High pressure is associated with clear skies and fair weather. This is ideal, but not always the case. In a forecast discussion you may come across the term "dirty high". This is in reference to a high pressure that has clouds and/or precipitation within its domain.

There are several ways clouds can occur in association with high pressure. A deck of low clouds (stratus) and/or fog could be within the domain of high pressure. This can occur as a cool area of high pressure moves over saturated land. Moisture evaporated into the low levels and cooler conditions cause a quick saturation of air which results in a low deck of clouds and/or fog (high pressure generally has light wind and clear skies at its core which is conducive to morning clouds and fog over night especially if soils are saturated). An inversion produced by the high pressure can trap the moisture in the PBL and can cause low level clouds to persist. Cloud can occur with high pressure when orographic lifting causes cloud development. Lifting mechanisms such as WAA or upper level divergence can produce clouds in close proximity to the high pressure. Much also depends on the strength of the high pressure and the verticality of the high pressure. A deep and very dry high pressure is less likely to have clouds located near its core, especially if the land underneath is fairly dry.