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.