1. WWRP/THORPEX WORKSHOP on 4D-VAR and ENSEMBLE KALMAN FILTER INTER-COMPARISONS BUENOS AIRES - ARGENTINA, 10-13 NOVEMBER 2008 Topics for Discussion in Session 5: Background error estimation L. Berre, C. Bishop, and T. Hamill Compiled by R. Todling

2. Topics for Discussion in Session 5: Background error estimation The issues identified by this group fall into four general categories: - Approach - Tuning - Balance - Scale with overlaps among them. WWRP/THORPEX WORKSHOP on 4D-VAR and EnKF INTER-COMPARISONS BUENOS AIRES - ARGENTINA, 10-13 NOVEMBER 2008

3. Topics for Discussion in Session 5: Background error estimation Approach Are there new approaches to classical localization, e.g., in spectral space, or multi-grid implementations of filters? (T. Hamill) Are there different ways to deal with the small sample size and noisy covariances other than localization, with less deleterious effects? (T. Hamill) Does it matter that in the EnKF use of serial processing of observations the posterior covariances are not updated, and consequently the update equation violates its optimal formulation? (C. Bishop) WWRP/THORPEX WORKSHOP on 4D-VAR and EnKF INTER-COMPARISONS BUENOS AIRES - ARGENTINA, 10-13 NOVEMBER 2008

4. Topics for Discussion in Session 5: Background error estimation Approach What are the consequences of localization via inflation of the observation error variances? (C. Bishop) Classical KF-like approaches parameterize P f equally in P f H T and HP f H T to guarantee P a > 0. Some EnKFs apply different localization function to each of these two terms. Does this inconsistent treatment affect results in ways not yet noticed? (R. Todling) Model-space localization: H(P f  C)H T & (P f  C)H T Obs-space localization: HP f H T  HCH T & P f H T  CH T What are the consequences of approx. former by latter? (C. Bishop) WWRP/THORPEX WORKSHOP on 4D-VAR and EnKF INTER-COMPARISONS BUENOS AIRES - ARGENTINA, 10-13 NOVEMBER 2008

5. Topics for Discussion in Session 5: Background error estimation Tuning Could it be possible to design objective estimation procedures to determine Schur localization parameters? (L. Berre) Could the above be done adaptively based on residual error covariances? Generally, how do “prescribed” and sampled residual covariances differ in EnKF? How does localization contribute to this difference? (R. Todling) Could one consider to combine ensemble- and innovation-based estimates of covariances, in order to estimate model error covariances? (L. Berre) WWRP/THORPEX WORKSHOP on 4D-VAR and EnKF INTER-COMPARISONS BUENOS AIRES - ARGENTINA, 10-13 NOVEMBER 2008

6. Topics for Discussion in Session 5: Background error estimation Balance Is imbalance introduced by localization a key issue or a red herring? To what extent does localization result in "off-attractor" initial conditions that go through transient adjustment periods during the short-term forecast, constraining the spread in the ensemble? (T. Hamill) Assuming that a given balance property is valid over a certain region, could local spatial averaging of covariances (over this region) preserve balance better than Schur localization techniques? (L. Berre) Once balance is addressed, say, along Kepert’s line, how will EnKF covs differ from the anisotropic covs specified in 4d-Var via ensemble of forecasts? (R. Todling) WWRP/THORPEX WORKSHOP on 4D-VAR and EnKF INTER-COMPARISONS BUENOS AIRES - ARGENTINA, 10-13 NOVEMBER 2008

7. Topics for Discussion in Session 5: Background error estimation Scales How do maps of variances and correlation length-scales look like in ensemble- and innovation-based estimates? Is there a predominance of some large-scale features related to data density contrasts and synoptic situations? (L. Berre) In a unified global and mesoscale data assimilation system, are different types, or tiers of localization necessary for treatment of the synoptic scales vs. the mesoscale? (T. Hamill) Are practical ensemble sizes capable of capturing broad correlation scales such as those in the stratosphere or from chemical species? Does localization make sense when the scales are very broad? (R. Todling) WWRP/THORPEX WORKSHOP on 4D-VAR and EnKF INTER-COMPARISONS BUENOS AIRES - ARGENTINA, 10-13 NOVEMBER 2008