.NICE

aNother Integrated Climate Economy model Tom Fiddaman, MIT System Dynamics Group (tomfid@mit.edu) Incorporates the structural experiments from: Fiddaman, Thomas (1995). Formulation Experiments with a Simple Climate-Economy Model. In 1995 System Dynamics Conference, Plenary Papers . Tokyo, Japan. including an explicit energy sector, behavioral investment rules, and an alternative carbon cycle. Based on the DICE model: Nordhaus, William D. (1992). The "DICE" Model: Background and Structure of a Dynamic Integrated Climate-Economy Model of the Economics of Global Warming Discussion Paper No. 1009). Cowles Foundation for Research in Economics at Yale University. Nordhaus, William D. (1992). An Optimal Transition Path for Controlling Greenhouse Gases. Science, 258(20), 1315-1319. Nordhaus, William D. (1994). Managing the Global Commons. Cambridge, MA: MIT Press. To use the model, you must: - Use a copy of Vensim DSS (or the DSS model reader) in order to read arrays and perform optmization. Notes: - For optimization runs, be sure to use a final time of at least 2305 to 2505 to prevent finite-horizon effects. Unlike Nordhaus' GAMS implementation, this model does not use transversality coefficients from longer runs. The results from 1965 to 2105 are generally insensitive to time horizons greater than 2305, though. - The efficiency of optimization can be increased by raising the absolute tolerances on the decision variables. - The investment path changes very little from run to run, so for most purposes it is acceptable to use a baseline investment path and optimize only the GHG reduction path. Alternatively, you can use the behavioral investment heuristic, which closely mimics the optimal time path. - It's a good idea to use random multi-start optimization to verify your solutions, especially with endogenous technological change active.

.capital

(001) Capital = INTEG(Investment - Depreciation, Reference_Capital)

Units: $

Capital ($) Capital stock in 1989 dollars. [Managing Global Commons, pg. 21]

Causes:

Uses:

(002) Capital_Energy_Coeff = (Capital_Energy_Elast-1)/Capital_Energy_Elast

Units: dmnl

Coefficient of capital-energy substitution.

Causes:

Uses:

(003) Capital_Energy_Elast = 0.7

Units: dmnl

Elasticity of subsitution between capital and effective energy inputs.

Uses:

(004) Capital_Labor_Ratio = Capital/Population

Units: $/person

Ratio of Capital Inputs to Labor Inputs ($/person)

Causes:

(005) Capital_Output_Ratio = Capital/Gross_Output

Units: $/($/year)

Capital per Unit Output ($ per $/year)

Causes:

(006) Capital_Share = 1-Energy_Share

Units: dmnl

Share of capital in producing effective capital.

Causes:

Uses:

(007) Depreciation = Capital*Depreciation_Rate

Units: $/year

Depreciation

Causes:

Uses:

(008) Depreciation_Rate = 0.065

Units: 1/year

Depreciation Rate [delta-k] (1/year) Nordhaus uses exp(-.1*10)=.65 to convert the assumed capital life of 10 years to a decadal depreciation rate of .65. This is generally a poor way to correct for integration error due to insufficient compounding, and is wrong as applied because the net rate (investment-depreciation) must be compounded; depreciation cannot be treated in isolation. Using the annual rate of .1 causes insufficient capital growth, so I have converted the decadal rate of .65 to an annual rate of .065. [Managing Global Commons, pg. 21]

Uses:

(009) Effective_Capital = Reference_Eff_Capital*(Capital_Share*(Capital/Reference_Capital )^Capital_Energy_Coeff +(1-Capital_Share)*(Energy_Serv_Demand/Ref_Energy_Serv_Demand)^Capital_Energy_Coeff )^(1/Capital_Energy_Coeff )

Units: $

Effective capital inputs to production, obtained by CES aggregation of capital and effective energy inputs.

Causes:

Uses:

(010) Energy_Int_Adj_Time = 10

Units: year

Energy intensity adjustment time; set shorter than capital life and decoupled from investment for simplicity; assumes costless retrofit potential.

Uses:

(011) Energy_Intens_Chg_Rt = (Ind_Energy_Cap_Ratio-Energy_Intens_of_Capital )/Energy_Int_Adj_Time

Units: GJ/year/$/year

Rate of change of energy intensity.

Causes:

Uses:

(012) Energy_Intens_Dec_Rt_Decline_Rt = Energy_Intens_Decline_Rt*Fact_Prod_Gr_Rt_Dec_Rt

Units: 1/year/year

Rate of decline of Rate of Decline of CO2 intensity (i.e. a second derivative or CO2 intensity).

Causes:

Uses:

(013) Energy_Intens_Decline_Rt = INTEG(- Energy_Intens_Dec_Rt_Decline_Rt, Init_Energy_Intens_Dec_Rt )

Units: 1/year

Rate of Decline of Greenhouse Gas Intensity of Output [g-sigma] (1/year) Note that Nordhaus decompounds the decadal rate of .1168 to yield an annual rate of .0125; I have simply divided by 10 to convert the decadal rate to an annual rate. [Managing Global Commons, pg. 21]

Causes:

Uses:

(014) Energy_Intens_of_Capital = INTEG(Energy_Intens_Chg_Rt,Ref_Energy_Serv_Demand /Capital)

Units: GJ/year/$

Energy intensity of capital stock.

Causes:

Uses:

(015) Energy_Serv_Demand = Energy_Intens_of_Capital*Capital

Units: GJ/year

Energy requirements of capital

Causes:

Uses:

(016) Energy_Share = INTEG(-Energy_Share*Energy_Intens_Decline_Rt,Initial_Energy_Share )

Units: dmnl

Share of energy in the capital-energy composite good. Declines at an exogenous rate.

Causes:

Uses:

(017) Ind_Energy_Cap_Ratio = Ref_Energy_Serv_Demand/Reference_Capital *(Energy_Price/Marg_Prod_Capital*Capital_Share/(1-Capital_Share) *Ref_Energy_Serv_Demand/Reference_Capital)^(1/(Capital_Energy_Coeff-1))

Units: GJ/year/$

Indicated energy-capital ratio. Equal to the CES optimal factor ratio at current prices. Terms can be rearranged to eliminate units error.

Causes:

Uses:

(018) Init_Energy_Intens_Dec_Rt = 0.015

Units: 1/year

Initial rate of decline of energy intensity (i.e. energy share of capital/energy composite good).

Uses:

(019) Initial_Energy_Share = 0.08

Units: dmnl

Initial share of energy in the composite capital-energy good.

