Numerical models used for weather and climate prediction have traditionally been formulated in a deterministic manner. In other words, given a particular state of the resolved scale variables, the most likely forcing from sub-grid scale motions and parametrised processes is estimated and used to predict the evolution of the large-scale flow. However, knowledge uncertainties, necessary simplifications in representing the physical processes in numerical models, and the lack of scale-separation in the Earth System mean that this approach is a large source of error in forecasts. Over recent years, an alternative paradigm has developed: the use of stochastic techniques to represent the effects of uncertain small-scale and parametrised processes. Instead of predicting the most likely forcing effect of these processes on the resolved scales, a Monte-Carlo approach is used. Integrations of the numerical model sample possible realisations of the forcing.

Stochastic parametrisations are now the norm in ensemble weather and seasonal forecasts worldwide. By accounting for uncertainty in the forecast due to the limitations of numerical models, stochastic parametrisations improve the reliability of ensemble forecasts. We are now seeing their adaptation for use in climate models, with stochastic parametrisations being developed to represent a wide range of processes in the Earth System, including processes in the atmosphere, oceans, and land surface.

This course will introduce the art and science of stochastic parametrisation, including

> Purpose: model uncertainty, ensemble forecasting, climate applications
> Foundations: stochastic processes
> Theory: how to design a stochastic scheme
> Realisation: the path from a well-designed scheme to an operational implementation in a numerical model

This course is aimed at PhD students, Early Career Scientists, and all those interested in an overview of key concepts in stochastic parametrisation. The course will be taught through a combination of presentations and interactive exercises using python notebooks. No prior knowledge of python is necessary.

Public information:
Due to the reduced length of time allocated to each short course this year, the short course will consist of presentations and Q&A, and will no longer include python exercises.

For further reading on this topic, please find useful references here:
https://mumip.web.ox.ac.uk/stochastic-parametrisation