Fluctuation spectrum and size scaling of river flow and level

TL;DR

This study analyzes the statistical properties of river flow and level fluctuations in the Danube and Mississippi, examining their scaling behaviors and testing the universality of the BHP PDF in river level data.

Contribution

It provides a comparative analysis of two major rivers' fluctuation spectra and evaluates the applicability of the BHP PDF to river level data, highlighting deviations and possible causes.

Findings

Flow moments scale with basin area

Seasonally adjusted flows show relative moment scaling

BHP PDF approximates some level data, but not consistently

Abstract

We describe the statistical properties of two large river systems: the Danube and the Mississippi. The properties of the two rivers are compared qualitatively to the general properties of a critical steady state system. Specifically, we test the recent suggestion by Bramwell, Fennell, Holdsworth and Portelli [{\it Europhys. Lett.} {\bf 57}, 310 (2002)] that a universal probability density function (PDF) exists for the fluctuations in river level, namely the Bramwell-Holdsworth-Pinton (BHP) PDF. The statistical properties investigated in this paper are: the PDF of the river flow and river level; moment scaling with basin area; moment to moment scaling or relative scaling; and power spectral properties of the data. We find that the moments of the flow scale approximately with basin area and that the seasonally adjusted flows exhibit relative moment scaling. Compared to the Mississippi, the Danube shows large deviations from spatial scaling and the power spectra show considerable dependence on system size. This might be due to water use and regulations as well as inhomogeneities in the basin area. We also find that the PDF of level data in some, but not all, cases can be qualitatively approximated by the BHP PDF. We discuss why this coincidence appears to be accidental.