Modelling of climate indicators - IMACLIM - Revision history

Eoin OBroin at 17:09, 14 December 2016

2016-12-14T17:09:39Z

← Older revision		Revision as of 19:09, 14 December 2016
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	The initial values of ''A'', ''B'', and ''O'', and the parameters ''a12'', ''a21'', ''a23'', and ''a32'' determine the fluxes between reservoirs. The main criticism which may be addressed to this Carbon-cycle model is that the transfer coefficients are constant. In particular, they do not depend on the carbon content of the reservoir (e.g. deforestation hindering biospheric sinks) nor are they influenced by ongoing climatic change (e.g. positive feedbacks between climate change and the carbon cycle).		The initial values of ''A'', ''B'', and ''O'', and the parameters ''a12'', ''a21'', ''a23'', and ''a32'' determine the fluxes between reservoirs. The main criticism which may be addressed to this Carbon-cycle model is that the transfer coefficients are constant. In particular, they do not depend on the carbon content of the reservoir (e.g. deforestation hindering biospheric sinks) nor are they influenced by ongoing climatic change (e.g. positive feedbacks between climate change and the carbon cycle).

	Nordhaus? original calibration has been adapted to reproduce both; data until 2010 and; results from the IMAGE model for a given trajectory of ''CO<sub>2</sub>'' emissions. This gives the following results (for a yearly time step): ''a12''= 0.02793, ''a21''=0.03427, ''a23''=0.007863, ''a32''=0.0003552, with the initial conditions: ''A''2010=830 ''GtC'' (i.e. 391ppm), ''B''2010=845 ''GtC'' and ''O''2010=19254 ''GtC''. The additional forcing caused by ''CO<sub>2</sub>'' and ''non-CO<sub>2</sub>'' gases is given by		Nordhaus' original calibration has been adapted to reproduce both; data until 2010 and; results from the IMAGE model for a given trajectory of ''CO<sub>2</sub>'' emissions. This gives the following results (for a yearly time step): ''a12''= 0.02793, ''a21''=0.03427, ''a23''=0.007863, ''a32''=0.0003552, with the initial conditions: ''A''2010=830 ''GtC'' (i.e. 391ppm), ''B''2010=845 ''GtC'' and ''O''2010=19254 ''GtC''. The additional forcing caused by ''CO<sub>2</sub>'' and ''non-CO<sub>2</sub>'' gases is given by

	[[File:35815689.png]]		[[File:35815689.png]]

Eoin OBroin at 14:28, 12 October 2016

2016-10-12T14:28:46Z

← Older revision		Revision as of 16:28, 12 October 2016
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	=== Carbon Cycle Model and Climate Model ===		=== Carbon Cycle Model and Climate Model ===

	The carbon cycle is a three-box model, after Nordhaus and Boyer (2010)[[CiteRef::nordhaus2003warming]]. The model is a linear three-reservoir model (atmosphere, biosphere + ocean mixed layer, and deep ocean). Each reservoir is assumed to be homogenous (well-mixed in the short run) and is characterized by a residence time inside the box and corresponding mixing rates with the two other reservoirs (for longer timescales). Carbon flows between reservoirs depend on constant transfer coefficients. GHGs emissions (CO<sub>2</sub> solely) accumulate in the atmosphere and are slowly removed by biospheric and oceanic sinks.		The carbon cycle is a three-box model, after Nordhaus and Boyer (2010)[[CiteRef::nordhaus2003warming]]. The model is a linear three-reservoir model (atmosphere, biosphere + ocean mixed layer, and deep ocean). Each reservoir is assumed to be homogenous (well-mixed in the short run) and is characterized by a residence time inside the box and corresponding mixing rates with the two other reservoirs (for longer timescales). Carbon flows between reservoirs depend on constant transfer coefficients. GHGs emissions (''CO<sub>2</sub>'' solely) accumulate in the atmosphere and are slowly removed by biospheric and oceanic sinks.

