The balance between mass and wind fields resulting from multivariate optimal interpolation

Abstract The relative importance of various sources of imbalance in analyses produced by multivariate optimal interpolation is determined. The experimental design uses the shallow-water equations and nonlinear normal mode initialization to define the correct balanced reference atmospheric state and thus restricts this study to horizontal aspects of the problem. The experiments show that the analysis procedure itself introduces systematic imbalances in lows due to the use of the geostrophic relationship to determine the height–wind covariances from the height–height covariances. Random observational errors introduce imbalances but not out of proportion to the observational errors themselves. Data-void areas are responsible for a region of imbalance with width approximately equal to the maximum radius of influence of the analysis on the data-void side of the data-void/data-rich boundary. Model errors in the form of equivalent depth errors do not introduce large imbalances.