Comparison GRAS outputs with Nordhaus's GAMS outputs
(GRAS version 1.1.3e, 2/27/2008)

* CO2 emission paths are only compared.
* Horizontal axis is a unit of 10 years, starting in 2005. Simulation results are compared 200 years.
* Vertical axis is a unit of gigatons of carbon.
*Some simulations have significantlly different parts. Though if the results of larger objective values is better,
some of GRAS's results are more reasonable, it is not so simple.


1. Hoteling Path
Hoteling path is constrained only by fossil fuel limitation. Global warming damage is not incorporated.
CO2 reduction rates of this path is used as upper limits or lower limits of following some simulations.
In this hoteling path, GRAS and GAMS paths of CO2 emission are almost coincided.



2. Emission paths fixed on hoteling CO2 reduction series for 250 years
Two pats are almost coincided.



3. Emission paths fixed on hoteling CO2 reduction series for 50 years
Although two pats are almost coincided for fifty years, after that, two paths are significantly
diverged.



4. Optimal Paths without any constraint condition
Generally, there is a tendency that GRAS path and GAMS path are diverge as lesser the constraint conditions.
In this case, as seen in the simulation results, the objective value of GRAS is greater than that of GAMS as 273.



5. Stern review
Only the first period is different. This reason is as follows. The simulation is performed twice
as show in the simulation page. In the second stage, the first period restriction is ineffective in the
GAMS simulation. The restriction is effective in GRAS simulation. However, the difference is not serious.
Just ignore.



6. Temperature rise since 1900 is limited to 1.5 C degree
Despite of complexity of the paths, almost coincided each other.



7. Temperature rise since 1900 is limited to 2.0 C degree
The difference of objective value is 139.



8. Temperature rise since 1900 is limited to 2.5 C degree
The difference of objective value is 212.



9. Temperature rise since 1900 is limited to 3.0 C degree
The difference of objective value is 254.



10. CO2 accumulation in atmosphere limited to 1.5 times of preindustrial CO2
The difference of objective value is 69. Two paths are almost coincided.


10. CO2 accumulation in atmosphere limited to 2.0 times of preindustrial CO2
The difference of objective value is 211. But two paths are almost coincided.



11. CO2 accumulation in atmosphere limited to 2.0 times of preindustrial CO2
The difference of objective value is 211. Two paths are slightly different.



12. GORE Proposal
Though the difference of objective value is 697, two paths are almost coincided.



13. Kyoto Protocol no US
Almost coincided.



14. Kyoto protocol with US
Almost coincided.



15. Strength Kyoto protocol
After 15th period, the sharp difference appears in the graph. I cannot catch that reason.



16. Reduction of backstop technology
The difference of the first period depend on the constraint of the first period. It is not important.