	The stocks of carbon (in the form of ''CO<sub>2</sub>'') in the atmosphere, in the biomass and upper ocean, and in the deep ocean are, respectively, ''A'', ''B'', and ''O''. The variable ''E'' is the ''CO<sub>2</sub>'' emissions. The evolution of ''A'', ''B'', and ''O'' is given by		The stocks of carbon (in the form of ''CO<sub>2</sub>'') in the atmosphere, in the biomass and upper ocean, and in the deep ocean are, respectively, ''A'', ''B'', and ''O''. The variable ''E'' is the ''CO<sub>2</sub>'' emissions. The evolution of ''A'', ''B'', and ''O'' is given by

Eoin OBroin at 11:13, 12 October 2016

2016-10-12T11:13:05Z

← Older revision		Revision as of 13:13, 12 October 2016
Line 16:		Line 16:
	The carbon cycle is a three-box model, after Nordhaus and Boyer (2010)[[CiteRef::nordhaus2003warming]]. The model is a linear three-reservoir model (atmosphere, biosphere + ocean mixed layer, and deep ocean). Each reservoir is assumed to be homogenous (well-mixed in the short run) and is characterized by a residence time inside the box and corresponding mixing rates with the two other reservoirs (for longer timescales). Carbon flows between reservoirs depend on constant transfer coefficients. GHGs emissions (CO<sub>2</sub> solely) accumulate in the atmosphere and are slowly removed by biospheric and oceanic sinks.		The carbon cycle is a three-box model, after Nordhaus and Boyer (2010)[[CiteRef::nordhaus2003warming]]. The model is a linear three-reservoir model (atmosphere, biosphere + ocean mixed layer, and deep ocean). Each reservoir is assumed to be homogenous (well-mixed in the short run) and is characterized by a residence time inside the box and corresponding mixing rates with the two other reservoirs (for longer timescales). Carbon flows between reservoirs depend on constant transfer coefficients. GHGs emissions (CO<sub>2</sub> solely) accumulate in the atmosphere and are slowly removed by biospheric and oceanic sinks.

	The stocks of carbon (in the form of CO<sub>2</sub>) in the atmosphere, in the biomass and upper ocean, and in the deep ocean are, respectively, A, B, and O. The variable E is the CO<sub>2</sub> emissions. The evolution of A, B, and O is given by		The stocks of carbon (in the form of ''CO<sub>2</sub>'') in the atmosphere, in the biomass and upper ocean, and in the deep ocean are, respectively, ''A'', ''B'', and ''O''. The variable ''E'' is the ''CO<sub>2</sub>'' emissions. The evolution of ''A'', ''B'', and ''O'' is given by

	[[File:35815687.png]]		[[File:35815687.png]]
Line 22:		Line 22:
	The fluxes are equal to<br />[[File:35815688.png]]		The fluxes are equal to<br />[[File:35815688.png]]

	The initial values of A, B, and O, and the parameters a12, a21, a23, and a32 determine the fluxes between reservoirs. The main criticism which may be addressed to this Carbon-cycle model is that the transfer coefficients are constant. In particular, they do not depend on the carbon content of the reservoir (e.g. deforestation hindering biospheric sinks) nor are they influenced by ongoing climatic change (e.g. positive feedbacks between climate change and the carbon cycle).		The initial values of ''A'', ''B'', and ''O'', and the parameters ''a12'', ''a21'', ''a23'', and ''a32'' determine the fluxes between reservoirs. The main criticism which may be addressed to this Carbon-cycle model is that the transfer coefficients are constant. In particular, they do not depend on the carbon content of the reservoir (e.g. deforestation hindering biospheric sinks) nor are they influenced by ongoing climatic change (e.g. positive feedbacks between climate change and the carbon cycle).

