A dust storm picked up by a front moving through Victoria has led to a downpour of "dirty rain" across Melbourne, forcing public swimming pools to close and leaving cars looking like they have been "sprayed with mud".

Key points: The dirty rain was the result of a cold front colliding with a dust storm

The dirty rain was the result of a cold front colliding with a dust storm The rain caused the temporary closure of Burnley station

The rain caused the temporary closure of Burnley station Melbourne has had its wettest January since 1996, with more than double its usual rainfall for the month

Bureau of Meteorology senior meteorologist Richard Carlyon said there had been many reports of brown rain across the city, which was the result of dust storms, not bushfire smoke.

"I didn't see it myself but it makes sense that we did have the active dust storms across northern Victoria yesterday," he said.

"Some of that dust must have been wrapped up in that front that moved through last night.

"Initially, the rain was fairly light so we did get that brown or dirty rain but we've had significant rain through the night that has washed that dirty rain away."

The Yarra River was browner than usual after the dirty rain. ( ABC News: Dylan Anderson )

ABC weather presenter Nate Byrne said the dust was picked up by a cold front and dragged down from South Australia and north-west Victoria.

"Rain is always a little bit dirty because at the heart of every single rain drop, and in fact every single particle or bit of water in the cloud, is a tiny little bit of either dust or bacteria or something," he said.

"Water doesn't like to condense out of being a gas into a liquid unless it's on something so it did it on the dust and then as the rain drops fell from this cold front they bumped into more dust on the way down it just got really muddy."

Byrne said by the time the dust reached Melbourne it was high up in the atmosphere, which is why the sky was tinged with orange, but there wasn't the reduced visibility seen in places like Broken Hill, in New South Wales, and Renmark, in South Australia.

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ABC Radio Melbourne listener Tony said the cool change was accompanied by strong winds as it moved through Point Cook on Wednesday.

"The sky turned into an eerie brown-y hue, just like when we had the smoke it was a red hue, but it was brown and it started raining mud," he said.

"The car looked like it had been sprayed with brown mud and it continued like that for a couple of hours but, as the night wore on, it got a bit cleaner."

Shona McAlpine said her pool in Brighton looked more like a pond.

"We are very lucky to have a swimming pool where we live and our pool is now a mud spa," she said.

"It's definitely brown, it just needs some ducks to put in it and some water plants."

Brunswick Baths closed its outdoor pool on Thursday due to poor visibility.

"We have had some much-needed rain overnight however, it has brought with it a lot of dust," the business posted on its Facebook page.

"Clarity is very poor and unsafe at this time."

Rowers glide through the muddy Yarra River after dusty rain fell across the city. ( ABC News: Dylan Anderson )

The City of Boroondara also closed its outdoor pools "due to the muddy rain that fell last night".

"We are working hard on getting the pools back to an acceptable level of clarity and will let you know when they are reopened," the council said.

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The rain also saw the closure of Burnley station, as specialist crews worked to clear flood water from the station's subway.

Melbourne has had its wettest January since 1996, with 23 millimetres of rain falling overnight, bringing the monthly rainfall total to 114mm.

The city's average January rainfall is 45mm.