THE CLIMATE FRAMEWORK FOR UNCERTAINTY, NEGOTIATION AND DISTRIBUTION (FUND), TECHNICAL DESCRIPTION, VERSION 3.9

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1 THE CLIMATE FRAMEWORK FOR UNCERTAINTY, NEGOTIATION AND DISTRIBUTION (FUND), TECHNICAL DESCRIPTION, VERSION 3.9 David Anthoff a and Richad S.J. Tol b,c,d a Enegy and Resouces Goup, Univesity of Califonia at Bekeley, USA b Depatment of Economics, Sussex Univesity, United Kingdom c Institute fo Envionmental Studies, Vije Univesiteit, Amstedam, The Nethelands d Depatment of Spatial Economics, Vije Univesiteit, Amstedam, The Nethelands Septembe 16, Resolution FUND 3.9 is defined fo 16 egions, specified in Table R. The model uns fom 1950 to 3000 in time-steps of a yea. 2. Population and income Population and pe capita income follow exogenous scenaios. Thee ae five standad scenaios, specified in Tables P and Y. The FUND scenaio is based on the EMF14 Standadised Scenaio, and lies some in between the IS92a and IS92f scenaios (Leggett et al., 1992). The othe scenaios follow the SRES A1B, A2, B1 and B2 scenaios (Nakicenovic and Swat, 2001), as implemented in the IMAGE model (IMAGE Team, 2001). We assume that all egions ae in a steady state afte the yea Fo the yeas pe capita income gowth ates ae constant and equal to the values of the yea 2300, while population does not change. 3. Emission, abatement and costs 3.1. Cabon dioxide (CO2) Cabon dioxide emissions ae calculated on the basis of the Kaya identity: (CO2.1) M E Y M P : Y t, t, t, t, t, t, t, t, Et, Yt, Pt, M denotes emissions, E denote enegy use, Y denotes GDP and P denotes population; t is the index fo time, fo egion. The cabon intensity of enegy use, and the enegy intensity of poduction follow fom: (CO2.2) and (CO2.3) Ψ t, = g Ψ t 1, Ψ t 1, α t 1, τ t 1, φ φ t, = g t 1, φ t 1, α t 1, τ t 1, τ is policy intevention and α is a paamete. The exogenous gowth ates g ae efeed to as the Autonomous Enegy Efficiency Impovement (AEEI) and the Autonomous 1

2 Cabon Efficiency Impovement (ACEI). See Tables AEEI and ACEI fo the five altenative scenaios (values fo the yeas again equal the values fo the yea 2300). Policy also affects emissions via (CO2.1 ) M t, t, t, t, t, t, (1 ) (CO2.4) t, t1, t1, t1, and (1 ) (CO2.5) t, t1, t1, t1, Y Thus, the vaiable 0<α <1 govens which pat of emission eduction is pemanent (educing cabon and enegy intensities at all futue times) and which pat of emission eduction is tempoay (educing cuent enegy consumptions and cabon emissions), fading at a ate of 0<κ<1. In the base case, κψ=κφ=0.9 and (CO2.6) t, t, t, So that α=0.5 if τ=$100/tc. One may intepet the diffeence between pemanent and tempoay emission eduction as affecting commecial technologies and capital stocks, espectively. The emission eduction module is a educed fom way of modelling that pat of the emission eduction fades away afte the policy intevention is evesed, but that anothe pat emains though technological lock-in. Leaning effects ae descibed below. The paametes of the model ae chosen so that FUND oughly esembles the behaviou of othe models, paticulaly those of the Enegy Modeling Foum (Weyant, 2004; Weyant et al., 2006). The costs of emission eduction C ae given by (CO2.7) C 2 t, t, t, g t, t, t Y H H H denotes the stock of knowledge. Equation (CO2.6) gives the costs of emission eduction in a paticula yea fo emission eduction in that yea. In combination with Equations (CO2.2)- (CO2.5), emission eduction is cheape if smeaed out ove a longe time peiod. The paamete β follows fom (CO2.8) M M t, min Y Y t, t, s s t, t, s That is, emission eduction is elatively expensive fo the egion that has the lowest emission intensity. The calibation is such that a 10% emission eduction cut in 2003 would cost 1.57% (1.38%) of GDP of the least (most) cabon-intensive egion; this is calibated to Houcade et al. (1996, 2001). An 80% (85%) emission eduction would completely uin the economy. Late emission eductions ae cheape by Equations (CO2.7) and (CO2.8). Emission eduction is elatively cheap fo egions with high emission intensities. The thought is that emission eduction is cheap in counties that use a lot of enegy and ely heavily on fossil fuels, while othe counties use less enegy and less fossil fuels and ae theefoe close to the technological fontie of emission abatement. Fo elatively small emission eduction, the costs in FUND coespond closely to those epoted by othe top-down models, but fo highe emission eduction, FUND finds highe costs, because FUND does not include backstop 2

