Carbon captured as a new instrument in forest management: some implications

Transcription

1 SCIENTIA FORESTALIS n. 63, p , jun Carbon capturd as a nw instrumnt in forst managmnt: som implications Captura d carbono como um novo instrumnto para o manjo florstal: algumas implicaçõs Luis Díaz-Baltiro Carlos Romro ABSTRACT: Th rcnt considration of forst cosystms as possibl sinks of carbon dioxid (CO 2 ) maks ncssary its inclusion in th forst managmnt modls. This typ of inclusion gnrats thortical changs in th systm of calculation of th rotation ags. In this sns, it is intrsting to rsarch if th currnt forst policis ncouraging afforstation programms "push th forst ownr" towards rotation ags that optimiss th captur of CO 2. It is also intrsting to not that th considration of this nw objctiv implis important changs in th traditional mthods of forst managmnt basd upon xclusivly in timbr production. Th main objctiv of this work is to chck if svral forst managmnt framworks (rotation ag, harvst schduling) modify thir valus whn carbon capturd is includd into th managmnt procss. Aftr rviwing th abov topics, som nw mthods basd on goal programming ar proposd. This typ of approach allows th dtrmination of harvst schduls that rprsnt snsibl and robust compromiss btwn conomic timbr rturns and th CO 2 capturd. KEYWORDS: Carbon sinks, Forst managmnt, Forst conomics RESUMO: A rcnt considração d cossistmas florstais como altrnativas lgívis para o sqüstro d dióxido d carbono (CO 2 ) torna ncssária a sua inclusão m modlos d manjo florstal. Ess tipo d inclusão gra mudanças tóricas nos sistmas d cálculo das idads d rotação. Nss sntido, é intrssant invstigar s as atuais políticas florstais qu ncorajam os programas d florstamnto incntivam o propritário florstal a adotar rotaçõs qu otimizam a captura d CO 2. Também é intrssant notar qu a considração dst novo objtivo implica m importants mudanças nos métodos tradicionais d manjo florstal voltados xclusivamnt para a produção d madira. O objtivo principal dst trabalho é confirmar s vários modlos d manjo florstal (nvolvndo scolha d rotaçõs agndamnto d colhitas) modificam os sus rsultados ao s considrar rgims qu sqüstram carbono. Após a rvisão dos tópicos acima, alguns métodos basados m programação por mtas são propostos. Est tipo d abordagm prmit a dtrminação d programas d colhitas qu rprsntam compromissos snsívis robustos ntr os rtornos conômicos a captura d CO 2. PALAVRAS-CHAVE: Sqüstro d carbono, Manjo florstal, Economia florstal

2 104 Captura d carbono m florstas INTRODUCTION In th last fw yars som intrnational principls of agrmnts lik Kyoto Protocol hav bn outlind in ordr to rduc th atmosphric missions of crtain gass. Th rason undrlying ths agrmnts is th crucial importanc of takn masurs facing a possibl global climatic chang. From th forstry point of viw, it is important to b awar that th Kyoto Protocol xplicitly considrs ARD (afforstation, rforstation and dforstation) activitis in ordr to account th carbon capturd; i.., th forst cological function as CO 2 sinks is totally considrd in th protocol as a masur to mitigat this problm. It is rathr obvious that th final balanc will b positiv or ngativ dpnding upon th volution of th afforstation and dforstation rats sinc In ordr to account proprly th carbon it is considrd not only th carbon stord in th commrcial parts of th tr but also th carbon stord in th soil, lavs, branchs tc. Evn som intrprtations of th articl 3.4 of th Kyoto Protocol might allow th considration of th carbon accumulatd in products drivd from timbr as th carbon capturd for th growth of th currnt stands (Nabuurs t al., 2000). Nvrthlss, dspit th inclusion of this objctiv in th Spanish and Europan forst policy stratgis, th currnt managmnt mchanisms do not considr its inclusion. Thus, at a stand lvl th usual procdurs to calculat th optimal rotation ar not applicabl whn th carbon capturd is considrd. Within this lin som works hav attmptd to adapt th Faustmann approach to a contxt whr th CO 2 capturd is considrd (Hon, 1994; Van Kootn t al., 1995; Romro t al., 1998). On th othr hand, if forst managmnt focuss at a forst lvl, thn is ncssary to incorporat dirctly this objctiv into th stratgic planning. On xampl in this dirction is th work by Hon and Solbrg (1994), whr a bi-objctiv function, with nt prsnt valu and CO 2 capturd as argumnts, is introducd. In this papr, th carbon capturd will b considrd as an xplicit managmnt objctiv at a stand