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Why are windward mountain slopes often wetter than leeward slopes?

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A car drives along the Trans-Canada Highway with Mount Sir Donald's sharp, snow-capped peak rising above forested slopes in the Selkirk Mountains, British Columbia. — mountain Mount Sir Donald in the Selkirk Mountains, British Columbia, looms above a segment of the Trans-Canada Highway.

Windward mountain slopes are typically wetter than leeward slopes due to a process known as orographic precipitation.

When moist air encounters a mountain range, it is forced upward along the windward slope. As the air rises, it expands and cools—a process called adiabatic cooling. Because cooler air has a reduced capacity to hold moisture, the water vapor condenses to form clouds and releases significant amounts of rain or snow on the windward side.12

By the time the air passes over the mountain ridge and begins to descend the leeward slope, it has lost much of its moisture. As this air descends, it warms and its capacity to hold moisture increases, leading to drier conditions on the leeward side. This relatively arid region is known as a rain shadow.2314