Although it may not seem obvious, a myriad of satellite data is being used by many of the popular numerical models. Satellite-derived winds, radiances, and other data provided by geostationary and polar-orbiting satellites provide a tremendous amount of information in areas that cannot be directly sampled. This is part of the reason why you can't just say "Yeah, but the trough is still over the eastern Pacific, outside of the RAOB/sounding network, so I don't believe the model forecast". In areas that are not sampled by in situ observations (e.g. much of the middle and upper troposphere, and most of the troposphere over ocean regions), there are typically
millions of data points provided by satellites that are used in analysis schemes for operational computer models; most of the data used in many numerical weather models are provided by satellites (certainly there are many more satellite observations than soundings, surface observations, etc.).
This ESRL presentation notes that, from one run of the ECMWF in 2007, "95% of assimilated data is from satellites".