	Nordhaus? original calibration has been adapted to reproduce both; data until 2010 and; results from the IMAGE model for a given trajectory of CO<sub>2</sub> emissions. This gives the following results (for a yearly time step): a12= 0.02793, a21=0.03427, a23=0.007863, a32=0.0003552, with the initial conditions: ~~A2010~~=830 GtC (i.e. 391ppm), ~~B2010~~=845 GtC and ~~O2010~~=19254 GtC. The additional forcing caused by CO<sub>2</sub> and non-CO<sub>2</sub> gases is given by		Nordhaus? original calibration has been adapted to reproduce both; data until 2010 and; results from the IMAGE model for a given trajectory of ''CO<sub>2</sub>'' emissions. This gives the following results (for a yearly time step): ''a12''= 0.02793, ''a21''=0.03427, ''a23''=0.007863, ''a32''=0.0003552, with the initial conditions: ''A''2010=830 ''GtC'' (i.e. 391ppm), ''B''2010=845 ''GtC'' and ''O''2010=19254 ''GtC''. The additional forcing caused by ''CO<sub>2</sub>'' and ''non-CO<sub>2</sub>'' gases is given by

	[[File:35815689.png]]		[[File:35815689.png]]

	where A<sub>PI</sub> is the pre-industrial CO<sub>2</sub> concentration (280 ppm), F<sub>2x</sub> is the additional radiative forcing for a doubling of the CO<sub>2</sub> concentration (3.71 W.m^-2^), and F<sub>non-CO2</sub> is the additional radiative forcing of non-CO<sub>2</sub> gases.		where ''A<sub>PI</sub>'' is the pre-industrial ''CO<sub>2</sub>'' concentration (280 ppm), ''F<sub>2x</sub>'' is the additional radiative forcing for a doubling of the ''CO<sub>2</sub>'' concentration (3.71 W.m^-2^), and ''F<sub>non-CO2</sub>'' is the additional radiative forcing of ''non-CO<sub>2</sub>'' gases.

	The temperature model is a two-box model, after Schneider and Thompson (1981)[[CiteRef::schneider1981atmospheric]] and Ambrosi ''et al.'' (2003)[[CiteRef::ambrosi2009optimal]], with the atmosphere temperature ''T<sub>A</sub>'' and the ocean temperature ''T<sub>O</sub>'' as follows:		The temperature model is a two-box model, after Schneider and Thompson (1981)[[CiteRef::schneider1981atmospheric]] and Ambrosi et al. (2003)[[CiteRef::ambrosi2009optimal]], with the atmosphere temperature ''T<sub>A</sub>'' and the ocean temperature ''T<sub>O</sub>'' as follows:

	[[File:35815690.png]]		[[File:35815690.png]]

	where T2x is the equilibrium temperature increase at the doubling of the CO<sub>2</sub> concentration, that is, it represents climate sensitivity. All parameters have been calibrated to reproduce results from CMIP5 from CNRM-CERFACS global climate model, CNRM-CM5, over the 21st century for RCP3-PD and RCP4.5 radiative forcing trajectories (using a least squares method). This calibration leads to the following parameter values for heat transfer rates (for a yearly time step): ''σ1''= 0.054''C.W<~~sub~~>-1</~~sub~~>-1.m<~~sub~~>2</~~sub~~>'', ''σ2''= 0.664 ''C.W<~~sub~~>-1</~~sub~~>-1.m<~~sub~~>2</~~sub~~>'' and ''σ3''= 0.0308, and a climate sensitivity of 2.6°C.		where ''T2x'' is the equilibrium temperature increase at the doubling of the ''CO<sub>2</sub>'' concentration, that is, it represents climate sensitivity. All parameters have been calibrated to reproduce results from CMIP5 from CNRM-CERFACS global climate model, CNRM-CM5, over the 21st century for RCP3-PD and RCP4.5 radiative forcing trajectories (using a least squares method). This calibration leads to the following parameter values for heat transfer rates (for a yearly time step): ''σ1''= 0.054''C.W<sup>-1</sup>-1.m<sup>2</sup>'', ''σ2''= 0.664 ''C.W<sup>-1</sup>-1.m<sup>2</sup>'' and ''σ3''= 0.0308, and a climate sensitivity of 2.6°C.