lvl as wll as a at forst lvl. Aftr analysing th ffct of carbon capturd on th optimal rotation ag of plantations, thn th othr objctivs considrd ar th following: to study th ffct of th considration of th carbon capturd in afforstation programs in spcis of short rotation (Populus sp.) and mdium rotation (Pinus radiata), as wll as to tst th rsults obtaind whn this nw critria is introducd on stratgic forst planning modls. Morovr, th main rsults drivd from a forst managmnt modl with multipl critria to a forst covrd with a long rotation spcis (Pinus sylvstris) in Spain will b prsntd. METHODOLOGY In ordr to includ th carbon capturd som prvious considrations should b mad. First, it is ncssary to dfin th form chosn for masuring th incrmnt in th carbon capturd. Thus, w hav th carbon accumulatd in th trs du to thir growth procss (gross carbon). This typ of carbon is th asist to masur. Th scond form is rlatd with th fficincy in th procss of carbon accumulation. Thus, if it is ncouragd that th final us of timbr will b products with a long lif, thn th r-mission of CO 2 to th atmosphr will b vry slow. In othr words, in this cas what is masurd is not gross carbon but nt carbon, that is calculatd as th diffrnc btwn th carbon capturd by th biomass and th carbon mittd according to th diffrnt uss of th timbr harvstd. Th abov considrations imply that th lction of th forst rotation is a basic dcision for two rasons. First, bcaus th rotation

3 Díaz-Baltiro Romro 105 chosn can incras th total carbon capturd. Scond, th cutting ag influncs th suitability of th products for a potntial rallocation of carbon from forsts to othr sourcs and sinks. In ordr to stimat th forst carbon contnt, it has bn assssd th carbon to b capturd ach yar, including th carbon du to th biomass growth as wll as th carbon rtaind in th products from timbr drivd from thinning oprations and from rgnration harvsts. To achiv this purpos thr typs of uss for timbr ar considrd: vnr, sawtimbr and nginrd wood composit. A possibl us for pulp is not considrd as wll as a possibl r-utilisation by a rcycling procss. Th calculation of th carbon capturd, for ach diffrnt timbr us, is mad by accpting th working hypothsis statd by Row and Phlps (1996). Finally, th usual way to fix a pric to th carbon capturd consists in th dtrmination of th willingnss to pay by th socity for a ton of CO 2 capturd. Howvr, in this papr w hav considrd th pric as th subsidy that maks qual th privat and th social optimum. Forst plantations To undrtak this analysis w hav considrd th usual mthodology for th dtrmination of th conomic optimum forst rotation. From a financial prspctiv it is wll accptd that th corrct procdurs is th on proposd by Faustmann (1849). This mthodology dfins th optimum rotation as th lif of th stand for which th nt prsnt valu of th undrlying invstmnt achivs a maximum valu, taking into account th land rnt. In ordr to apply proprly th Faustmann formula to our contxt th procdur suggstd by Díaz Baltiro and Romro (1995) and Mutk t al. (2000) has bn followd. Thus, a sals rvnu function I(t)= p f(t) is introducd, bing p th timbr pric and f(t) th growth curv. K rprsnts th plantation costs, G th gnral annual managmnt paymnts, Y S th cultural oprations and C l th rcipts drivd from thinning oprations. Bsids th abov paymnts and rcipts it is also ncssary to introduc th financial subsidis providd by th currnt Europan forstry policy. Ths typs of financial aids hav considrably ncouragd nw plantations in th last fw yars (Hrruzo, 2001). In this sns thr ar thr catgoris of aids. A maintnanc prmium P m rcivd during th first fiv yars of th plantation cycl; a compnsatory prmium P c rcivd during th first twnty yars of th plantation cycl and a subsidy K 1 to mitigat afforstation costs. Taking into account all ths componnts, and bing awar that th diffrnt subsidis ar prcivd only in first plantation cycl, th Nt Prsnt Valu (NPV) attachd to th invstmnt will b qual to: I( t) NPV = with: α = β = ( i 1) ( i 20) ( 1) γ = ( i1) ( 1) K 1 =1272 /ha K=1272 /ha ( i 1) ( ( i 1) ( ( ( i 1) ( 1) ( i 1) ( 1) Y s =1190 /ha i t i t) 1) ( i 5) K G α 1) G=30 /ha*yar Pm=150 /ha * yar 1 Y s s i t C (1) + K + P β + P γ Figur 1 Diagrammatic prsntation of th invstmnt procss (Populus sp.) (Rprsntação gráfica do procsso d invstimnto (Populus sp.)) i s + l l i l 1 m c I(t)=35814 /ha

