)1 State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, 36 Bochubeilu, Hangzhou 310012, China; [EMAIL_ADDRESS] (D.P. ); 11638023@zju. about radiative coupling between different regions of the system. [PERSON] et al. [4; 5] presented three MC programs of polarized light transport into scattering media; comparison between MC runs and Adding Doubling program yielded less than 1% error. [PERSON] et al. [6] investigated scattering and multiple scattering of a typical laser beam in a turbid environment and obtained good agreement between experimental measurements and results from MC simulations. [PERSON] [7] studied multiple scattering effects by solving the RTE via MC techniques. The effective attenuation coefficient of this exponential decay is found to be strongly dependent on the parameters of the lidar system and on the optical properties of the water. [PERSON] et al. [8] described a semi-analytic MC radiative transfer model (SALMON), which is particularly well-suited for addressing oceanographic lidar systems. It is based on the method of expected values in which an analytical estimate is made of the probability of collection by a remote receiver of scattered or emitted photons at appropriate points in the stochastically constructed underwater photon trajectory. [PERSON] et al. [9] also developed a semi-analytic MC radiative transfer model to study laser propagation in inhomogeneous sea water within the subsurface plankton layer. Besides, there are many other MC studies for simulating photons propagating in a scattering medium [10; 11; 12; 13]. The probability density function (pdf) for a random variable that can have values only between 0 and 1 is fundamental to MC simulation. Scattering phase function (spf) can be interpreted as a pdf: \(\tilde{\beta}(\psi)\sin(\psi)\). The Henyey-Greenstein (HG) spf [14] has been widely used in many studies. The HG phase function, however, does not work well at small or large scattering angles. Though other spfs work well, e.g., Fournier-Forand phase function (FF) [15], solving cumulative distribution function (cdf) of spf \(P_{\Psi}(\psi)\) as Equation 1 for scattering angle \(\psi\) (even if possible), namely inverse cdf (ICDF), would give a complicated formula. Besides, in almost all of these studies, they assume the water is optically vertical homogeneous; a few studies focus on simulating light propagation in inhomogeneous water. For some use cases there is a need to extend and improve existing MC methods to apply to inhomogeneous water, for instance, the ocean with subsurface chlorophyll maximum layer. \[P_{\Psi}(\psi)=2\pi\int\limits_{0}^{\psi}\tilde{\beta}(\psi^{\prime})\sin\psi^ {\prime}d\psi^{\prime} \tag{1}\]  
This study introduces an improved semi-analytic MC radiative transfer model based on the lookup table (LUT) method and an analytically lidar geometric model to describe photons scattering event for oceanographic lidar systems. The new model presented in this study is based on a lidar geometric model for analytically estimating the probability of photon scatter back to a remote receiver, and inhomogeneous layers are divided into voxels with different optical properties with a resolution as high as 0.11 m. The LUT method is used for solving complicated or even unsolvable inverse cumulative distribution function of various spfs. Multiple scattering and wind-driven sea surface condition effects are also studied. Finally, we compared our simulation results with measurements of airborne lidar.