Figure 8. A scatter diagram of hourly temperature and CO2 concentration levels at BRW, 1 Jan 1985 – 31 Dec 2015
The autocorrelative nature of hourly temperature is an important characteristic of the data (Figure 9). As the figure indicates, the magnitude and the duration of the autocorrelative process are significant. In terms of magnitude, the estimated one-hour autocorrelation in temperature equals 0.9970, a value that is so large that it is reasonable to wonder if there is a unit root issue. If this is indeed the case, the results of this study could be spurious for the reasons explained by Kennedy ( 2008, p. 301).
Fortunately, an Augmented Dickey-Fuller test yields a P -value that is less than 0.0001 both with and without a possible trend, and thus the null hypothesis of a unit root is rejected. Consistent with this finding, the Phillips-Perron test for a unit root also yields aP -value less than 0.0001 both with and without a possible trend. Consideration was given to further unit root testing using the DF-GLS test developed by Elliot et al. (1996). This test is regarded as a leading “second-generation” unit root test that avoids some of the shortcomings of the Augmented Dickey-Fuller and Phillips-Perron tests (Baum and Hurn, 2021, pp. 117-120 ). The application of this methodology requires a data series without any gaps. The Barrow data set has 325 gaps in terms of temperature, and thus, the DF-GLS test cannot be applied.
Fortunately, hourly temperature data analysis at another observatory in the polar region may be instructive. One of the few stations in the polar region that substantially meets the zero data gap requirements of the DF-GLS test is the Syowa station on East Ongle Island, located about 4km from the Antarctic continent with a latitude 69.0125° South and a longitude of 39.5900° East. This station is supported by the National Institute of Polar Research in Japan. The data from this station was obtained from NASA’s CERES/ARM Validation Experiment (https://ceres-tool.larc.nasa.gov/ord-tool/jsp/SYN1degEd41Selection.jsp).
From 14 Apr 2002 through 31 Jan 2016, a period with 120,982 hours and no data gaps, the mean temperature at the Syowa Observatory was about -10.7 °C, with the hourly values ranging from 41.25 °C to 7.65 °C. At one hour lagged, the autocorrelation in temperature equals 0.9959, a value seemingly suggestive of a unit root issue. This possible suspicion is not supported by the Augmented Dickey-Fuller, Phillips–Perron, or the DF-GLS tests.
While the available tests do not support the null hypothesis of a unit root in the hourly temperature data, a quantitative analysis of hourly time-series temperature data needs to control its time-series nature to effectively extract the signal from the noise in the data. The method of ordinary least squares is woefully deficient in this regard. This point is consistent with a warning by Granger and Newbold (1974, p. 117), who note the following: “In our opinion the econometrician can no longer ignore the time series properties of the variables with which he is concerned ‐ except at his [ or her ] peril.” The consequences of ignoring their warning include inefficient estimates of the regression coefficients, suboptimal forecasts, and invalid tests of statistical significance. Unfortunately, an inspection of “Statistical Methods in the Atmospheric Sciences,” authored by Wilks (2019), suggests that this warning has not been fully heeded in the atmospheric sciences.