Effects of sample density on the assimilation performance of an explicit four-dimensional variational data assimilation method

The concepts of sample sphere radius and sample density are proposed in this paper to help illustrate that different vector transformations result in diverse sample density with the same sample ensemble, which finally affects their assimilation performance. Several numerical experiments using a one-dimensional (1-D) soil water equation and synthetic observations are conducted to evaluate this new theory in land data assimilation.