An improved polarization-sensitive semi-analytic monte carlo simulation method for bathymetric lidar considering complex water-column stratification

Bathymetric lidar simulation has long treated seawater as an optically uniform medium, so existing models cannot reproduce how a thermocline, a turbidity layer, or a subsurface chlorophyll maximum reshapes the polarized echo. This paper develops an improved polarization-sensitive semi-analytic Monte Carlo (SMC) method for vertically stratified water. Earlier semi-analytic treatments either keep the polarization state but collapse the column to a homogeneous medium, or resolve the vertical structure but carry only a scalar photon weight; here the photon engine itself is rebuilt around layer-aware free-path marching and a layer-resolved local estimate, the forced-scoring weight is rederived so that it remains unbiased where the attenuation coefficient and the Mueller matrix change discontinuously, and the full Stokes state is carried through every scattering event. Importance sampling, adaptive step control near boundaries, and a GPU-mapped multiple-scattering synthesis keep the cost within reach of parameter sweeps. Against an analytic small-angle solution the method agrees to better than 1% inside the quasi-single-scattering window where that solution is valid, and against a converged conventional Monte Carlo reference it holds waveform and degree-of-polarization errors below 1% at roughly a tenth of the photon budget. Under stratified scenes it reproduces the layer-specific pulse broadening, peak delay, and co- and cross-polarized depolarization signatures that homogeneous models cannot generate. Reading the two polarization channels jointly reduces the stratification-induced bottom-detection bias from about 0.34 m to about 0.10 m once the waveform signal-to-noise ratio exceeds 25 dB, and it supports a preliminary retrieval of layer depth and optical contrast, although absorption and scattering remain strongly correlated. The evidence is entirely numerical, and the flat-layer geometry, the static sea surface, the neglect of wave-facet refraction, and the absence of any comparison with field-measured airborne waveforms bound what can be claimed from it.