3 technologies, that is, a cabon-fee enegy supply that is available in unlimited quantities at fixed aveage costs. The egional and global knowledge stocks follow fom (CO2.9) H, H 1, 1 1, and t t R t G G (CO2.10) H H 1 1, t t G t Knowledge accumulates with emission abatement. Moe knowledge implies lowe emission eduction costs. The paametes γ detemine which pat of the knowledge is kept within the egion, and which pat spills ove to othe egions as well. In the base case, γr=0.9 and γg=0.1. The model is simila in stuctue and numbes to that of Goulde and Schneide (1999) and Goulde and Mathai (2000). Emissions fom land use change and defoestation ae exogenous, and cannot be mitigated. Numbes ae found in Tables CO2F, again fo five altenative scenaios Methane (CH4) Methane emissions ae exogenous, specified in Table CH4 (emissions fo the yeas ae equal to emissions in the yea 2300). Thee is a single scenaio only, based on IS92a (Leggett et al., 1992). The costs of emission eduction ae quadatic. Table OC specifies the paametes, which ae calibated to USEPA (2003) Nitous oxide (N2O) Nitous oxide emissions ae exogenous, specified in Table N2O (emissions fo the yeas ae equal to emissions in the yea 2300). Thee is a single scenaio only, based on IS92a (Leggett et al., 1992). The costs of emission eduction ae quadatic. Table OC specifies the paametes, which ae calibated to USEPA (2003) Sulfuhexafluoide (SF6) SF6 emissions ae linea in GDP and GDP pe capita. Table SF6 gives the paametes. The numbes fo 1990 and 1995 ae estimated fom IEA data ( Thee is no option to educe SF6 emissions Dynamic Biosphee Emissions fom the teestial biosphee follow B (DB.1) E T T t t 2010 Bt B with B (DB.2) Bt Bt 1 Et 1 3 max

4 E B ae emissions (in million metic tonnes of cabon); T is the global mean tempeatue (in degee Celsius); Bt is the emaining stock of potential emissions (in million metic tonnes of cabon, GtC; Bmax is the total stock of potential emissions; Bmax = 1,900 GtC; β is a paamete; β = 2.6 GtC/ºC (with a gamma distibution with shape=4.9 and scale=662.8). The model is calibated to the eview of (Denman et al. 2007). Emissions fom the teestial biosphee befoe the yea 2010 ae zeo. 4. Atmosphee and climate 4.1. Concentations Methane, nitous oxide and sulphu hexafluoide ae taken up in the atmosphee, and then geometically depleted: (C.1) C t = C t-1+ E t - Ct-1 -C pe C denotes concentation, E emissions, t yea, and pe pe-industial. Table C displays the paametes α and β fo all gases. Paametes ae taken fom Foste et al. (2007). The atmospheic concentation of cabon dioxide follows fom a five-box model: (C.2a) Box i,t = iboxi, t i Et with (C.2b) C = t 5 i Box i=1 i,t i denotes the faction of emissions E (in million metic tonnes of cabon) that is allocated to Box i (0.13, 0.20, 0.32, 0.25 and 0.10, espectively) and the decay-ate of the boxes ( = exp(-1/lifetime), with life-times infinity, 363, 74, 17 and 2 yeas, espectively). The model is due to Maie-Reime and Hasselmann (1987), its paametes ae due to Hammitt et al. (1992). Thus, 13% of total emissions emains foeve in the atmosphee, while 10% is on aveage emoved in two yeas. Cabon dioxide concentations ae measued in pats pe million by volume Radiative focing Radiative focing is specified as follows: (C.3) RF t = 5.35 ln CO2 t ( CH4 t 790) ( N2O t 285) 0.47 ln( CH4 t CH4 t ) 0.47 ln( N2O t N2O t 1.52 ) ln( ) (SF6 t 0.04) + fso2 t Paametes ae taken fom Ramaswamy et al. (2001) and Foste et al. (2007) fo the indiect effect of methane on topospheic ozone. Radiative focing fom SO2 at time t (fso2 t ) is 4

5 exogenous; the FUND scenaio uses the focing fom RCP85 and the SRES scenaios use the focing as intepeted by IMAGE Tempeatue and sea level ise The global mean tempeatue T is govened by a geometic build-up to its equilibium (detemined by adiative focing RF). In the base case, global mean tempeatue T ises in equilibium by 3.0 C fo a doubling of cabon dioxide equivalents, so: (C.4) T t = (1 1 φ ) T t CS φ 5.35 ln 2 RF t CS is climate sensitivity, set to 3.0 (with a gamma distibution with shape=6.48 and scale=0.55). φ is the e-folding time and set to (C.5) φ = max(α + β l CS + β q CS 2, 1) α is set to -42.7, β l is set to 29.1 and β q is set to 0.001, such that the best guess e- folding time fo a climate sensitvitiy of 3.0 is 44 yeas. Regional tempeatue is deived by multiplying the global mean tempeatue by a fixed facto (see Table RT) which coesponds to the spatial climate change patten aveaged ove 14 GCMs (Mendelsohn et al. 2000). Global mean sea level is also geometic, with its equilibium level detemined by the tempeatue and a life-time of 500 yeas: (C.6) S t = (1 1 ρ ) S t 1 + γ 1 ρ T t ρ = 500 (with a tiangula distibution bounded by 250 and 1000) is the e-folding time. γ = 2 (with a gamma distibution with shape=6 and scale=0.4) is sea-level sensitivity to tempeatue. Tempeatue and sea level ae calibated to the best guess tempeatue and sea level fo the IS92a scenaio of Kattenbeg et al. (1996). 5. Impacts 5.1. Agicultue The impacts of climate change on agicultue at time t in egion ae split into thee pats: impacts due to the ate of climate change A t, ; impacts due to the level of climate change A t, and impacts fom cabon dioxide fetilisation A f t, : (A.1) A t, = A t, l + A t, f + A t, The fist pat (ate) is always negative: As fames have impefect foesight and ae locked into poduction pactices, climate change implies that fames ae maladapted. Faste climate change means geate damages. The thid pat (fetilization) is always positive. CO2 fetilization means that plants gow faste and use less wate. The second pat (level) can be positive o negative. Thee is an optimal climate fo agicultue. If climate change moves a egion close to (away fom) the optimum, impacts ae positive (negative); and impacts ae smalle neae to the optimum. l ; 5

