Ensemble of Data Assimilations (EDA)

An Ensemble of Data Assimilations (EDA) is an ensemble of independent 4D-Var data assimilations which aims to:

• give estimates of analysis and short-range forecast uncertainty.
• provide flow-dependent background error estimates for the deterministic 4D-Var system.

In the EDA, we have an ensemble of perturbed members that are used to prepare background errors for the next analysis cycle and that are also part of the initial conditions of ensemble forecasts (ENS).  The 'Soft re-centring’ concept was brought into operation with Cy49r1 in autumn 2024.  It incorporates information from the control member of the ensemble as input to a perturbed member’s analysis.  Thus the control analysis becomes part of the cycling of the perturbed members’ analyses.

The EDA analyses are generated by randomly perturbing the main analysis error sources according to their estimated accuracy:

• observation errors are represented by perturbing observations.  The observations are assumed unbiased (once any dynamic bias correction has been applied) and observation errors are assumed to have a normal distribution.
• model errors are represented by perturbing the forecast model.  Model error is simulated using the Stochastically Perturbed Parameterisation scheme (SPP).  
• boundary condition errors are represented by perturbing soil moisture, sea-surface temperature, and sea ice across appropriate length scales.

Differences between pairs of analyses (and forecast) fields have the statistical characteristics of analysis (and forecast) error. 

Fig5.1.1-1: An idealized schematic showing how the 12 hour assimilation window used by 4D-Var (left part of the diagram) modifies the initial trajectories of the members of the ensemble of data assimilations EDA (in blue) to reflect the information from the assimilated observations (black dots with error bars).  The analysis trajectories (in green) have taken into account the new observations and thus are confined within a narrower ensemble.  Assimilating the new observations reduces the spread.  Also a bias has been corrected by reducing the magnitude of some of the largest values in the original ensemble.

At the end of the assimilation window the ensemble of data assimilations EDA is used to provide:

• background error information for the following deterministic analysis update.
• the initial perturbations, around the control analysis, for the next ensemble forecasts
  

The advantages of the ensemble of data assimilations EDA system are:

• it provides perturbations more widely and uniformly over the globe than SVs, with larger amplitudes over the tropics.
• it attempts to explicitly model analysis uncertainty, incorporating observation coverage and accuracy.

A disadvantage of the current ensemble of data assimilations EDA system is:

• the variability of the perturbations does not grow sufficiently through the forecast (perturbations are currently under-dispersive).

Scale-selective EDA re-centring

Generally small-scale structures come directly from the EDA but there were some problems with larger scale structures.   For theses features, scale-selective EDA re-centring introduced in Cy50r1 improves the realism of initial conditions, particularly for tropical cyclones.  Scale-selective EDA re-centring is only applied to large-scale upper-air fields, centring them on the control forecast.  This helps avoid unrealistic 'double-centred' tropical cyclones from appearing at the start of the ENS forecasts.

Fig5.1.1-2: Mean sea level pressure  ENS members 36 and 45 at forecast step T+0 h for Tropical Cyclone Freddy 00UTC 17 Feb 2023. Top panels show results with EDA re-centring (Cycle 49r1) producing unrealistic double centre; bottom panels use scale-selective EDA re-centring (Cycle 50r1) and unrealistic 'double centre' feature doesn't appear.

Additional Sources of Information

(Note: In older material there may be references to issues that have subsequently been addressed)

• Read more about quantifying forecast uncertainty.
• Read more on the ensemble of data assimilations EDA at ECMWF.
• Read more about Stochastically Perturbed Parametrization (SPP) scheme.

(FUG Associated with Cy50r1)