Commercial Fixed Wing
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
ATC Issue All Types; Deviation / Discrepancy - Procedural Clearance; Ground Incursion Taxiway
ATC Equipment / Nav Facility / Buildings; Airport; Weather; Human Factors
Landed in foggy conditions that got worse as we rolled down Runway 1 left. Tower told us to exit on Runway 31. The runway lights were not on and rolled past it. Then told to exit at Taxiway V and then take G; cross 31/13 and Bravo to the gate. There were no taxiway signs for Taxiway Golf that could be seen. Continued on Taxiway Victor and crossed Runway 31/13 at Victor instead of Golf. Tower then said just to proceed down Victor to Bravo and to the gate. No further problems. The visibility on the last half of Runway 1 Left kept getting worse and was probably less than 500 feet at times. [Caused by] fog and inadequate signage and no lights on the runway we were told to taxi off onto (13/31). Should have just asked for progressive taxi due to the worsening visibility.
After landing from a CAT II approach; we taxied off the runway. We were cleared to cross Runway 31 on G and we accidentally crossed on victor. When told to cross another active runway without any ground navigation aids to confirm which taxiway we were on; we believed we crossed the runway at G. We actually crossed the runway at V. The controller informed us after the crossing that we crossed on the wrong taxiway. Preceded to the gate without any incident. Visibility conditions got worse the further down the runway we taxied. The cause of the event was due to low visibility after landing from a CAT II. There weren't any signs to indicate the taxiway to which we were crossing a runway. Lights for the runway we were assigned to cross weren't on. The taxiway for which we exited the active led to a three way intersection to cross the runway for which we crossed at the wrong intersection. Ask for a progressive taxi when visibility conditions are low. Better signage on the airport. Lead off lights from the active runway to a taxiway and a marking on the ground for which taxiway we were on. Ground navigation on the iPad to show which taxiway we are on to use during times of low visibility.
Air Carrier Flight Crew reported runway lights and taxiway signage inoperative.