I thought that I would take a look a closer look at the weather conditions over recent days (9-12 February 2020) that caused the icing problems on the Queensferry crossing close to Edinburgh (why they don’t simply call it the Queensferry bridge and be done with it beats me). It was closed on Monday because falling ice from the cables damaged eight vehicles. It was the first time the bridge had been closed since it was opened in August 2017 but reopened again on Wednesday. They don’t employ any kind of sophisticated sensors to detect any build up of ice on the cables, but rely instead on the mark one human eyeball and a pair of decent 50 x 20 binoculars.
I hadn’t realised that it had been that cold over recent days to allow for ice to build up on the cables even if the towers do reach up to 207 metres (779 feet). Fortunately there has been a ship that has been anchored very close to the bridge for the last four days, it’s callsign is AMOUK36. There are many of these AMOUK vessels that ply the inshore waters around the UK, what they, what they do and who operate them is a complete mystery to me. Anyway the temperatures they report have always looked pretty accurate and as you can see the thermograph trace from AMOUK36 (~4 M amsl) the hourly air temperature only fell below 2°C three times in the last four days. Nearby, and close to Edinburgh airport at Gogarbank (57M amsl), it was a bit colder, but there again hourly temperatures only fell below 1°C once. Of course the towers are much higher than that, but I’m afraid apart from observations from GlenOgle (564 M amsl) which is quite distant, there are no nearby observations at the 200 M level that could give us an insight to the temperatures at the top of the tower.
So the temperature on the upper part of the cable obviously was quite a bit colder that those hourly temperatures at Gogarbank, and obviously cold enough to freeze any of the icy deposits from heavy sleet or snow showers into a veneer of ice around the cales. I was going to speculate that because the temperatures looked quite borderline it might have been melting snow rather than hard ice that had fallen from the bridge, and then I saw this pictures of the damage the ice had caused in the BBC News!
You could estimate what the temperature at the top of the towers was by means of the lapse rate.
The lapse rate is the rate at which an atmospheric variable, normally temperature in Earth’s atmosphere, falls with altitude. Lapse rate arise from the word lapse, in the sense of a gradual fall.Wikipedia
There are several different types of lapse rate, the dry adiabatic lapse rate is a constant 9.8°C per kilometre, the moist adiabatic lapse rates varies with temperature, but a typical value for it would be -5°C per kilometre. Because the towers stand 207 metres above the Firth of Forth and the temperature aboard AMOUK36 was generally between two and four degrees, the temperature at the top of the towers was likely between one or two degrees colder than this. It’s also important to realise that temperatures in the heavier showers would have lowered the freezing level quite easily by a couple of degrees, which would have been enough for ice to have formed from sleet or snow adhering to the cables and body of the towers.