Inaccurate weather measurement so close to an airport take off or landing flight path would seem unlikely.
Even in the wettest Scottish months there are 12-15 rain free days a month in the central belt. Considerably different in Oban of course, where you may enjoy 50% more rainy than days than the wettest Edinburgh month.
So the reality is it's a drainage problem. Unlike the Severn Tunnel though, the trackbed at Winchburgh is around 70 metres *above* sea level. There's probably potential there to deliver a gravity based solution, with a 70 metre drop, perhaps even generate power when it rains.
Edinburgh Park, which is not that far East, is about 50m above sea level so a track-side drain could be a viable proposition. The trouble starts with where the run-off goes.
Another alternative would be a drainage tunnel towards Abercorn. Again, the problem is where to put the run-off?