Use of 'That" rather than "the"

The weather reports on the BBC frequently use the word "That" when I was expecting either no article or possibly "the". For example 'There will be more of that cold weather.' when no cold weather has been referred to, unless they meant yesterday, or last week, possibly. Am I wrong, or is this just another silly attempt to sound vaguely colloquial? This use of "That" seems very common currently in what might be called reporter speak, the weather men are not the only example, but they seem to do it a lot. Over the last few weeks I have also heard "that sunshine", "that rain", "that fog". I have hunted around some grammar web resources and can't find any justification for this use of "That". Have I missed something?

Demonstrative determiners can have both anaphoric and cataphoric reference. That is, they can refer to something already mentioned or something which follows. The reference can be implied rather than explicit.

In a sentence such as There will be more of that cold weather the speaker means ‘more of the cold weather with which we are unfortunately so familiar in this country, and which you and I both know we’ve got to put up with because we’re British and we don’t really mind it, but like to pretend that we do.’

You frequently hear that in contexts where it implies a shared understanding of a particular item:

We got some of that good apple cider you like.

[Song] Gimme That Old-Time Religion

They're going to close that good diner.

In each case, it is more specific than the in the sense that it makes something of a personal statement. The persons addressed will think back to items that have some personal significance between them and the speaker. In your case, cold weather or sunshine will have a general meaning to the audience.