Information Content of Observations in Variational Data Assimilation

Data assimilation is needed to generate an analysis, which i s used as the initial conditions for numerical weather prediction. Four-dimensional variatio nal data assimilation (4D-Var) is the most advanced data assimilation algorithm to be used operat ionally; it uses observations that are distributed in time through the use of the model equation s. The aim of this thesis is to understand the extent to which 4DVar can develop the structures needed for the growth and decay of baroclinic systems. Such mid-latitude storms can cause severe damage and play a key role in the evolution of the atmospheric flow. The approach taken isolates the important mechanisms in 4D-Var by considering a simple model of baroclinic instability. Idealized case studies using the 2D Eady model consider the u se of a time-sequence of observations to reconstruct the state in unobserved region s. A novel technique using the singular value decomposition of the 4D-Var observability matr ix is developed, based on methods that are commonly used in satellite retrieval studies. It is used here to provide a new and useful understanding of the information content of observations i n 4D-Var. It is shown that the information that is propagated to the uno bserved regions is strongly penalized by the background state and is also extremely sens itiv to observational noise. This is understood by establishing a link with the literature on T ikhonov Regularization. An analysis increment will result in growth if the observations are give n at only the end of the window, or if a relatively large weight is given to the background state. T his may result in a poor forecast if the required analysis increments lead to decay. Two ways to m aximize the benefits of 4D-Var are identified: the initial and final observations should be f ar apart in time, and appropriate values for the regularization parameters should be specifie d.

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