6 Fo the impact of the ate of climate change (i.e., the annual change of climate) on agicultue, the assumed model is: (A.2) A t, = α ( ΔT β t 0.04 ) + (1 1 ρ ) A t 1, A denotes damage in agicultual poduction as a faction due the ate of climate change by time and egion; denotes egion; ΔT denotes the change in the egional mean tempeatue (in degees Celsius) between time t and t 1; α is a paamete, denoting the egional change in agicultual poduction fo an annual waming of 0.04 C (see Table A, column 2-3); β = 2.0 ( ) is a paamete, equal fo all egions, denoting the non-lineaity of the eaction to tempeatue; β is an expet guess; ρ = 10 (5-15) is a paamete, equal fo all egions, denoting the speed of adaptation; ρ is an expet guess. The model fo the impact due to the level of climate change since 1990 is: (A.3) l A t, = δ l T t + δ q 2 T t A l denotes the damage in agicultual poduction as a faction due to the level of climate change by time and egion; denotes egion; T denotes the change (in degee Celsius) in egional mean tempeatue elative to 1990; δ l and δ q ae paametes (see Table A), that follow fom the egional change (in pe cent) in agicultual poduction fo a waming of 2.5 C above today o 3.2 C above pe-industial and the the optimal tempeatue (in degee Celsius) fo agicultue in each egion. CO2 fetilisation has a positive, but satuating effect on agicultue, specified by (A.4) A f t, = γ ln CO2 t 275 A f denotes damage in agicultual poduction as a faction due to the CO2 fetilisation by time and egion; denotes egion; 6

7 CO2 denotes the atmospheic concentation of cabon dioxide (in pats pe million by volume); 275 ppm is the pe-industial concentation; γ is a paamete (see Table A, column 8-9). The paametes in Table A ae calibated, following the pocedue descibed in Tol (2002a), to the esults of Kane et al. (1992), Reilly et al. (1994), Moita et al. (1994), Fische et al. (1996), and Tsigas et al. (1996). These studies all use a global computable geneal equilibium model, and epot esults with and without adaptation, and with and without CO2 fetilisation. The egional esults fom these studies ae assumed to hold fo each county in the espective egions. They ae aveaged ove the studies and the climate scenaios fo each county, and aggegated to the FUND egions. The standad deviations in Table A follow fom the spead between studies and scenaios. Equation (A.4) follows fom the diffeence in esults with and without CO2 fetilization. Equation (A.3) follows fom the esults with full adaptation. Equation (A.2) follows fom the diffeence in esults with and without adaptation. Equations (A.1-4) expess the impact of climate change as a pecentage of agicultual poduction. In ode to expess this as a pecentage of income, we need to know the shae of agicultual poduction in total income. This is assumed to fall with pe capita income, that is, (A.5) GAP t, Y t, = GAP 1990, Y 1990, ( y ε 1990, ) y t, GAP denotes goss agicultual poduct (in 1995 US dolla pe yea) by time and egion; Y denotes goss domestic poduct (in 1995 US dolla pe yea) by time and egion; y denotes goss domestic poduct pe capita (in 1995 US dolla pe peson pe yea) by time and egion; denotes egion; ε = 0.31 ( ) is a paamete; it is the income elasticity of the shae of agicultue in the economy; it is taken fom Tol (2002b), who egessed the egional shae in agicultue on pe capita income, using 1995 data fom the Wold Resouces Institute ( Foesty The model is: (F.1) F t, y t, Tt CO2, t ln y 1990, F denotes the change in foesty consume and poduce suplus (as a shae of total income); 7

8 denotes egion; y denotes pe capita income (in 1995 US dolla pe peson pe yea); T denotes the global mean tempeatue (in degee centigade); is a paamete, that measues the impact of climate change of a 1ºC global waming on economic welfae; see Table EFW; = 0.31 ( ) is a paamete, and equals the income elasticity fo agicultue; = 1 ( ) is a paamete; this is an expet guess; γ = 0.44 ( ) is a paamete; γ is such that a doubling of the atmospheic concentation of cabon dioxide would lead to a change of foest value of 15% (10-30%); this paamete is taken fom Gitay et al., (2001). The paamete α is estimated as the aveage of the estimates by Peez-Gacia et al. (1995) and Sohngen et al. (2001). Peez-Gacia et al. (1995) pesent esults fo fou diffeent climate scenaios and two management scenaios, while Sohngen et al. (2001) use two diffeent climate scenaio and two altenative ecological scenaios. The esults ae mapped to the FUND egions assuming that the impact is unifom elative to GDP. The impact is aveaged within the study esults, and then the weighted aveage between the two studies is computed and shown in Table EFW. The standad deviation follows Wate esouces The impact of climate change on wate esouces follows: (W.1) W t 2000 y t, P t, T Y t t, t, min Y1990, (1 ), y 1990, P 1990, W denotes the change in wate esouces (in 1995 US dolla) at time t in egion ; denotes egion; y denotes pe capita income (in 1995 US dolla) at time t in egion ; P denotes population at time t in egion ; T denotes the global mean tempeatue above pe-industial (in degee Celsius) at time t; is a paamete (in pecent of 1990 GDP pe degee Celsius) that specifies the benchmak impact; see Table EFW; = 0.85 (0.15, >0) is a paamete, that specifies how impacts espond to economic gowth; η = 0.85 (0.15,>0) is a paamete that specifies how impacts espond to population gowth; = 1 (0.5,>0) is a paamete, that detemines the esponse of impact to waming; 8