4 106 Captura d carbono m florstas A diagrammatic prsntation of th invstmnt procss was includd in Figur 1. Th optimal forst rotation as wll as th profitability of th diffrnt plantations is obtaind by maximising xprssion (1). Howvr, whn w ar considring a joint production procss timbr-carbon capturd, th abov procdur is not applicabl. Evn th xtnsion of Faustmann formula introducd by Hartman (1976) is nithr applicabl sinc this approach rquirs th stimation of a flow of srvics masurd in montary trms. To circumvnt this problm w hav followd in this papr a mthodology proposd by Romro t al. (1998). With this purpos in mind a subsidy A ( pr ton of carbon capturd) will b introducd. In th sam way, a tax of A will b lvid for ach ton of carbon mittd to th atmosphr. Taking into account this nw contxt quation (1) turns into: I( t) NPV = + K + P β + P γ 1 with : α = γ = ( β = ( i i 1 ) ( i t ) ( 1) ( i 1 ) ( 1) i 1) ( i 5) ( 1) ( i 1 ) ( 1) ( m i t 1 ) ( i 20) ( 1) ( i 1) ( 1) K G α c s Y s i s + 1 C (2) + A C A C Whr C a (ton C/ha) rprsnts th carbon capturd whn th ag of th stand is r. C rprsnts th carbon mittd in th yar v. It should b notd that w hav only considrd th carbon stord in th marktabl timbr in th final cut as wll as in th thinnings. Howvr, w hav not considrd th carbon capturd in othr typ of biomass nor th variation of carbon in th soil. Th discount rat chosn is 7% and no taxs will b considrd. In all th cass studid th NPV, th optimal forst rotation as wll as th amount of carbon capturd will b calculatd for th privat optimum (corrsponds to th Faustmann optimum) and th nvironmntal optimum l l i t i l r a ir v iv (corrsponds to th maximum captur of carbon). Although som xcptions ar citd in th litratur (Rodriguz t al., 1997) th longst rotation corrsponds to th nvironmntal optimum and th shortst rotation to th conomic optimum. Prmannt stands Traditionally th primary objctiv of forst managmnt in Spain and in othr Europan countris has consistd in achiving crtain timbr volum targts. Howvr, in th last fw yars nw objctivs hav bn incorporatd in th managmnt of th forst, and th traditional Europan forst managmnt mthodologis can only dal with timbr objctivs. For this rason is compltly ncssary to rsort to th tools of th Oprational Rsarch disciplin in ordr to incorporat svral objctivs in th forst managmnt planning. Consquntly, th multi-critria mthodology known as Goal Programming will b usd to tackl this typ of problm. Th first stp in our work will consist in dfining th diffrnt goals considrd in this typ of problm. Thus, w hav considrd an conomic goal (to minimis th ngativ dviation with rspct to th maximum NPV). Morovr, thr forstry goals hav also bn considrd to minimis th unwantd dviations with rspct to an vn-flow policy: obtaining a rgulatd forst and scuring a satisfactory final invntory. Finally, an nvironmntal goal has bn considrd. This goal minimiss th unwantd dviations with rspct to th maximum carbon capturd by th forst along th planning horizon considrd (100 yars). Onc th diffrnt goals hav bn dfind, th achivmnt function minimising th unwantd dviation variabls is introducd. In ordr to minimis th achivmnt function subjctd to th corrsponding constraints, two Lxicographic Goal Programming modls hav

5 Díaz-Baltiro Romro 107 bn usd. Th tchnical dtails about ths modls can b found in Díaz-Baltiro and Romro (2003). Basically, both lxicographic modls groupd th goals into thr priority lvls. Th first priority lvl corrsponds to th goal that scurs a satisfactory final invntory. Th scond priority lvl includs th goal corrsponding to th rgulation condition. Th last priority lvl includs th othr thr goals corrsponding to th NPV, th vn-flow policy and th carbon capturd. In th first modl th wightd and normalisd sum of unwantd dviation variabls is minimisd whil in th scond modl th maximum dviation is minimisd. Tchnical aspcts as wll as th rational undrlying to this typ of optimisation approachs can b sn in Romro (1991) and Ignizio and Cavalir (1994). RESULTS W ar going to prsnt sparatly th rsults corrsponding to plantations with rspct to th rsults corrsponding to prmannt stands.in th Annx 1 appar th main charactristics of th afforstation program considrd, whil in th Annx 2 th basic aspcts of th forst analysd ar prsntd. Annx 1 Charactristics of th afforstations with Populus sp. and Pinus radiata. (Caractrísticas d florstamntos com Populus sp. Pinus radiata) Populus sp. Pinus radiata afforstation cost 1,272 /ha 1,563 /ha annual cost 30 /ha*yar 12 /ha*yar cultural oprations costs* 1,190 /ha 1,966 /ha K 1 1,272 /ha 