Abstract/Summary

Every numerical model of a real-world system will contain errors. This errors may arise due to a lack of scientific understanding or a lack of computing power available to address all the known physical processes. In general, model errors are often not well understood and hence are large sources of uncertainty in a model. This thesis presents an overview of model improvement through the use of data assimilation. Data assimilation can be used to reduce model errors, either by finding and correcting systematic model errors or by improving the conditions that numeri-cal models are initialised with. This thesis explores both of these options for model improvement. New methods of estimating systematic errors through the use of data assimilation are developed. The data assimilation analysis is used to estimate the model errors over the whole domain at all timesteps. The structure of this estimated model error is analysed for physically realistic structures that allow us to improve the model. A parameter estimation method and a parameterisation estimation method are both developed inthis thesis. Experiments on a linear advection model using the new parameter estimation method, Derivative-based Parameter Estimation (DerPE), with a localised stochastic Ensemble Kalman Smoother (EnKS) and the Localised Ensemble Transform Kalman Smoother (LETKS), two state of the art data assimilation methods, were performed and compared to an established method of parameter estimation, state augmentation. These experiments showed that a reduction in model error arising from the incorrectly specified parameters can be achieved with the new DerPE method. The performance of the new parameterisation estimation method is tested on a non-linear advection model. The parameterisation recreated nonlinear functional estimates for the model error, where state augmentation cannot, given the same prior information. This method also produces consistent estimates of the uncertainty associated with each of the terms estimated for the model error arising from parameterisation errors. These results demonstrate that this method has the potential to estimate functional model errors accurately for more complex models. Advanced data assimilation methods are applied to a solar wind model for the first time with the ultimate aim to use data assimilation to improve the initial conditions for solar wind forecasting. The EMPIRE (Employing Message Passing Interface for Researching Ensembles) data assimilation system is coupled to the ENLIL solar wind model and twin experiments are performed using the Localised Ensemble Transform Kalman Filter(LETKF) in both the steady solar wind and when a Coronal Mass Ejection (CME) is propagated through the domain. The LETKF is shown to have to reduce the Root Mean Squared Errors (RMSEs) at the observation point, especially when the observation is near the Sun. Further, the LETKF is shown to have the potential to recreate CMEs from observations. When the observation is closer to the Earth, the LETKF is less effective at estimating the true state, in both the steady solar wind and when a CME is propagated through the domain. This is due to the collapse of the LETKF ensemble. Potential strategies to mitigate this are proposed so that the LETKF can be used with real observations. New techniques for model improvement are found that seem to be accurate enough to apply to more realistic systems than the applications explored in this thesis. Additionally, a new field of application of data assimilation, the solar wind and its disturbances, is opened up. Both of these require much more work, but the expectation is that useful first steps have been made in this thesis.