A icle
Fo ecas ing Va ia ions in P o i abili y and Sil icul u e unde
Clima e Change o Radia a Pine Plan a ions h ough
Di e en iable Op imiza ion
Miguel A. González-Rod íguez 1,2,* , Miguel E. Vázquez-Méndez 3and Ulises Diéguez-A anda 2
Ci a ion: González-Rod íguez, M.A.;
Vázquez-Méndez, M.E.;
Diéguez-A anda, U. Fo ecas ing
Va ia ions in P o i abili y and
Sil icul u e unde Clima e Change o
Radia a Pine Plan a ions h ough
Di e en iable Op imiza ion. Fo es s
2021,12, 899. h ps://doi.o g/
10.3390/ 12070899
Academic Edi o : Ma hias Neumann
Recei ed: 7 June 2021
Accep ed: 8 July 2021
Published: 10 July 2021
Publishe ’s No e: MDPI s ays neu al
wi h ega d o ju isdic ional claims in
published maps and ins i u ional a il-
ia ions.
Copy igh : © 2021 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
1
CERNA Ingenie ía y Aseso ía Medioamben al S.L., R/Illas Cíes n
º
52-54-56, G ound Floo ,
27003 Lugo, Spain
2
Unidade de Xes ión Ambien al e Fo es al Sos ible, Depa amen o de Enxeña ía Ag o o es al, Uni e sidade de
San iago de Compos ela, Escola Poli écnica Supe io de Enxeña ía, R/Benigno Ledo, Campus Te a,
27002 Lugo, Spain; [email p o ec ed]
3
Depa amen o de Ma emá ica Aplicada, Ins i u o de Ma emá icas, Uni e sidade de San iago de Compos ela,
Escola Poli écnica Supe io de Enxeña ía, R/Benigno Ledo, Campus Te a, 27002 Lugo, Spain;
[email p o ec ed]
*Co espondence: miguelangel.gonzalez. [email p o ec ed]
Abs ac :
Clima e change migh en ail signi ican al e a ions in u u e o es p oduc i i y, p o i abili y
and managemen . In his wo k, we es ima ed he inancial p o i abili y (Soil Expec a ion Value, SEV)
o a se o adia a pine plan a ions in he no hwes o Spain unde clima e change. We op imized
sil icul u al in e en ions using a di e en iable app oach and p ojec ed u u e p oduc i i y using a
machine lea ning model basing on he clima ic p edic ions o 11 Global Clima e Models (GCMs) and
wo Rep esen a i e Concen a ion Pa hways (RCPs). The o ecas ed mean SEV o u u e clima e
was lowe han cu en SEV (
∼
22% lowe o RCP 4.5 and
∼
29% o RCP 6.0, wi h in e es
a e = 3%
).
The dispe sion o he u u e SEV dis ibu ion was e y high, al e na i ely o ecas ing inc eases
and dec eases in p o i abili y unde clima e change depending on he chosen GCM. Sil icul u al
op imiza ion conside ing u u e p oduc i i y p ojec ions e ec i ely mi iga ed he po en ial economic
losses due o clima e change; howe e , i s abili y o pe o m his mi iga ion was s ongly dependen
on in e es a es. We conclude ha he inancial p o i abili y o adia a pine plan a ions in his egion
migh be signi ican ly educed unde clima e change, hough u he esea ch is necessa y o clea ing
he unce ain ies ega ding he high dispe sion o p o i abili y p ojec ions.
Keywo ds:
di e en iable op imiza ion; Pinus adia a; s and-le el managemen ; clima e change; isk
modelling
1. In oduc ion
Clima e change is in ended o shi o es dynamics in he ollowing decades [
1
]. De-
clines in o es p oduc i i y and as changes in species sui abili y a e among he po en ial
nega i e consequences o global wa ming [
2
–
4
]. These consequences may comp omise he
abili y o o es ecosys ems o p oducing goods and se ices, leading o socioeconomic all-
ou s, such as sca ci y in imbe supply chains [
5
], u ns in imbe land alue app ecia ion [
6
],
and ood and ene gy sho ages in u al ulne able communi ies [7].
