Abstract/Summary

Data assimilation is the process of combining observations with a model’s first guess to determine the best estimate of the current state of the atmosphere. In the case of numerical weather prediction the data assimilation step is carried out using various types of Kalman filter equations, which are developed based on the Gaussian assumption and are therefore unable to deal with non-Gaussianity. Particle filters, by definition, can deal with non-Gaussianity and are well known in statistics. They have a long tradition in the framework of ensemble data assimilation (EDA) as well as Markov-Chain Monte Carlo (MCMC) methods. A key challenge today is to employ such methods in a high-dimensional environment, since the naive application of the classical particle filter usually leads to filter divergence or filter collapse when applied within the very high dimensionality of many practical assimilation problems (known as the curse of dimensionality). In the first part of this thesis we introduce the Localised Adaptive Particle Filter (LAPF), which follows closely the idea of the classical MCMC or bootstrap type particle filter, but overcomes the problems of filter collapse and divergence using localisation in the sense of the Local Ensemble Transformed Kalman Filter (LETKF) and adaptivity with an adaptive Gaussian resampling or rejuvenation scheme in ensemble space. We have implemented the particle filter in the data assimilation system for the global forecast model ICON at the German Meteorological Service (DWD). We carry out simulations over a period of one month with a global horizontal resolution of 52 km and 90 vertical layers. With four variables analysed per grid point, this results in 6.6 · 106 degrees of freedom. The LAPF can be run stably and shows a reasonable performance. We compare its results with the operational LETKF implementation of DWD for the ICON model. Based on this work, we investigate the implementation of the Gaussian uncertainty of individual particles in the assimilation step of the localised adaptive particle filter. We obtain a local representation of the prior distribution as a mixture of basis functions. In the assimilation step, the filter calculates the individual weight coefficients and new particle locations. It can be thought of as a combination of the LAPF and a localised version of a Gaussian mixture filter, i.e., a Localised Mixture Coefficients Particle Filter (LMCPF). Again, we have implemented the LMCPF within the global operational framework ICON of the DWD and evaluate the relationship between prior and posterior distributions and observations. Our simulations are carried out in the same standard pre-operational experimental setup as for the LAPF and additionally in a setup closer to the currently operational system. We are able to show that the mixture approach is able to deal with the discrepancy between the prior distribution and the observation location in ensemble space in a real-world framework and to pull the particles towards the observations. This shows that the use of Gaussian uncertainty can be an important tool to improve the analysis and forecast quality in a particle filter framework.