Uses:

(020) Investment = Output*Investment_Frac

Units: $/year

Gross Investment ($/year)

Causes:

Uses:

(021) Marg_Prod_Capital = Marg_Prod_Eff_Capital*(Reference_Eff_Capital/Reference_Capital ) *(Capital_Share*(Capital/Reference_Capital)^Capital_Energy_Coeff +(1-Capital_Share)*(Energy_Serv_Demand/Ref_Energy_Serv_Demand)^Capital_Energy_Coeff ) ^(1/Capital_Energy_Coeff-1) *Capital_Share*(Capital/Reference_Capital)^(Capital_Energy_Coeff-1)

Units: 1/year

Marginal Productivity of Capital (gross, not including depreciation).

Causes:

Uses:

(022) Marg_Prod_Eff_Capital = Capital_Elast_Output*Gross_Output/Effective_Capital

Units: 1/year

Marginal Productivity of Capital

Causes:

Uses:

(023) Marg_Prod_Energy = Marg_Prod_Eff_Capital*(Reference_Eff_Capital/Ref_Energy_Serv_Demand ) *(Capital_Share*(Capital/Reference_Capital)^Capital_Energy_Coeff +(1-Capital_Share)*(Energy_Serv_Demand/Ref_Energy_Serv_Demand) ^Capital_Energy_Coeff)^(1/Capital_Energy_Coeff-1) *(1-Capital_Share)*(Energy_Serv_Demand/Ref_Energy_Serv_Demand)^(Capital_Energy_Coeff -1)

Units: $/GJ

Marginal Productivity of Energy

Causes:

(024) Marg_Return_Capital = Marg_Prod_Eff_Capital-Depreciation_Rate

Units: 1/year

Marginal Return to Capital Equals the marginal product of capital less depreciation.

Causes:

Uses:

(025) Ref_Energy_Serv_Demand = INIT(Energy_Share*Capital_Elast_Output*Output_in_1965 /Energy_Price)

Units: GJ/year

Reference demand for energy services.

Causes:

Uses:

(026) Reference_Capital = 1.6e+013

Units: $

Reference capital input in composite capital/energy good.

Uses:

(027) Reference_Eff_Capital = 1.6e+013

Units: $

Reference value (output) of composite capital/energy good. Selected to have same value as initial capital in Nordhaus for comparability.

Uses:

.Carbon

Carbon cycle from DICE model.

(028) Atmos_Retention = (CO2_Net_Emiss-CO2_Storage)/CO2_Net_Emiss

Units: dmnl

Total (average) atmospheric retention in Nordhaus carbon cycle.

Causes:

(029) Carbon_Cycle_Switch = 0

Units: dmnl

0 = Nordhaus, 1 = modified

Uses:

(030) CO2_Content[carbon] = 0.01773 CO2_Content[non_carbon] = 0 CO2_Content[alt_carbon] = 0.01773

Units: TonC/GJ

CO2 content of energy sources. Corresponds to .065 TonCO2/GJ.

Uses:

(031) CO2_Emissions = SUM(Energy_CO2_Emiss[source!])+Nonenergy_CO2_Emiss

Units: TonC/year

Total CO2 emissions.

Causes:

Uses:

(032) CO2_in_Atmos = INTEG(CO2_Net_Emiss - CO2_Storage, Init_CO2_in_Atm)

Units: TonC

Greenhouse Gases in Atmosphere [M(t)] (tons carbon equivalent) [Cowles, pg. 21]

Causes:

Uses:

(033) CO2_Int_of_Output = CO2_Emissions/Gross_Output

Units: TonC/$

Carbon Intensity of Output

Causes:

(034) CO2_Net_Emiss = Marginal_Atmos_Retention*CO2_Emissions

Units: TonC/year

Net Greenhouse Gas Emissions (tons carbon equivalent/year) Greenhouse gas emissions less short-run uptake from the atmosphere. Where does the portion not retained go in the long run? [Cowles, pg. 21]

Causes:

Uses:

(035) CO2_Rad_Force_Coeff = 4.1

Units: watt/meter/meter

Coefficient of Radiative Forcing from CO2 (W/m^2) Coeff. of additional surface warming from accumulation of CO2. [Cowles, pg. 22]

Uses:

(036) CO2_Rad_Forcing = CO2_Rad_Force_Coeff*LOG(IF_THEN_ELSE(Carbon_Cycle_Switch =0, CO2_in_Atmos,CO2_in_Atmosphere)/Preindustrial_CO2,2)

Units: watt/meter/meter

Radiative Forcing from CO2 [F(t)] (W/m^2) Additional surface warming from accumulation of CO2. [Cowles, pg. 22]

Causes:

Uses:

(037) CO2_Storage = (CO2_in_Atmos-Preindustrial_CO2)*Rate_of_CO2_Transfer

Units: TonC/year

Greenhouse Gas removal from the atmosphere and storage by long-term processes. (tons carbon equivalent/year) [Cowles, pg. 21]

Causes:

Uses:

(038) Emiss_Stabilization = Emiss_Stabilization_LOOKUP(Time)

Units: dmnl

Fraction of CO2 and CFC Emissions Controlled (dimensionless) Stabilization of Emissions. Estimated from graph in [Science, Fig. 1]. (000)Time - Internally defined simulation time.

Causes:

Uses:

(039) Emiss_Stabilization_LOOKUP( (1965, 0), (1975, 0), (1985, 0), (1995, 0.13 ), (2005, 0.27), (2015, 0.36 ), (2025, 0.45), (2035, 0.51), (2045, 0.55), (2055, 0.59), (2065, 0.62), (2075 , 0.64), (2085, 0.66), (2095, 0.68), (2105, 0.7) )

Units: dmnl

Fraction of CO2 and CFC Emissions Controlled (dimensionless) Stabilization of Emissions. Estimated from graph in [Science, Fig. 1].

Uses:

(040) Emissions_Scenario = 1

Units: dmnl

1 = no control; 2 = optimal control; 3 = emissions stabilization; 4 = temperature stabilization

Uses:

(041) Energy_CO2_Emiss[source] = Production[source]*CO2_Content[source]

Units: TonC/year

Causes:

Uses:

(042) IPCC_CO2_CFC_Rad_Force = IPCC_CO2_CFC_Rad_Force_LOOKUP(Time)

Units: watt/meter/meter

IPCC Scenario for Radiative Forcing from CO2 and CFCs (W/m^2) As interpolated by Nordhaus. [Cowles, Table III.E-5] (000)Time - Internally defined simulation time.