1,266 /ha Europan aids P m 150 /ha 180 /ha P c 0 /ha 166 /ha volum obtaind at privat optimum 356 m m 3 Thinnings no ys timbr pric /m 3 51 /m 3 *discountd to zro yar Annx 2 Main charactristics of th "Pinar d Navafria" forst and managmnt (Principais caractrísticas florstais d manjo do "Pinar d Navafria") ara asignd to ach sit indx sit indx Sit I Sit II Sit III Sit IV Sit V ara (ha) 754,85 426,53 771,38 444,86 105,25 ara asignd to ach ag class ag class ara (ha) 42,37 347,16 133,44 355,82 58,4 356,81 230,11 49,56 352,71 139,2 392,06 46,73 Planning horizon: tim unit intrval final ag class 100 yars 10 yars 20 yars discount rat 0,02 maintnanc cost 24 /ha*yar timbr pric 71,4-94,7 /m 3

6 108 Captura d carbono m florstas Forst plantations Lt us start with th cas of poplar plantations without considring any typ of subsidy. Within this contxt th optimal forst rotation is 14 yars, corrsponding a NPV around 17,000 /ha. For this typ of privat optimum th gross carbon capturd is around 44.7 ton C/ha. Within an nvironmnt of financial subsidis th forst rotation raiss up to 15 yars, du to th possibility of rciving th maintnanc prmium. In this nw contxt th profitability incrass a littl, achiving a NPV pr hctar of 18,243. Th incras in th forst rotation producs a tiny incras in th carbon capturd of ton C/ha. On th othr hand, th nvironmntal optimum implis a forst rotation of 18 yars, providing a maximum carbon capturd of ton C/ha. Howvr, if w considr a cycl of plantations th optimum will not corrspond to this maximum ag but to th ag for which th avrag carbon capturd rachs a maximum valu. This ag is 17 yars with a carbon captur of ton/ha. For this rotation th NPV achivs th figur of 14,246 /ha without subsidis and of 16,132 /ha whn th Europan aids ar considrd. In othr words, to nlarg th forst rotation up to this ag implis to giv up th 16% of th NPV whn thr ar not subsidis and th 12% in a contxt of financial aids. If w considr th nt carbon instad of th gross carbon, this optimum dos not altr. Thus, th nt carbon has bn calculatd by accpting th abov statd hypothsis and by assuming that all th stord carbon is r-mittd to th atmosphr aftr 150 yars. Th figurs obtaind for th nt carbon oscillat btwn th 15% and th 20% of th gross carbon aftr 200 yars of plantation. Tabl 1 shows th gross and th nt carbon according to th afforstations considrd. Tabl 2 shows th rsults obtaind in trms of profitability. Tabl 1 Balanc of gross and nt accumulatd carbon in 100, 120, 150 y 180 yars, in 2 spcis: Populus sp. and Pinus radiata. (Balanço do acúmulo bruto líquido d carbono m 100, 120, anos d duas spécis, Populus sp. Pinus radiata.) Populus sp. GROSS CARBON (tm/ha) NET CARBON (tm/ha) Rotation 100 yars 120 yars 150 yars 200 yars 100 yars 120 yars 150 yars 200 yars ,12 376,20 460,92 626,44 111,33 119,26 106,85 112, ,03 388,85 488,64 648,89 129,04 118,52 130,39 128, ,35 382,22 479,88 645,85 106,01 109,55 108,35 110, ,81 393,91 492,39 642,79 111,01 116,76 118,12 106, ,39 371,29 471,08 627,77 100,77 100,32 106,98 99, ,60 359,55 448,28 601,94 92,45 89,54 93,36 90, ,06 345,09 419,44 565,27 77,02 88,38 80,06 83,47 Pinus radiata GROSS CARBON (tm/ha) NET CARBON (tm/ha) Rotation 100 yars 120 yars 150 yars 200 yars 100 yars 120 yars 150 yars 200 yars ,99 388,71 493,74 647,85 94,73 107,26 120,32 110, ,56 386,92 505,55 662,76 111,41 95,75 110,99 102, ,16 397,00 498,74 692,12 115,61 92,00 94,90 117, ,63 409,72 510,36 697,27 100,56 96,05 96,03 105, ,34 415,06 517,45 681,24 87,77 101,39 96,85 85, ,33 418,76 522,96 680,52 76,75 101,85 100,36 82, ,59 420,14 525,17 686,06 68,98 88,95 89,08 78, ,15 390,44 492,66 674,77 74,41 74,05 74,12 83, ,16 381,75 489,25 652,33 75,30 72,11 78,38 78,73

7 Díaz-Baltiro Romro 109 Tabl 2 Profitability taking into account a subsidy pr ton of carbon capturd of 25 /ton, in two afforstation programs: Populus sp. and Pinus radiata. (Rntabilidad considrando-s um subsídio d 25?