They have less-runny lava, meaning that it doesn't travel as far before cooling, meaning that the layers build up more steeply, but don't go out as far. You also get layers of ash on the composite volcano to help build it up too
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The climate of any particular place is influenced by a host of interacting factors. These include latitude, elevation, nearby water, ocean currents, topography, vegetation, and prevailing winds. The global climate system and any changes that occur within it also influence local climate.