Causes:

(043) IPCC_CO2_CFC_Rad_Force_LOOKUP( (1965, 0.92), (1975, 1.19), (1985, 1.57 ), (1995, 2), (2005, 2.46), (2015 , 2.93), (2025, 3.4), (2035, 3.97), (2045, 4.54), (2055, 5.11), (2065, 5.68 ), (2075, 6.25), (2085, 6.79 ), (2095, 7.33), (2105, 7.87) )

Units: watt/meter/meter

IPCC Scenario for Radiative Forcing from CO2 and CFCs (W/m^2) As interpolated by Nordhaus. [Cowles, Table III.E-5]

Uses:

(044) Marginal_Atmos_Retention = 0.64

Units: dmnl

Atmospheric Retention Fraction [beta] (dimensionless) Fraction of Greenhouse Gas Emissions which accumulate in the atmosphere. [Cowles, pg. 21]

Uses:

(045) No_Controls = 0

Units: dmnl

Fraction of CO2 and CFC Emissions Controlled (dimensionless) Uncontrolled scenario.

Uses:

(046) Nord_CO2_in_Atm = Nord_CO2_in_Atm_LOOKUP(Time)

Units: GTonC

Nordhaus' CO2 & CFC Concentrations (Gt Carbon Equivalent) Uncontrolled scenario [Cowles, Table IV-4]. (000)Time - Internally defined simulation time.

Causes:

(047) Nord_CO2_in_Atm_LOOKUP( (1965, 677), (1975, 698), (1985, 727), (1995, 764), (2005, 809), (2015, 0), (2025, 921), (2035, 0), (2045, 0), (2055, 0), (2065, 0), (2075, 1293), (2085 , 0), (2095, 0), (2105, 0) )

Units: GTonC

Nordhaus' CO2 & CFC Concentrations (Gt Carbon Equivalent) Uncontrolled scenario [Cowles, Table IV-4].

Uses:

(048) Nord_CO2_Intensity = Nord_CO2_Intensity_LOOKUP(Time)

Units: GTonC/year

(000)Time - Internally defined simulation time.

Causes:

(049) Nord_CO2_Intensity_LOOKUP( (1965, 0.519), (1975, 0.465), (1985, 0.421 ), (1995, 0.385), (2005, 0.356) , (2015, 0), (2025, 0.312), (2035, 0), (2045, 0), (2055, 0), (2065, 0), (2075 , 0.249), (2085, 0), (2095 , 0), (2105, 0) )

Units: GTonC/year

Uses:

(050) Nord_Emiss = Nord_Emiss_LOOKUP(Time)

Units: GTonC/year

Nordhaus' CO2 & CFC Emissions (Gt Carbon Equivalent) Uncontrolled scenario [Cowles, Table IV-4]. (000)Time - Internally defined simulation time.

Causes:

(051) Nord_Emiss_LOOKUP( (1965, 4.42), (1975, 5.89), (1985, 7.53), (1995, 9.28 ), (2005, 11.1), (2015, 0), (2025, 14.6), (2035, 0), (2045, 0), (2055, 0), (2065, 0), (2075, 22), (2085 , 0), (2095, 0), (2105, 0 ) )

Units: GTonC/year

Nordhaus' CO2 & CFC Emissions (Gt Carbon Equivalent) Uncontrolled scenario [Cowles, Table IV-4].

Uses:

(052) Nord_GHG_Reduction_Frac = IF_THEN_ELSE(Emissions_Scenario=1,No_Controls , IF_THEN_ELSE(Emissions_Scenario=2,Optimal_Controls, IF_THEN_ELSE(Emissions_Scenario=3,Emiss_Stabilization,Temp_Stabilization)))

Units: dmnl

Fraction of Greenhouse Gas Emissions Abated [mu(t)] (dimensionless) Selects one of three scenarios. [Cowles, pg. 20]

Causes:

(053) Optimal_Controls = Optimal_Controls_LOOKUP(Time)

Units: dmnl

Fraction of CO2 and CFC Emissions Controlled (dimensionless) Optimal control scenario. [Cowles, table IV-3] (000)Time - Internally defined simulation time.

Causes:

Uses:

(054) Optimal_Controls_LOOKUP( (1965, 0), (1975, 0), (1985, 0), (1995, 0.088 ), (2005, 0.096), (2015, 0.103 ), (2025, 0.111), (2035, 0.116), (2045, 0.12), (2055, 0.125), (2065, 0.129) , (2075, 0.134), (2085, 0.139 ), (2095, 0.143), (2105, 0.148) )

Units: dmnl

Fraction of CO2 and CFC Emissions Controlled (dimensionless) Optimal control scenario. [Cowles, table IV-3]

Uses:

(055) Preindustrial_CO2 = 5.9e+011

Units: TonC

Preindustrial atmospheric stock of carbon.

Uses:

(056) Rate_of_CO2_Transfer = 0.008333

Units: 1/year

Rate of Storage of Atmospheric Greenhouse Gases [delta-m] (1/year) Inverse yields average residence time of gases (120 years). Note that the validity and stability of this factor is highly questionable. [Cowles, pg. 21]

Uses:

(057) Temp_Stabilization = Temp_Stabilization_LOOKUP(Time)

Units: dmnl

Fraction of CO2 and CFC Emissions Controlled Stabilization of temperature. Estimated from graph. [Science, Fig. 1]. (000)Time - Internally defined simulation time.

Causes:

Uses:

(058) Temp_Stabilization_LOOKUP( (1965, 0), (1975, 0), (1985, 0), (1995, 0.45 ), (2005, 0.585), (2015, 0.72 ), (2025, 0.855), (2035, 0.99), (2045, 0.99), (2055, 0.97), (2065, 0.95), ( 2075, 0.95), (2085, 0.95) , (2095, 0.99), (2105, 0.92) )

Units: dmnl

Fraction of CO2 and CFC Emissions Controlled (dimensionless) Stabilization of temperature. Estimated from graph in [Science, Fig. 1].

Uses:

.climate

Climate sector from DICE model.