/ton d carbono sqüstrado, m dois programas: Populus sp. Pinus radiata) Populus sp. NPV without afforstation grants [ /ha] NPV with afforstation grants [ /ha] Rotation NPV, no C NPV + gross C NPV + nt C NPV, no C NPV + gross C NPV + nt C Pinus radiata NPV without afforstation grants [ /ha] NPV with afforstation grants [ /ha] Rotation NPV, no C NPV + gross C NPV + nt C NPV, no C NPV + gross C NPV + nt C As it was commntd abov, to circumvnt th diffrnc btwn th privat and th nvironmntal optimum a subsidy ranging btwn 20 and 220 pr ton of carbon capturd has bn usd. It is assumd that th forst ownr maximiss th sals rvnu of th joint production using th sam discount rat. Th rsults obtaind clarly show how th figur of forst rotation obtaind is th sam whn gross or nt carbon is considrd. Th subsidis do not incras th captur of carbon but incrass considrabl th privat profitability. In fact, th NPV incras in a 27% if th gross carbon is considrd with a subsidy of 200 /ton. It is intrsting to not that th rsults obtaind ar rathr inlastic to changs in th discount rat. This inlasticity is rmarkabl whn subsidis ar considrd. Thus, for discount rats changing btwn 4-8%, th rotation ag dos not vary. Whn th discount rat achivs th 9%, th rotation ag rducs to 13 yars, incrasing th gap with rspct to th nvironmntal optimum. For this discount rat, th considration of subsidis incrass th rotation ag up to 15 yars, Morovr, for a discount rat of 10% both rotation ags (with and without subsidis) coincids in 13 yars.

8 110 Captura d carbono m florstas For Pinus radiata plantations and within a scnario without subsidis this typ of plantation is not financially viabl. In fact, for an optimum forst rotation of 30 yars a NPV of -881 /ha is obtaind (s Tabl 2). Th considration of subsidis dos not influnc in th rotation ag but allows th achivmnt of a positiv NPV of 2,965 /ha. For this privat optimum a captur of gross carbon of ton/ha is obtaind. In this cas, it is important to not th importanc of th sals rvnu providd by th thinning oprations. This typ of rvnu rprsnts th 16% of th NPV whn th subsidis ar considrd. For th sit indx considrd and taking into account th growth curv prviously introducd, th rotation ag providing th maximum sustainabl yild achivs th figur of 33 yars. To nlarg th rotation up to this ag implis, ctris paribus, to rduc th NPV in a 15% without subsidis and around 5% in a contxt of subsidis. This rotation ag corrsponds to th nvironmntal optimum, providing a gross carbon capturd of ton /ha. In trms of nt carbon, if th priod of tim considrd is long (200 yars), thn th figur obtaind is rathr similar with rspct to th poplar plantations. If w try to mitigat th divrgnc btwn both optima through an incras in th subsidy th rotation ag dos not chang. Th incras in th subsidy onc a crtain thrshold is surpassd can mak th invstmnt profitabl considring only th gross carbon and without th Europan financial aids. Thus, a subsidy of 90 /ton C implis that th NPV rfrrd to th gross carbon rachs th figur of 24 /ha. It is intrsting to not that ths rsults ar robust to changs in th discount rat. Prmannt stands Lt us start obtaining th pay-off matrix. This is a squar matrix with dimnsion qual to th numbr of goals considrd (fiv in our application). Th diffrnt rows of th matrix show th rsults obtaind whn ach goal is optimisd sparatly. S Tabl 3 for th rsults of our particular cas. Th main intrst of this tabl consists in th information providd about th dgr of conflict btwn th diffrnt goals considrd. Thus, from Tabl 3 is asy to dduc that thr is an important dgr of conflict btwn th captur of carbon and th othr goals considrd. In fact, th captur of carbon is clarly lss (it rducs narly to on third) whn th vn-flow goal holds. Similar rsults ar obtaind whn th forst rgulation goal holds or whn th goal rlatd to th final forst invntory is mt. On th contrary, th solution providing th maximum captur of carbon (s last column of Tabl 2) implis th worst rsults with rspct to th othr goals. Finally, in ordr to incras th informativ charactr of this matrix two additional rows hav bn addd to inform about th total harvst volum and th avrag rotation that corrsponds to ach goal. Th diffrnt solutions providd by th payoff matrix do not sm nough attractiv from a managrial point of viw. For this rason, th Lxicographic Goal Programming modls outlind abov hav bn applid in ordr to obtain satisficing or bst-compromis solutions. It is intrsting to not that a snsitivity analysis with th prfrntial wights has bn implmntd. Th diffrnt rsults obtaind ar shown in Tabl 4. Th main information drivd from Tabl 4 can b summarisd as follows. Th goals placd in th first two priority lvls ar fully achivd in all th scnarios considrd. In othr words, in all th solutions obtaind th goals rlatd to th forst rgulation and th final invntory compltly achivd th aspiration lvls stablishd. On th contrary, for th goals placd in th third priority lvl thr ar dviations with rspct to th corrsponding aspiration lvls.

