1 research outputs found
Ensemble Kalman Filter with perturbed observations in weather forecasting and data assimilation
Data assimilation provides algorithms for widespread applications in various
fields. It is of practical use to deal with a large amount of information in
the complex system that is hard to estimate. Weather forecasting is one of the
applications, where the prediction of meteorological data are corrected given
the observations. Numerous approaches are contained in data assimilation. One
specific sequential method is the Kalman Filter. The core is to estimate
unknown information with the new data that is measured and the prior data that
is predicted. As a matter of fact, there are different improved methods in the
Kalman Filter. In this project, the Ensemble Kalman Filter with perturbed
observations is considered. It is achieved by Monte Carlo simulation. In this
method, the ensemble is involved in the calculation instead of the state
vectors. In addition, the measurement with perturbation is viewed as the
suitable observation. These changes compared with the Linear Kalman Filter make
it more advantageous in that applications are not restricted in linear systems
any more and less time is taken when the data are calculated by computers. The
thesis seeks to develop the Ensemble Kalman Filter with perturbed observation
gradually. With the Mathematical preliminaries including the introduction of
dynamical systems, the Linear Kalman Filter is built. Meanwhile, the prediction
and analysis processes are derived. After that, we use the analogy thoughts to
lead in the non-linear Ensemble Kalman Filter with perturbed observations.
Lastly, a classic Lorenz 63 model is illustrated by MATLAB. In the example, we
experiment on the number of ensemble members and seek to investigate the
relationships between the error of variance and the number of ensemble members.
We reach the conclusion that on a limited scale the larger number of ensemble
members indicates the smaller error of prediction