Efficient forward modelling by matrix representation of sensor responses

The polarization, frequency and spatial responses of the sensor can be considered by calculating the Stokes vector of monochromatic pencil beam radiances for a set of frequencies and viewing directions, and weight these radiances with the instrument responses. This paper presents a highly efficient solution for this calculation procedure. The basic idea is to pre-calculate a matrix that represents the mapping from polarisation, frequency and spatial values to measured data. Sensor impacts can then be included by a simple matrix multiplication. The full sensor matrix can be obtained by determining the response matrix for the sensor parts individually. Data reduction methods can also be incorporated. A simple method for optimizing the calculation grids is further presented. The described approach for sensor modeling has been implemented in two public available softwares for atmospheric radiative transfer simulations.