Global Invariance in Yearly Temperature Volatility: A Conservation Property Implicit in Governing Climate PDEs?

26 November 2013, 13:00-17:00

**Organisers**: Chris Huntingford *(Centre for Ecology and Hydrology)* and Peter Cox *(Exeter)*

in association with the Newton Institute programme Mathematics for the Fluid Earth

(21 October - 20 December 2013)

Three years ago, the Isaac Newton Institute held the programme Mathematical and Statistical Approaches to Climate Modelling and Prediction. This led directly to a paper entitled No increase in global temperature variability despite changing regional patterns, Nature 2013 doi:10.1038/nature12310.

In this analysis, for the ECWMF re-analysis product, local timeseries of yearly annual mean temperatures are de-trended by 11-year running means. The standard deviation of the remaining anomalies provides a metric of local interannual climate variability. When the time-evolutions of this number are studied over the last few decades, then very significant changes (sometimes > 20%) have occurred. In particular, there has been a marked decrease in tropically yearly variability. This is concurrent with major increases in fluctuations at mid-latitudes, and occurring over much of Europe and the USA.

However, when for each year an area-weighted global mean standard deviation is calculated, this single timeseries shows a particularly small < 2% variation throughout the entire ECMWF model-data period. This is remarkable, given the huge geographical variations. The suggestion therefore is that a global conservation property exists in the governing PDEs that acts to constrain total variability on yearly timescales. If true, then to prove this would confirm more formally a very exciting and important policy-relevant attribute of the contemporary climate system.

Looking ahead, using Global Circulation Models to project to year 2100, then our statistic of total variability shows a tendency to decrease. This is true for almost all models in the CMIP5 ensemble. This is again a surprise, given the perception that human-induced climatic change will most likely be associated with overall increases in climate volatility. Hence any conservation law valid for present times may, ultimately, be modulated. We conjecture that this is due to decreases in sea-ice suppressing its ability to inject variability into weather systems. Again, this is presented as an open mathematical problem, awaiting possible proof.

This afternoon workshop is open to anyone interested in exploring how mathematical machinery could be built to explain better our findings in both the ECWMF re-analysis product, and in the suite of CMIP5 climate models.

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