O'Connell et al. (2016) Scientific Legacy of Harold Edwin Hurst
P. E. O'Connell, D. Koutsoyiannis, H. F. Lins, Y. Markonis, A. Montanari and T. Cohn, 2106, The scientific leagacy of Harold Edwin Hurst, Hydrological Sciences Journal, 61: 1571-1590.
The impact of the Hurst Phenomenon on hydrology and other disciplines in discussed, including attempts to explain the phenomenon (by Langbein and hurst, Feller, Anis and Lloyd, Moran, Mattel's and Huzzen, and Fiering) before the mathematical explanation provided by Benoit Mandelbrot and Jim Wallis in the 1968 paper in Water Resources Research (Noah, Joseph and Operational Hydrology) based on fractional Brownian motion. The development of methods of generating fractional Gaussian noise is then discussed, including methods based on Box-Jenkins ARMA models (O'Connell, Wallis and O'Connell) and the arguments of Klemes (1974) against infinite memory assumptions. It is noted that Kolmogorov first proposed the power law variance form in 1940. The explanation of Hurst-Kolmogorov dynamics by Koutsoyiannis and others is outlined, before a section seeking physical explanations for the H-K dynamics in the climate system. Further sections outline Hurst's legacy to other disciplines including climate variability and change. The final section discusses some unresolved issues.