(059) A_UO_Heat_Cap = 44.248

Units: watt*year/DegreesC/(meter*meter)

Atmosphere & Upper Ocean Heat Capacity per Unit Area [1/R1] (W-yr/m^2/degrees C) Note: equals 1/0.0226 [Managing the Global Commons, pg. 21]

Uses:

(060) Atmos_UOcean_Temp = INTEG(Chg_A_UO_Temp, 0.2)

Units: DegreesC

Temperature of the Atmosphere and Upper Ocean [T] (degrees C) [Cowles, pg. 24]

Causes:

Uses:

(061) Chg_A_UO_Temp = (Radiative_Forcing-Feedback_Heating-Heat_Transfer)/A_UO_Heat_Cap

Units: DegreesC/year

Change in the Atmosphere & Upper Ocean Temperature (degrees C/yr) [Cowles, pg. 27]

Causes:

Uses:

(062) Chg_DO_Temp = Heat_Transfer/DO_Heat_Cap

Units: DegreesC/year

Change in the Deep Ocean Temperature (degrees C/yr) [Cowles, pg. 30]

Causes:

Uses:

(063) Climate_Damage_Frac = 1-1/(1+Climate_Damage_Scale*(Atmos_UOcean_Temp/ Reference_Temperature)^Climate_Damage_Nonlinearity )

Units: dmnl

Fraction of Output lost to combating Climate Change (1/Degrees C^2)

Causes:

Uses:

(064) Climate_Damage_Nonlinearity = 2

Units: dmnl

Nonlinearity of Climate Damage Cost Fraction [Theta2] (dimensionless) [Cowles, pg. 13 & 24]

Uses:

(065) Climate_Damage_Scale = 0.013

Units: dmnl

Climate Damage Fraction at Reference Temperature [part of Nordhaus' variable Theta1] (dimensionless) [Managing Global Commons, pg. 18 and 21]

Uses:

(066) Climate_Feedback_Param = 1.41

Units: watt/meter/meter/DegreesC

Climate Feedback Parameter [lambda] (W-m^2/degree C) The crucial climate sensitivity parameter - determines feedback effect from temperature increase. The Schneider-Thompson 2-stock model uses 1.33 [Cowles, Table III-B1]. [Managing Global Commons, pg. 21]

Uses:

(067) Deep_Ocean_Temp = INTEG(Chg_DO_Temp, 0.1)

Units: DegreesC

Temperature of the Deep Ocean [T*] (degrees C) [Cowles, pg. 24]

Causes:

Uses:

(068) DO_Heat_Cap = Heat_Capacity_Ratio*Heat_Trans_Coeff

Units: watt*year/DegreesC/meter/meter

Deep Ocean Heat Capacity per Unit Area [R2] (W-yr/m^2/degrees C) Note: Managing Global Commons uses .44*Heat_Trans_Coeff = 220; Cowles report uses 223.7 (page 30). [Managing Global Commons, pg. 21]

Causes:

Uses:

(069) Feedback_Heating = Atmos_UOcean_Temp*Climate_Feedback_Param

Units: watt/meter/meter

Feedback Heating (W/m^2) Additional heating of the atmosphere/upper ocean system from feedback effects of warming. [Cowles, pg. 27]

Causes:

Uses:

(070) Heat_Capacity_Ratio = 0.44

Units: watt/(meter*meter*DegreesC)

Ratio of Thermal Capacity of Deep Ocean to Heat Transfer Time Constant [R2/Tau12] [Managing Global Commons, pg. 21]

Uses:

(071) Heat_Trans_Coeff = 500

Units: year

Heat Transfer Coefficient [tau12] (years) Coefficient of heat transfer between the atmosphere & upper ocean and the deep ocean. May be interpreted as a mixing time constant. Schneider & Thompson use a slightly higher estimate of 550. [Cowles, pg. 31]

Uses:

(072) Heat_Transfer = Temp_Diff*DO_Heat_Cap/Heat_Trans_Coeff

Units: watt/meter/meter

Heat Transfer from the Atmosphere & Upper Ocean to the Deep Ocean

Causes:

Uses:

(073) Nord_Temp = Nord_Temp_LOOKUP(Time)

Units: DegreesC

Nordhaus' Atmospher & Upper Ocean Temperature Difference (degrees C) Uncontrolled scenario [Cowles, Table IV-5]. (000)Time - Internally defined simulation time.

Causes:

(074) Nord_Temp_LOOKUP( (1965, 0.2), (1975, 0.4), (1985, 0.58), (1995, 0.76 ), (2005, 0), (2015, 0), (2025, 1.4), (2035, 0), (2045, 0), (2055, 0), (2065, 0), (2075, 2.68), (2085, 0), (2095, 0), (2105, 3.4) )

Units: DegreesC

Nordhaus' Atmospher & Upper Ocean Temperature Difference (degrees C) Uncontrolled scenario [Cowles, Table IV-5].

Uses:

(075) Other_GHG_Rad_Forcing = Other_GHG_Rad_Forcing_LOOKUP(Time)

Units: watt/meter/meter

Radiative Forcing from Other GHGs (W/m^2) Additional surface warming from accumulation of other GHGs (NOx and Methane). [Table 4.9B, Managing Global Commons, pg. 73] (000)Time - Internally defined simulation time.

Causes:

Uses:

(076) Other_GHG_Rad_Forcing_LOOKUP( (1965, 0.41), (1975, 0.5), (1985, 0.6), (1995, 0.7), (2005, 0.78), (2015 , 0.87), (2025, 0.96), (2035, 1.05), (2045, 1.14), (2055, 1.2), (2065, 1.25 ), (2075, 1.29), (2085, 1.32 ), (2095, 1.35), (2105, 1.36) )

Units: watt/meter/meter

Radiative Forcing from Other GHGs (W/m^2) Additional surface warming from accumulation of other GHGs (NOx and Methane). [Table 4.9B, Managing Global Commons, pg. 73]

Uses:

(077) Radiative_Forcing = CO2_Rad_Forcing+Other_GHG_Rad_Forcing

Units: watt/meter/meter

Radiative Forcing from All GHGs (W/m^2) Additional surface warming from accumulation of CO2 & CFCs. [Cowles, Sec. III.F]

Causes:

Uses:

(078) Reference_Temperature = 3

Units: DegreesC

Reference Temperature for Calculation of Climate Damages [part of Nordhaus' variable theta1] [Managing Global Commons, pg. 18 and 21]

Uses:

(079) Temp_Diff = Atmos_UOcean_Temp-Deep_Ocean_Temp

Units: DegreesC

Temperature Difference between Upper and Deep Ocean (degrees C)

Causes:

Uses:

.control

(080) FINAL_TIME = 2105

Units: year

Uses:

(081) Init_Policy_Times[T] = 1965,1980,1995,2000,2005,2015,2025,2050,2075,2100 ,2200

Units: year

Year of implementation of Tth policy.

