Data assimilation with a barotropically unstable shallow water system using representer algorithms

Abstract

The cycling representer algorithm of Xu and Daley (2000) is a weak constraint four-dimensionalvariational data assimilation algorithm. It was successfully applied to a one-dimensional transportproblem and was able to successfully extract the signal from noisy and sparse observations.The algorithm, however, has not previously been applied to a multivariate, multidimensionalsystem with dynamic instability. The algorithm is also very computationally demanding andawaits considerable enhancement in computer power before being practical for operationalforecast models.We have two objectives in this paper. The first is to apply the cycling representeralgorithm to a two-dimensional, multivariate barotropically unstable linear shallow watersystem. The second objective is to formulate and test an accelerated representer algorithm thatis much more computationally tractable than the cycling representer algorithm itself. A linearshallow water system with a barotropically unstable basic state was used as a test bed toconduct data assimilation experiments. The evolution of a ‘neutral’ eastward-propagating singularvector was selected as the ‘truth’, against which all data assimilation experiments were tobe evaluated. The results indicated that the cycling representer algorithm was capable of providingsatisfying state estimates for a multivariate, multidimensional system. The results from theaccelerated representer algorithm were very encouraging because it is sufficiently computationallytractable to be used on present day multi-processor machines for operationalapplications.