1) Even small variations in the sun's output, such as the 0.1% change over the sun's 11-year solar cycle, can significantly impact Earth's climate through complex interactions between the atmosphere and ocean.
2) The sun's extreme ultraviolet radiation varies by much larger factors of 10 over the solar cycle, strongly affecting the chemistry and temperature of the upper atmosphere in ways that can influence surface weather patterns.
3) Recent studies provide evidence that solar variability leaves an imprint on regional climates like the Pacific Ocean through both "top-down" and "bottom-up" atmospheric and oceanic mechanisms.