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- For each year in which data was reported, the Collaboratorium team plotted five points, with each point corresponding to one of the emissions scenarios (e.g. Reference, 750 ppm, 650 ppm, etc.) Atmospheric concentrations of CO2 were plotted on the x-axis and reduction in global GDP on the y axis. The team then derived an equations that described a curve that fit these points, with one equation for each year for which data was reported. The equation took the form of y = ax^4 + bx^3 + cx^2 + dx + e, where x was the atmospheric concentration of CO2 in the focal year and y the reduction in global GDP against the baseline scenario. The resulting equations and R^2 values for the fit of the curves are provided below. The values in the tables are the coefficients of the x^n terms of the function:
Year | x^4 | X^3 | x^2 | x^1 | X^0x^0 | R^2 value |
|---|---|---|---|---|---|---|
2020 | 0 | 0 | -0.00774736369371996 | 6.48339888803732 | -1356.42001161487 | 0.9994 |
2030 | 0 | 0.000007410494 | -0.011949554906 | 6.25574082933 | -1070.58675338772 | 1.0000 |
2040 | 0 | 0.000007055543 | -0.01069478523 | 5.406617511459 | -911.538271418181 | 1.0000 |
2050 | 0 | 0.000001924732 | -0.003345734941 | 1.930460246553 | -369.923946524369 | 1.0000 |
2060 | 0 | 0.000001868923 | -0.003231531858 | 1.871037762599 | -362.985855742092 | 0.9997 |
2070 | -0.000000007 | 0.000016708072 | -0.014999782691 | 6.017224944268 | -912.694432159844 | 1.0000 |
2080 | -0.000000003017 | 0.000007998976 | -0.007961624697 | 3.53639427401 | -593.731272082939 | 1.0000 |
2090 | -0.000000001997 | 0.00000564627 | -0.00599287884 | 2.839906550908 | -509.522167717593 | 1.0000 |
2100 | -0.000000001686 | 0.000005024812 | -0.0056041183 | 2.783336996545 | -522.639645387934 | 1.0000 |
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