On the Use of Variational Adjoint Approach on Wide-Angle Approximation of Parabolic Equation with the Method of Split-Step Wavelet

Abstract : This paper introduces a validation step for inferring atmosphere from RF data in an effort towards an 'refractivity from clutter' (RFC) system. The method retrieves the vertical refractive index distribution point-by-point in the lower troposphere from the measurements sampled in bistatic configuration. The new method utilizes wide-angle parabolic equation (WAPE) solved with the method of split-step wavelet (SSW) as the forward model, which is less computationally costly than the typical method used in the literature. The gradient of the cost function is estimated via the adjoint SSW solver developed by means of the variational adjoint approach. The high-dimensional problem is taken into account via gradient based optimization method. Thus the validation of the gradient is crucial. The accuracy of the new method is validated by comparing the gradient to the method of finite differences.