A comparison of the hybrid and EnSRF analysis schemes in the presence of model errors due to unresolved scales

A hybrid analysis scheme is compared with an ensemble square root filter

(EnSRF) analysis scheme in the presence of model errors, as a follow-up to a previous

perfect-model comparison. In the hybrid scheme, the ensemble perturbations are updated

by the ensemble transform Kalman filter (ETKF) and the ensemble mean is updated with

a hybridized ensemble and static background-error covariance. The experiments were

conducted with a two-layer primitive equation model. The true state was a T127

simulation. Data assimilation experiments were conducted at T31 resolution,

assimilating imperfect observations drawn from the T127 nature run. By design, the

magnitude of the truncation error was large, which provided a test on the ability of both

schemes to deal with model error. Additive noise was used to parameterize model errors

in the background ensemble for both schemes. In the first set of experiments, additive

noise was drawn from a large inventory of historical forecast errors and in the second set

of experiments, it was drawn from a large inventory of differences between forecasts and

analyses. The static covariance was computed correspondingly from the two inventories.

The hybrid analysis was statistically significantly more accurate than the EnSRF

analysis. The improvement of the hybrid over the EnSRF was smaller when differences

of forecasts and analyses were used to form the random noise and the static covariance.

The EnSRF analysis was more sensitive to the size of the ensemble than the hybrid. A

series of tests were conducted to understand why the EnSRF performed worse than the

hybrid. It was shown that the inferior performance of the EnSRF was likely due to the

sampling error in the estimation of the model-error covariance in the mean update and the

less balanced EnSRF initial conditions due to the extra localizations used in the EnSRF.