In ecen yea s, he conce n o p oac i ely adap ing o shi s in o es p oduc i i y has
p o oked a scien i ic u na ound in he ield o empi ical g ow h and yield modelling [
1
,
8
].
The cu en esea ch end aims a de eloping g ow h-en i onmen ela ionships h ough
p edic i e modelling, mainly ocusing on he si e index (
SI
), he mos equen empi ical
indica o o o es p oduc i i y [
9
]. A a ie y o supe ised lea ning echniques ha e been
used o his pu pose [10–12], yielding, o e all, success ul esul s (R2∼0.3–0.7).
E en so, connec ing u u e o es p oduc i i y p edic ions wi h i s economic and
sil icul u al epe cussions is s ill an unce ain ask. In his ega d, se e al ecen s udies
ha e e alua ed inancial isks associa ed wi h unce ain u u e p oduc i i y basing on
Fo es s 2021,12, 899. h ps://doi.o g/10.3390/ 12070899 h ps://www.mdpi.com/jou nal/ o es s
Fo es s 2021,12, 899 2 o 14
op imiza ion a s and-le el [
13
,
14
] and o es -le el [
15
,
16
]. These s udies consis , in sum-
ma y, on he nume ical op imiza ion o a ce ain inancial indica o (e.g., he soil expec a ion
alue), which depends on decision a iables associa ed wi h sil icul u e and in es men s,
unde a ying economic and clima ic condi ions. Acco ding o Pasalodos-Ta o
[17]
, mos
o he p e ious esea ch on s and-le el managemen op imiza ion has elied ei he on
dynamic p og amming me hods o on di ec sea ch me hods. Dynamic p og amming was
he ea lies o bo h echniques [
18
] and consis ed basically o simpli ying he op imiza ion
p oblem by di iding i in o a se ies o simple p oblems ha we e sol ed ecu si ely.
Though i had he majo ad an age o ensu ing con e gence o he global maximum, i
also implied some impo an disad an ages, such as he need o disc e izing decision and
s a e a iables [
19
]. Di ec sea ch me hods we e applied o i s ime in o es y by Kao
and B odie
[20]
and since hen ha e been ex ensi ely used o s and-le el op imiza ion.
In compa ison wi h dynamic p og amming, di ec sea ch me hods p o ide easonably
good solu ions as e and can implemen con inuous decision and s a e a iables. Howe e ,
di ec sea ch me hods do no ensu e he con e gence owa ds he global maximum [
21
].
Se e al amilies o di ec sea ch me hods ha e been applied in ecen decades o op i-
mizing s and-le el managemen , including he one solu ion ec o me hods, such as he
Hooke and Jee es algo i hm [
22
], and he popula ions-based me hods, such as Di e en ial
E olu ion [23], Pa icle Swa m Op imiza ion [24] and E olu ion S a egy [25].
To cope wi h some o he disad an ages o hese echniques, [
26
] p oposed he use
o di e en ial op imiza ion me hods. The la e allow wo king wi h con inuous decision
a iables, hus a oiding he in o ma ion loss due o disc e iza ion, and p oduce good
solu ions in a ela i ely sho compu ing ime. In hei compa a i e analysis, [
26
] ound
ha a di e en iable me hod was be ween
∼
3 and
∼
20 imes mo e e icien , in e ms o
compu ing cos s, han Hooke and Jee es and Di e en ial E olu ion, espec i ely. Mo eo e ,
some o he obse ed compu ing limi a ions o dynamic p og amming and di ec sea ch
seem o scale sha ply as we inc ease he numbe o decision a iables [
21
,
26
], as i can be he
case when hinnings a e implemen ed in addi ion o clea cu ing- ela ed decision a iables.
