Comparison of different assimilation schemes in a sequential Kalman filter assimilation system

Abstract

In this paper, four assimilation schemes, including an intermittent assimilation scheme (INT) and three incremental assimilation schemes (IAU 0, IAU 50 and IAU 100), are compared in the same assimilation experiments with a nonlinear ocean circulation model using the Ensemble Kalman Filter as assimilation method. The three IAU schemes differ from each other in the position of the increment update window that has the same size as the assimilation window. 0, 50 and 100 correspond to the degree of superposition of the increment update window on the current assimilation window. Twin experiments are performed. Firstly, the assimilation experiments are initialised on the same number of ensemble members and with analysis every 2 and 6days respectively in order to investigate the behaviours of different assimilation schemes against the assimilation cycles with different mixing and adjustment processes. In addition to the constant increment update, weighting functions with time scales in accord with the observation decorrelation are also applied. Secondly, the assimilation experiments are performed with the same computational cost, thus different number of ensemble members for different assimilation schemes. The relevance of each assimilation scheme is evaluated through analyses on four control variables including the sea surface height, the temperature, the zonal and meridional velocities and two diagnostic variables, the vertical velocity and the vertical eddy diffusivity. The comparisons between these assimilation schemes are performed at both global and local scales. The advantages and shortcomings of each assimilation scheme are highlighted. According to the results obtained: with the same number of ensemble members, for the control variables, the difference between the four schemes exists essentially at local scale. At global scale, no large difference is observed. Thus, the model error reduction by the IAU schemes with respect to the INT scheme is not observed in these experiments. The IAU schemes outperform the INT scheme on one hand at level of vertical advection where the IAU schemes suppress to a large extent the spurious geostrophic adjustment analysis-induced oscillation, on the other hand at level of vertical diffusion where much smaller instability is induced by gradual increment update in the IAU schemes. The application of the time scale in accord with the observation decorrelation during increment update is beneficial to the instability reduction with the schemes IAU 0 and IAU 50. With the same computational cost, thus less ensemble members for the schemes IAU 50 and IAU 100, the reduced ensemble members degrade the performance of the schemes IAU 50 and IAU 100. Therefore, taken into account the analysis-induced oscillation and instability reduction, as well as the computational cost, the scheme IAU 0 is preferred.