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Some weather providers like Yahoo give a visibility percentage while others like OpenWeather.org give cloudiness percentage.

To normalize would it be acceptable to say that visibility = 100 - cloudiness?

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    Different things. Visibility - horizontal distance – FelixIP Jan 22 '15 at 20:05
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I think it depends a lot on your target audience, but I don't think you can say this in general.

In aviation (ICAO) and "real" weather (WMO) definitions, visibility is a distance. There is a pretty good wikipedia article on Visibility. It is also possible to represent visibility as a probability of a certain distance being achieved (e.g. probability of 5km visibility), but that is much less common - I've only seen it as a parameter in some numerical ensemble forecasts.

By contrast, cloudiness is a ratio (amount of sky covered by cloud as ratio of the total sky). Again, Wikipedia has a good article on cloud cover.

There is an example in the WMO document on "forms" like METAR that describes a scenario where a SPECI is for an both increasing visibility and lowering clouds (which often represents an increase in effective cover, because the same clouds closer means greater coverage).

To think about this in terms of phenomena, consider that visibility can be affected by lots of things other than cloud (haze, smoke, other aerosols). Also, a lot of high cloud (maybe above an inversion layer) may be unaffected by some surface wind that comes in to clear away a low fog/cloud bank that is limiting visibility.

So unless you know that the Yahoo definition of visibility is something other than what is (generally) defined as visibility, I think you should avoid that particular normalisation.

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