9 τ = (0.005, >0) is a paamete, that measues technological pogess in wate supply and demand. These paametes ae fom calibating FUND to the esults of Downing et al. (1995, 1996) Enegy consumption Fo space heating, the model is: (E.1) atan T t SH t, = α Y 1990, atan 1.0 ( y ε t, ) ( P t, ) y 1990, P 1990, 9 t AEEI s, s=1990 SH denotes the decease in expenditue on space heating (in 1995 US dolla) at time t in egion ; denotes egion; Y denotes income (in 1995 US dolla) at time t in egion ; T denotes the change in the global mean tempeatue elative to 1990 (in degee Celsius) at time t; y denotes pe capita income (in 1995 US dolla pe peson pe yea) at time t in egion ; P denotes population size at time t in egion ; α is a paamete (in dolla pe degee Celsius), that specifies the benchmak impact; see Table EFW, column 6-7 ε is a paamete; it is the income elasticity of space heating demand; ε = 0.8 (0.1,>0,<1); AEEI is a paamete (cf. Tables AEEI and Equation CO2.3); it is the Autonomous Enegy Efficiency Impovement, measuing technological pogess in enegy povision; the global aveage value is about 1% pe yea in 1990, conveging to 0.2% in 2200; its standad deviation is set at a quate of the mean. These paametes ae fom calibating FUND to the esults of Downing et al. (1995, 1996). Savings on space heating ae assumed to satuate. The income elasticity of heating demand is taken fom Hodgson and Mille (1995, cited in Downing et al., 1996), and estimated fo the UK. Space heating demand is linea in the numbe of people fo want of scenaios of numbe of households and house sizes. Enegy efficiency impovements in space heating ae assumed to be equal to the aveage enegy efficiency impovements in the economy. Fo space cooling, the model is: (E.2) SC t, = α Y 1990, ( T β t 1.0 ) ( y ε t, ) ( P t, ) y 1990, P 1990, t AEEI s, s=1990 SC denotes the incease in expenditue on space cooling (1995 US dolla) at time t in egion ;

10 denotes egion; Y denotes income (in 1995 US dolla) at time t in egion ; T denotes the change in the global mean tempeatue elative to 1990 (in degee Celsius) at time t; y denotes pe capita income (in 1995 US dolla pe peson pe yea) at time t in egion ; P denotes population size at time t in egion ; α is a paamete (see Table EFW, column 8-9); β is a paamete; β = 1.5 ( ); ε is a paamete; it is the income elasticity of space heating demand; ε = 0.8 ( ); AEEI is a paamete (cf. Tables AEEI and Equation CO2.3) ; it is the Autonomous Enegy Efficiency Impovement, measuing technological pogess in enegy povision; the global aveage value is about 1% pe yea in 1990, conveging to 0.2% in 2200; its standad deviation is set at a quate of the mean. These paametes ae fom calibating FUND to the esults of Downing et al. (1995, 1996). Space cooling is assumed to be moe than linea in tempeatue because cooling demand acceleates as it gets wame. The income elasticity of cooling demand is taken fom Hodgson and Mille (1995, cited in Downing et al., 1996), and estimated fo the UK. Space cooling demand is linea in the numbe of people fo want of scenaios of numbe of households and house sizes. Enegy efficiency impovements in space cooling ae assumed to be equal to the aveage enegy efficiency impovements in the economy Sea level ise Table SLR shows the accumulated loss of dylands and wetlands fo a one mete ise in sea level. The data ae taken fom Hoozemans et al. (1993), supplemented by data fom Bijlsma et al. (1995), Leatheman and Nicholls (1995) and Nicholls and Leatheman (1995), following the pocedues of Tol (2002a). Potential cumulative dyland loss without potection is assumed to be a function of sea level ise: (SLR.1) γ CD t, = min[δ S t, ζ ] CD t, is the potential cumulative dyland lost at time t in egion that would occu without potection; denotes egion; δ is the dyland loss due to one mete sea level ise (in squae kilomete pe mete) in egion ; S t is sea level ise above pe-industial levels at time t; note that is assumed to equal fo all egions; 10

