Have you read Umbrella by Taro Yashima? It's wonderful! It's about a Japanese girl named Momo ("the peach") living in New York City who receives rubber boots and an umbrella for her third birthday. Momo longs for a rainy day . . . a rainy day where she can wear her rubber boots and use her umbrella. Yashima's rhythmic use of language echos the "bon polo" (pitter-patter) of raindrops falling on an umbrella, making the textual imagery a bit musical to read aloud. The illustrations also evoke the look of falling rain in its composition. In addition, Japanese characters and their definitions are sprinkled throughout the text. So read this one aloud, and then help your children unveil the riddle at the end!
Also of noteworthy mention, Yashima's Umbrella was a 1959 Caldecott Honor Winner.