Ms Smith’s father Martin Knowles said the family was “still praying and hoping Sophie will walk through her mum’s door, just so we can put our arms around her and tell her how much we enjoy her”.
He described his daughter as “happy-go-lucky, full of life, quite popular, liked by a lot of people”.
“She’s had a bit of hard time recently but I imagine all juveniles do. It’s hard being young, ” Mr Knowles said.
A police helicopter, the coastguard and lifeboats had been involved in examines all over the beach at Gorleston on Tuesday and Wednesday.
“We have diligently searched for Sophie and have investigated a range of scenarios but unfortunately “theres been” no confirmed sightings or contact since she left her dimension, ” said Insp Will Drummond.
“We have a possible CCTV image of Sophie heading towards the seafront but, despite all our efforts, we have found no further draw of her.”
Insp Drummond said police officers were in “close contact with Sophie’s family”.
“However, due to the circumstances in which she left home with negligible apparel , no mobile phone, her mental state and the weather conditions, the the expectations of receiving Sophie safe and well decreases as meter gone on, ” he said.
Ms Smith’s family has led a inquiry around the Britannia pier in Great Yarmouth, and police and the Norfolk Fire and Rescue Service were involved in a nine-hour search effort on Tuesday.
The search of the beach continues in Wednesday and has involved the membership of the Norfolk Lowland Search and Rescue.
Manager Paul Webber said his volunteers would return to the town in an effort to find Ms Smith, who vanished from Avondale Road without her mobile phone.
“We methodically searched areas within the town, ” he said. “We have about 15 members going back to continue the search.”
Norfolk Police said on Wednesday they were becoming “increasingly concerned” for University of East Anglia student Ms Smith and wanted to hear from anyone who may have determined her or knew where she was.
She is described as about 5ft 8in tall( 1.72 m ), of slim structure with long blonde hair.