Variational data assimilation schemes used in NWP are effectively univariate near the equator. On the other hand, a significant part of the large-scale tropical variability can be represented by equatorial waves coupled to convection. It is therefore justified to attempt applying their (im)balance relationships in data assimilation.
Two questions posed here are: what fraction of the tropical forecast error fields can be represented in terms of equatorial waves with the observed phase speeds and how is this error variance distributed among the various modes. We compare this variance distribution for average error statistics, as used in the variational assimilation with flow-dependent tropical error variances based on the ensemble Kalman filter.