11 γ is a paamete, calibated to a digital elevation model; ζ is the maximum dyland loss in egion, which is equal to the aea in the yea Potential dyland loss in the cuent yea without potection is given by potential cumulative dyland loss without potection minus actual cumulative dyland lost in pevious yeas: (SLR.2) D t, = CD t, CD t 1, D t, is potential dyland loss in yea t and egion without potection; CD t, is the potential cumulative dyland lost at time t in egion that would occu without potection; CD t, is the actual cumulative dyland lost at time t in egion. Actual dyland loss in the cuent yea depends on the level of potection: (SLR.3) D t, = (1 P t, )D t, D t, is dyland loss in yea t and egion ; P t, is the faction of the coastline potected in yea t and egion ; D t, is potential dyland loss in yea t and egion without potection. Actual cumulative dyland loss is given by: (SLR.4) CD t, = CD t 1, + D t, CD t, is the actual cumulative dyland lost at time t in egion ; D t, is dyland loss in yea t and egion. The value of dyland is assumed to be linea in income density ($/km 2 ): (SLR.5) VD Y A t, t, t, YA0 VD is the unit value of dyland (in million dolla pe squae kilomete) at time t in egion ; denotes egion; Y is the total income (in billion dolla) at time t in egion ; A is the aea (in squae kilomete) at time t of egion ; φ is a paamete; φ = 4 (2,>0) million dolla pe squae kilomete (Dawin et al., 1995); YA0=0.635 (million dolla pe squae kilomete) is a nomalisation constant, the aveage incomde density of the OECD in 1990; ε is a paamete, the income density elasticity of land value; ε = 1 (0.25). 11

12 Wetland loss is assumed to be a linea function of sea level ise: S M (SLR.6) W, S P, S t t t t Wt, is the wetland lost at time t in egion ; denotes egion; Pt, is faction of coast potected against sea level ise at time t in egion ; ΔSt is sea level ise at time t; note that is assumed to equal fo all egions; ω S is a paamete, the annual unit wetland loss due to sea level ise (in squae kilomete pe mete) in egion ; note that is assumed to be constant ove time; ω M is a paamete, the annual unit wetland loss due to coastal squeeze (in squae kilomete pe mete) in egion ; note that is assumed to be constant ove time. Cumulative wetland loss is given by C C M (SLR.7) Wt, min Wt 1, Wt 1,, W W C is cumulative wetland loss (in squae kilomete) at time t in egion W M is a paamete, the total amount of wetland that is exposed to sea level ise; this is assumed to be smalle than the total amount of wetlands in Wetland loss (SLR.6) goes to zeo if all wetland theatened by sea-level ise in a egion is lost. Wetland value is assumed to incease with income and population density, and fall with wetland size: (SLR.8) VW t, = α ( y β t, ) ( d γ t, ) y 0 d 0 ( W C δ 1990, W t, ) W 1990, VW is the wetland value (in dolla pe squae kilomete) at time t in egion ; denotes egion; y is pe capita income (in dolla pe peson pe yea) at time t in egion ; d is population density (in peson pe squae kilomete) at time t in egion ; W C is cumulative wetland loss (in squae kilomete) at time t in egion ; W 1990 is the total amount of wetlands in 1990 in egion ; α is a paamete, the net pesent value of the futue steam of wetland sevices; note that we thus account pesent and futue wetland values in the yea that the wetland is lost; α = α 1+ρ+ηg t, = α = ρ+ηg t, α 12

13 α = 280,000 $/km 2, with a standad deviation of 187,000 $/km 2 ; α is the aveage of the meta-analysis of Bande et al. (2006); the standad deviation is based on the coefficient of vaiation of the intecept in thei analysis; β is a paamete, the income elasticity of wetland value; β = 1.16 (0.46,>0); this value is taken fom Bande et al. (2006); y 0 is a nomalisation constant; y 0 = 25,000 $/p/y (Bande, pesonal communication); d 0 is a nomalisation constant; d 0 = 27.59; γ is a paamete, the population density elasticity of wetland value; γ = 0.47 (0.12,>0,<1); this value is taken fom Bande et al. (2006); δ is a paamete, the size elasticity of wetland value; δ = (0.05,>-1,<0); this value is taken fom Bande et al. (2006); If dyland gets lost, the people living thee ae foced to move. The numbe of foced migants follows fom the amount of land lost and the aveage population density in the egion. The value of this is set at 3 (1.5,>0) times the egional pe capita income pe migant (Tol, 1995). In the eceiving county, costs equal 40% (20%,>0) of pe capita income pe migant (Cline, 1992). Table SLR displays the annual costs of fully potecting all coasts against a one mete sea level ise in a hunded yeas time. If sea level would ise slowe, annual costs ae assumed to be popotionally lowe; that is, costs of coastal potection ae linea in sea level ise. The level of potection, that is, the shae of the coastline potected, is based on a cost-benefit analysis: (SLR.9) P 1 NPVVP NPVVW t, t, t, max 0,1 2 NPV VD t, P is the faction of the coastline to be potected; NPVVP is the net pesent value of the potection if the whole coast is potected (defined below); NPVVW is the net pesent value of the wetland lost due to coastal squeeze if the whole coast is potected (defined below); NPVVD is the net pesent value of the land lost without any coastal potection (defined below). Equation (SLR.9) is due to Fankhause (1994). See below. Table SLR epots aveage costs pe yea ove the next centuy. NPVVP is calculated assuming annual costs to be constant. This is based on the following. Fistly, the coastal potection decision makes anticipate a linea sea level ise. Secondly, coastal potection entails lage infastuctual woks which last fo decades. Thidly, the consideed costs ae diect investments only, and technologies fo coastal potection ae matue. Thoughout the analysis, a pue ate of time pefeence,, of 1% pe yea is used. The actual discount ate lies thus 1% above the gowth ate of the economy, g. The net pesent costs of potection PC equal (SLR.10) st 1 1 gt, t, t t st 1 g t, gt, NPVVP S S 13

