Meaning: The sun appeared and made the ground dry.
Choice of Words: Sun came out, drying the ground.
Meaning: This sentence tells us that the sun appeared for a short time, and it's making the ground less wet.
Choice of Words: Peeked out means the sun appeared for a short time, like when you look around a corner. Less soggy means not as wet.
Meaning: This sentence tells us that the sun became visible, and it's making the ground less wet.
Choice of Words: Appeared means the sun became visible. Causing means making something happen. Become dry means to lose moisture.