Conce ning he speci ic p oblem o managemen op imiza ion unde unce ain u u e
p oduc i i y, he usual app oach consis s on he use o isk me ics de i ed om a co a i-
ance analysis be ween isk ac o s (i.e., p oduc i i y) and p o i abili y. Unde his app oach,
especially equen in he ield o mode n po olio op imiza ion [
6
,
13
], he co a iance anal-
ysis is based on a simula ion-based p ocedu e in which he objec i e unc ion is e alua ed
exhaus i ely, encompassing a wide ange o combina ions o sil icul u al, economic and
clima ic condi ions. Conside ing he high numbe o simula ions ha his ask migh imply,
compu a ional e iciency becomes an impo an conce n ha should guide he selec ion
o he op imiza ion me hod. In his con ex , he use o dynamic p og amming and di ec
sea ch me hods can lead o a ce ain le el o o e simpli ica ion in he p oblem se up (i.e.,
a educ ion in he numbe o decision a iables and possible solu ions ia disc e iza ion) o
educe compu ing cos s.
In his a icle, we simula ed he de elopmen o o es plan a ions in he no hwes o
Spain unde di e en clima e change scena ios. Fo each scena io, we op imized economic
p o i abili y using s and-le el di e en ial op imiza ion. We ocused ou scope on a se o
adia a pine (Pinus adia a D. Don) s ands dis ibu ed mainly in he Spanish p o ince o
Lugo. A e he simula ions, we e alua ed he changes in inancial p o i abili y and isk
be ween cu en and u u e clima ic condi ions. As a side goal, we analyzed he changes in
op imum sil icul u e a iables, such as he o a ion leng h.
2. Ma e ials and Me hods
2.1. Op imiza ion App oach
We op imized o es s and managemen ollowing a simila me hodology o ha
used by A ias-Rodil e al.
[26]
in he NW o Spain o pu e, e en-aged s ands o Pinus
pinas e Ai . In i , he de elopmen o a o es s and is simula ed using he dynamic
sys ems-based amewo k ( equen ly e e ed o as “s a e-space” app oach) i s used in
Fo es s 2021,12, 899 3 o 14
o es y by Ga cía
[27]
. Acco ding o i , he o es s and is cha ac e ized a each momen
by s a e a iables whose e olu ion, desc ibed by ime-dependen ansi ion unc ions, is
conside ed independen o p e ious s a es. These unc ions ep esen na u al dynamics
(g ow h and mo ali y), a e a ec ed by con ol a iables which encapsula e he impac
o sil icul u al ea men s on he s a e, and a e complemen ed by ou pu unc ions ha
ansla e s a e a iables in o ou comes (e.g., imbe olume). An economic model p o ides
he objec i e unc ion alue co esponding o hese con ol a iables and ini ial s and
condi ions (see Figu e 1).
SIMULATOR
Ou pu unc ions
Objec i e unc ion
Con ol a iables (managemen p esc ip ion)
u iIiRi n +1
=
Ou comes Vd
( , )u ...
Vi
,d
( )u
Objec i e alue SEV( )u
DYNAMIC SYSTEM MODEL
S a e a iables a an ini ial age 0
H0N0G0
T ansi ion unc ions
S a e a iables a age
H ( ) N ( , )uG ( , )u
ECONOMIC MODEL P ices ( ) and cos s ( )p C
j
Figu e 1.
Flow diag am o he simula o de eloped o compu ing he objec i e alue (SEV) o a gi en managemen p esc ip ion.
We used he mos equen se ing unde his app oach, which cha ac e izes he s and
using h ee s a e a iables: dominan heigh (mean heigh o dominan ees in he s and,
in me es),
H( )
, numbe o s ems pe hec a e,
N( )
, and s and basal a ea ( o al a ea o
s em sec ions a 1.3 m, in m
2
/ha),
G( )
. The dynamic o hese a iables is desc ibed by
species-speci ic ansi ion unc ions
h
,
n
,
g
:
R+×R+×R+−→ R
, so ha , i o an ini ial
age
0≥
0 he e is a known s a e whe e
H( 0) = H0
,
G( 0) = G0
and
N( 0) = N0
, and no
sil icul u al ea men s a e applied in
[ 0
,
]
, hen i is e i ied ha
H( ) = h( 0
,
H0
,
)
,
N( ) = n( 0,N0, )and G( ) = g( 0,G0, ).