Uses:

(082) INITIAL_TIME = 1965

Units: year

Uses: (000)Time - Internally defined simulation time.

Uses:

(083) Policy_Interval = max(0,(Time-Policy_Times[T1])/(Policy_Times[T2]-Policy_Times [T1]))

Units: dmnl

Fractional weight for policy value interpolation. (000)Time - Internally defined simulation time.

Causes:

Uses:

(084) Policy_Time_Shift[TL] = IF_THEN_ELSE(Time >= Policy_Times[T2],(Policy_Times [TU]-Policy_Times[TL])/TIME_STEP ,0) Policy_Time_Shift[TT] = IF_THEN_ELSE(Time &gt= Policy_Times[T2],(FINAL_TIME- Policy_Times[TT])/TIME_STEP ,0)

Units: year/year

Shift in policy time vector. (000)Time - Internally defined simulation time.

Causes:

Uses:

(085) Policy_Times[T] = INTEG(Policy_Time_Shift[T],Init_Policy_Times[T])

Units: year

Year of implementation of Tth policy, in reverse order.

Causes:

Uses:

(086) SAVEPER = 5

Units: year

(087) T : (T1-t11) Subscript for policy optimization arrays

(088) TIME_STEP = 0.5

Units: year

Uses:

(089) TL : (T1-T10) -> TU Lower subscripts for policy optimization arrays

(090) TT : t11 Top subscript of array.

(091) TU : (T2-t11) -> TL Upper subscripts for policy optimization arrays

.Energy

Simple energy sector with conventional and alternative carbon fuels and a noncarbon fuel.

(092) Actual_Energy_Share = Total_Energy_Expend/Gross_Output

Units: dmnl

Actual share of energy expenditures in output.

Causes:

(093) Auton_Energy_Tech_Gr_Rt[source] = 0

Units: 1/year

Autonomous energy technology growth rate (cost reducing).

Uses:

(094) Auton_Tech_Multiplier[source] = EXP(-Auton_Energy_Tech_Gr_Rt[source]* (Time - INITIAL_TIME))

Units: dmnl

Cumulative autonomous energy technology progress. (000)Time - Internally defined simulation time.

Causes:

Uses:

(095) Average_Price = SUM(Weighted_Price[source!])

Units: $/GJ

Weighted average price of physical energy.

Causes:

Uses:

(096) Cumulative_Production[source] = INTEG(Production[source],Init_Cum_Prod [source])

Units: GJ

Cumulative production of energy, by source.

Causes:

Uses:

(097) Depletion_Coeff[carbon] = 2 Depletion_Coeff[non_carbon] = 0 Depletion_Coeff[alt_carbon] = 0

Units: dmnl

Coefficient of depletion nonlinearity; higher values indicate more abrubt depletion.

Uses:

(098) Depletion_Multiplier[source] = Low_Lim_Depletion[source]+(1-Low_Lim_Depletion [source])/(1+(Cumulative_Production [source]/Reference_Resource[source])^Depletion_Coeff[source])

Units: dmnl

Effect of depletion on unit cost of energy production. A decreasing function of cumulative production, approaching a lower limit as cumulative production becomes large with respect to the reference cumulative production level.

Causes:

Uses:

(099) Energy_Demand = Energy_Serv_Demand/Energy_Serv_Ratio

Units: GJ/year

Energy demand in physical terms

Causes:

Uses:

(100) Energy_Expend[source] = Production[source]*Price[source]

Units: $/year

Energy expenditures (including taxes).

Causes:

Uses:

(101) Energy_Intensity_of_Output = Energy_Serv_Demand/Gross_Output

Units: GJ/$

Energy Intensity of Output

Causes:

(102) Energy_Price = Average_Price/Energy_Serv_Ratio

Units: $/GJ

Price of energy services.

Causes:

Uses:

(103) Energy_Serv_Ratio = SUM(Share_Exp[source!])^(1/Energy_Subst_Coeff)

Units: dmnl

Ratio of energy services output (CES aggregate) to physical energy input

Causes:

Uses:

(104) Energy_Subst_Coeff = (Energy_Subst_Elast-1)/Energy_Subst_Elast

Units: dmnl

Coefficient of substitution for CES aggregate

Causes:

Uses:

(105) Energy_Subst_Elast = 2

Units: dmnl

Elasticity of substitution among energy sources.

Uses:

(106) Indicated_Share[source] = Price_Exp[source]/SUM(Price_Exp[source!])

Units: dmnl

Indicated share of energy sources in total output

Causes:

Uses:

(107) Init_Cum_Prod[carbon] = 5e+012 Init_Cum_Prod[non_carbon] = 2.5e+011 Init_Cum_Prod[alt_carbon] = 5e+011

Units: GJ

Initial cumulative production, by source.

Uses:

(108) Learning_Coeff[source] = LOG(1-Learning_Rate[source],2)

Units: dmnl

Learning curve coefficient.

Causes:

Uses:

(109) Learning_Rate[source] = 0.1

Units: dmnl

Learning rate, expressed as fractional reduction per doubling of experience.

Uses:

(110) Low_Lim_Depletion[carbon] = 0 Low_Lim_Depletion[non_carbon] = 1 Low_Lim_Depletion[alt_carbon] = 1

Units: dmnl

Lower limit to depletion effect Set to .25 for carbon energy, implying that a total shift to coal and non-conventional carbon fuels would involve a quadrupling of cost. Value for non-carbon energy is 1, indicating that there is no depletion effect.

Uses:

(111) Price[source] = Energy_Carbon_Tax[source]+Unit_Cost[source]

Units: $/GJ

Energy price.

Causes:

Uses:

(112) Price_Exp[source] = (Price[source]/Std_Price/Share_Coeff[source])^(-Energy_Subst_Elast )

Units: dmnl

Contribution of source prices to aggregate price.

Causes:

Uses:

(113) Production[source] = Energy_Demand*Indicated_Share[source]

Units: GJ/year

Physical energy production.

Causes:

Uses:

(114) Reference_Price[carbon] = 0.9 Reference_Price[non_carbon] = 5.4 Reference_Price[alt_carbon] = 3.6

Units: $/GJ

Initial or reference price of energy sources.

Uses:

(115) Reference_Resource[carbon] = 6e+013 Reference_Resource[non_carbon] = 1 Reference_Resource[alt_carbon] = 6e+014

Units: GJ

Initial resources of energy. Alt carbon value corresponds with total fossil resources, while carbon value is approximately 2x oil & gas resources.

Uses:

(116) Share_Coeff[source] = 1

Units: dmnl

Energy share coefficients, assumed equal for each source, so that initial share differences must be attributed to price.