14 NPVVP is the net pesent costs of coastal potection at time t in egion ; denotes egion; π is the annual unit cost of coastal potection (in million dolla pe vetical mete) in egion ; note that is assumed to be constant ove time; ΔSt is sea level ise at time t; note that is assumed to equal fo all egions; g is the gowth ate of pe capita income at time t in egion ; ρ is a paamete, the ate of pue time pefeence; ρ = 0.03; η is a paamete, the consumption elasticity of maginal utility; η = 1; NPVVW is the net pesent value of the wetlands lost due to full coastal potection. Wetland values ae assumed to ise in line with Equation (SLR.8). All gowth ates and the ate of wetland loss ae as in the cuent yea. The net pesent costs of wetland loss WL follow fom (SLR.11) NPV VW W VW t, t, 1 W VW 1 g 1 g t, t, s, st t, t, g g p w t, t, t, t, NPVVW denotes the net pesent value of wetland loss. at time t in egion ; denotes egion; ω is the annual unit wetland loss due to full coastal potection (in squae kilomete pe mete sea level ise) in egion ; note that is assumed to be constant ove time; ΔSt is sea level ise at time t; note that is assumed to equal fo all egions; g is the gowth ate of pe capita income at time t in egion ; p is the population gowth ate at time t in egion ; w is the gowth ate of wetland at time t in egion ; note that wetlands shink, so that w < 0; ρ is a paamete, the ate of pue time pefeence; ρ = 0.03; η is a paamete, the consumption elasticity of maginal utility; η = 1; β is a paamete, the income elasticity of wetland value; β = 1.16 (0.46,>0); this value is taken fom Bande et al. (2006); γ is a paamete, the population density elasticity of wetland value; γ = 0.47 (0.12,>0,<1); this value is taken fom Bande et al. (2006); δ is a paamete, the size elasticity of wetland value; β = (0.05,>-1,<0); this value is taken fom Bande et al. (2006); st 14

15 NPVVD denotes the net pesent value of the dyland lost if no potection takes place. Land values ae assumed to ise at the ate of income gowth. All gowth ates and the ate of wetland loss ae as in the cuent yea. The net pesent costs of dyland loss ae s t ) 1 + ρ + ηg t, (SLR.12) NPVVD t, = D t, VD t, ( 1 + εd t, s=t NPVVD is the net pesent value of dyland loss at time t in egion ; denotes egion; D is the cuent dyland loss without potection at time t in egion ; VD is the cuent dyland value; g is the gowth ate of pe capita income at time t in egion ; ρ is a paamete, the ate of pue time pefeence; ρ = 0.03; = D t, VD t, 1 + ρ + ηg t, ρ + ηg t, εd t, η is a paamete, the consumption elasticity of maginal utility; η = 1; ε is a paamete, the income elasticity of dyland value; ε = 1.0, with a standad deviation of 0.2; d is the cuent income density gowth ate at time t in egion. Potection levels ae bounded between 0 and Ecosystems Tol (2002a) assesses the impact of climate change on ecosystems, biodivesity, species, landscape etcetea based on the "wam-glow" effect. Essentially, the value, which people ae assumed to place on such impacts, ae independent of any eal change in ecosystems, of the location and time of the pesumed change, etcetea although the pobability of detection of impacts by the geneal public is inceasing in the ate of waming. This value is specified as (E.1) E yt, T b t y B0 P 1 y T 1 1 B t, t, t, t t b y E denotes the value of the loss of ecosystems (in 1995 US dolla) at time t in egion ; denotes egion; y denotes pe capita income (in 1995 dolla pe peson pe yea) at time t in egion ; P denotes population size (in millions) at time t in egion ; ΔT denotes the change in tempeatue (in degee Celsius); 15

16 B is the numbe of species, which makes that the value inceases as the numbe of species falls using Weitzman s (1998) anking citeion and Weitzman s (1992, 1993) biodivesity index, the scacity value of biodivesity is invesely popotional to the numbe of species; =50 (0-100, >0) is a paamete such that the value equals $50 pe peson if pe capita income equals the OECD aveage in 1990 (Peace and Moan, 1994); y b = is a paamete; y b = $30,000, with a standad deviation of $10,000; it is nomally distibuted, but knotted at zeo. τ=0.025ºc is a paamete; σ=0.05 (tiangula distibution,>0,<1) is a paamete, based on an expet guess; and B0=14,000,000 is a paamete. The numbe of species follows (E.2) B T Bt B max, t1 1 2 ρ = ( , >0.0) is a paamete; γ = ( , >0.0) is a paamete; and These paametes ae expet guesses. The numbe of species is assumed to be constant until the yea 2000 at 14,000,000 species Human health: Diahoea The numbe of additional diahoea deaths (HD.1) D y d d t, t, t, Pt, y 1990, T peindustial, P,t denotes population, indexes egion t indexes time, T d D, t in egion and time t is given by y,t is the pe capita income in egion and yea t in 1995 US dollas, T,t is egional tempeatue in yea t, in degees Celcius (C); μ d is the ate of motality fom diahoea in 2000 in egion, taken fom the WHO Global Buden of Disease (see Table HD, column 3); ε = (0.23)is the income elasticity of diahoea motality η = 1.14 (0.51) is a paamete, the degee of non-lineaity of the esponse of diahoea motality to egional waming. 16