Eoin OBroin: /* Modelling of Climate indicators */

2016-10-12T11:07:06Z

Modelling of Climate indicators

← Older revision		Revision as of 13:07, 12 October 2016
Line 34:		Line 34:
	[[File:35815690.png]]		[[File:35815690.png]]

	where T2x is the equilibrium temperature increase at the doubling of the CO<sub>2</sub> concentration, that is, it represents climate sensitivity. All parameters have been calibrated to reproduce results from CMIP5 from CNRM-CERFACS global climate model, CNRM-CM5, over the 21st century for RCP3-PD and RCP4.5 radiative forcing trajectories (using a least squares method). This calibration leads to the following parameter values for heat transfer rates (for a yearly time step): ?1= 0.~~054C~~.W-1.m2, ?2= 0.664 C-1.W.m-2 and ?3= 0.0308, and a climate sensitivity of 2.6°C.		where T2x is the equilibrium temperature increase at the doubling of the CO<sub>2</sub> concentration, that is, it represents climate sensitivity. All parameters have been calibrated to reproduce results from CMIP5 from CNRM-CERFACS global climate model, CNRM-CM5, over the 21st century for RCP3-PD and RCP4.5 radiative forcing trajectories (using a least squares method). This calibration leads to the following parameter values for heat transfer rates (for a yearly time step): ''σ1''= 0.054''C.W<sub>-1</sub>-1.m<sub>2</sub>'', ''σ2''= 0.664 ''C.W<sub>-1</sub>-1.m<sub>2</sub>'' and ''σ3''= 0.0308, and a climate sensitivity of 2.6°C.

Eoin OBroin at 15:40, 11 October 2016

2016-10-11T15:40:08Z

← Older revision		Revision as of 17:40, 11 October 2016
Line 14:		Line 14:
	=== Carbon Cycle Model and Climate Model ===		=== Carbon Cycle Model and Climate Model ===

	The carbon cycle is a three-box model, after Nordhaus and Boyer (2010). The model is a linear three-reservoir model (atmosphere, biosphere + ocean mixed layer, and deep ocean). Each reservoir is assumed to be homogenous (well-mixed in the short run) and is characterized by a residence time inside the box and corresponding mixing rates with the two other reservoirs (for longer timescales). Carbon flows between reservoirs depend on constant transfer coefficients. GHGs emissions (CO<sub>2</sub> solely) accumulate in the atmosphere and are slowly removed by biospheric and oceanic sinks.		The carbon cycle is a three-box model, after Nordhaus and Boyer (2010)[[CiteRef::nordhaus2003warming]]. The model is a linear three-reservoir model (atmosphere, biosphere + ocean mixed layer, and deep ocean). Each reservoir is assumed to be homogenous (well-mixed in the short run) and is characterized by a residence time inside the box and corresponding mixing rates with the two other reservoirs (for longer timescales). Carbon flows between reservoirs depend on constant transfer coefficients. GHGs emissions (CO<sub>2</sub> solely) accumulate in the atmosphere and are slowly removed by biospheric and oceanic sinks.

	The stocks of carbon (in the form of CO<sub>2</sub>) in the atmosphere, in the biomass and upper ocean, and in the deep ocean are, respectively, A, B, and O. The variable E is the CO<sub>2</sub> emissions. The evolution of A, B, and O is given by		The stocks of carbon (in the form of CO<sub>2</sub>) in the atmosphere, in the biomass and upper ocean, and in the deep ocean are, respectively, A, B, and O. The variable E is the CO<sub>2</sub> emissions. The evolution of A, B, and O is given by
Line 30:		Line 30:
	where A<sub>PI</sub> is the pre-industrial CO<sub>2</sub> concentration (280 ppm), F<sub>2x</sub> is the additional radiative forcing for a doubling of the CO<sub>2</sub> concentration (3.71 W.m^-2^), and F<sub>non-CO2</sub> is the additional radiative forcing of non-CO<sub>2</sub> gases.		where A<sub>PI</sub> is the pre-industrial CO<sub>2</sub> concentration (280 ppm), F<sub>2x</sub> is the additional radiative forcing for a doubling of the CO<sub>2</sub> concentration (3.71 W.m^-2^), and F<sub>non-CO2</sub> is the additional radiative forcing of non-CO<sub>2</sub> gases.

