E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
To rain cats and dogs. In northern mythology the cat is supposed to have great influence on the weather, and English sailors still say, The cat has a gale of wind in her tail, when she is unusually frisky. Witches that rode upon the storms were said to assume the form of cats; and the stormy north-west wind is called the cats-nose in the Harz even at the present day.
The dog is a signal of wind, like the wolf, both which animals were attendants of Odin, the storm-god. In old German pictures the wind is figured as the head of a dog or wolf, from which blasts issue.
The cat therefore symbolises the downpouring rain, and the dog the strong gusts of wind which accompany a rainstorm; and a rain of cats and dogs is a heavy rain with wind. (See CAT AND DOG.)
The French catadoupe or catadupe means a waterfall.