Weather and climate simulations produce petabytes of high-resolution data that are later analyzed by researchers to understand climate change or severe weather. We propose an efficient data compression method dedicated to weather and climate data. It consists of two components: one base compressor utilizing the JPEG2000 image codec, and a residual compressor based on sparse wavelets. With compression ratios ranging from 10x to more than 3,000x, our method can achieve better accuracy than existing methods. It can faithfully preserve important large-scale atmosphere structures and does not introduce significant artifacts. Due to the introduction of the residual compressor, it can achieve error-bounded compression without sacrificing compression ratios.