On the nature of persistence in dendrochronologic records with implications for hydrology

Abstract Hydrologic processes are generally held to be persistent and not secularly independent. Impetus for this view was given by Hurst in his work which dealt with properties of the rescaled range of many types of long geophysical records, in particular dendrochronologic records, in addition to hydrologic records. Mandelbrot introduced an infinite memory stationary process, the fractional Gaussian noise process (F), as an explanation for Hurst's observations. This is in contrast to other explanations which have been predicated on the implicit non-stationarity of the process underlying the construction of the records. In this work, we introduce a stationary finite memory process which arises naturally from a physical concept and show that it can accommodate the persistence structures observed for dendrochronological records more successfully than an F or any other of a family of related processes examined herein. Further, some question arises as to the empirical plausibility of an F process. Dendrochronologic records are used because they are widely held to be surrogates for records of average hydrologic phenomena and the length of these records allows one to explore questions of stochastic process structure which cannot be explored with great validity in the case of generally much shorter hydrologic records.