Underdispersiveness of EnKF posterior spread when p >> K as revealed by diagnostics of information content measured by Degrees of Freedom for Signal (DFS)

Daisuke Hotta* and Yoichiro Ota
Japan Meteorological Agency

Degrees of Freedom for Signal (DFS) quantify how much of information is extracted from observations in a Data Assimilation System (DAS). Although DFS has become one of the standard diagnostics on variational DASs routinely monitored by many operational centers, it has not been applied to any EnKF in an operational context. In this study, DFS diagnostics formulated by Liu et al. (2009) is applied, perhaps for the first time, to a quasi-operational EnKF with real observations using the EnKF component of the JMA’s pre-operational global hybrid 4D-Var, and is compared with the DFS computed for the variational component using the method of Lupu et al. (2011). The same diagnostics is also performed using the NCEP’s GSI-EnKF hybrid 3D-EnVar. It is found that the information content extracted from observations by EnKF is an order of magnitude smaller than that by 4D-Var; this underestimation is particularly striking for densely observed data types such as satellite hyperspectral soundings (AIRS and IASI). The reason turns out to be the fact that, in a situation where the number of locally assimilated observations exceeds the ensemble member size (p>>K), the DFS is bounded from above by the member size (DFS < K-1). Since DFS coincides with analysis spread measured in observation space divided by the observation error variance, underestimation of DFS is directly related to underdispersion of error covariances. The fact that DFS is automatically underestimated when p>>K has many implications on a broad aspect of EnKF, inclu ding covariance localization and inflation, observation thinning and in what order the observations should be assimilated. In particular, it will allow theoretical justification as to why the relaxation-to-prior inflation of Zhang et al. (2004) and Whitaker and Hamil (2012) are so successful, and why drastic observation thinning does not harm performance of EnKF (Hamrud et al., 2015).

*email: hotta.d@gmail.com
*Preference: Oral