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. Key Points: Lake‐level spectra are globally power‐law over periods of 20 days to 27 years Spectral slope of lake‐levels are a nonlinear function of logarithm of surface area Numerical modeling shows lake‐level variability can be internally generated