### Abstract

For all points of the globe, in the ECWMF re-analysis product, 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-latitudues, and occurring over much of Europe and the USA (Huntingford et al, Nature, 2013), thus with clear impacts implications.

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 constrains total variability on yearly timescales. This would potentially provide a very exciting and important policy-relevant attribute of the Earth system, waiting to be discovered in the governing PDEs.

When using Global Circulation Models to project forward, then our statistic of total variability across almost all simulations shows a tendency to decrease. 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 may, ultimately, be modulated. We conjecture that this is due to decreases in sea-ice suppressing its ability to inject variability in to weather systems. Again, this is presented as an open mathematical problem, awaiting possible formal proof.