Uses:

(117) Share_Exp[source] = Share_Coeff[source]*Indicated_Share[source]^Energy_Subst_Coeff

Units: dmnl

Weighted contribution of energy sources to energy services, for calculation of ratio of physical energy input to energy services output.

Causes:

Uses:

(118) source : carbon,non_carbon,alt_carbon Energy sources.

(119) Std_Price = 1

Units: $/GJ

Reference price (for unit consistency).

Uses:

(120) Technology_Multiplier[source] = (Cumulative_Production[source]/Init_Cum_Prod [source])^Learning_Coeff [ source]

Units: dmnl

Effect of learning on unit costs.

Causes:

Uses:

(121) Total_Energy_Expend = SUM(Energy_Expend[source!])

Units: $/year

Total expenditures on energy production, including taxes.

Causes:

Uses:

(122) Total_Energy_Prod = SUM(Production[source!])

Units: GJ/year

Total physical energy production.

Causes:

(123) Unit_Cost[source] = Reference_Price[source]/Depletion_Multiplier[source ] *Technology_Multiplier[source]*Auton_Tech_Multiplier[source]

Units: $/GJ

Unit cost of energy sources, dependent on technology, depletion, and initial price.

Causes:

Uses:

(124) Weighted_Price[source] = Indicated_Share[source]*Price[source]

Units: $/GJ

Weighted contribution of energy sources to average energy price.

Causes:

Uses:

.investment

(125) Behav_Inequal_Aversion = 1

Units: dmnl

Rate of inequality aversion characterizing behavior.

Uses:

(126) Behav_Invest_Frac = INTEG(Chg_Invest_Frac,0.22)

Units: dmnl

Investment fraction indicated by behavioral savings rule.

Causes:

Uses:

(127) Behav_Time_Pref = 0.03

Units: 1/year

Rate of time preference characterizing behavior.

Uses:

(128) Chg_Invest_Frac = (Desired_Invest_Frac-Behav_Invest_Frac)/Invest_Adj_Time

Units: 1/year

Rate of change of investment fraction (savings rate).

Causes:

Uses:

(129) Desired_Invest_Frac = Behav_Invest_Frac*(Desired_Return_on_Capital/Marg_Return_Capital )^Invest_Adj_Coeff

Units: dmnl

Desired savings rate, anchored to current savings rate and adjusted for prevailing returns.

Causes:

Uses:

(130) Desired_Return_on_Capital = Behav_Inequal_Aversion*Perceived_Growth_Rt +Behav_Time_Pref

Units: 1/year

Desired rate of return, assuming Ramsey equilibrium optimal investment conditions, in which interest rate = elast of marginal utility * growth rate + discount rate

Causes:

Uses:

(131) Growth_Trend_Avg_Time = 3

Units: year

Averaging time for perception of growth trend.

Uses:

(132) Init_Growth_Rt = 0.045

Units: 1/year

Initial perceived economic growth rate.

Uses:

(133) Init_Invest_Fracs[T] = 0.219,0.206,0.196,0.194,0.192,0.19,0.182,0.175 ,0.171,0.168,0.168

Units: dmnl

Investment fractions at time T. Default values from Nordhaus. Generally replaced by optimization.

Uses:

(134) Invest_Adj_Coeff = -1

Units: dmnl

Coefficient of adjustment of desired investment fraction.

Uses:

(135) Invest_Adj_Time = 10

Units: year

Savings rate adjustment time.

Uses:

(136) Invest_Fracs[T] = INTEG(Invest_Shift[T],Init_Invest_Fracs[T])

Units: dmnl

Investment Fractions at policy time T.

Causes:

Uses:

(137) Invest_Shift[TL] = IF_THEN_ELSE(Time >= Policy_Times[T2],(Invest_Fracs [TU]-Invest_Fracs[TL])/TIME_STEP ,0) Invest_Shift[TT] = 0

Units: 1/year

Shift in policy time vector. Top element (last time period) stays fixed. (000)Time - Internally defined simulation time.

Causes:

Uses:

(138) Investment_Frac = IF_THEN_ELSE(Investment_Switch=1,Optimal_Invest_Frac , IF_THEN_ELSE(Investment_Switch=0,Nord_Investment_Frac,Behav_Invest_Frac))

Units: dmnl

Fraction of Output Invested (savings rate)

Causes:

Uses:

(139) Investment_Frac_LOOKUP( (1965, 0.219), (1975, 0.21), (1985, 0.202), ( 1995, 0.196), (2005, 0.193), (2015 , 0.19), (2025, 0.182), (2035, 0.18), (2045, 0.178), (2055, 0.175), (2065, 0.173), (2075, 0.171), (2085 , 0.17), (2095, 0.168), (2105, 0.168) )

Units: dmnl

Fraction of Output allocated to Investment (dimensionless) Time path derived from results of optimization reported in [Cowles, Table IV-2, Optimal]. Intermediate points interpolated linearly. Points after 2075 estimated from [Cowles, Fig. IV-5].

Uses:

(140) Investment_Switch = 1

Units: dmnl

0 = Nordhaus reference path, 1 = Path from optimization, 2 = Behavioral

Uses:

(141) Net_Investment = Investment-Depreciation

Units: $/year

Net Investment Investment less depreciation

Causes:

Uses:

(142) Net_Savings_Rate = Net_Investment/Output

Units: dmnl

Net Savings Rate Equal to the ratio of net investment to output.

Causes:

(143) Nord_Investment_Frac = Investment_Frac_LOOKUP(Time)

Units: dmnl

Fraction of Output allocated to Investment (dimensionless) Time path derived from results of optimization reported in [Cowles, Table IV-2, Optimal]. Intermediate points interpolated linearly. Points after 2075 estimated from [Cowles, Fig. IV-5]. (000)Time - Internally defined simulation time.

Causes:

Uses:

(144) Optimal_Invest_Frac = Invest_Fracs[T2]*Policy_Interval+Invest_Fracs[T1 ]*(1-Policy_Interval)

Units: dmnl

Investment Fraction derived from optimization.

Causes:

Uses:

(145) Perceived_Growth_Rt = TREND(Output,Growth_Trend_Avg_Time,Init_Growth_Rt )

Units: 1/year

Perceived economic growth rate.

