In this talk, I deliver two case studies for pursuing the innovative application and development of statistical methodology to address problems faced in geophysical sciences. In the first case, I present statistical methods for climate prediction. Prediction of future climate change are issues of global importance affecting the whole ecosystem and human community. In the second problem, I propose a novel method to estimate the period and the light curve (or periodic function) of a variable star and classify the stars. The careful analysis of variable stars can provide an important clue to understand the structure of galaxy and stellar evolution.