A Variational Adjoint Approach on Wide-Angle Parabolic Equation for Refractivity Inversion

Abstract

Radar systems performance under anomalous propagation conditions can be predicted if the atmosphere is properly known. This paper introduces a tomographic approach to estimate refractivity in the troposphere with an adjoint-based inversion method. A new adjoint model is developed for the two-dimensional wide-angle parabolic equation using variational adjoint approach, to invert refractivity from phaseless data measured with an array of radio receivers in open-sea environment. The obtained adjoint model is validated considering propagation through range-independent medium over flat perfectly-electricconducting surface at horizontal polarization. The ill-posedness of the regarded inverse problem is shown with the optimization landscapes. The parametric study indicates the potential use of this method as a refractivity gradient retrieval system under certain circumstances.Index Terms-Refractivity inversion, inverse problem, wideangle parabolic equation, adjoint model.

A Two-Way Split-Step Wavelet Scheme for Tropospheric Long-Range Propagation in Various Environments

“…To conclude, we note that using this approach allows us to model more precisely the effects of the sea. This is of high importance for the RFC inverse problem [2,3], where an accurate and fast forward model is needed. This latter is studied in Section 3.8 for various sea conditions.…”

“…In this last numerical test, we study the propagation above the sea from the antenna of a ship, which corresponds to the forward model of RFC [2,3]. The main objective is to show that the surface geometry must be taken into account in this context.…”

“…As can be seen in Figure 16d, we only have one lobe for a high wind speed. In the RFC scenario [2,3], we measure the field at the last iteration in order to retrieve the refractive index. Thus, if the sea geometry is not accounted for, one can see that error would be introduced in the forward model.…”

“…This is also particularly important for predicting the coverage of new systems or the impact of man-made structures on the coverage of existing systems (e.g., the impact of solar panels or wind turbines on system performance) [1]. Fast and accurate modeling of the electromagnetic wave propagation is also important for inverse problems such as refractivity from clutter (RFC) [2,3] or radio-occultation [4,5]. In this context, one must consider different interactions of electromagnetic waves with the propagation medium, such as relief, atmospheric ducts, or rough surfaces.…”

An inverse problem of reconstructing the refractive index interrain parabolic equations ∗

“…In [38,39], the inverse problem of retrieving the atmospheric duct structure in equation (1.1) is investigated by the adjoint approach with the regularization technique, where the adjoint is derived from the split-step Fourier parabolic equation method. Then, these methods are extended in [22,23] to the Helmholtz equation in cylindrical coordinates…”