FORUM (Far-infrared Outgoing Radiation Understanding and Monitoring) will fly as the ninth ESA's Earth Explorer mission, and an end-to-end simulator (E2ES) has been developed as a support tool for the mission selection process and the subsequent development phases. The current status of the FORUM E2ES project is presented together with the characterization of the capabilities of a full physics retrieval code applied to FORUM data.

E-commerce is a continuously growing sector worldwide, with important repercussions on the delivery system in urban areas and especially in the Business to Consumer (B2C) sector. The delivery of a package to a consumer's address involves not only high costs for couriers (greater number of kilometres travelled), but also increased congestion and greater environmental pollution (greater volume of pollutants released into the air).

High quality long-term data sets of altitude-resolved measurements of the atmospheric composition areimportant because they can be used both to study the evolu-tion of the atmosphere and as a benchmark for future mis-sions. For the final ESA reprocessing of MIPAS (MichelsonInterferometer for Passive Atmospheric Sounding) on ENVISAT (ENViromental SATellite) data, numerous improve-ments were implemented in the Level 2 (L2) processor Op-timised Retrieval Model (ORM) version 8.22 (V8) and itsauxiliary data.

For the finite weighted Hilbert transform we consider two different product integration rules, the VP rule and the L-rule, based on the same nodes and obtained by approximating the density function with filtered de la Vallée Poussin and classical Lagrange interpolation polynomials, respectively. The L-rule is well known and widely studied.