The gradient transfer theory for turbulent diffusion is reformulated in order to obtain an improved method for applied dispersion studies. The basic innovation is that diffusivity of single Fourier components of the concentration field is treated separately, i.e., spectral turbulent diffusivity coefficients are introduced. The value of the diffusivity decreases with increasing wave vector k of the concentration spectrum. The rate of growth of an expanding cloud of material thus becomes dependent on the stage of growth. This is in qualitative agreement with the statistical dispersion theory. It is shown that the assumption of k-dependent diffusivity leads to a nonlocal flux-gradient relation. A new function, the turbulent diffusivity transfer function, is introduced. The turbulent diffusive flux depends on concentration gradients at all points in the space. The diffusion equation is written in terms of the turbulent diffusivity transfer function. The width of the turbulent diffusivity transfer fun... Abstract The gradient transfer theory for turbulent diffusion is reformulated in order to obtain an improved method for applied dispersion studies. The basic innovation is that diffusivity of single Fourier components of the concentration field is treated separately, i.e., spectral turbulent diffusivity coefficients are introduced. The value of the diffusivity decreases with increasing wave vector k of the concentration spectrum. The rate of growth of an expanding cloud of material thus becomes dependent on the stage of growth. This is in qualitative agreement with the statistical dispersion theory. It is shown that the assumption of k-dependent diffusivity leads to a nonlocal flux-gradient relation. A new function, the turbulent diffusivity transfer function, is introduced. The turbulent diffusive flux depends on concentration gradients at all points in the space. The diffusion equation is written in terms of the turbulent diffusivity transfer function. The width of the turbulent diffusivity transfer fun...