Conce ning he simula ion o sil icul u al ea men s, each (
i
- h) hinning is cha ac-
e ized by i s in ensi y (p opo ion o s ems emo ed),
Ii
, emo al ela ion ( a io be ween
he p opo ion o s and basal a ea emo ed and he p opo ion o s ems emo ed),
Ri
,
and iming,
i
. Then, a managemen p esc ip ion is de ined by he numbe o hinnings,
n ∈N
, and he ec o (con ol a iable)
u= (I1
,
R1
,
1
,...,
In
,
Rn
,
n
,
n +1)∈R3n +1
,
de e mining hese hinnings and he o a ion age
n +1
. As
Ri
is usually kep in he in e al
(
0,1
]
, he dominan heigh is no a ec ed by ea men s (no e ha a alue o
Ri>
1 would
lead o hinning om abo e). The s a e a iables
H( )
,
N(u
,
)
and
G(u
,
)
can be p e-
dic ed a any age wi h he ansi ion unc ions
h
,
n
,
g
, and he con ol a iable
u
(see [
26
],
o de ails). Ou pu s a e hen ob ained om he p edic ed alues o he s a e a iables.
Fo ins ance, he me chan able imbe olume (in m
3
/ha) o a ce ain p oduc (de ined by
a limi diame e
d
, in cm) can be ob ained om a known ou pu unc ion
(H
,
N
,
G
,
d)
: o
any ≥0,
Vd(u, ) = (H( ),N(u, ),G(u, ),d)
Fo es s 2021,12, 899 4 o 14
gi es he me chan able imbe olume wi h diame e g ea e han
d
a age
. F om his
unc ion, he emo ed imbe olume a he i- h hinning is calcula ed as
V ,d
i(u) = Vd(u, −
i)−Vd(u, +
i),
whe e
−
i
and
+
i
deno e, espec i ely, he ins an s be o e and a e he
i
- h hinning. In he
same way, he emo ed imbe olume a he o a ion age is gi en by
V ,d
n +1(u) = Vd(u, n +1).
Conside ing ha he pu pose is o compa e he p o i abili y o managemen al e na-
i es wi h di e en o a ion leng hs, he economic model conside s as objec i e unc ion
he soil expec a ion alue (SEV, [28]):
SEV(u) = R(u)−C
(1+ ) n +1−1, (1)
whe e
R(u)
and
C
a e he discoun ed e enues and cos s, and
is he in e es a e. Fo
each imbe p oduc conside ed, e enues we e compu ed as he discoun ed p oduc o
s umpage p ices and ex ac ed olumes a each hinning and a inal ha es :
R(u) =
n +1
∑
i=1
1
(1+ ) i na
∑
j=1
pj
iV ,dj
i(u)−V ,dj+1
i(u)!(2)
whe e
na
is he numbe o di e en imbe p oduc s,
V ,dna+1
i(u) =
0,
In +1=Rn +1=
1,
and
pj
i
is he s umpage p ice (
e
/m
3
) o p oduc
j
in he
i
- h cu . I
pj
is he s umpage p ice
a clea cu ing, we assume a dep ecia ion in hinning p ice due o i s lowe in ensi y and,
maybe, lowe emo ed ela ion, such ha
pj
i=pj
a(2−Ri)(1−Ii),
whe e a>1 is a pa ame e ha measu es he s umpage p ice dep ecia ion in hinnings.
