Self-affinity and surface-area-dependent fluctuations of lake-level time series

Abstract

We performed power-spectral analyses on 133 globally distributed lake-level time series after removing annual variability. Lake-level power spectra are found to be power-law functions of frequency over the range of 20 d 21 to 27 yr 21 , suggesting that lake levels are globally a f 2b -type noise. The spectral exponent (b), i.e., the best-fit slope of the logarithm of the power spectrum to the logarithm of frequency, is a nonlinear function of lake surface area, indicating that lake size is an important control on the magnitude of water-level variability over the range of time scales we considered. A simple cellular model for lake-level fluctuations that reproduces the observed spectral-scaling properties is presented. The model (an adaptation of a surface-growth model with random deposition and relaxation) is based on the equations governing flow in an unconfined aquifer with stochastic inputs and outputs of water (e.g., random storms). The agreement between observation and simulation suggests that lake surface area, spatiotemporal stochastic forcing, and diffusion of the groundwater table are the primary factors controlling lake water-level variability in natural (unmanaged) lakes. Water-level variability is generally considered to be a manifestation of climate trends or climate change, yet our work shows that an input with short or no memory (i.e., weather) gives rise to a long-memory nonstationary output (lake water-level). This work forms the basis for a null hypothesis of lake water-level variability that should be disproven before water-level trends are to be attributed to climate.

Temporal Analysis of Ground Movement at a Metal Mine in China

“…To quantify the temporal correlations and the strength of persistence in self-affine time series, the spectral exponents, β, must be analyzed [42]. The spectral exponent quantifies how variability is distributed across the frequency domain and is a measure of the strength of persistence or anti-persistence in a time series [14,15]. When β > 0, the time series is long-range persistent, and the correlations between neighbored values become stronger.…”

“…If β > 1, strong persistence exists in the time series, which is nonstationary with mean and variance changes in the recorded length [43]. If β = 0, the time series corresponds to white noise, and the correlations between the values are nonexistent [15,43]. A self-affine time series with β < 0 exhibits long-range anti-persistence.…”

Environmental signal shredding on sandy coastlines

“…Drawing on the physics of turbulent fluid flows (Frisch and Kolmogorov, 1995), Jerolmack and Paola (2010) used time series of sediment flux from physical and numerical experiments -bedload transport in a flume channel (Singh et al, 2009), a canonical rice-pile experiment (Frette et al, 1996), and a numerical rice-pile model -to illustrate their argument. Beyond source-to-sink sedimentary systems (Romans et al, 2016), signal shredding has since been extended to spatio-temporal changes in lake levels (Williams and Pelletier, 2015) and methane release from peatlands (Ramirez et al, 2015).…”

Environmental signal shredding on sandy coastlines

“…Drawing on the physics of turbulent fluid flows (Frisch and Kolmogorov, 1995), Jerolmack and Paola (2010) use sediment flux time-series from physical and numerical experiments -bedload transport in a flume channel (Singh et al, 2009), a canonical rice-pile experiment (Frette et al, 1996), and a numerical rice-pile model -to illustrate their argument. Beyond source-to-sink sedimentary systems (Romans et al, 2016), signal shredding has since been extended to spatio-temporal changes in lake levels (Williams and Pelletier, 2015) and methane release from peatlands (Ramirez et al, 2015).…”