8 Summary and Conclusion
This paper employed an ARCH/ARMAX model with statistical controls for total downward solar irradiance and 426 binary variables to examine the relationship between CO2 concentrations and hourly temperature at the Barrow Atmospheric Observatory in Alaska. The model was estimated using hourly data over the time interval of 1 Jan 1985 - 31 Dec 2015. The model was evaluated using hourly data from 1 Jan 2016 through 31 Aug 2017. The predictive R-square equivalence of 0.9962 over the evaluation period suggests that the model has reduced the attribution challenge associated with the significant natural meteorological variability in the Arctic. Consistent with this view, the predictions over the evaluation period are more accurate than the highly regarded ERA5 values for the same general vicinity. Thus, though the model fails to achieve the metric of “white noise” in the standardized residuals, the accuracy of its predictions over the evaluation period indicates that the model is “useful.” These results are consistent with the physics that indicates that rising CO2concentrations have consequences for temperature, a point that even climate deniers such as Richard Lindzen, William Happer, Roy Spencer, Patrick Michaels, and the other members of the CO2Coalition have conceded. What is different is that the model also offers useful insights into the magnitude of the relationship between CO2 concentrations and hourly temperature. Specifically, the predictions over the evaluation period are significantly more accurate when they reflect the estimated and statistically significant CO2 coefficients compared to when those coefficients are ignored. The out-of-sample results indicate that CO2concentrations have nontrivial implications for hourly temperature. The modeling results also addressed the possible contribution of factors other than CO2 being drivers of increased temperature over the sample. The mean of the out-of-sample predicted temperature over the evaluation period is not materially affected by these variables, even though some of those variables are statistically significant.
Given that all models are “wrong,” it is a picayune task to dismiss the estimation results reported in Table 1. It is much more challenging to rationally dismiss the implications of the large decline in the out-of-sample predictive accuracy when the estimated CO2effects are ignored. One possibility is that some unknown natural factor at work is the true culprit of the decline in predictive accuracy. While climate deniers may find this an attractive explanation for the results presented in this paper, the model’s high level of predictive out-of-sample accuracy suggests that unknown factors are not an important driver of temperature. There is also the point that attributing the large decline in the out-of-sample predictive accuracy when the estimated CO2 effects are ignored to an “unknown variable” is highly likely to represent obscurantism as opposed to a conclusion that represents the best of all competing explanations as explained by Lipton (2004, p. 56). In short, the beliefs of the climate change deniers are not supported by the hourly temperature data at NOAA’s Barrow Observatory in Alaska. Considering the inadequate results of COP26, this suggests that the current outlook for the Earth’s future is quite grim. Research that further illuminates the shortcomings of the views by climate deniers might help matters. One approach being considered is an analysis of the drivers of the hourly surface energy imbalance, a metric that is easily understood as being important but that climate deniers almost never mention. This research path appears feasible using the methods presented here in light of a preliminary analysis indicating that the hourly surface energy imbalance at Barrow and other locations is autoregressive and heteroskedastic. It is not overly optimistic to believe that modeling these properties will facilitate the recognition of CO2’s “signal” in the data.