Acco ding o all p e ious conside a ions, a simula o o compu ing he SEV co e-
sponding o each managemen p esc ip ion was de eloped (see Figu e 1). In addi ion,
economic and logis ic cons ain s we e conside ed, and uppe and lowe bounds o he
decision a iables we e se , de e mining he admissible se
Un ⊂R3n +1
o possible alues
o
u
. The e o e, he o es s and managemen p oblem was o mula ed as he ollowing
Mixed-In ege Nonlinea P oblem (MINLP):
max SEV(u)(3)
subjec o u∈Un , (4)
0≤n ≤n max, (5)
whe e n max is he maximum numbe o hinnings allowed.
2.2. T ansi ion Func ions and Pa ame e s
As ansi ion unc ions o es ima ing he ime-dependen changes in he s a e a i-
ables we used he dynamic equa ions de eloped by Diéguez-A anda e al.
[29]
and Cas edo-
Do ado e al. [30] o adia a pine in his egion:
h( 0,H0, ) = H01−exp(−0.06738 )
1−exp(−0.06738 0)1.755+12.44/A1, (6)
Fo es s 2021,12, 899 5 o 14
wi h
A1=0.5log H0+1.755A2+q(log H0+1.755A2)2−49.76A2,
A2=log(1−exp(−0.06738 0));
n( 0,N0, ) = (N−0.3161
0+1.053 −100 −1.053 0−100)−1/0.3161; (7)
g( 0,G0, ) = exp(A3)exp−(−276.1 +1391/A3) −0.9233, (8)
wi h
A3=0.5 −0.9233
0−276.1 + 0.9233
0log(G0) + q5564 0.9233
0+276.1 − 0.9233
0log(G0)2.
The ini ial alues o he be o e- hinning s a e we e se as ollows: (i) o
h( 0
,
H0
,
)
,
0=
20, which is he e e ence age o he species acco ding o Diéguez-A anda e al.
[29]
,
and
H0
is he si e index (
S
); (ii) o
n( 0
,
N0
,
)
,
0=
0 and
N0
is he plan a ion densi y; and
(iii) o g( 0,G0, ), 0=10 and G0is gi en by
G0=exp(A4)exp−(−276.1 +1391/A4)10−0.9233, (9)
wi h
A4=4.331S0.03594 −114.3
n(0, N0,10).
Thus, o es p oduc i i y was implemen ed wi hin he simula ions h ough
S
, which
a ec s he ini ial basal a ea and dominan heigh . The inpu s o o es p oduc i i y used in
his s udy a e explained in Sec ion 2.3.
The ou pu unc ion o he me chan able imbe olume was [31]
(H,N,G,d) = 0.4046H1.013G0.9776 exp(−0.2933D−2.818
gd3.192), (10)
whe e he quad a ic mean diame e is gi en by Dg=100 4G
πN.
The necessa y in o ma ion o implemen ing sil icul u al in e en ions and economic
pa ame e s wi hin he simula ions was p o ided by he Spanish o es consul ancy com-
pany CERNA SL. The p oposed managemen p og am comp ised he ini ial plan a ion,
sc ub clea ance, and low p uning. Conside ing ha plan a ion densi ies o adia a pine
use o a y om 800 o 1100 s ems/ha in his egion, we chose as ini ial alue o
N0
he mean o ha in e al, 950 s ems/ha. The imbe p oduc conside ed we e chip and
pulpwood, sawlog and o a y enee . The cos o managemen in e en ions and s umpage
p ices by p oduc a clea cu ing a e shown in Table 1. Conce ning hinnings, we exe-
cu ed simula ions o managemen p esc ip ions o one and wo hinnings (
n max =
2).
The cons ain s o hinning- ela ed decision a iables men ioned in Sec ion 2.1 we e se as
(minimum-maximum): 15%–45% o in ensi y (
I
), 0.35 ( hinning o below)-1 (sys ema ic
hinning) o emo al ela ion (
R
), and 10–60 yea s o iming, wi h a minimal in e al
o i e yea s be ween cu ings. Mo eo e , o discoun ing he es ima ed e enues, we
compa ed he esul s o in e es a es o 1%, 3% and 5%.
