Sensitivity Analysis on the Reconstruction of the Attenuation Function for Short Time-Windows Measurements

Abstract:
By relying on suitable propagation models, lightning electromagnetic fields can be computed from the knowledge of the channel-base current (CBC) and of the attenuation function. While the CBC is measured by means of instrumented towers, a parametric attenuation function is usually assumed a priori and then compared with the measured fields in order to find optimal values for the CBC parameters. Unlike this approach, the present paper proposes a methodology for the reconstruction of the attenuation function whereby the latter is obtained as the solution of an inverse problem (while maintaining the same kind of input data). Moreover, for the sake of generality, the framework is formulated by considering possibly short time-windows, so that meaningful information can be recovered even when a complete recording of the lightning discharge process is not available. The inversion method is based on an iterative Tikhonov regularization procedure. The proposed approach is then applied to simulated data of electric and magnetic fields, as well as of CBC current, blurred by numerical noise in the time domain. The resulting algorithm turns out to provide a good accuracy in reconstructing a fictitious attenuation function. Finally, a short sensitivity analysis on the electromagnetic field noise and on the radial distance error is presented.