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

Abstract:

Variability in lake water level time series is commonly attributed to variability in climatic and hydrologic forcing. We present a spectral analysis of water level time series for 185 globally distributed lakes that suggests a previously unidentified source of internal variability within coupled lake-aquifer systems. Water level fluctuations universally follow a power law scaling of the power spectrum over the range of 30 days to 10 years indicating that lake levels are a 1/f type noise. The slope of the log transformed power spectrum is shown to be a linear function of the logarithm (base 10) of lake surface area. To understand the processes underlying these spectral characteristics, we develop a simple numerical model for lake fluctuations based on the governing equations for groundwater flow in an unconfined aquifer with stochastic forcing. The model robustly produces 1/f type power spectra across all lake sizes and predicts surface area dependence of the power spectrum. The close agreement between simulation and natural data suggests that spatial and temporal stochasticity of mass inputs and diffusion of the groundwater table are key processes for understanding lake level variability.