Correlated diffusive processes have been previously considered in a hydrological context when examining the Hurst effect, which leads to persistence in hydrologic time-series.

Systems with no memory have a value for the Hurst exponent *H* of 0.5. However, as noted by Klemes [1974], typical values for hydrologic time-series appear to be *H* » 0.7, implying a fractal structure to the data, memory or a steadily changing mean.

Kirkby (1987) discussed the implications of this for the extrapolation of process rates – ‘tricky’.

Kirkby
M.J. 1987. The Hurst effect and its implications for extrapolating process
rates. *Earth Surface Processes and Landforms *12, 57-67.