Fo es s 2021,12, 899 6 o 14
Table 1. Economic pa ame e s used o he simula ions.
Desc ip ion Value
Cos s
Plan a ion ( =0) 1300 e/ha
Sc ub clea ing ( =3) 450 e/ha
Sc ub clea ing ( =10) 450 e/ha
Low p uning ( =10) 750 e/ha
P ices
Chip and pulpwood (d1= 7 cm) 16 e/m3
Sawlog (d2= 16 cm) 24 e/m3
Ro a y enee (d3= 25 cm) 30 e/m3
S umpage p ice dep ecia ion pa ame e in hinnings 2
2.3. Fu u e Fo es P oduc i i y
P edic ions o
S
o u u e clima ic scena ios we e ob ained om a Suppo Vec o Re-
g ession (SVR, [
32
]) model de i ed om a p e ious p ojec [
33
]. The model was de eloped
wi h da a om he esea ch plo s ne wo k es ablished by he Sus ainable En i onmen al
and Fo es Managemen Uni (UXAFORES) o he Uni e si y o San iago de Compos ela,
Spain. As p edic o s o o es p oduc i i y, he model inco po a es ou a iables om
he Wo dclim 2 bioclima ic da ase [
34
]: mean annual empe a u e, mean diu nal ange
(mean di e ence be ween maximum and minimum daily empe a u es), iso he mali y
a io (p opo ion be ween mean diu nal ange and maximum di e ence be ween mean
mon hly empe a u es) and mean empe a u e o he coldes mon h. Fo p edic ing u u e
S
, we used he p ojec ions o hese ou a iables de eloped by he Wo ldclim p ojec [
35
]
o he pe iod 2041–2060. Speci ically, we used he downscaled p ojec ions o a se o
11 Global Clima e Models (GCMs) included in he Coupled Model In e compa ison P ojec
Phase 5 [
36
] o he Rep esen a i e Concen a ion Pa hways (RCPs) 4.5 and 6.0. These
pa hways ep esen he o ecas ed clima e dynamics unde he assump ion o eaching a
adia i e o cing (p opo ion o inciden sola i adiance and adia ed ene gy om Ea h) o
4.5 W/m2
and
6 W/m2,
espec i ely, by he yea 2100. The u u e clima ic p ojec ions and
o es p edic i i y p edic ions we e ob ained o a se o 128 adia a pine s and loca ions in
he no hwes o Spain o which cu en p oduc i i y da a we e a ailable.
2.4. Nume ical Resolu ion and Analysis
Taking in o accoun ha only a ew hinnings a e allowed (
n max
is small),
MINLP (3)–(5)
can be sol ed by exhaus i e sea ch on he in ege a iable
n
. The e o e, o each
n =
1,
. . .
,
n max
, he nonlinea p oblem (NLP) (3)–(4) is sol ed wi h he ixed alue o
n
, and he
bes o he n max ob ained solu ions is aken as he op imal solu ion o p oblem (3)–(5).
Conce ning o NLP (3)–(4), due o he smoo hness o ansi ion unc ions (6)–(8) and
he ou pu unc ion (10), he di e en iabili y o he objec i e unc ion (1) can be p o ed
(see [
26
]), and g adien - ype me hods can be used o sol ing he p oblem. In his s udy, we
used he mos widesp ead amily: Sequen ial Quad a ic P og amming (SQP). Speci ically,
we used he implemen a ion in he nlop package [
37
]o R[
38
], wi h a andom mul i-s a
and compu ing g adien s by a ini e di e ence me hod [
39
]. To speed up calcula ions, we
did pa alleliza ion wi h he doPa allel package [40].
