Abstract
ABSTRACTA 4-dimensional variational data assimilation (4D-Var) scheme for the HIgh Resolution Limited Area Model (HIRLAM) forecasting system is described in this article. The innovative approaches to the multi-incremental formulation, the weak digital filter constraint and the semi-Lagrangian time integration are highlighted with some details. The implicit dynamical structure functions are discussed using single observation experiments, and the sensitivity to various parameters of the 4D-Var formulation is illustrated. To assess the meteorological impact of HIRLAM 4D-Var, data assimilation experiments for five periods of 1 month each were performed, using HIRLAM 3D-Var as a reference. It is shown that the HIRLAM 4D-Var consistently out-performs the HIRLAM 3D-Var, in particular for cases with strong mesoscale storm developments. The computational performance of the HIRLAM 4D-Var is also discussed.The review process was handled by Subject Editor Abdel Hannachi
Highlights
The 4-dimensional variational data assimilation (4D-Var) was first suggested by Le Dimet and Talagrand (1986) and Lewis and Derber (1985)
The model initial state is obtained by minimising a cost function, which consists of one term measuring the distance between the 3-dimensional model initial state and a model background state at the beginning of the assimilation window, and another term measuring the distance between the observations distributed over the assimilation window and the corresponding model state values evaluated in the observation points
The incremental 4D-Var approach (Courtier et al, 1994) is based on a linearisation of the forecast model equations around a model trajectory being sufficiently close to the true development of the atmosphere, such that the resulting analysis would be within the estimation error of the truth
Summary
The 4-dimensional variational data assimilation (4D-Var) was first suggested by Le Dimet and Talagrand (1986) and Lewis and Derber (1985). There exist possibilities to partly compensate for this weakness of 4D-Var. The original idea of Lewis and Derber (1985) to use some quantity representing model errors, for example, a tendency bias, in the assimilation control vector has recently received renewed interest (Tremolet, 2006) and can be applied in the HIRLAM 4D-Var. The incremental 4D-Var approach (Courtier et al, 1994) is based on a linearisation of the forecast model equations around a model trajectory being sufficiently close to the true development of the atmosphere, such that the resulting analysis would be within the estimation error of the truth. There must be access to a range of regularised and simplified TL and AD physical parameterisation schemes that can be applied during different phases of the minimisation Another weakness of 4D-Var in its original formulation is the lack of flow dependency of the assimilation structure functions at the start of the assimilation window.
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