When studying light propagation through the atmosphere, it is usual to rely on widely used spectra such as the modified von Karman or Andrews-Hill. These are relatively tractable models for the fluctuations of the refractive index, and are primarily used because of their mathematical convenience. They correctly describe the fluctuations behaviour at the inertial range yet lack any physical basis outside this range. In recent years, deviations from the Obukhov-Kolmogorov theory (e. g. interminttency, partially developed turbulence, etc.) have been built upon these models through the introduction of arbitrary spectral power laws. Here we introduce a quasi-wavelet model for the refractive index fluctuations which is based on a phenomenological representation of the Richardson cascade. Under this model, the atmospheric refractive index has a correct spectral representation for the inertial range, behaves as expected outside it, and even accounts for non-Kolmogorov behaviour; moreover, it has non-Gaussian statistics. Finally, we are able to produce second order moments under the Rytov approximation for the complex phase; we estimate the angle-of-arrival as an example of application.