	The temperature model is a two-box model, after Schneider and Thompson (1981) and Ambrosi ''et al.'' (2003), with the atmosphere temperature ''T<sub>A</sub>'' and the ocean temperature ''T<sub>O</sub>'' as follows:		The temperature model is a two-box model, after Schneider and Thompson (1981)[[CiteRef::schneider1981atmospheric]] and Ambrosi ''et al.'' (2003)[[CiteRef::ambrosi2009optimal]], with the atmosphere temperature ''T<sub>A</sub>'' and the ocean temperature ''T<sub>O</sub>'' as follows:

	[[File:35815690.png]]		[[File:35815690.png]]

	where T2x is the equilibrium temperature increase at the doubling of the CO<sub>2</sub> concentration, that is, it represents climate sensitivity. All parameters have been calibrated to reproduce results from CMIP5 from CNRM-CERFACS global climate model, CNRM-CM5, over the 21st century for RCP3-PD and RCP4.5 radiative forcing trajectories (using a least squares method). This calibration leads to the following parameter values for heat transfer rates (for a yearly time step): ?1= 0.054C.W-1.m2, ?2= 0.664 C-1.W.m-2 and ?3= 0.0308, and a climate sensitivity of 2.6°C.		where T2x is the equilibrium temperature increase at the doubling of the CO<sub>2</sub> concentration, that is, it represents climate sensitivity. All parameters have been calibrated to reproduce results from CMIP5 from CNRM-CERFACS global climate model, CNRM-CM5, over the 21st century for RCP3-PD and RCP4.5 radiative forcing trajectories (using a least squares method). This calibration leads to the following parameter values for heat transfer rates (for a yearly time step): ?1= 0.054C.W-1.m2, ?2= 0.664 C-1.W.m-2 and ?3= 0.0308, and a climate sensitivity of 2.6°C.

Rineke Oostenrijk: Text replacement - "(Image:.IMPORT\/attachments\/[0-9]\/[0-9]*.png\|)" to "File:"

2016-08-24T11:51:03Z

Text replacement - "(Image:.*IMPORT\/attachments\/[0-9]*\/[0-9]*.png\|)" to "File:"

← Older revision		Revision as of 13:51, 24 August 2016
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	The stocks of carbon (in the form of CO<sub>2</sub>) in the atmosphere, in the biomass and upper ocean, and in the deep ocean are, respectively, A, B, and O. The variable E is the CO<sub>2</sub> emissions. The evolution of A, B, and O is given by		The stocks of carbon (in the form of CO<sub>2</sub>) in the atmosphere, in the biomass and upper ocean, and in the deep ocean are, respectively, A, B, and O. The variable E is the CO<sub>2</sub> emissions. The evolution of A, B, and O is given by

	[[~~Image~~:~~IMACLIMIMPORT/attachments/34379251/35815687.png\|~~35815687.png]]		[[File:35815687.png]]

	The fluxes are equal to<br />[[~~Image~~:~~IMACLIMIMPORT/attachments/34379251/35815688.png\|~~35815688.png]]		The fluxes are equal to<br />[[File:35815688.png]]

