The role of spatial interactions for prediction of the spectral structure of the atmospheric phase screen

The atmospheric phase screen is one of the main error sources that affect the precise phase measurements in many fields of earth remote sensing. The atmospheric effects can be mitigated if a precise knowledge of the power spectral density of the process is available and if same sample observations can be retrieved on a sparse grid. At smaller scales, where interactions are no longer isotropic, the behaviour is not easily predicted by the ultimate dissipative behaviour of turbulence eddies. We start by assuming that the propagation of the electromagnetic wave in the lower atmosphere can be represented by a ray travelling in a layered medium where the refractive index is constant along each layer. In a turbulent atmosphere, the interaction among eddies induces a diffusion process that propagates with different rates in both vertical and horizontal direction with the final effect of ruling the number of effective layers in the atmosphere. In this way, the overall path travelled by the electromagnetic wave is governed by the accumulated number of such effective layers whose interactions play a primary role in our model. A good model for the interactions among different layers is the linear interaction model. The power spectrum of the process can be found by solving a differential equation with given initial conditions. It can be demonstrated that an asymptotic power law decay is found under binomial competitive interactions and that, at a smaller scale, the behaviour observed in the observed data is naturally induced by the interaction process itself. The model predictions have been tested using samples of the atmospheric phase screen extracted from Synthetic Aperture Radar interferograms. To this end, the model parameters have been estimated from the data set and the predicted spectrum has been compared with the measured one.