This study reports the development of tangent-linear and adjoint models for a vector radiative transfer model called TAMU-VRTM. This vector radiative transfer model is further validated in the case of the atmosphere–ocean coupled system, although previous validation was conducted for single and multiple layers. The TAMU-VRTM and tangent-linear and adjoint models can be applied to remote sensing and data assimilation based on spaceborne and airborne polarimetric observations. The tangent-linear and adjoint models accurately and efficiently compute the derivatives of output Stokes parameters with respect to input variables of the TAMU-VRTM. An inversion algorithm can straightforwardly compute the Jacobian matrix from the derivatives of Stokes parameters using the chain rule. We validate the tangent-linear and adjoint models by comparing them with the finite-difference method, and show that the finite-difference results converge to the tangent-linear and adjoint results. Furthermore, the adjoint model can efficiently compute the derivatives of observables with respect to the scattering phase matrix elements. This capability can be used to evaluate the scattering phase matrix assumed in an inversion algorithm and has potential for applications to inferring scattering phase matrix elements of cloud, aerosol, and hydrosol particles.
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