9 Díaz-Baltiro Romro 111 Tabl 3 Pay-off matrix for th fiv critria considrd (Matriz d pagamntos dos cinco critérios considrados) Nt Prsnt Volum Ara Ending Carbon Valu [NPV] Control Control Forst Invntory Balanc nnpv nih+pih nif+pif nki+pki ncb NPV (*10 6 ) 35,08 26,98 25,02 28,22 25,36 nnpv 0 8,10 10,06 6,86 9,72 nih+pih nif+pif nki+pki Carbon Balanc (Tm) ncb Volum (m 3 ) Avrag Rotation nnpv ngativ dviation variabl for th nt prsnt valu critrion (*10 6 ) nih+pih: ngativ and positiv dviation variabls for th volum control goal (m 3 ) nif+pif: ngativ and positiv dviation variabls for th ara control goal (ha) nki+pki: ngativ and positiv dviation variabls for th nding forst invntory goal (m 3 ) Carbon Balanc: nt carbon along th planning horizon (ton C) ncb: ngativ dviation for th carbon balanc critrion (ton C) Volum: Total volum along th planning horizon (m 3 ) Tabl 4 Rsults of th GP modls (bst-compromis or satisficing schduls) (Rsultados dos modlos d programação por mtas (mlhor compromisso ou satisfação d programas)) w1=w2=w3=1 w2=w3=1; w1=2 w1=w3=1; w2=2; w1=w2=1; w3=2; wightd minmax wightd minmax wightd minmax wightd minmax NPV (*10 6 ) 31,11 28,93 31,20 31,57 31,05 28,85 31,00 25,99 nih+pih (m3) nif+pif (ha) nki+pki (m3) Carbon Balanc (Tm) Volum (m 3 ) Avrag rotation w1: valu of th prfrntial wight assignd to th first propority lvl w2: valu of th prfrntial wight assignd to th scond propority lvl w3: valu of th prfrntial wight assignd to th third propority lvl wightd: Lxicographic wightd goal programming modl minmax: Lxicographic minmax goal programming modl It is important to not that whil th diffrncs in trms of carbon capturd ar important, howvr th diffrncs in trms of NPV, total volum or avrag rotation ar not significant. In short, it sms that som of th goals usually introducd in forst managmnt ar inlastic to changs in th valu of th wights or vn to th typ of mthod usd. Finally, it should b notd that th solutions prsntd ar robust to changs in th valus of th prfrntial wights as it is shown in Tabl 4.

