The time-singularity multifractal spectrum distribution

► We propose the time-singularity multifractal spectrum distribution (TS-MFSD). ► We introduce temporal information into the singularity spectrum. ► The TS-MFSD of Devil Staircases is a convex function with the maxima value 1. ► Simulation shows there are some time intervals in the TS-MFSD of real sea clutter. ► The TS-MFSD of real sea clutter reveals the spatial dynamic character of fractal systems.