The Second Derivative of CO₂: How the Atmosphere Governs Climate ✎

Original: "Correlations of the first and second derivatives of atmospheric CO2 with global surface temperature and the El Nino-Southern Oscillation respectively"
· L. M. W. Leggett, D. A. Ball
arXiv:1402.6316 · 2014-02-25 · arXiv non-exclusive · independent analysis · 2 min
The rate of change of atmospheric CO₂ explains both temperature and El Niño.

An interpreter gets distracted by every rustle in the hall, and a one-hour meeting stretches into two. The atmosphere is like such an interpreter: it hears not only the biosphere's words but also its tone. When plants change the pace at which they absorb carbon dioxide, the air responds not to the gas itself but to how quickly and how abruptly its amount changes.

Since 1960, the Mauna Loa observatory in Hawaii has measured CO₂ concentration every month. If you look not at the level itself but at its rate of change, the first derivative, it almost perfectly matches tropical temperatures. But the most interesting part begins with the second derivative, that is, the acceleration. It turns out that the acceleration of CO₂ change leads the Southern Oscillation by two months. The Southern Oscillation is the pressure difference between the eastern and western Pacific, the atmospheric part of El Niño. The correlation between them was 0.315, higher than for any other factor.

The biosphere receives about 130 terawatts of energy through photosynthesis, which is 10–20% of the power of all atmospheric winds. Plants influence climate not only chemically but also through energy and water fluxes.

Previously, El Niño was explained as an independent ocean mode, but now it appears that it may be a response of the biosphere to the acceleration of CO₂ change. This ties together the carbon cycle, vegetation, and large-scale atmospheric circulation. In a regression model, the rate of CO₂ change explains temperature as well as a standard set of four predictors, and the volcanic factor becomes insignificant. After correcting for autocorrelation, the relationships remain statistically significant: p = 0.0013 for the pair "CO₂ rate and temperature" and p = 0.001 for the pair "CO₂ acceleration and Southern Oscillation."

This work also explains the warming pause since 1998: models did not account for the rate of CO₂ change, and it is this rate, not the level itself, that turns out to be key. Including it in forecasts could improve predictions of both El Niño and global temperature. An interpreter who hears the tone does not need to wait for the biosphere to finish its sentence.

The energy that the biosphere obtains through photosynthesis is about 130 terawatts, which is 10–20% of the power of all winds in the atmosphere. That means plants can influence climate not only chemically but also through energy and water fluxes.

Concepts
ENSO La Niña Southern Oscillation El Niño-Southern Oscillation El Niño Jin-Timmermann model spring predictability barrier natural variability Multivariate ENSO Index ERSST TAO/TRITON moorings ocean-atmosphere coupling zebiak cane model equatorial wave propagation Warm water volume seasonal cycle global warming relative ONI NOAA CPC North Equatorial Countercurrent