The Judge in the Climate Trial ✎

Original: "Quantitative assessment of drivers of recent climate variability: An information theoretic approach"
arXiv:1607.01529 · 2016-07-06 · arXiv non-exclusive · independent analysis · 1 min
The judge doesn't listen to who shouts loudest, but to who prompts whom. This revealed that CO₂, methane, and volcanic dust almost equally controlled the planet's temperature.

The judge in the climate trial doesn't listen to who shouts loudest. Instead, he watches who prompts whom. Nine 'witnesses', from carbon dioxide to cosmic rays, testified from 1984 to 2005. Their statements were recorded every month. The judge doesn't trust mere coincidences, because two witnesses might echo each other without knowing who started first. He looks for a one-way flow of information.

Transfer entropy is a way to measure how much information about the future of one series is contained in the past of another. If one series 'prompts' another, it is the driver.

The records were cleaned of slow trends, leaving fast fluctuations. Then, for each pair of 'suspect and temperature', they calculated who prompts whom, with delays from zero to ten months. To filter out random coincidences, the records were shuffled a hundred times to see if the signal persisted. If the prompt disappeared after shuffling, it meant the real data had a genuine signal.

The judge delivered a verdict: carbon dioxide, methane, and volcanic aerosols prompted temperature almost equally, accounting for 24%, 19%, and 23% of the total information flow. Ultraviolet and El Niño also prompted, but more weakly. Cosmic rays, nitrous oxide, and total solar radiation remained silent. Previously, correlations could not distinguish cause from effect: a warmer ocean also releases more CO₂. The judge hears the direction of the prompt. This method does not require model assumptions, so it can serve as an independent check for climate models. Now the judge is ready to hear new cases.

Nitrous oxide (N₂O) has a strong radiative effect per molecule and stays in the atmosphere for about 120 years, yet its contribution turned out to be marginal due to low concentration. Volcanic aerosols from the 1982 El Chichón and 1991 Pinatubo eruptions produced an optical depth spike that the method confidently identified as a temperature driver.

In Kim Stanley Robinson's novel The Ministry for the Future, climatologists try to separate natural fluctuations from the anthropogenic signal to justify geoengineering measures. The entropy transfer method from this paper resembles their tool for identifying causal links in climate data.

TE_{x\to y}(\tau) = \sum P(y(t+\tau), y(t), x(t)) \log_2 \left( \frac{P(y(t+\tau), y(t), x(t)) P(y(t))}{P(x(t), y(t)) P(y(t+\tau), y(t))} \right)
The amount of information about the future of y provided by knowing the past of x, beyond what is already known from the past of y.
NTE_{x\to y}(\tau) = \frac{TE_{x\to y}(\tau)}{\sqrt{H_x H_{y+\tau}}}
Entropy transfer divided by the geometric mean of the entropies of x and y, allowing comparison across different variable pairs.
D_{x\to y}(\tau) = NTE_{x\to y}(\tau) - NTE_{y\to x}(\tau)
The difference in normalized information flows; a positive value indicates that x is a driver of y.
Concepts
natural variability North Atlantic Oscillation interannual variability seasonal cycle ENSO NOAA CPC Multivariate ENSO Index climate Jin-Timmermann model El Niño-Southern Oscillation ERSST spring predictability barrier TAO/TRITON moorings climate model UAH satellite record information theory El Niño index Teleconnection granger causality IRI