Rainfall Propagation Effects and Distortion Compensation for Cross-Polarized Radar Signatures of Aircraft Wake Vortices

Aircraft wake vortices pose a hazard to following aircraft, yet their forward-looking radar detection in rain is complicated by propagation through intervening precipitation. In a near-axial geometry, the weak line-of-sight projection of wake rotational velocity motivates a complementary polarimetric observable. This study numerically investigates how wake-induced raindrop redistribution and reorientation form a two-core linear depolarization ratio (LDR) signature, how intervening rain distorts this signature, and whether full-matrix propagation retrieval and compensation can recover it. A physics-guided convolutional neural network (CNN) combined with bidirectional long short-term memory (BiLSTM) retrieves range-resolved forward-scattering matrices from polarimetric echo profiles and reconstructs the cumulative propagation matrix for two-sided echo compensation. Under the modeled Boeing 747-class wake, a rain rate of 10 mm h−1, and a 20 m × 20 m transverse averaging footprint, the intrinsic wake-to-background LDR contrast is 9.92 dB. For the prescribed sustained path-orientation-bias scenario, full-matrix propagation reduces the contrast to 2.87 dB, while network-based compensation restores it to 8.89 dB. A separate numerical evaluation using disjoint calibration and test physical-background fields further shows improved two-core detection under the tested strong-path conditions, with the benefit governed jointly by propagation coupling and received path and target signal-to-noise ratios (SNRs). These results provide numerical evidence for full-matrix propagation compensation as a means of recovering the cross-polarized wake signature under the modeled conditions.