I have two comments on this:
1) If the 10-16 day forecast is only slightly better than a shot in the dark, then why does the GFS model run that far out?
2) If nanotechnology continues to grow, I can conceive of billions of "nano-sensors" being released into the atmosphere, Conceivably, the entire globe at all levels could be covered. Each nano-bot would need to be programmed for a specific area of the atmosphere, and to communicate with the group it belongs to, and then relay the data they have collected either to Earth stations, or satellites for relay to ground stations.
This would give us the data we need - then all we have to do is build the model that can run with all the data.
Of course - with all those nano-bots flying around, our view of the sky might change - and they might even interfere with sunlight reaching the ground - thus changing the weather patterns. If the bots can be made small enouogh, and have enough power to fly a large enough area to collect data, then the number required might be low enough so as not to cause interference.