Modeling any climate phenomena should consider relevant physics, however, it should not ignore approximations commonly made to simplify these constructs. The validity of these approximations must be verified in the presence of data. Physics provide a starting point for our research, but there are gaps in the physics knowledge relating to (i) use of extreme values, (ii) lack of random effects and latent variables, and (iii) spatial-temporal dependence. This thesis addresses the statistical challenges in properly modeling (i), (ii) and (iii) using climate data. Specifically, the research focuses on case studies of worldwide tropical cyclones and Indian summer monsoon precipitation.