10 112 Captura d carbono m florstas DISCUSSION Th mthodologis usd in this papr show a grat potntiality in forst managmnt whn th classic scop is incrasd with th considration of additional goals lik th captur of carbon. This conclusion is valid for a plantation cas as wll as for an stablishd stand. Lt us now compar th rsults obtaind in th two cass studid. Thus, th carbon capturd dos not dpnd of th spci usd, if th tmporal horizon is larg. As Harmon (2001) stats, th scal considrd has a strong influnc whn th carbon capturd by diffrnt stands is compard. Nvrthlss, du to th diffrnt timbr dnsitis gross carbon is slightly largr for Pinus radiata. That is, th poplar although has a shortr cycl with rspct to th pin, prsnts a lowr carbon balanc bcaus of th dnsity of both typ of woods (0.30 kg/ m 3 for poplar and kg/m 3 for pin). This fact should b takn into account in ordr to choos th right spci whn th maximisation of th captur of carbon is a primary goal. Whn th planning horizon is largr than 100 yars th nt carbon in both spcis is rathr constant, although slightly suprior in th cas of th poplar. This rsult is du to th fact that th numbr of conscutiv harvsts for th pin is not still nough to achiv a balanc with rspct to th carbon. On th othr hand, thinning oprations imply an incras in th nt carbon sinc thy ar ssntial in ordr to obtain logs with a longr lif final us. Howvr, this fact is compnsatd for th largr amount of carbon mittd in th short run. Thus, in ordr to maximis th carbon capturd by this typ of plantations thinning oprations should b avoidd (Batman and Lovtt, 2000). Howvr, it is rathr obvious that this typ of policy is not viabl from a privat point of viw. In fact, this typ of policy would lad to an incras in th figur of gross carbon as wll as an nlargmnt of th rotation ag but with a vry bad conomic prformanc. In th last sctions it has bn provd that th Europan subsidis for afforstation programs as wll as th implmntation of subsidis pr ton of carbon capturd ar not fficint policis in ordr to approximat th privat and th nvironmntal optima. A possibl solution for this problm will consist in stablishing mor spcific aids by supplmnting, for xampl, th timbr pric. That is, to ncourag th nlargmnt of th rotation ag by subsidising th timbr pric. Without ntring in a dp discussion about how to implmnt this policy, th two cass studid clarly show how du to th proximity btwn both optima th ncssary amount of mony to support this typ of policy will not b too larg. Thus, in th cas of afforstation with Pinus radiata and in a contxt with subsidis it would b ncssary a pric subsidy around 3 /m 3. Altrnativly, it is intrsting to not that most profitabl plantations (.g., poplar) prsnt an nvironmntal optimum slightly inlastic to incrass in th figur of subsidis. Dspit th proximity btwn both optima in th cass analysd, if th rotation ag incrass, th divrgnc btwn thm also incrass. Thus, in Romro t al. (1998) can b vrifid how in an afforstation cas with Fagus sylvatica considring th carbon capturd th rotation ag corrsponding to th privat optimum is around 50 yars, whil th nvironmntal optimum is achivd at 150 yars. In th cas of prmannt stands whn th carbon capturd is considrd, th managmnt guidlins ar vry diffrnt with rspct th traditional ons. Thus, traditionally th primary objctiv in forst managmnt has consistd in th maximisation of th timbr volum looking

11 Díaz-Baltiro Romro 113 for an vn-flow policy and a rgulatd forst (i.., th hypothsis of "normal forst"). Howvr, th rsults shown in th pay-off matrix clarly show how th maximisation of th carbon capturd is incompatibl with ths traditional objctivs. Finally, is important to not that th two Lxicographic Goal Programming modls provid similar solutions, which rprsnt attractiv lins of action from a managrial point of viw. CONCLUSIONS Th Goal Programming modls usd in this papr hav rvald as a powrful approach to intgrat th carbon capturd in conjunction with othr critria in forst managmnt problms. It is important to not that if w account only th carbon stord in th logs, thr is a grat disparity btwn gross and nt carbon. Morovr, th amount of carbon capturd is strongly influncd by factors lik th timbr dnsity, th silvicultural systms, or th planning horizon chosn. In th two cass studid in trms of rotation ag, NPV and vn gross carbon thr ar not significant diffrncs for th privat and nvironmntal optima. Howvr, if w account th nt carbon th diffrncs ar rlvant for th two spcis. Th currnt Europan subsidis as wll as th introduction of a subsidy pr ton of carbon capturd dos not guarant a largr gross or nt captur. Th only ffct of this typ of policy is to incras th profitability of th forst ownr. Ths rsults sm to suggst th ncssity to dsign diffrnt public policis