Non-linear model for Keeling Data

This is the sample variogram formula:

${S=\sum_{c=1}^{N_c}{N_h\over{N_p}}\left[{1\over{2N_h}}\sum_{(i,j)\epsilon{P_c}}^{N_h}(x_{i}-x_j)^2\right]}$ I use it for modeling the variograms of the vostok ice cores, illustrating the Milankovich effect.

This is the model I proposed for the Keeling data:

${CO_2(t)=\beta_0+\beta_1t+\beta_2t^2+ A\sin(\frac{2\pi}{T}(t-t_0))$

${CO_2(t)=\beta_0+\beta_1t+\beta_2t^2+ A[\sin(\alpha{t})\cos(\alpha{t_0})-\cos(\alpha{t})\sin(\alpha{t_0})]$

${\alpha\equiv\frac{2\pi}{365.25}}$

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