Speeding up the DISORT solver: mathematical approach and application to radiance simulations of FORUM

New remote sensing satellite sensors for the measurements of atmospheric radiation offer the advantage of very high spectral resolution and spectral and/or spatial and temporal coverage. The analysis of these measurements often requires a forward model (FM) for the simulation of the radiation collected by the sensor. The FM should model all the processes affecting the radiance, such as absorption and scattering by molecules and particles. Despite the advancement in sensor technology, the radiative transfer solvers are almost the same since several decades. Among these, the DISORT solver is still one of the most widely used. The DISORT code was developed 30 years ago, and while the code is maintained and updated regularly, the improvements are more geared towards new features than to a revision of the original setup. While the implementation was the best possible at the time, the memory constrains and language limitations of the time are nowadays considerably changed. On the other hand there is still the need of NRT retrievals, and the computing time of the multiple scattering needed in cloudy sky conditions is still the bottleneck of the FM calculation. We modified the DISORT algorithm in three directions: 1) Language improvements. Making use of dynamical assignment and modularity of modern fortran reduces execution time.  2) Algorithm improvements. By approaching the delta-m transformation on a per-layer basis, many computations were saved, expecially when the cloud pattern does not cover all the atmospheric range. 3) Numerical analysis improvements. While these improvements do not shorten the computational time, they improve the precision of the solution of the eigenvalue sub-problems that arises in the multiple scattering calculations. The modifications in the DISORT solver produce an improvement in calculation performances of a factor 3 with respect to the original version.  The new solver is named as fast-DISORT (fDISORT).