Evidence of Causality between the Atmospheric Concentration Level of Carbon Dioxide and Hourly Temperature

This paper addresses the issue of causality between CO₂ and hourly temperature by following the research of the Nobel Laureate Clive Granger [1969], who defined causality in terms of whether lagged values of a variable lead to more accurate predictions of some other variable. This study embraces this view of causality by examining whether lagged values of hourly CO₂ concentration levels lead to more accurate predictions of hourly temperature. The specific approach adopted here is to exploit the diurnal nature of the variation in the hourly CO₂ concentration levels by using the CO₂ concentration level in hour t – 24 as an explanatory variable. This variable has a 0.971 correlation with the CO₂ level in hour t but is obviously itself unaffected by the temperature in hour t given that it is lagged by 24 hours. Thus, this variable can provide evidence of causality between CO₂and temperature that is not tainted by possible two-way causality between the two variables.

The study employs hourly data on the hourly atmospheric concentration level of CO₂ as reported by the Mauna Loa Observatory (MLO) over the period 7 August 2009 through 31 December 2015. MLO is an atmospheric station of the Earth System Research Laboratory (ESRL), Global Monitoring Division (GMD), of the National Oceanic and Atmospheric Administration (NOAA). The hourly CO₂ data were downloaded from the ESRL website. The variable of interest in the analysis is the hourly temperature at the nearby Hilo International Airport. The data were obtained from NOAA’s National Climatic Data Center.

The starting point of the analysis is the observation that there is significant conflict among meteorologists on the issue of climate change (Stenhouse, et al., 2017). This lack of consensus provides an opportunity to test for the effect of CO₂ on temperature while statistically controlling for the weather conditions expected by meteorologists. Specifically, the analysis controls for the day-ahead forecasted probability of precipitation, forecasted temperature, forecasted dew point, forecasted humidity, forecasted visibility, forecasted wind speeds, and measures of forecasted sky conditions. The analysis also makes use of a series of binary variables to represent the season. The day-ahead forecast data for each hour were obtained from CustomWeather, a San Francisco based weather forecasting firm that generates forecasts for approximately 70,000 locations in 200 countries (http://customweather.com/).

In terms of methodology, a two-step time-series estimation approach is employed. In the first step, the functional form is identified. The Box-Cox procedure is used to assess whether it is appropriate to model the variable of interest, hourly temperature, using a linear specification. The presumption of linearity in terms of the explanatory variables (e.g. the hourly CO₂ concentration level) is also scrutinized. Based on this analysis, hourly temperature and several explanatory variables are entered into the statistical model with nonlinear specifications.

The purpose of the second step in the estimation is to obtain parameter estimates that give rise to a white noise error structure that also has the property of an asymptotic Gaussian distribution. The resulting estimating equation has a structural component driven by CO₂, forecasted weather, and the seasonality variables. There is also an autoregressive component that considers that the temperature in hour t is not independent from the temperature in previous hours. Step two of the estimation is accomplished by making use of an autoregressive conditionally heteroscedastic (ARCH) model. This is a useful method in modeling times series data that exhibit time-varying volatility i.e. periods of turbulence (e.g. storms) followed by periods of relative calm. The second step in the modeling also makes use of an autoregressive–moving-average with exogenous inputs model specification (ARMAX) with the transformed CO₂ concentration level, forecasted weather, and the seasonality variables from the first step being included as the exogenous inputs and where the disturbance terms are presumed to follow an autoregressive moving-average (ARMA) specification.

The multivariate estimation yields a statistically significant relationship between the atmospheric CO₂ concentration level and hourly temperature. The estimated effect of CO₂ is not uniform across hours but is instead highly contingent on the day-ahead forecasted temperature and humidity. Specifically, the overall estimated marginal effect of CO₂ on temperature is larger the higher the day-ahead forecasted temperature. It is also larger the higher the day-ahead forecasted level of humidity.

The estimated model is used to generate out-of-sample temperature predictions for each hour over the period 1 April 2013 – 31 December 2015. Two sets of predictions are generated. The first set of predictions ignore the estimated contribution of CO₂ while the second recognizes the estimated contribution. Consistent with CO₂ having a causal effect on temperature, the predictions that recognize the estimated contribution of CO₂ are more accurate (Figure 2 vs. Figure 1). Specifically, the predictions that ignores the estimated contribution of CO₂ has a root-mean-squared error (RMSE) of about 21.40 ^oC while the predictions that incorporate the estimated effect of CO₂ has a RMSE of about 1.43 ^o C . In short, the out-of-sample predictions are consistent with the view that CO₂ concentrations have causal implications for temperature.