When a scale-dependent fractal dispersivity is introduced in the convective-dispersive equation of transport in subsurface flow, the Fokker-Planck equation (FPE), also known as the second diffusion equation, is derived. Similarity solutions of the one-dimensional FPE, subject to a Dirac delta function input, are also presented. The similarity solution is shown to function as a kernel in the convolution integral to yield an output on a real timescale. The input function is derived by a procedure known as the inverse problem with the aid of Laplace transform. The FPE and its solutions contain a fractal dimension D and cutoff limit ϵ, two shape parameters &bgr; and &ggr; in the FPE, and other parameters that appear in Darcy's law. A two-dimensional FPE and its solutions have been presented elsewhere. It is reasoned that the scale-dependent dispersion in unsaturated flow is also an issue for investigation. ¿ American Geophysical Union 1995