Adjoint methods for adjusting three-dimensional atmosphere and surface properties to fit multi-angle/multi-pixel polarimetric measurements

This talk presents an efficient procedure for using the three-dimensional (3D) vector radiative transfer equation (VRTE) to adjust atmosphere and surface properties and improve their fit with multi-angle/multi-pixel radiometric and polarimetric measurements of scattered sunlight. The proposed adjoint method uses the 3D VRTE to compute the measurement misfit function and the adjoint 3D VRTE to compute its gradient with respect to all unknown parameters. In the remote sensing problems of interest, the scalar-valued misfit function quantifies agreement with data as a function of atmosphere and surface properties, and its gradient guides the search through this parameter space.  Remote sensing of the atmosphere and surface in a three-dimensional region may require thousands of unknown parameters and millions of data points.  Many conventional approaches would require calls to the 3D VRTE solver in proportion to the number of unknown parameters or measurements.  To avoid this issue of scale, we focus on computing the gradient of the misfit function instead of the Jacobian of the measurement operator. The resulting adjoint methods provide a way to adjust 3D atmosphere and surface properties with only two calls to the 3D VRTE solver for each spectral channel, regardless of the number of retrieval parameters, measurement view angles or pixels. This gives a viable procedure for adjusting atmosphere and surface parameters that will scale to the large problems of 3D remote sensing.  For certain types of multi-angle/multi-pixel polarimetric measurements, this encourages the development of a new class of three-dimensional retrieval algorithms with more flexible parameterizations of spatial heterogeneity, less reliance on data screening procedures, and improved coverage in terms of the resolved physical processes in the Earth's atmosphere.