Variational data assimilation in the tropics:: The impact of a background-error constraint

Geostrophic adjustment theory predicts that wind information is a primary information source in the tropics. We ask whether this is true when variational data assimilation including a background-error constraint is applied. The question is investigated by carrying out three- and four-dimensional variational (4D-Var) data assimilation experiments with nonlinear shallow-water equations and idealized waves. The contribution to the analysis from mass and wind field observations is contrasted to that of spectral characteristics and multivariate relationships of equatorial waves built into a background-error covariance matrix. A background-error term for the analysis is built by using the tropical eigenmodes and the observed variability is used to determine the relative weights for different modes. Single observation sensitivity experiments illustrate an important impact of Kelvin and mixed Rossby-gravity waves in reducing the coupling between the mass and wind fields, found when only equatorial Rossby Waves are utilized in the background-error constraint. The assimilation experiments demonstrate two main features. First, the wind field information is of greater value than the mass field information, in spite of the known error statistics. A second intriguing feature is that the assimilation of wind observations better resolves smaller-scale features of the height field than the assimilation of height data. When height data are used, a somewhat different analysis response is obtained for the zonal and meridional wind components. due to the strong projection onto the Kelvin wave structure for height observations. Finally, a comparison of different time windows for 4D-Var illuminates the sensitivity of height field assimilation to the length of the assimilation window.