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Joint state and parameter estimation to address model error in convective scale numerical weather prediction systems
Joint state and parameter estimation to address model error in convective scale numerical weather prediction systems
Numerical weather prediction models need initial conditions to produce weather forecasts. These initial conditions are computed through a process called data assimilation, where previously computed model states are updated using newly obtained observations of the atmosphere. The data assimilation system (KENDA) employed at the German Weather Service for regional forecasts is based on the Ensemble Kalman Filter (EnKF), which was designed under the assumption of a perfect model in a stochastic sense and Gaussian error statistics. As neither of these assumptions is valid for operational convection permitting weather prediction models, improvement can be gained by developing methods and algorithms for which these assumptions can be relaxed. In this thesis we investigate the feasibility of addressing model error by perturbing and estimating uncertain static model parameters using data assimilation techniques. In particular we use the augmented state approach, where parameters are updated by observations via their correlation with observed state variables. This online approach offers a flexible, yet consistent way to better fit model variables affected by the chosen parameters to observations, while ensuring feasible model states. A key challenge is to design the probability distribution of the parameters, which should reflect the uncertainty of the targeted model error. We show in an operational setup that the representation of clouds in COSMO-DE is improved if the two dimensional roughness length parameter is estimated with the augmented state approach. Here, the targeted model error is the roughness length itself and the surface fluxes, which influence the initiation of convection. The probability density function of the roughness length, and by extension the model error corresponding to the surface fluxes, is assumed Gaussian with a certain covariance matrix. The results are highly sensitive to the choice of covariance matrix, and strongly suggest the importance of assimilating surface wind measurements. In addition we evaluate two recently developed modifications of the EnKF that either explicitly incorporate constraints such as mass conservation and positivity of precipitation by solving constrained minimization problems (QPEns), or introduce higher order moments such as skewness (QF) to deal with non-Gaussian error statistics. We show in a idealized setup that the estimation of parameters benefits from the QF (even for moderate ensemble sizes) and that the QPEns generally outperforms the EnkF significantly. To reduce the high computational costs of the QPEns we propose an new algorithm that exploits properties of the minimization problems that need to be solved. We also explore a different approach where we train a neural network to reproduce the initial conditions generated by the QPEns from those generated by the EnKF. Besides the encouraging finding that even in a near operational setup model error is significantly reduced by estimating appropriate model parameters, we provide various suggestions for further research that can lead to further improvements.
data assimilation, parameter estimation, model error, Ensemble Kalman Filter, non-Gaussianity
Ruckstuhl, Yvonne
2019
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Ruckstuhl, Yvonne (2019): Joint state and parameter estimation to address model error in convective scale numerical weather prediction systems. Dissertation, LMU München: Faculty of Physics
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Abstract

Numerical weather prediction models need initial conditions to produce weather forecasts. These initial conditions are computed through a process called data assimilation, where previously computed model states are updated using newly obtained observations of the atmosphere. The data assimilation system (KENDA) employed at the German Weather Service for regional forecasts is based on the Ensemble Kalman Filter (EnKF), which was designed under the assumption of a perfect model in a stochastic sense and Gaussian error statistics. As neither of these assumptions is valid for operational convection permitting weather prediction models, improvement can be gained by developing methods and algorithms for which these assumptions can be relaxed. In this thesis we investigate the feasibility of addressing model error by perturbing and estimating uncertain static model parameters using data assimilation techniques. In particular we use the augmented state approach, where parameters are updated by observations via their correlation with observed state variables. This online approach offers a flexible, yet consistent way to better fit model variables affected by the chosen parameters to observations, while ensuring feasible model states. A key challenge is to design the probability distribution of the parameters, which should reflect the uncertainty of the targeted model error. We show in an operational setup that the representation of clouds in COSMO-DE is improved if the two dimensional roughness length parameter is estimated with the augmented state approach. Here, the targeted model error is the roughness length itself and the surface fluxes, which influence the initiation of convection. The probability density function of the roughness length, and by extension the model error corresponding to the surface fluxes, is assumed Gaussian with a certain covariance matrix. The results are highly sensitive to the choice of covariance matrix, and strongly suggest the importance of assimilating surface wind measurements. In addition we evaluate two recently developed modifications of the EnKF that either explicitly incorporate constraints such as mass conservation and positivity of precipitation by solving constrained minimization problems (QPEns), or introduce higher order moments such as skewness (QF) to deal with non-Gaussian error statistics. We show in a idealized setup that the estimation of parameters benefits from the QF (even for moderate ensemble sizes) and that the QPEns generally outperforms the EnkF significantly. To reduce the high computational costs of the QPEns we propose an new algorithm that exploits properties of the minimization problems that need to be solved. We also explore a different approach where we train a neural network to reproduce the initial conditions generated by the QPEns from those generated by the EnKF. Besides the encouraging finding that even in a near operational setup model error is significantly reduced by estimating appropriate model parameters, we provide various suggestions for further research that can lead to further improvements.