The Interaction between Model Resolution, Observation Resolution and Observation Density in Data Assimilation: a Two-dimensional Study

In variational data assimilation, an optimal analysis is derived from the knowledge of background and observation error statistics. According to Daley (1993), the observation error can be divided into two components: the instrumental error of a measuring device and the representativeness error of an observation operator. The first one is often considered to be a white Gaussian noise, whereas the second is thought to be responsible for spatial correlations in the observational error. The representativeness error depends on a resolution function of the measuring instrument, observation density, model grid resolution, and specification of an observation operator. This dependency was investigated by Liu and Rabier (2002) in a simple onedimensional (1D) framework. They have found an approximate relation of the aforementioned parameters corresponding to an optimal analysis. However in operational practice, the optimal analysis is usually not achievable, since the observation-error correlations are difficult to estimate and expensive to specify in the assimilation procedure. Therefore, a suboptimal assimilation scheme is often used, in which the observation errors are assumed to be uncorrelated. In this scheme, the observations with strongly correlated errors must be filtered out prior to assimilation, in order to achieve a good analysis quality. This error-decorelation operation is called observation thinning. Although it is commonly used in operational practice by most of the weather prediction centers nowadays, the question of optimal thinning that provides the best balance between the observation-error correlation and the forecast error is still not well understood. Liu and Rabier have investigated the thinning of observations with