Sonar altimeter measurements of bed level change were made in conjunction with instantaneous measurements of sea surface elevation and currents at a fixed position in a saturated surf zone (water depths less than 1 m). Two types of bed behavior were observed, classified as progressive, where mean bed level showed a steady increase or decrease with time, and oscillatory, where the bed level took a periodic motion (amplitudes 0.5--1.5 cm, periods 10--30 min). Mixed combinations of the two behaviors were also observed. Comparisons between bed behavior and a wave-based mobility number parameter (Ψ) observed oscillatory beds for Ψ 1 and Euig > 0.05 m2s-2) and strong mean current (>0.1 ms-1). A fractal analysis of the bed level time series was used to test the hypothesis that the process of ripple migration is nonlinear (self-organised) rather than a direct response to variations in the forcing component. For low wave energy conditions, when ripples were observable (oscillatory and mixed time series), values of the Local Hurst Exponent (0 < HL < 1) suggested fractal behavior at ripple migration timescales, indicating that the process by which ripples migrate is nonlinear and is allowed to flourish when the hydrodynamic forcing is weak.