High pressure systems are much more likely to consist of cool dry air.
Above the blanketing effect of greenhouse gases in the lower atmosphere, high altitude air cools as IR radiates into space. Its humidity deposits into clouds of ice crystals as the air cools through the dew point. The volume occupied by the air mass decreases and its density increases. The dense air sinks and accumulates at ground level until increasing pressure counterbalances the sinking air. Winds flow outwards from the high pressure cell and twist with the Coriolis effect. The outflowing air may be replaced by more sinking dry air maintaining the system.