17 Equation (HD.1), specifically paametes ε and η, was estimated based on the WHO Global Buden of Diseases data ( Diahoea mobidity has the same equation as motality, but with ε=-0.42 (0.12) and η=0.70 (0.26); base mobidity is given in Table HD, column 4. Table HD gives impact estimates, ignoing economic and population gowth. See section fo a desciption of the valuation of motality and mobidity Human health: Vecto-bone diseases The numbe of additional deaths fom vecto-bone diseases, v D, t is given by: t, t, 1990, t 1990 y 1990, v v v (HV) D D T T v D t, D v 1990, y denotes climate-change-induced motality due to disease v in egion at time t; denotes motality fom vecto-bone diseases in egion in 1990 (see Table HV, column base ); denotes egion; v denotes vecto-bone disease (malaia, schistosomiasis, dengue feve); α is a paamete, indicating the benchmak impact of climate change on vecto-bone diseases (see Table HV, column impact ); the best guess is the aveage of Matin and Lefebve (1995), Matens et al. (1995, 1997) and Moita et al. (1995), while the standad deviation is the spead between models and the scenaios. y,t denotes pe capita income; Tt denotes the egional mean tempeatue in yea t, in degees Celcius (C); β = 1.0 (0.5) is a paamete, the degee of non-lineaity of motality in waming; the paamete is calibated to the esults of Matens et al. (1997); γ = (0.69) is the income elasticity of vecto-bone motality, taken fom Link and Tol (2004), who egess malaia motality on income fo the 14 WHO egions.. See section fo a desciption of the valuation of motality and mobidity. Mobidity is popotional to motality, using the facto specified in Table HM Human health: Cadiovascula and espiatoy motality Cadiovascula and espiatoy disodes ae wosened by both exteme cold and exteme hot weathe. Matens (1998) assesses the incease in motality fo 17 counties. Tol (2002a) extapolates these findings to all othe counties, based on fomulae of the shape: (HC.1) c c c D T B 17

18 D c denotes the change in motality (in deaths pe 100,000 people) due to a one degee global waming; c indexes the disease (heat-elated cadiovascula unde 65, heat-elated cadiovascula ove 65, cold-elated cadiovascula unde 65, cold-elated cadiovascula ove 65, espiatoy); TB is the cuent tempeatue of the hottest o coldest month in the county (in degee Celsius); and ae paametes, specified in Table HC.1. Equation (HC.1) is specified fo populations above and below 65 yeas of age fo cadiovascula disodes. Cadiovascula motality is affected by both heat and cold. In the case of heat, TB denotes the aveage tempeatue of the wamest month. In the case of cold, TB denotes the aveage tempeatue of the coldest month. Respiatoy motality is not agespecific. Equation (HC.1) is eadily extapolated. With waming, the baseline tempeatue TB changes. If this change is popotional to the change in the global mean tempeatue, the equation becomes quadatic. Summing county-specific quadatic functions esults in quadatic functions fo the egions: (HC.2) c D t, D T T c c c 2 t, t t denotes climate-change-induced motality (in deaths pe 100,000 people) due to disease c in egion at time t; c indexes the disease (heat-elated cadiovascula unde 65, heat-elated cadiovascula ove 65, cold-elated cadiovascula unde 65, cold-elated cadiovascula ove 65, espiatoy); indexes egion; t indexes time; T denotes the change in egional mean tempeatue (in degee Celsius); and ae paametes, specified in Tables HC.2-4 (in pobabilistic mode all pobablitiy distibutions ae constained so that only values with the same sign as the mean can be sampled). One poblem with (HC.2) is that it is a non-linea extapolation based on a data-set that is limited to 17 counties and, moe impotantly, a single climate change scenaio. A global waming of 1C leads to changes in cadiovascula and espiatoy motality in the ode of magnitude of 1% of baseline motality due to such disodes. Pe cause, the total change in motality is esticted to a maximum of 5% of baseline motality, an expet guess. This estiction is binding. Baseline cadiovascula and espiatoy motality deives fom the shae of the population above 65 in the total population. If the faction of people ove 65 inceases by 1%, cadiovascula motality inceases by % (0.0096%). Fo espiatoy motality, the change is % (0.0005%). These paametes ae estimated fom the vaiation in population above 65 and cadiovascula and espiatoy motality ove the nine egions in 1990, using data fom 18

