Formulations for Estimating Spatial Variations of Analysis Error Variance to Improve Multiscale and Multistep Variational Data Assimilation

Figure 1

Benchmark analysis error variance plotted by red solid curve and estimated analysis error variance in (7) plotted by blue dotted curve. The green dashed line shows the constant analysis error variance estimated from the spectral formulation. The purple + signs show the observation error variance ( m²s⁻²) at the locations of (=10) uniformly distributed coarse-resolution observations with (=11.04 km). The background error covariance has the double-Gaussian form with ,  m²s⁻² and  km. The analysis domain length is  km with and  km, and the number of coarse-resolution observations is .