The intensity of the rain at certain points caused particular problems, with the Scottish Environment Protection Agency reporting up to 4mm falling in the space of an hour during the height of the rain.

The downpour had stopped early this morning, but some roads remained closed and water levels, particularly in the Arbroath area, remained high.

The A92 was still closed this morning at Inverkeilor due to flooding on the railway line, which was also closed, resulting in trains being held at Montrose and Dundee and a replacement bus service put on to Aberdeen.

Meanwhile, clear-up operations got under way across Tayside and Fife as the authorities kept a nervous eye on the weather forecast, which predicted further rainfall tonight.

A spokesman for Tayside Police said, “River levels on a number of rivers throughout Tayside are high and fast flowing but appear to be levelling out and have not been affected by the incoming tide.

“Rivers have been monitored overnight and will continue to be monitored until river levels subside.

“But the forecast is that it is going to rain again later today and that is a bit of a concern.”

However, some comfort was provided by SEPA, who said the west coast of Scotland would be worse hit by the predicted rain.

A spokeswoman said, “More rain is expected later, but will be most frequent across western Scotland. The rain will cross the country later tonight and clear from eastern areas in the morning.

“Rain levels are expected to be lower than those experienced in the last few days at around 5 to 10mm, with most of the heaviest rain confined to western areas.

“River levels in the North East remain high, but most rivers have now peaked or are falling.”

Tayside Police asked motorists not to contact them directly to check on road conditions, but to visit the SEPA website or contact Traffic Scotland for travel information. However, if drivers are experiencing hazardous conditions they should contact Tayside Police on 0300 111 2222.

More misery was heaped on Dundee’s motorists as one of the city’s largest car park was closed due to the flooding.

Dundee City Council confirmed Bell Street, which has 930 spaces, has been shut off to the public until further notice.

A number of electrical control systems for the building have been affected by water after yesterday’s heavy rain.

Temporary signs warning of the closure have been put up, but some drivers complained to the Tele the signage did not give enough notice of the closure and there had been traffic congestion.

A spokesman for Dundee City Council apologised for any inconvenience the closure would cause and reminded monthly ticket holders they can use any of the council’s other long stay car parks while Bell Street is out of action.

Energy supplier Scottish Hydro Electric Power Distribution said a power cut affecting thousands of homes in the east of Dundee on Sunday was caused by the torrential downpours.

A total of 4000 homes and businesses were left in the dark after heavy rain affected the network, leaving some residents without electricity for up to six hours.

A spokesman for the company said that “extraordinary” rain had affected advanced security equipment which shuts down the system if it senses moisture as a safety measure.

He explained, “Scottish Hydro Electric Power Distribution makes every effort to ensure that its network is as robust and resilient as possible. There are occasions, as was the case in Dundee yesterday, when exceptional weather conditions can cause our safety equipment to operate.

“We would like to apologise to our customers whose supplies were interrupted yesterday and thank them for their patience as our engineers worked to restore their power as quickly as possible.”

The spokesman added the faults of the weekend had been repaired and stressed they were confident that there would be no further power cuts.

The power cut on Sunday was unrelated to a blackout on Saturday evening, which was linked to a problem at Scottish Hydro Electric’s Milton of Craigie site.