Climate modelling tasks involve assimilating large amounts of geospatial data from different sources, such as simulators and measurements from weather stations and satellites. These sources of data are weighted according to their uncertainty, so good quality uncertainty estimates are essential. Gaussian processes (GPs) offer flexible models with uncertainty estimates, and have a long track record of use in geospatial modelling. However, much of the research effort, including recent work on scalability, is focused on statistically stationary models, which are not suitable for many climatic variables, such as precipitation. Here we propose a novel, scalable, nonstationary GP model based upon discrete wavelets, and evaluate them on toy and real world data.