alme iensis. Second g aph co esponds o Dunaliella
e iolec a. Thi d g aph co esponds o Nannochlo opsis oceanica. Fou h g aph co esponds o
Chlo ella py enoidosa, while i h g aph co esponds o Spi ulina pla ensis. Six h g aph ep esen s
he es ima ed empe a u e in he aceway eac o (dashed line). Fo he co ec isualiza ion o he
colo s in he g aphs, e e o he web e sion o he pape .
Nannochlo opsis oceanica would no esis he summe pe iod bu i shows good esul s du ing
he es o he yea , especially in win e , whe e i s p oduc i i y exceeds he o he s ains analyzed.
Bo h Chlo ella py enoidosa and Spi ulina pla ensis s ains show a good empe a u e index du ing
he summe pe iod, oge he wi h la e sp ing and he ea ly au umn, as o Dunaliella e iolec a,
in con as o p ac ically no g ow h in win e due o low empe a u es. The esul s ob ained show
a clea ela ionship wi h he cha ac e is ic alues o each s ain ep esen ed in Table 4 allowing an
es ima ion o he iabili y o each s ain o he s udied loca ion.
Discussion
The e o ob ained in Figu es 3 and 5 deno es a p omising accu acy in he model ob ained om
he mal balances. F om he biological poin o iew, he e o ela ed o he es ima ed and he ac ual
empe a u e would no be a p oblem acco ding o he global p ocess dynamics. The model is able
21

o accu a ely ep esen he empe a u e du ing he whole day. Howe e , no ice ha in some days
he e o is la ge han in o he s. These misma ches may be due o he exis ence o non-measu able
e ms o dis u bances ha ha e no been con empla ed in he he mal balances, such as punc ual
e o s in he measu emen s, i egula ope a ions in he eac o o empe a u e o cul u e medium
o eplacemen . On he o he hand, he calib a ion by means o gene ic algo i hms allows o ob-
ain mean alues o pa ame e s used in he equa ions ha a e subjec ed o unce ain y, as hey a e
in lumped-pa ame e s ep esen a ions o balances ha should equi e dis ibu ed pa ame e ep e-
sen a ions and hus a e in gene al di icul o ob ain om ables. In gene al, he esul s ob ained
ha e been posi i e and no able o he use o he model in he de elopmen o mic oalgae g ow h
models whe e i s dynamics and o he pa ame e s such as p oduc i i y, pe o mance, consump ion
o CO2, and e olu ion o pH a e es ima ed.
The esul s o he empe a u e analysis o he cul i a ion o mic oalgae in Alme ía using
he empe a u e model o aceway eac o s ha e de e mined ha Scenedesmus alme iensis and
Dunaliella e iolec a mic oalgae a e sui able o p oduc ion du ing mos pa o he yea , espe-
cially du ing summe , due o i s high empe a u e index. Bo h Chlo ella py enoidosa and Spi ulina
pla ensis s ains a e also sui able o cul i a ion du ing he sp ing, summe and au umn pe iods,
due o a good empe a u e index beha iou bu less sui able han hose desc ibed abo e. On he
o he hand, he mic oalgae Nannochlo opsis oceanica is no capable o wi hs anding he empe -
a u es eached du ing la e sp ing and summe pe iods, being a mic oalgae di icul o cul i a e in
hese pe iods, bu being he mos sui able o cul i a ion in au umn and win e because i shows
he highes empe a u e index o all s ains o his seasonal pe iod.
The en i onmen al condi ions depend on he wea he and can be e y di e en om one season
o ano he . This ac has been aken in o accoun in he calib a ion o he model so ha i can adjus
o all he en i onmen al condi ions o each mon h, wi hou changing he pa ame e s o inc easing
he model complexi y. On he o he hand, being a model designed o all mon hs o he yea , he e
a e ce ain e o s due o a gene aliza ion o pa ame e s, bu a adeo be ween pe o mance and
complexi y has been ound.
22
The empe a u e es ima ion is eally use ul in he mic oalgae p oduc ion p ocess. The em-
pe a u e model can be combined wi h exis ing mic oalgae biomass p oduc ion models o add he
e ec o empe a u e on g ow h and hus make mo e accu a e and comple e mic oalgae p oduc ion
models. On he o he hand, empe a u e es ima ion can be used as a design ool when ins alling
a eac o in a de e mined loca ion. F om he g ow h p oduc i i y model and he en i onmen al
condi ions, i is possible o es ima e he empe a u e o a eac o in ha a ea and es ablish i s max-
imum biomass p oduc ion o he mic oalgae s ain iabili y. In his way, i is possible o assess he
sui abili y o ins all a aceway eac o in any speci ic a ea o es ablish di e en mic oalgae cul u es
depending on he season. Mo eo e , i can also be used o design con ol algo i hms o op imize
he eac o empe a u e.
Conclusions
This wo k p esen s a empe a u e model o aceway eac o s based on a he mal balance om
measu able condi ions in he en i onmen . The esul s o he dynamic empe a u e e olu ion ob-
ained om he model show sa is ac o y pe o mance ha closely esemble he ac ual empe a u e
alues, measu ed in he eac o . The g ea impac o empe a u e on he p oduc i i y o mic oalgae
has been demons a ed in he li e a u e and, he e o e, his ype o models has a undamen al ole in
he de elopmen o new and mo e comple e models o mic oalgae ha allow us o ully unde s and
all he pa ame e s ha a ec i s g ow h. The use o indus ial scale models ha ake in o accoun
all he a iables a ec ing he mic oalgae g ow h is sca ce in p ac ice, and hus, his empe a u e
model aims o complemen he use o mo e comple e models ha allow he de elopmen o p ecise
e alua ion applica ions in he ield o mic oalgae, such as op imal eac o con ol, a iable impac
s udies, pe o mance imp o emen o pa ame e es ima ion. In u u e wo k, he use ulness o he
model o es ima e he p oduc i i y o mic oalgae om di e en condi ions will be analyzed, in
addi ion o i s use as a design ool.
23
Acknowledgemen
This wo k has been pa ially unded by he ollowing p ojec s: DPI2017 84259-C2-1-R ( inanced
by he Spanish Minis y o Science and Inno a ion and EU-ERDF unds), and he Eu opean
Union’s Ho izon 2020 Resea ch and Inno a ion P og am unde G an Ag eemen No. 727874
SABANA.
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