The op imiza ions we e execu ed o he 128 loca ions assuming
n max =
2. Fo each
loca ion, 22 (11 GCMs and wo RCPs)
S
p edic ions and h ee in e es a es we e conside ed,
leading o a o al o 8448 MINLPs (op imiza ion scena ios), i.e., 16,896 NLPs. Finally, we
analyzed he empi ical dis ibu ion o SEV o each loca ion and compu ed he expec ed
sho all (ES, [
41
,
42
]), a inancial isk indica o p e e ed o o he me ics (e.g., he alue a
isk) o non-no mal dis ibu ions [
43
]. Following he de ini ion gi en by P a
[44]
, we
compu ed ES o a con idence le el = 1 −αas
ESα=1
αZα
0qu(FSEV)du, (11)
Fo es s 2021,12, 899 7 o 14
whe e
qu(FSEV)
is he quan ile unc ion o he SEV dis ibu ion. This indica o can be in e -
p e ed as he mean SEV below he quan ile de ined by
α
, which we ixed as 0.025 in his
s udy, and ha is equi alen o he mean inancial loss abo e he 97.5% h eshold, acco ding
o he nomencla u e used by P a
[44]
. Fo discussing he po en ial sensi i eness o SEV o
a o able u u e clima e scena ios, we also compu ed he symme ic o ES2.5, ES97.5.
Finally, we compa ed he SEV es ima ed o cu en p oduc i i y (assuming no a ia ions
in u u e
S
, i.e., no clima e change), SEV
CP
, wi h he mean SEV o clima e change scena ios
(
SEVCC
), ES
2.5
and ES
97.5
. In addi ion, we also es ed he economic e ec o no adap ing
sil icul u e o clima e change, i.e., o apply he op imum sil icul u al p og ams o cu en
p oduc i i y o RCP 4.5 and RCP 6.0 scena ios (he ea e , “clima e-
insensi i e” sil icul u e
).
3. Resul s
3.1. P oduc i i y and Economic Indica o s
The conside ed u u e clima e models o ecas ed, on a e age, an inc ease in he ou
S
clima ic p edic o s excep o he iso he mali y, which expe ienced a sligh dec ease.
The mos no able shi in clima ic a iables was he mean empe a u e o he coldes mon h,
which inc eased
∼
40% wi h espec o p e ious condi ions. Howe e , hese o ecas s a ied
no ably o e clima e models, being he mean empe a u e o he coldes mon h he spa ses
o bo h RCPs ( ela i e dispe sion
∼
15%). The o es p oduc i i y p edic ions de i ed om
hese clima ic p ojec ions e ealed a dec easing end in mean
S
unde clima e change.
The mean
S
educed om 20.8 m (obse ed p oduc i i y) o 18.8 m (RCP 4.5) and 17.3 m
(RCP 6.0). Mo eo e , he a iabili y o hese p edic ions inc eased no ably, wi h
S
anges
(min.–max.) o 7.9–32.1 m o RCP 4.5 and 7.1–29.4 m o RCP 6.0 ha con as he obse ed
ange o 12.8–27.7 m.
The esul ing SEV unde op imum sil icul u e o cu en p oduc i i y a ied om
−
1150
e/
ha ( o
= 0.05) o
∼
52,000
e/
ha ( o
= 0.01), wi h a mean alue o
12,800 e/ha.
Conce ning clima e change scena ios, he
SEVCC
anged, o e all, om
−
750 o
∼35,000 e/ha
wi h a mean alue o 10,500
e/
ha o RCP 4.5 and 9000
e/
ha o RCP 6.0. Wi h ega d o he
ails o he
SEVCC
dis ibu ion, he ES
2.5
a ied om
−
1800
e/
ha o 27,000
e/
ha, while he
ES
97.5
a ied om 130
e/
ha o 56,000
e/
ha. Plo s o SEV unde cu en p oduc i i y s.
SEV unde clima e change o each in e es a e-RCP combina ion a e shown in Figu e 2.
