Dynamical response of equatorial waves in four-dimensional variational data assimilation

In this study we question the relative importance of direct wind measurements in the tropics by investigating limits of four-dimensional variational assimilation (4D-Var) in the tropics when only wind or mass field observations are available. Typically observed equatorial wave motion fields (Kelvin, mixed Rossby-gravity and n= 1 equatorial Rossby waves) are assimilated in a non-linear shallow water model. Perfect observations on the full model grid are utilized and no background error term is used. The results illustrate limits of 4D-Var with only one type of information, in particular mass field information. First, there is a limit of information available through the internal model dynamics. This limit is defined by the length of the assimilation window, in relation to the characteristics of the motion being assimilated. Secondly, there is a limit related to the type of observations used. In all cases of assimilation of wind field data, two or three time instants with observations are sufficient to recover the mass field, independent of the length of the assimilation time window. Assimilation of mass field data, on the other hand, although capable of wind field reconstruction, is much more dependent on the dynamical properties of the assimilated motion system. Assimilating height information is less efficient, and the divergent part of the wind field is always recovered first and more completely than its rotational part.