Way too often, observations from weather stations fall outside of the ensemble generated by initial uncertainty in weather models. This is because as of yet, many important physical processes that contribute to the weather dynamics are not resolved in numerical models, despite the increase in computing power in recent years. It is therefore necessary to incorporate uncertainty at the level of the model, without destroying the underlying physics. To this end, we introduce SALT (Stochastic Advection by Lie Transport), a framework that derives stochastic PDEs for weather models from a variational principle. This introduces a stochastic term that models the statistics of sub-grid scale turbulence, which is to be learned from data, while still preserving fundamental invariants of the flow. Techniques from machine learning are necessary to learn such stochastic parameterisations. I will also briefly discuss at the end a recent work we did on representing the climate system (as opposed to weather) as a stochastic PDE that is non-local in probability space, and its connection to turbulence closure theory.