Six cases of models

The previous post included an attempt to explain land surface temperatures as estimated by the BEST project using a dynamic linear model including regressions on both quarterly CO2 concentrations and ocean heat content. The idea was to check the explanatory power of these independent variables in the context of a strong assault on the viability of doing anything like that, even challenging the very notion of attempting to demonstrate a connection.

But to properly assess how good or bad these predictors are, CO2 concentrations and ocean heat content, it’s necessary to fit and calculate AICc values (see previous post) for six additional cases. The seventh case, with local level, CO2 regression, and ocean heat content regression, was reported in the previous post, and had this result:

This had an AICc of -718.3.

Note the AICc values are comparable for the land only temperature data. The smallest value is judged to be the best model of the bunch compared.

The six cases are:

1. a local level model only
2. regression on only the quarterly atmospheric CO2 series
3. regression on only the ocean heat content series
4. regression on quarterly atmospheric CO2 and on ocean heat content without local level
5. local level with regression on quarterly atmospheric CO2 series
6. local level with regression on quarterly ocean heat content series

The result from the local level only model, AICc = -534.9:

The result from the CO2 series regression only model, AICc = -534.9:

Note that the AICc is no different than the local level model only.

The result from the ocean heat content regression only model, AICc = -534.9, also no better than local level only, or CO2 only:

The result from the regression on atmospheric CO2 concentration series and ocean heat content, without local level, AICc = -592.8:

The result from the regression on atmospheric CO2 concentration series with the local level model, AICc = -685.7:

And, finally, the result from the regression on ocean heat content with the local level model, AICc = -690.0: