The interaction between model resolution, observation resolution and observation density in data assimilation: A one-dimensional study

In this paper, the optimal configurations of model resolution, observation resolution and observation density are investigated in a simple one-dimensional framework. In this context, the representativeness error is formalized and estimated before being used in the analysis-error formulation. Some optimal and suboptimal assimilation-schemes, differing from different approximations of observation-error covariance and observation operator, are compared. The optimal observation-extent is determined as a function of model resolution. Increasing the observation density is usually beneficial, except for suboptimal schemes similar to the ones used in operational practice. The impact of thinning the observations with correlated error is also studied from a suboptimal viewpoint.