Four-dimensional variational data assimilation for a limited area model

Huang, Yang, Gustafsson, Mogensen and Lindskog

Abstract

A 4-dimensional variational data assimilation (4D-VAR) scheme for the HIgh Resolution Limited Area Model (HIRLAM) forecasting system is described in this report. The HIRLAM 4D-VAR is based on the minimization of a cost function that consists of one term, Jb, which measures the distance between the resulting 4-dimensional analysis and a background at the beginning of the assimilation interval, and another term, Jo, which measures the distance between the resulting 4-dimensional analysis and observations over the assimilation interval. As HIRLAM 4D-VAR is a temporal extension of HIRLAM 3-dimensional variational data assimilation (3D-VAR), the general formulation of the cost function, the background constraint and the observation operators of HIRLAM 3D-VAR are kept. The temporal extension is introduced by using the HIRLAM tangent linear and adjoint models in the Jo calculations. Data assimilation experiments using realistic system configurations, such as domain size and resolution, are described. The computational performance of the HIRLAM 4D-VAR and its operational feasibility are assessed. The cost of the selected 4D-VAR  configuration is about 7 times the cost of 3D-VAR or about the same as the cost of a 72h forecast. In order to assess the meteorological impact of HIRLAM 4D-VAR, data assimilation experiments for three periods are performed, using HIRLAM 3D-VAR as a reference. Both subjective evaluation and observation verification are applied. From the few storm cases in December 1999, 4D-VAR analyses produce deeper and more realistic lows than 3D-VAR. While the forecasts from 4D-VAR and 3D-VAR are of the same accuracy for the the storm that hit Denmark in the beginning of December 1999, the forecasts for the storm over France on 27 December from 4D-VAR  are clearly better. The subjective evaluation is in favour of 4D-VAR. For the first 10 days of December 1999 and the whole month of February 2002, the observation verification scores for 4D-VAR are on the average comparable with those for 3D-VAR. For the last 10 days of December 1999, when the two French storms occurred, 4D-VAR has improved scores in general and in particular significantly better scores in the mean sea level pressure, 2 meter temperature and 10 meter wind forecasts.

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