On forecast errors in variational data assimilation using high resolution advection schemes of the Lin-Rood finite volume shallow water model
S. Akella, I. M. Navon
We used the the Lin-Rood finite volume shallow water model in the framework of 4-D Var data assimilation addressing first the hierarchical implementation of high resolution (van Leer and PPM) advection schemes in both forward and adjoint models. The results obtained show that using the various advection schemes consistently improves variational data assimilation (VDA) in the strong constraint form, which does not include model error, but the cost functional included efficient and physically meaningful construction of the background term, J b using balance and diffusion equation based correlation operators. This was then followed by an in-depth study of various approaches to model the systematic component of model error in the framework of a weak constraint VDA. Three simple forms, decreasing, invariant, and exponentially increasing in time forms of evolution of model error were tested. The inclusion of model error provides a substantial reduction in forecasting errors, in particular the exponentially increasing form in conjunction with the piecewise parabolic high resolution advection scheme provided the best results. Results presented in this article can be used to formulate sophisticated model error forms.