Climate Informatics is emerging as a compelling application of machine learning. This is due in part to the urgent nature of climate change, and its many remaining uncertainties (e.g. how will a changing climate affect severe storms and other extreme weather events?). Meanwhile, progress in climate informatics is made possible in part by the public availability of vast amounts of data, both simulated by large-scale physics-based models, and observed. Not only are time series at the crux of the study of climate science, but also, by definition, climate change implies non-stationarity. In addition, much of the relevant data is spatiotemporal, and also varies over location. In this talk, I will discuss our work on learning in the presence of spatial and temporal non-stationarity, and exploiting local dependencies in time and space. Along the way, I will highlight open problems in which machine learning, including deep learning methods, may prove fruitful.