The Spatial Scale Dependence of The Hurst Coefficient in Global Annual Precipitation Data, and Its Role in Characterising Regional Precipitation Deficits within a Naturally Changing Climate

Hurst's seminal characterisation of long-term persistence (LTP) in geophysical records more than seven decades ago continues to inspire investigations into the Hurst phenomenon, not just in hydrology and climatology, but in many other scientific fields. Here, we present a new theoretical development based on stochastic Hurst-Kolmogorov (HK) dynamics that explains the recent finding that the Hurst coefficient increases with the spatial scale of averaging for regional annual precipitation. We also present some further results on the scale dependence of H in regional precipitation, and reconcile an apparent inconsistency between sample results and theory. LTP in average basin scale precipitation is shown to be consistent with LTP in the annual flows of some large river basins. An analysis of the crossing properties of precipitation deficits in regions exhibiting LTP shows that the Hurst coefficient can be a parsimonious descriptor of the risk of severe precipitation deficits. No evidence is found for any systematic trend in precipitation deficits attributable to anthropogenic climate change across the regions analysed. Future precipitation deficit risk assessments should, in the first instance, be based on stochastic HK simulations that encompass the envelope of uncertainty synonymous with LTP, and not rely exclusively on GCM projections that may not properly capture long-term natural variability in the climate. Some views and opinions are expressed on the implications for policy making in sustainable water resources management.