	The initial values of A, B, and O, and the parameters a12, a21, a23, and a32 determine the fluxes between reservoirs. The main criticism which may be addressed to this Carbon-cycle model is that the transfer coefficients are constant. In particular, they do not depend on the carbon content of the reservoir (e.g. deforestation hindering biospheric sinks) nor are they influenced by ongoing climatic change (e.g. positive feedbacks between climate change and the carbon cycle).		The initial values of A, B, and O, and the parameters a12, a21, a23, and a32 determine the fluxes between reservoirs. The main criticism which may be addressed to this Carbon-cycle model is that the transfer coefficients are constant. In particular, they do not depend on the carbon content of the reservoir (e.g. deforestation hindering biospheric sinks) nor are they influenced by ongoing climatic change (e.g. positive feedbacks between climate change and the carbon cycle).
Line 26:		Line 26:
	Nordhaus? original calibration has been adapted to reproduce both; data until 2010 and; results from the IMAGE model for a given trajectory of CO<sub>2</sub> emissions. This gives the following results (for a yearly time step): a12= 0.02793, a21=0.03427, a23=0.007863, a32=0.0003552, with the initial conditions: A2010=830 GtC (i.e. 391ppm), B2010=845 GtC and O2010=19254 GtC. The additional forcing caused by CO<sub>2</sub> and non-CO<sub>2</sub> gases is given by		Nordhaus? original calibration has been adapted to reproduce both; data until 2010 and; results from the IMAGE model for a given trajectory of CO<sub>2</sub> emissions. This gives the following results (for a yearly time step): a12= 0.02793, a21=0.03427, a23=0.007863, a32=0.0003552, with the initial conditions: A2010=830 GtC (i.e. 391ppm), B2010=845 GtC and O2010=19254 GtC. The additional forcing caused by CO<sub>2</sub> and non-CO<sub>2</sub> gases is given by

	[[~~Image~~:~~IMACLIMIMPORT/attachments/34379251/35815689.png\|~~35815689.png]]		[[File:35815689.png]]

	where A<sub>PI</sub> is the pre-industrial CO<sub>2</sub> concentration (280 ppm), F<sub>2x</sub> is the additional radiative forcing for a doubling of the CO<sub>2</sub> concentration (3.71 W.m^-2^), and F<sub>non-CO2</sub> is the additional radiative forcing of non-CO<sub>2</sub> gases.		where A<sub>PI</sub> is the pre-industrial CO<sub>2</sub> concentration (280 ppm), F<sub>2x</sub> is the additional radiative forcing for a doubling of the CO<sub>2</sub> concentration (3.71 W.m^-2^), and F<sub>non-CO2</sub> is the additional radiative forcing of non-CO<sub>2</sub> gases.
Line 32:		Line 32:
	The temperature model is a two-box model, after Schneider and Thompson (1981) and Ambrosi ''et al.'' (2003), with the atmosphere temperature ''T<sub>A</sub>'' and the ocean temperature ''T<sub>O</sub>'' as follows:		The temperature model is a two-box model, after Schneider and Thompson (1981) and Ambrosi ''et al.'' (2003), with the atmosphere temperature ''T<sub>A</sub>'' and the ocean temperature ''T<sub>O</sub>'' as follows:

	[[~~Image~~:~~IMACLIMIMPORT/attachments/34379251/35815690.png\|~~35815690.png]]		[[File:35815690.png]]

	where T2x is the equilibrium temperature increase at the doubling of the CO<sub>2</sub> concentration, that is, it represents climate sensitivity. All parameters have been calibrated to reproduce results from CMIP5 from CNRM-CERFACS global climate model, CNRM-CM5, over the 21st century for RCP3-PD and RCP4.5 radiative forcing trajectories (using a least squares method). This calibration leads to the following parameter values for heat transfer rates (for a yearly time step): ?1= 0.054C.W-1.m2, ?2= 0.664 C-1.W.m-2 and ?3= 0.0308, and a climate sensitivity of 2.6°C.		where T2x is the equilibrium temperature increase at the doubling of the CO<sub>2</sub> concentration, that is, it represents climate sensitivity. All parameters have been calibrated to reproduce results from CMIP5 from CNRM-CERFACS global climate model, CNRM-CM5, over the 21st century for RCP3-PD and RCP4.5 radiative forcing trajectories (using a least squares method). This calibration leads to the following parameter values for heat transfer rates (for a yearly time step): ?1= 0.054C.W-1.m2, ?2= 0.664 C-1.W.m-2 and ?3= 0.0308, and a climate sensitivity of 2.6°C.

