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Self‐affinity and surface‐area‐dependent fluctuations of lake‐level time series
Author(s) -
Williams Zachary C.,
Pelletier Jon D.
Publication year - 2015
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2015wr017254
Subject(s) - environmental science , forcing (mathematics) , water level , series (stratigraphy) , water table , scaling , surface water , range (aeronautics) , precipitation , logarithm , hydrology (agriculture) , climatology , groundwater , geology , mathematics , meteorology , geography , paleontology , geometry , cartography , geotechnical engineering , environmental engineering , mathematical analysis , materials science , composite material
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 20d − 1to 27yr − 1, suggesting that lake levels are globally af − β‐type noise. The spectral exponent ( β ), 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.