the times climate module progress report

THE TIMES CLIMATE MODULEProgress Report

AMIT KANUDIA, MARYSE LABRIET, ANTTI LEHTILA, RICHARD LOULOU, UWE REMNE

ETSAP Workshop, Nov 2004, Firenze

ETSAP Firenze Nov 2004 2

OBJECTIVES

1. Endogenize CO2 concentrations in TIMES

2. Calculate Total Change in Radiative forcing due to GHG emissions

3. Calculate global Temperature Change due to GHG emissions

4. Keep entire model linear

5. Extension to Multigas ?


APPROACH• Calculate CO2 concentrations in three

reservoirs as functions of global emissions

• Calculate CO2 radiative forcing as function of atmospheric concentration

• Add (exogenous) radiative forcing from other gases

• Calculate Global temperature changes in two reservoirs as functions of forcing


CO2 CONCENTRATIONS(adapted from Nordhaus and Boyer 1999)

1. CO2atm(t) = Emiss(t) + CO2atm(t-1)*(1-fatm,up)

+ CO2up(t-1)*fup,atm

2. CO2up(t) = CO2up(t-1)*(1-fup,atm -fup,lo)

+ CO2lo(t-1)* flo,up

+ CO2atm(t-1)*fatm,up

3. CO2lo(t) = CO2lo(t-1)*(1-flo,up)

+ CO2up(t-1)* fup,lo

Units for t : years; Units for CO2: Gt Carbon


ATMOSPHERE

UPPER OCEAN

LOWER OCEAN

THREE RESERVOIR MODEL FOR CONCENTRATION CHANGES(Adapted from Nordhaus and Boyer)

EMISSIONS


CHANGE IN RADIATIVE FORCING(from IPCC 2001)

DELTA_F(t) =

(γ/ln2)*ln[CO2atm(t)/CO2atm(pre-ind)] + O(t)

Units for t : yearsUnits for DELTA_F: W/m2

Where O(t) is the exogenous forcing from other gases (Methane, N2O, aerosols, etc). Represents less than 15% of total forcing until 2100.

- 0.1965 + 0.013465 *(t-1995) , if 1995 ≤ t ≤ 2095 O(t) =

+1.15 , if t > 2095


TEMPERATURE CHANGES(adapted from Nordhaus and Boyer, 1999)

1. DTup(t) = σ1*DELTA_F(t)

+ DTup(t-1)*g1,1

+ DTlo (t-1)*g2,1

2. DTlo(t) = DTup(t-1)* g1,2

+ DTlo (t-1)* g2,2

Units for DT: oC above pre-industrial equilibrium temperatures


ATMOSPHERE

AND UPPER OCEAN

LOWER OCEAN

TWO RESERVOIR MODEL FOR TEMPERATURE CHANGES(Adapted from Nordhaus and Boyer, 1999)

RADIATIVE FORCING


Calibration• The coefficients have been adapted to

provide a best fit with Nordhaus and Boyer 1999, itself calibrated to more detailed climate models

• The coefficients depend on the TIMES period lengths. Therefore they are internally calculated in TIMES

• Initial concentrations are user provided, with default values for 1995


Use of Module• Currently, only CO2 concentration equations

may be used as constraints. User may specify bounds on CO2 concentration variables

• Non-linear Radiative forcing equation is only for reporting purposes, same for Temperature changes.

• Possible further work: Linearize radiative forcing equation and implement an iterative optimization scheme to endogenize Forcing and Temperature Changes (useful for imposing constraints on speed of temperature change)


Use of Module Cont’d

• The module may be used even if the model is not global. In such a case, the exogenous forcing O(t) should represent forcing from other gases plus forcing from CO2 in the non modeled regions


PROGRESS REPORT

• Variables, parameters, equations: finalized

• GAMS code: written and tested

• Documentation: written

• Parameters in VEDA_FE: in progress

• Results in VEDA_BE: in progress

• Full experimentation: to be done


Possible Extension

1. Approximate Forcing via linear function, tangent to forcing surface at some ‘guessed’ point.

2. If guessed point is right, stop

3. Else, modify guessed point, and GOTO 1

Remark: if forcing is to be endogenized at a single time: only 1 guessed point is needed. If forcing is to be endogenized at all times, more guesses are needed.


Linear approximation of CO2 forcing

0

1

2

3

4

5

6

200.0 300.0 400.0 500.0 600.0 700.0 800.0

CO2 concentration

Fo

rcin

g (

W/s

q m

)

forcing

approx forcing

Guessed Point

the times climate module progress report

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