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

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-1 to 27 yr-1, suggesting that lake levels are globally a f-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.