This contribution will present recent advances in understanding of dynamical aspects of the tropical data assimilation. In contrast with the mid-latitudes, there is no a well-defined approach for the tropical data assimilation in numerical weather prediction (NWP) community which has traditionally been concentrated on the mid-latitude analysis problem. In particular, the impact of the equatorial Rossby, inertio-gravity, and mixed Rossby-gravity waves on the tropical forecast errors is difficult to quantify. Various tropical waves are characterized by different couplings between the mass field and the wind field. The average mixture of these waves, built into the background-error covariance matrix for data assimilation provides analysis increments which appear nearly univariate even though they result from the advanced multivariate assimilation methodology. This is a non-existing problem for mid-latitude planetary and synoptic scales for which the quasi-geostrophic balance is the backbone of data assimilation systems. These properties are illustrated by using dry and moist idealized tropical systems as well as 4D-Var NWP global assimilation system.