Abstract
What exactly is the short-time rate of change (growth rate) in the trend of text {CO}_2 data such as the Keeling curve? The answer to this question will obviously depend very much on the duration in time over which the trend has been defined, as well as the smoothing technique that has been used. As an estimate of the short-time rate of change we propose to employ a very simple and robust definition of the trend based on a centered 1-year sliding data window for averaging and a corresponding centered 1-year difference (2-year data window) to estimate its rate of change. In this paper, we show that this simple strategy applied to weekly data of the Keeling curve (1974–2020) gives an estimated rate of change which is perfectly consistent with a more sophisticated regression analysis technique based on Taylor and Fourier series expansions. From a statistical analysis of the regression model and by using the Cramér–Rao lower bound, it is demonstrated that the relative error in the estimated rate of change is less than 5 %. As an illustration, the estimates are finally compared to some other publicly available data regarding anthropogenic text {CO}_2 emissions and natural phenomena such as the El Niño.
Highlights
The National Oceanic and Atmospheric Administration (NOAA) estimate shown here is based on a long-term trend and where a smoothing of the residual data has been employed with a Full Width at Half Maximum (FWHM) of 1.4 year to match the amplitude of the short-time estimates
We have proposed a simple strategy for estimating the short-time rate of change in the trend of the Keeling curve
This estimate is based on a centered 1-year sliding average to estimate the trend, and a corresponding centered 2-year sliding data window with differencing to determine its rate of change. We have compared it to a more sophisticated regression analysis based on a combined Taylor and Fourier series expansion and found a very good agreement based on 3 Taylor coefficients, 8 Fourier series coefficients (4 yearly harmonics) and a 2-year data window to determine the parameters
Summary
Define a time window of T years covering exactly M weeks ( M + 1 week-points) and where M is an even integer. Due to the centered 2-year data window which is required in order to obtain a reliable estimate of the rate of change, we can conclude that we will have to wait until 2021 to see any conclusive effects of the COVID-19 outbreak in the atmospheric CO2 data
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