At one point last night, both bridges were closed. Now its just the old bridge but it will increase traffic congestion in the area. Its always bad on a Monday morning anyway, and today will be worse.
I can remember pre-1996, when the only bridge was shut, South Wales was paralysed for at least 15 miles westwards. Similar problems on the English side. The only alternative to using the bridge was a very long, extremely congested trip up to Gloucester and down the other side of the Severn.
The difficulty with the old bridge is that it was very exposed to high winds. It was actually only closed altogether very few times in its 1st 30 years but was closed to high-sided vehicles rather more often, which had a similar effect to traffic, as big lorries and trucks had to be filtered off at both ends, causing chaos.
The new Bridge is much more resilient to bad weather, with "baffle plates" either side of the carriageway, shielding it from the worst of the winds. Its also not really a suspension bridge, like the old one, so is inherently more stable. Its also three lanes in each direction. The way that it is linked to the M4 and the old bridge means that over 90% of traffic now uses this rather than the original bridge.
But we seem to have escaped most of what was predicted by the weather forecasters. In Swansea were I live, we have had no storm whatsoever, not even a light breeze. Its raining of course, but that is nothing unusual for us in Wales !