A comparison of probabilistic forecasts from bred, singular-vector, and perturbed observation ensembles

The statistical properties of analysis and forecast errors from commonly used ensemble perturbation methodologies are explored. A quasigeostrophic channel model is used, coupled with a 3D-variational data assimilation scheme. A perfect model is assumed. Three perturbation methodologies are considered. The breeding and singular-vector (SV) methods approximate the strategies currently used at operational centers in the United States and Europe, respectively. The perturbed observation (PO) methodology approximates a random sample from the analysis probability density function (pdf) and is similar to the method performed at the Canadian Meteorological Centre. Initial conditions for the PO ensemble are analyses from independent, parallel data assimilation cycles. Each assimilation cycle utilizes observations perturbed by random noise whose statistics are consistent with observational error covariances. Each member's assimilation/forecast cycle is also started from a distinct initial condition. Relative to breeding and SV, the PO method here produced analyses and forecasts with desirable statistical characteristics. These include consistent rank histogram uniformity for all variables at all lead times, high spread/ skill correlations, and calibrated, reduced-error probabilistic forecasts. It achieved these improvements primarily because 1) the ensemble mean of the PO initial conditions was more accurate than the mean of the bred or singular-vector ensembles, which were centered on a less-skilful control initial condition - much of the improvement was lost when PO initial conditions were recentered on the control analysis; and 2) by construction, the perturbed observation ensemble initial conditions permitted realistic variations in spread from day to day, while bred and singular-vector perturbations did not. These results suggest that in the absence of model error. an ensemble of initial conditions performs better when the initialization method is designed to produce random samples from the analysis pdf. The perturbed observation method did this much more satisfactorily than either the breeding or singular-vector methods. The ability of the perturbed observation ensemble to sample randomly from the analysis pdf also suggests that such an ensemble can provide useful information on forecast covariances and hence improve future data assimilation techniques.