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The accuracy variations of the EKF prior state in the Lorenz model

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Title: The accuracy variations of the EKF prior state in the Lorenz model
Author(s): Hasu, Mikael
Contributor: University of Helsinki, Faculty of Science
Degree program: Master's Programme in Atmospheric Sciences
Specialisation: Meteorology
Language: English
Acceptance year: 2022
This thesis investigates how the Lorenz model state sensitivity appears on the prior state error of the Extended Kalman Filter (EKF) process. The Lorenz model is a well-known ordinary differential equation system. Its simple nonlinear equations show that a chaotic system, like the atmosphere, does not have a single deterministic solution. Edward N. Lorenz also showed that the predictability of the state depends on the flow itself, and numerical weather prediction models, therefore, cannot always be trusted equally. For this reason, when computing a forecast, it is necessary to consider both the model and observations with their weight uncertainties to get the most probabilistic analysis state. The EKF is an algorithm that provides a powerful data assimilation method for nonlinear systems. Its operating principle is based on the evolution of prior state (model evolution) and observation updates. Each observation update calculates the most likely state based on the prior state and observation errors. The process continues from the new analysis state by evolving the model until the next observation update. In this study, I made the EKF utilizing the Lorenz model and sent ensembles from the analysis states on the Lorenz attractor. I calculated the variance of evolved ensembles and compared them to the magnitude of prior state error at the observation update time levels. The results showed that these two parameters are positively correlated. For the 18-timestep observation interval, Pearson’s correlation coefficient was 0.850, which indicates a very high correlation. Therefore, it can be concluded that when the prior state error is small, the ensemble on the Lorenz attractor indicates good predictability (i.e., dispersion of ensemble members is small) and vice versa.
Keyword(s): Numerical meteorology Lorenz model Extended Kalman Filter

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