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 hydrology and climatology, but many other scientific fields. Here, we present a new theoretical development based on stochastic Hurst–Kolmogorov (HK) dynamics that explains recent finding coefficient increases with spatial scale averaging for regional annual precipitation. We also some further results dependence H precipitation, reconcile an apparent inconsistency between sample theory. LTP average basin precipitation is shown be consistent flows large river basins. An analysis crossing properties deficits regions exhibiting shows can parsimonious descriptor risk severe deficits. No evidence found any systematic trend attributable anthropogenic climate change across analysed. Future deficit assessments should, first instance, HK simulations encompass envelope uncertainty synonymous LTP, rely exclusively GCM projections may properly capture natural variability climate. Some views opinions are expressed implications policy making sustainable water resources management.