A stochastic, particle based model for testing the impact of correlated representation error on data assimilation

Semrau, Florian (2024): A stochastic, particle based model for testing the impact of correlated representation error on data assimilation. Dissertation, LMU München: Fakultät für Physik

Abstract

In many disciplines, a common problem is to estimate the state of a system by combining a forecast or prediction with observations. Addressing this issue is the central goal of Data Assimilation (DA). In this context, the uncertainties and error correlations of individual observations are encoded in the observation error covariance matrix, and those of the forecast are encoded in the background error covariance matrix. The observation error usually consists of multiple components, originating from the measurement process, the mapping of the state space used to model the system to the observations and the so-called representation error. The latter one originates from the difference between the model used to describe the system and physical reality and will be the focus of this thesis. Despite the fact that the observation error covariance matrix plays a crucial role in DA, the role of its spatial structure and temporal development is still poorly understood and estimating it is extremely difficult for most practical applications. Thus in many cases a diagonal observation error covariance matrix is employed, requiring an uncorrelated data set and often leading to a large percentage of the available data being discarded. To be able to systematically study the role of the observation error covariance matrix in DA, in this thesis we construct the Stochastic Particle Model (SPM), a simple particle based toy model for liquid water content and number density with well-defined covariances. After constructing the SPM, we numerically calculate the according covariance matrices and relate their features to gravitational sorting and particle geometry. Subsequently, we use the covariance matrices obtained from the SPM in a series of DA experiments, in which we compare the results obtained when using dynamic and static, as well as full, diagonal and block diagonal observation error covariance matrices. In these experiments, we find that correctly specifying the temporal evolution of the observation error covariance matrix is far more important than accounting for its spatial structure. A further important aspect relevant for the choice between using diagonal or non-diagonal observation error covariance matrices in DA is non-negativity preservation. Thus we consider several strongly simplified examples to show that with non-diagonal background and observation error covariances, we can not ensure that the analysis of the Kalman filter (a common DA algorithm) is non-negative. Furthermore, we carry out a series of numerical experiments to investigate, how using non-diagonal observation error covariance matrices affects the frequency of non-negativity violations.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Keywords: data assimilation, representation error
• Themengebiete: 500 Naturwissenschaften und Mathematik ; 500 Naturwissenschaften und Mathematik > 530 Physik
• Fakultäten: Fakultät für Physik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 15. November 2024
• 1. Bericht­erstatter:in: Janjić, Tijana