Causes:

Uses:

.Modified

Alternative carbon cycle representation, using a box-diffusion structure. Developed by analytically reducing a more complex model to eliminate time constants shorter than 5 years. The full model is available from the author, and is based on: Goudriaan, J., & Ketner, P. (1984). A Simulation Study for the Global Carbon Cycle, Including Man's Impact on the Biosphere. Climatic Change, 6, 167-192. Oeschger, H., Siegenthaler, U., Schotterer, U., & Gugelmann, A. (1975). A Box Diffusion Model to Study the Carbon Dioxide Exchange in Nature. Tellus, XXVII(2), 167-192. Rotmans, Jan (1990). IMAGE: An Integrated Model to Assess the Greenhouse Effect. Boston: Kluwer Academic Publishers.

(146) Atmospheric_Retention = (Emissions-Diffusion_Flux[layer1]-Flux_AtmMix_to_Biosphere )/Emissions

Units: dmnl

Average atmospheric retention of CO2

Causes:

(147) Biosphere_Res_Time = 25

Units: year

Residence time of CO2 in the biosphere. Trees and soils have longer residence times.

Uses:

(148) Biostim_Coeff = 0.3

Units: dmnl

Sensitivity of primary production to changes in atmospheric CO2 concentration.

Uses:

(149) bottom5 : (layer6-layer10) Bottom 5 (thick) ocean layers.

(150) Buffer_Factor = 10

Units: dmnl

Revelle or Buffer factor; relates increase in ocean CO2 partial pressure to ocean carbon concentration.

Uses:

(151) CO2_in_AtmMix = INTEG(Emissions-Diffusion_Flux[layer1]-Flux_AtmMix_to_Biosphere , Init_CO2_in_Atm+Init_CO2_in_Mixed_Layer)

Units: TonC

CO2 in atmosphere and mixed ocean layer.

Causes:

Uses:

(152) CO2_in_Atmosphere = (CO2_in_AtmMix-Init_CO2_in_Mixed_Layer*(1-1/Buffer_Factor )) /(1+Init_CO2_in_Mixed_Layer/Init_CO2_in_Atm/Buffer_Factor)

Units: TonC

CO2 in atmosphere, from equilibrium solution to more complex model with explicit atmosphere and mixed layer stocks.

Causes:

Uses:

(153) CO2_in_Biosphere = INTEG(Flux_AtmMix_to_Biosphere,Init_NPP*Biosphere_Res_Time )

Units: TonC

CO2 in terrestrial biota.

Causes:

Uses:

(154) CO2_in_Deep_Ocean[upper] = INTEG(Diffusion_Flux[upper]-Diffusion_Flux [lower], Init_CO2_in_Deep_Ocean*Thickness[upper]/Deep_Ocean_Depth) CO2_in_Deep_Ocean[layer10] = INTEG(Diffusion_Flux[layer10], Init_CO2_in_Deep_Ocean*Thickness[layer10]/Deep_Ocean_Depth)

Units: TonC

CO2 in deep ocean, by layer.

Causes:

Uses:

(155) CO2_in_Mixed_Layer = CO2_in_AtmMix-CO2_in_Atmosphere

Units: TonC

CO2 in mixed ocean layer, from equilibrium solution to more complex model with explicit atmosphere and mixed layer stocks.

Causes:

Uses:

(156) Concentration[layers] = CO2_in_Deep_Ocean[layers]/Thickness[layers]

Units: TonC/meter

CO2 concentration in deep ocean layers.

Causes:

Uses:

(157) Deep_Ocean_Depth = 3800

Units: meter

Total thickness of the deep ocean.

Uses:

(158) Diffusion_Flux[layer1] = (CO2_in_Mixed_Layer/Mixed_Depth-Concentration [layer1])*Eddy_Diff_Coeff *2/(Mixed_Depth+Thickness[layer1]) Diffusion_Flux[lower] = (Concentration[upper]-Concentration[lower])*Eddy_Diff_Coeff *2/(Thickness[upper]+Thickness[lower])

Units: TonC/year

Diffusion flux of CO2 between ocean layers.

Causes:

Uses:

(159) Eddy_Diff_Coeff = 4000

Units: meter*meter/year

Ocean diffusion flux coefficient.

Uses:

(160) Emissions = CO2_Emissions

Units: TonC/year

Total anthropogenic CO2 emissions to the atmosphere.

Causes:

Uses:

(161) Flux_AtmMix_to_Biosphere = Init_NPP*(CO2_in_Atmosphere/Preindustrial_CO2 )^Biostim_Coeff - CO2_in_Biosphere/Biosphere_Res_Time

Units: TonC/year

Net flow of carbon from the atmosphere and mixed layer to the biosphere.

Causes:

Uses:

(162) Init_CO2_in_Atm =6.77e+011

Units: TonC

CO2 in Atmosphere in 1965 (Preindustrial level is 5.9e11)

Uses:

(163) Init_CO2_in_Deep_Ocean = Init_CO2_in_Mixed_Layer*Deep_Ocean_Depth/Mixed_Depth

Units: TonC

Initial CO2 in deep ocean

Causes:

Uses:

(164) Init_CO2_in_Mixed_Layer = 7.678e+011

Units: TonC

Initial CO2 in mixed ocean layer

Uses:

(165) Init_NPP = 6e+010

Units: TonC/year

Initial net primary production

Uses:

(166) layers : (layer1-layer10) Deep ocean layers.

(167) lower : (layer2-layer10) -> upper Lower 9 deep ocean layers.

(168) Mixed_Depth = 75

Units: meter

Depth of mixed ocean layer.

Uses:

(169) Thickness[top5] = 200 Thickness[bottom5] = 560

Units: meter

Layers chosen to be relatively thick, as fast dynamics are not of interest.

Uses:

(170) top5 : (layer1-layer5) Top 5 (thin) ocean layers.

(171) upper : (layer1-layer9) -> lower Upper 9 deep ocean layers.

.Nonenergy

Emissions from nonenergy sources are treated using the emissions reduction cost curve from DICE and equating the carbon tax with the marginal cost of reductions.

(172) Decline_Nonenergy_CO2_Intens = Nonenergy_CO2_Int_of_Output*Nonenergy_CO2_Intens_Decline_Rt

Units: TonC/$/year

Decline of GHG Intensity of Output (tons carbon equivalent/$/year) [Cowles, pg. 20]

Causes:

Uses:

(173) GHG_Reduction_Frac = IF_THEN_ELSE(Carbon_Tax > 0, MIN(1,(Carbon_Tax*Nonenergy_CO2_Int_of_Output/Red_Cost_Scale/Red_Cost_Nonlinearity ) ^(1/(Red_Cost_Nonlinearity-1))), 0)

Units: dmnl

Fraction of Nonenergy Greenhouse Gas Emissions Abated Set so that the marginal productivity of nonenergy carbon equals the carbon tax. IF statement added to prevent floating point error on Windows platform.