As shown in Figu e 2, in mos o he loca ions
SEVCC <SEVCP
(poin s a e mainly
loca ed o he igh side o he iden i y line). In o he wo ds, in mos loca ions, simula ions
unde clima e change led o a d op in p o i abili y in compa ison wi h he scena io o
cu en p oduc i i y. The a e age ela i e dec ease in p o i abili y om cu en p oduc i i y
o clima e change scena ios a ied in he anges 15–64% o RCP 4.5 and 22–89% o RCP
6.0. These wide anges o a ia ion we e mos ly d i en by in e es a es, being he highes
dec eases in p o i abili y associa ed wi h high alues o
. Inc eases in SEV om cu en
p oduc i i y o clima e change (i.e., whe e
SEVCC >SEVCP
) we e sca ce and mos ly ound
in some loca ions wi h cu en low-a e age p oduc i i y. A high deg ee o co espondence
was ound be ween
SEVCC
and ES
2.5
, meaning ha loca ions wi h highe
SEVCC
had also
high ES
2.5
alues. Howe e , he e we e cases wi h high
SEVCC
and low ES
2.5
, and ice e sa,
which accoun o he a ying dispe sion a es o SEV among he di e en loca ions. The
e olu ion o SEV om cu en p oduc i i y o
SEVCC
, ES
2.5
and ES
97.5
unde RCPs 4.5 and
6.0 is shown in Figu e 3. Al oge he , a descending end in SEV was no iced in he di ec ion
cu en p oduc i i y-RCP 4.5-RCP 6.0. A sligh ly dec easing end was also ound in ES
2.5
be ween RCP 4.5 and RCP 6.0. The es ima ed ela i e dec eases o p o i abili y based on
ES
2.5
, om cu en p oduc i i y o clima e change scena ios, we e o 47–142% (also a ying
wi h
) o RCP 4.5 and 55–156% o RCP 6.0. In con as , ES
97.5
e ealed an inc ease in SEV
unde clima e change scena ios, wi h ela i e alues o up o 40% o RCP 4.5 and 47% o
RCP 6.0.
Fo es s 2021,12, 899 8 o 14
Figu e 2.
Sca e plo s o SEV unde cu en p oduc i i y (
SEVCP
) s. mean SEV unde clima e change o he wo RPC’s
and he h ee in e es a es conside ed. The dashed line in each plo ep esen s he iden i y.
Fo es s 2021,12, 899 9 o 14
Figu e 3.
Pa allel coo dina es plo s ep esen ing he change om SEV unde cu en p oduc i i y (
SEVCP
) o (
A
) mean SEV
unde clima e change (SEVCC), (B) u u e ES2.5 and (C) u u e ES97.5 o an in e es a e = 0.03.
3.2. Op imum Sil icul u e
Conce ning sil icul u al decision a iables, he op imum numbe o hinnnings was
one (
n
= 1) in all he op imiza ion scena ios (MINLPs). Howe e , he di e ences in SEV
be ween op imum sil icul u al p og ams o one and wo hinnings we e e y sligh , being
he mean di e ence = 180
e/
ha. Clima ic scena ios had a no iceable in luence on he
op imum o a ion leng h, which ended o each highe alues unde clima e change
(RCP 6.0
>
RCP 4.5, in mos o cases) in compa ison o cu en p oduc i i y (Figu e 4).
As expec ed, he o a ion leng h also showed a nega i e co ela ion wi h
. The hinning
in ensi ies and emo al ela ions we e sca cely in luenced by clima ic scena ios and, o e all,
expe imen ed low a iabili y. Conce ning he i s hinning (o he only hinning when
n
= 1), he esul s o mos o NLPs yielded alues e y close o he lowe bounds o
hese decision a iables, implying low in ensi ies (
I1∼
0.15) and hinning om below
(
R1∼
0.35). The op imum in ensi ies o he second hinning ( o hose NLP wi h
n
= 2) had
a b oade a ia ion ange, wi h some o he NLPs eaching
I2∼
0.45. As wi h he o a ion
leng h, he op imum hinning imings su e ed a no iceable a ia ion ac oss op imiza ion
scena ios, especially in luenced by
. The mean iming o he i s hinning was, o e all,
19 yea s and he mean iming o he second hinning was 31 yea s.
