Winds in the area reached speeds of more than 50mph on Saturday night.
Coastal and flood-prone communities across Wales are preparing themselves for another battering from the weather this weekend
Ceredigion Council estimates that damage in Aberystwyth and elsewhere in the country will top £1.5m.
Network Rail says it will have to take "a phased approach" to reopening the Cambrian Coast line.
The line is expected to reopen as far as Barmouth by February, but the stretch from Barmouth to Pwllheli will not be fully repaired until May.
"This has been an extremely challenging period, but the rebuilding operation is underway and our priority is to safely re-open the railway as soon as is possible" says Network Rail's Mark Langman.
"I would like to take this opportunity to apologise for the on-going inconvenience and also thank rail passengers for their patience as we repair this unprecedented damage.”
Repairs to the Cambrian Coast railway will take months, say Network Rail.
The line is closed between Dovey Junction and Pwllheli after recent storms left debris strewn across the tracks.
Engineers intend to have the route open by mid-May.
The council dealing with the clean-up operation in Aberystwyth have said they are still trying to remove large debris from roads and beaches caused by storm damage over the last few days.
Ceredigion County Council says despite receiving numerous offers, 'it's not yet appropriate' for members of the public to be involved in the operation due to the heavy machinery required to complete the first stage of the clean-up.
But, the council added it would be more than happy for volunteers to assist towards the end of the week depending on it's progress and the weather.
It said information and further updates will be released through social media as to where and when the cleaning work will need to be done.
Marine Terrace is closed becasue of debris on the road between Victoria Terrace and New Promenade.
Marine Terrace is closed because of debris on the road between Victoria Terrace and New Promenade.
There's a replacement bus service running on Arriva Trains Wales between Machynlleth and Aberystwyth because of flooding.
Owing to flooding between Machynlleth and Aberystwyth all lines are currently blocked. For all service info visit http://t.co/O1CNZNTMbW
Aberystwyth RNLI Lifeboat crew have rescued a man they believe was taking photographs of the waves. Despite public warnings to stay away from the coastline, it seems the man walked to the end of the wooden jetty. Rescuers say he became trapped due to the force of the waves.
At 10am on 4th January the lifeboat was called in after the police and coastguard were unable to get to him. He was rescued and returned safely to the RNLI boathouse.
In a statement, a spokesperson for Aberystwyth RNLI Lifeboat said:
“Whilst the extreme sea conditions are attracting people to the coastline, we repeat our warning to the public stay safe and to keep away from the shore line and dangerous waves."
A small earthquake measuring 1.9 on the richter scale, which was centred on Llanwrtyd Wells in Powys, was felt as far away as Aberystwyth.
According to the British Geological Survey, the tremor occurred at 9.30am this morning.