in ordr to intrnalis this typ of positiv xtrnality. Morovr, it has bn dmonstratd how th maximisation of th carbon capturd clarly conflicts with th traditional objctivs that lad to th ida of "normal forst". Evn though, this important rsult drivs from a singl cas, it sms intrsting bcaus opn th doors to th us of th modrn tchniqus of optimisation in forst managmnt. Finally, th modls introducd provid solutions that can b implmntd by th forst managr. Thus, th bst-compromis or satisficing solutions gnratd by th lxicographic GP modls sm attractiv. This is spcially tru whn th solutions shown in Tabl 4 ar compard with th singl optimisation solutions containd in th pay-off matrix shown in Tabl 3. For instanc, if w compar th solution that maximiss th nt prsnt valu (column 1 of Tabl 3) with th lxicographic wightd GP solution for qual wights (column 1 of Tabl 4), th lattr solution prsnt important advantags in trms of th thr forstry goals considrd. Thus, th opportunity costs for ths improvmnts ntail a rduction of around 11% of nt prsnt valu and an incras of around 24% in th total carbon balanc. Morovr, th timbr volum harvstd and forst rotation ags for th ight solutions obtaind ar rathr similar. In short, solutions prsntd in Tabl 4 sm quit accptabl from a managrial point of viw. AUTHOR AND ACKNOWLEDGEMENTS LUIS DÍAZ-BALTEIRO é Psquisador na E.T.S. Ingnirías Agrarias - Avda. Madrid, Palncia - Espanha - baltiro@iaf.uva.s CARLOS ROMERO é Psquisador na E.T.S. Ingniros d Monts - Ciudad Univrsitaria s/n Madrid - Espanha - auggigp@monts.upm.s Thanks ar givn to Luis García (Tchnical Univrsity of Madrid) for th calculations of carbon contnt in som sampls of Pinus sylvstris. Th information providd by Antonio Prito and Santiago Vignot (Tchnical Univrsity

12 114 Captura d carbono m florstas of Madrid) and by Luis Acuña (Univrsity of Valladolid) is highly apprciatd. This rsarch was undrtakn with th support of th Spanish "Comisión Intrministrial d Cincia y Tcnología (CICYT)" of "Fundación BBVA". REFERENCES BATEMAN, I.J.; LOVETT, A.A. Estimating and valuing th carbon squstrd in softwood and hardwood trs, timbr products and forst soils in Wals. Journal of nvironmntal managmnt, v.60, p , DÍAZ-BALTEIRO, L.; ROMERO, C. Forst managmnt optimisation modls whn carbon capturd is considrd: a goal programming approach. Forst cology and managmnt, v.174, p , DÍAZ-BALTEIRO, L.; ROMERO, C. Rntabilidad conómica d spcis arbóras d crciminto mdio y lnto: algunas rflxions d política forstal. Rvista spañola d conomía agraria, v.171, p , FAUSTMANN, M. Brchung ds wrts wlchn waldbodn sowi noch nicht haubar holzbständ für di waldwirtschaft bsitzn. Allgmin forst und jagd zitung, n.15, (Also includd in: FAUSTMANN, M. Calculation of th valu which forst land and immatur stands possss for forstry. Journal of forst conomics, v.1, p.7-44, HARMON, M.E. Carbon squstration in forsts: addrssing th scal qustion. Journal of forstry, v.99, n.4, p.24-29, HARTMAN, R. Th harvsting dcision whn a standing forst has valu. Economic inquiry, v.16, p.52-58,1976. HERRUZO, A.C. La forstación d tirras agrarias y l dsarrollo rural n la unión uropa: una visión dsd España. Séri técnica IPEF, n.34, p , HOEN, H.F.; SOLBERG, B. Potntial and conomic fficincy of carbon squstration in forst biomass through silvicultural managmnt. Forst scinc, v.40, p , IGNIZIO, J.P.; CAVALIER, I. Linar programming. Nw Jrsy: Prntic Hall,1994. MUTKE REGNERI, S.; DÍAZ BALTEIRO, L.; GORDO ALONSO, J. Análisis comparativo d la rntabilidad comrcial privada d plantacions d Pinus pina L. n tirras agrarias d la provincia d Valladolid. Invstigacions agrarias: sri rcursos y sistmas forstals, v.9, n.2, p , NABUURS, G.J.; MOHREN, F.; DOLMAN, H. Monitoring and rporting carbon stocks and fluxs in Dutch forsts. Biotchnol. Agron. Soc. Environ., v.4, p , RODRÍGUEZ, L.C.E.; BUENO, A.R.B; RODRÍGUEZ, F. Rotaçôs d ucaliptos mais longas: anális volumétrica conômica. Scintia forstalis, v.51, p.15-28, ROMERO, C. Handbook of critical issus in goal programming. Oxford: Prgamon Prss,1991. ROMERO, C.; RÍOS, V.; DÍAZ-BALTEIRO, L. Optimal forst rotation ag whn carbon capturd is considrd: thory and applications. Journal of th oprational rsarch socity, v.49, p , ROW, C.; PHELPS, R.B. Wood carbon flows and storag aftr timbr harvst. In: SAMPSON, R.N.; HAIR, D., d. Forsts and global chang. Washington: Amrican Forsts Socity, v.2, p VAN KOOTEN, G.C.; BINKLEY, C.S.; DELCOURT, G. Effct of carbon taxs and subsidis on optimal forst rotation ag and supply of carbon srvics. Amrican journal of agricultural conomics, v.77, p , HOEN, H.F. Th Faustmann rotation in th prsnc of a positiv CO 2 -pric. In: LINDAHL, M.; HELLES, F., d. Procdings of th Binnial Mting of th Scandinavian Socity of Forst Economics. Gilllj, p