Rineke Oostenrijk: 1 revision imported

2016-08-17T09:41:54Z

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Revision as of 11:41, 17 August 2016

Rineke Oostenrijk at 10:12, 16 August 2016

2016-08-16T10:12:23Z

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{{ModelDocumentationTemplate
|IsDocumentationOf=IMACLIM
|IsEmpty=No
|DocumentationCategory=Modelling of climate indicators
}}
== Modelling of Climate indicators ==

The impact of emissions scenarios on climate indicators is computed using a simplified 3-box carbon cycle model and a simplified 2-box climate model (Ambrosi, 2003).

=== Radiative Forcing from Other Gases ===

The radiative forcing from other gases are taken as exogenous assumptions. 

=== Carbon Cycle Model and Climate Model ===

The carbon cycle is a three-box model, after Nordhaus and Boyer (2010). The model is a linear three-reservoir model (atmosphere, biosphere + ocean mixed layer, and deep ocean). Each reservoir is assumed to be homogenous (well-mixed in the short run) and is characterized by a residence time inside the box and corresponding mixing rates with the two other reservoirs (for longer timescales). Carbon flows between reservoirs depend on constant transfer coefficients. GHGs emissions (CO2 solely) accumulate in the atmosphere and are slowly removed by biospheric and oceanic sinks.

The stocks of carbon (in the form of CO2) in the atmosphere, in the biomass and upper ocean, and in the deep ocean are, respectively, A, B, and O. The variable E is the CO2 emissions. The evolution of A, B, and O is given by

[[Image:IMACLIMIMPORT/attachments/34379251/35815687.png|35815687.png]]

The fluxes are equal to [[Image:IMACLIMIMPORT/attachments/34379251/35815688.png|35815688.png]]

The initial values of A, B, and O, and the parameters a12, a21, a23, and a32 determine the fluxes between reservoirs. The main criticism which may be addressed to this Carbon-cycle model is that the transfer coefficients are constant. In particular, they do not depend on the carbon content of the reservoir (e.g. deforestation hindering biospheric sinks) nor are they influenced by ongoing climatic change (e.g. positive feedbacks between climate change and the carbon cycle).

Nordhaus? original calibration has been adapted to reproduce both; data until 2010 and; results from the IMAGE model for a given trajectory of CO2 emissions. This gives the following results (for a yearly time step): a12= 0.02793, a21=0.03427, a23=0.007863, a32=0.0003552, with the initial conditions: A2010=830 GtC (i.e. 391ppm), B2010=845 GtC and O2010=19254 GtC. The additional forcing caused by CO2 and non-CO2 gases is given by

[[Image:IMACLIMIMPORT/attachments/34379251/35815689.png|35815689.png]]

where API is the pre-industrial CO2 concentration (280 ppm), F2x is the additional radiative forcing for a doubling of the CO2 concentration (3.71 W.m^-2^), and Fnon-CO2 is the additional radiative forcing of non-CO2 gases.

The temperature model is a two-box model, after Schneider and Thompson (1981) and Ambrosi ''et al.'' (2003), with the atmosphere temperature ''TA'' and the ocean temperature ''TO'' as follows:

[[Image:IMACLIMIMPORT/attachments/34379251/35815690.png|35815690.png]]

where T2x is the equilibrium temperature increase at the doubling of the CO2 concentration, that is, it represents climate sensitivity. All parameters have been calibrated to reproduce results from CMIP5 from CNRM-CERFACS global climate model, CNRM-CM5, over the 21st century for RCP3-PD and RCP4.5 radiative forcing trajectories (using a least squares method). This calibration leads to the following parameter values for heat transfer rates (for a yearly time step): ?1= 0.054C.W-1.m2, ?2= 0.664 C-1.W.m-2 and ?3= 0.0308, and a climate sensitivity of 2.6°C.