19 Motality as in equations (HC.1) and (HC.2) is expessed as a faction of population size. Cadiovascula motality, howeve, is sepaately specified fo younge and olde people. In 1990, the pe capita income elasticity of the shae of the population ove 65 is 0.25 (0.08). This is estimated using data fom Heat-elated motality is assumed to be limited to uban populations. Ubanisation is a function of pe capita income and population density: (HC.3) U t, yt, PDt, 1 y PD t, t, U is the faction of people living in cities; y is pe capita income (in 1995 US$ pe peson pe yea); PD is population density (in people pe squae kilomete); t is time; is egion; α and β ae paametes, estimated fom a coss-section of counties fo the yea 1995, using data fom α=0.031 (0.002) and β= (0.005); R 2 =0.66. See section fo a desciption of the valuation of motality and mobidity. Mobidity is popotional to motality, using the facto specified in Table HM Exteme weathe: Topical stoms The economic damage TD due to an incease in the intensity of topical stoms (huicanes, typhoons) follows y 1 1 y 1990, t, (TS.1) TDt, Yt, Tt, denotes egion TD is the damage due to topical stoms (1995 US$ pe yea) in egion at time t; Y is the goss domestic poduct (in 1995 US$ pe yea) in egion at time t; α is the cuent damage as faction of GDP, specified in Table TS; the data ae fom the CRED EM-DAT database; y is pe capita income (in 1995 US$ pe peson pe yea) in egion at time t; ε is the income elasticity of stom damage; ε = (0.027;>-1,<0) afte Toya and Skidmoe (2007); δ is a paamete, indicating how much wind speed inceases pe degee waming; δ=0.04/ºc (0.005) afte WMO (2006); 19

20 T is the tempeatue incease since pe-industial times (in degee Celsius) in egion at time t; γ is a paamete; γ=3 because the powe of the wind in the cube of its speed. The motality TM due to an incease in the intensity of topical stoms (huicanes, typhoons) follows y 1 1 y 1990, t, (TS.2) TM t, Pt, Tt, denotes egion TM is the motality due to topical stoms (in people pe yea) in egion at time t; P is the population (in people) in egion at time t; β is the cuent motality (as a faction of population), specified in Table TS; the data ae fom the CRED EM-DAT database; y is pe capita income (in 1995 US$ pe peson pe yea) in egion at time t; η is the income elasticity of stom damage; η = (0.051;<0) afte Toya and Skidmoe (2007); δ is paamete, indicating how much wind speed inceases pe degee waming; δ=0.04/ºc (0.005) afte WMO (2006); T is the tempeatue incease since pe-industial times (in degee Celsius) in egion at time t; γ is a paamete; γ=3 because the powe of the wind in the cube of its speed. See section fo a desciption of the valuation of motality and mobidity Exteme weathe: Extatopical stoms The economic damage due to an incease in the intensity of extatopical stoms follows the equation below: (ETS.1) ETD Y y C t, CO2, t t, t, y1990, CCO 2, pe 1 ETDt, is the damage fom extatopical cyclones at time t in egion ; Yt, is GDP in egion and time t; α is benchmak damage fom extatopical cyclones fo egion ; 20

21 y is pe capita income at time t in egion ; ε=-0.514(0.027,>-1,<0) is the income elasticity of extatopical stom damages (Toya and Skidmoe 2007); δ is the stom sensitivity to atmospheic CO2 concentations fo egion ; CCO2,t is atmospheic CO2 concentations; CCO2, pe is the CO2 concentations in the pe-industial ea; γ=1 is a paamete. (EST.2) ETM P y C t, CO2, t t, t, y1990, CCO 2, pe 1 ETMt, is the motality fom extatopical cyclones at time t in egion ; Pt, is population in egion and time t; β is benchmak motality fom extatopical cyclones fo egion ; y is pe capita income at time t in egion ; φ=-0.501(0.051,>-1,<0) is the income elasticity of extatopical stom motality (Toya and Skidmoe 2007); δ is the stom sensitivity to atmospheic CO2 concentations fo egion ; CCO2,t is atmospheic CO2 concentations; CCO2, pe is the CO2 concentations in the pe-industial ea; γ=1 is a paamete. See section fo a desciption of the valuation of motality and mobidity Motality and Mobidity The value of a statistical life is given by 21

22 (MM.1) VSL t, y t, y0 VSL is the value of a statistical life at time t in egion ; α= ( ,>0) is a paamete; y is pe capita income at time t in egion ; y0=24963 is a nomalisation constant; ε=1 (0.2,>0) is the income elasticity of the value of a statistical life; This calibation esults in a best guess value of a statistical life that is 200 times pe capita income (Cline, 1992). The value of a yea of mobidity is given by (MM.2) VM t, y t, y0 VM is the value of a statistical life at time t in egion ; β= (29955,>0) is a paamete; y is pe capita income at time t in egion ; y0=24963 is a nomalisation constant; η=1 (0.2,>0) is the income elasticity of the value of a yea of mobidity; This calibation esults in a best guess value of a yea of mobidity that is 0.8 times pe capita income (Navud, 2001). Acknowledgements We thank Adiana Ciccone fo helpful comments on this documentation. Refeences Nakicenovic, N. and R.J. Swat (eds.) (2001), IPCC Special Repot on Emissions Scenaios Cambidge Univesity Pess, Cambidge. Bijlsma, L., C.N.Ehle, R.J.T.Klein, S.M.Kulshestha, R.F.McLean, N.Mimua, R.J.Nicholls, L.A.Nuse, H.Peez Nieto, E.Z.Stakhiv, R.K.Tune, and R.A.Waick (1996), 'Coastal Zones and Small Islands', in Climate Change 1995: Impacts, Adaptations and Mitigation of Climate Change: Scientific-Technical Analyses -- Contibution of Woking Goup II to the Second Assessment Repot of the Integovenmental Panel on Climate Change, 1 edn, R.T. Watson, M.C. Zinyowea, and R.H. Moss (eds.), Cambidge Univesity Pess, Cambidge, pp Cline, W.R. (1992), The Economics of Global Waming Institute fo Intenational Economics, Washington, D.C. 22

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