1. Based on the sketches he drew outside, Degas painted in his studio.
2. As/While he was based on the sketches he drew outside, Degas painted in his studio.
3. When he was based on the sketches he drew outside, Degas painted in his studio.
4. Because based on the sketches he drew outside, Degas painted in his studio.
(What does #1 mean? Which one is similar to #1? The participle phrase can be changed into an adverbial clause, right?)
#1 is correct; the others are not.
Again, the problem is the word "based" --
Degas based his paintings on the sketches he drew outside.
Degas' paintings, based on his sketches, were painted in his studio.
Because he had sketches that he had drawn outside, Degas could paint the scenes in his studio.