## Final Report Summary - PESM (Towards the Prototype Probabilistic Earth-System Model for Climate Prediction)

Comprehensive models of weather and climate play an increasingly important role in helping society become resilient to our changing climate. However, societal decisions based on output from such models is of value only if these models are trustworthy. Since such models are necessarily approximations of the underlying equations of physics, predictions of weather and climate are necessarily uncertain. Moreover, since these equations are nonlinear, the impact of such uncertainties is itself variable. In PESM we have developed an approach to the representation of model uncertainty, pioneered by the PI, to the point where a comprehensive suite of programs for the atmosphere, oceans, land surface and sea ice components has been developed for the premier pan-European climate model EC-Earth. This approach treats the mathematical form for representing processes which cannot be resolved by the model (such as clouds, turbulence and wave-like disturbances over small-scale topography) by stochastic schemes rather than traditional deterministic formulae. Such stochastic schemes, by their nature, contain elements of randomness. Using a technique called “coarse-graining” we have shown rigorously in PESM that stochastic representations of unresolved processes are necessarily more accurate than any set of conventional deterministic parametrisation formulae – this technique has also, for the first time, provided rigorous estimates of the spatial and temporal characteristics of the random noise in these stochastic schemes. The impact of stochastic parametrisation is manifest in three different ways. Firstly, the dispersion of an ensemble of integrations of a weather and climate model will generally be larger with stochastic parametrisation that without. In general, this has been shown to improve the trustworthiness of weather and climate models. Secondly, the nonlinearity of the underlying equations of motion means that stochasticity in the parametrisation process can in principle help reduce the systematic errors of climate models. Such errors have been difficult to eliminate and stochastic parametrisation provides a completely new approach to reducing model bias. In PESM we have shown that a broad range of climatic processes, from the subseasonal Madden-Julian Oscillation and statistics of extratropical weather regimes, to the El Nino/Southern Oscillation and internal decadal variability in the deep ocean, are all improved with stochastic parametrisation. As a result of PESM climate modelling groups around the world are beginning to develop stochastic schemes for their models. The final impact of stochastic parametrisation is being developed in a new ERC proposal. Again, because of the nonlinearity of the underlying equations of motion, stochasticity associated with uncertainty in the unresolved processes will percolate to affect resolved-scale circulations. This means that not all of the 64 bits that are used in contemporary climate models to represent resolved-scale variables contain real information. It was shown in PESM that there is the potential to reduce significantly the number of bits used to represent resolved-scale circulations, but exactly by how much is the topic of a new ERC Advanced Grant ITHACA. The amount of information communicated within a computer is a determinant of how well-resolved a weather or climate model can be. By reducing communication to the bits which contain real information, computer resources can be reallocated to increase the resolution of the model. Overall in PESM, through the European EC-Earth model, we have developed the Prototype Probabilistic Earth-System Model, we have shown that stochastic parametrisation is beneficial for improving the trustworthiness of climate models, and begun a revolution in the way climate models are formulated worldwide, for the benefit of society.