Stochastic parametrisation and model uncertainty
Keywords: Stochastic models
Atmospheric models
Model uncertainty
Atmospheric physics

Representing model uncertainty in atmospheric simulators is essential for the production of reliable probabilistic forecasts, and stochastic parametrisation schemes have been proposed for this purpose. Such schemes have been shown to improve the skill of ensemble forecasts, resulting in a growing use of stochastic parametrisation schemes in numerical weather prediction. However, little research has explicitly tested the ability of stochastic parametrisations to represent model uncertainty, since the presence of other sources of forecast uncertainty has complicated the results.
This study seeks to provide firm foundations for the use of stochastic parametrisation schemes as a representation of model uncertainty in numerical weather prediction models. Idealised experiments are carried out in the Lorenz `96 (L96) simplified model of the atmosphere, in which all sources of uncertainty apart from model uncertainty can be removed. Stochastic parametrisations are found to be a skilful way of representing model uncertainty in weather forecasts in this system. Stochastic schemes which have a realistic representation of model error produce reliable forecasts, improving on the deterministic and the more "traditional" perturbed parameter schemes tested.
The potential of using stochastic parametrisations for simulating the climate is considered, an area in which there has been little research. A significant improvement is observed when stochastic parametrisation schemes are used to represent model uncertainty in climate simulations in the L96 system. This improvement is particularly pronounced when considering the regime behaviour of the L96 system - the stochastic forecast models are significantly more skilful than using a deterministic perturbed parameter ensemble to represent model uncertainty. The reliability of a model at forecasting the weather is found to be linked to that model's ability to simulate the climate, providing some support for the seamless prediction paradigm.
The lessons learned in the L96 system are then used to test and develop stochastic and perturbed parameter representations of model uncertainty for use in an operational numerical weather prediction model, the Integrated Forecasting System (IFS). A particular focus is on improving the representation of model uncertainty in the convection parametrisation scheme. Perturbed parameter schemes are tested, which improve on the operational stochastic scheme in some regards, but are not as skilful as a new generalised version of the stochastic scheme. The proposed stochastic scheme has a potentially more realistic representation of model error than the operational scheme, and improves the reliability of the forecasts.
While studying the L96 system, it was found that there is a need for a proper score which is particularly sensitive to forecast reliability. A suitable score is proposed and tested, before being used for verification of the forecasts made in the IFS.
This study demonstrates the power of using stochastic over perturbed parameter representations of model uncertainty in weather and climate simulations. It is hoped that these results motivate further research into physically-based stochastic parametrisation schemes, as well as triggering the development of stochastic Earth-system models for probabilistic climate prediction.