Causes:

Uses:

(174) Nonenergy_CO2_Emiss = (1-GHG_Reduction_Frac)*Nonenergy_CO2_Int_of_Output *Gross_Output

Units: TonC/year

Greenhouse Gas Emissions [E(t)] (tons carbon equivalent/year) [Cowles, pg. 20]

Causes:

Uses:

(175) Nonenergy_CO2_Int_of_Output = INTEG(- Decline_Nonenergy_CO2_Intens, Ref_Nonenergy_CO2_Emiss /Output_in_1965 )

Units: TonC/$

Greenhouse Gas Intensity of Output [sigma(t)] (tons carbon equivalent/$) Conflicts with value reported on Cowles, pg. 24: .5368*.9875^(TIME-1990)/1000 = .7352/1000 [Managing Global Commons, pg. 21]

Causes:

Uses:

(176) Nonenergy_CO2_Intens_Dec_Rt_Decline_Rt = Nonenergy_CO2_Intens_Decline_Rt *Fact_Prod_Gr_Rt_Dec_Rt

Units: 1/year/year

Rate of decline of nonenergy CO2 intensity decline rate (2nd derivative).

Causes:

Uses:

(177) Nonenergy_CO2_Intens_Decline_Rt = INTEG(- Nonenergy_CO2_Intens_Dec_Rt_Decline_Rt , 0.01168)

Units: 1/year

Rate of Decline of Greenhouse Gas Intensity of Output [g-sigma] (1/year) Note that Nordhaus decompounds the decadal rate of .1168 to yield an annual rate of .0125; I have simply divided by 10 to convert the decadal rate to an annual rate. [Managing Global Commons, pg. 21]

Causes:

Uses:

(178) Nonenergy_CO2_Red_Cost = Gross_Output*Nonenergy_CO2_Red_Cost_Frac

Units: $/year

Cost of nonenergy CO2 emissions abatement.

Causes:

Uses:

(179) Nonenergy_CO2_Red_Cost_Frac = IF_THEN_ELSE(GHG_Reduction_Frac>0, Red_Cost_Scale*GHG_Reduction_Frac^Red_Cost_Nonlinearity, 0)

Units: dmnl

Fraction of Output devoted to cost of GHG emissions reductions (dimensionless) IF statement added to prevent floating point error on Windows platform.

Causes:

Uses:

(180) Red_Cost_Nonlinearity = 2.887

Units: dmnl

Nonlinearity of GHG Reduction Cost [b2] (dimensionless) [Cowles, pg. 13 & 24]

Uses:

(181) Red_Cost_Scale = 0.0211

Units: dmnl

Scale of Nonenergy CO2 Reduction Cost Equals Nordhaus' figure of .0686 multiplied by the initial share of nonenergy emissions in total emissions.

Uses:

(182) Ref_Nonenergy_CO2_Emiss = 1.36e+009

Units: TonC/year

Uses:

.output

From DICE, with explicit intangibles from: Tol, Richard S.J. (1994). The Damage Costs of Climate Change: a Note on Tangibles and Intangibles, Applied to DICE. Energy Policy, 22(5), 436-438.

(183) Capital_Elast_Output = 0.25

Units: dmnl

Capital Elasticity of Output [alpha] (dimensionless) Derived from share of capital in national income. [Cowles, pg. 17]

Uses:

(184) Climate_Damage_Cost = Climate_Damage_Frac*Gross_Output

Units: $/year

Output lost or diverted due to climate change.

Causes:

Uses:

(185) Consumption = Output-Investment

Units: $/year

Consumption ($/year) Output less investment (savings).

Causes:

Uses:

(186) Consumption_per_Cap = Output/Population

Units: $/person/year

Consumption of goods per Capita ($/person/year)

Causes:

(187) Eff_Consumption_per_Cap = Effective_Consumption/Population

Units: $/person/year

Consumption of goods less climate damages per Capita ($/person/year)

Causes:

Uses:

(188) Effective_Consumption = Consumption-Intangible_Damage_Cost

Units: $/year

Consumption of goods less losses from environmental damage due to climate change.

Causes:

Uses:

(189) Fact_Prod_Gr_Rt_Dec_Rt = 0.011

Units: 1/year

Rate of Decline of Factor Productivity Growth Rate [delta-A] (1/year/year) Factor productivity growth rate declines 11% per decade. [Cowles, pg. 18]

Uses:

(190) Fact_Prod_Gr_Rt_Decline_Rt = Fact_Prod_Growth_Rt*Fact_Prod_Gr_Rt_Dec_Rt

Units: 1/year/year

Decline of Factor Productivity Growth Rate (1/year/year)

Causes:

Uses:

(191) Fact_Prod_Growth_Rt = INTEG(- Fact_Prod_Gr_Rt_Decline_Rt, 0.015)

Units: 1/year

Growth Rate of Factor Productivity [gA(t)] (1/year) Growth rate declines over time. Value reported in [Cowles, pg. 17]: .0152 for period 1965-1987, matches statement in [Science, pg. 1317] that average was 1.3% from 1965-1989, with an 11%/decade rate of decline. Note that Nordhaus decompounds the decadal rate of .150 to yield an annual rate of .014; I have simply divided by 10 to convert the decadal rate to an annual rate. [Managing Global Commons, pg. 21] [Managing the Global Commons, pg. 21]

Causes:

Uses:

(192) Fact_Prod_Incr_Rt = Factor_Productivity*Fact_Prod_Growth_Rt

Units: 1/year

Change in Factor Productivity (1/year)

Causes:

Uses:

(193) Factor_Productivity = INTEG(Fact_Prod_Incr_Rt, 1)

Units: dmnl

Total Factor Productivity [A(t)] (dimensionless) May be interpreted as level of technology. [Cowles pg. 17]

Causes:

Uses:

(194) Frac_Clim_Dam_Tangible = 1

Units: dmnl

Fraction of climate change damage costs which are tangible (that is, those which appear on national accounts and may be substituted with other goods).

Uses:

(195) Gross_Output = Output_in_1965*Factor_Productivity*(Effective_Capital/ INIT(Effective_Capital))^Capital_Elast_Output *(Population/INIT(Population))^(1-Capital_Elast_Output)

Units: $/year

Reference Output before effects of climate damage and emissions abatement are considered

Causes:

Uses: