The impact of dynamical constraints on the selection of initial conditions for ensemble predictions: Low-order perfect model results

A number of operational atmospheric prediction centers now produce ensemble forecasts of the atmosphere. Because of the high-dimensional phase spaces associate with operational forecast models, many centers use constraints derived from the dynamics of the forecast model to define a greatly reduced subspace from which ensemble initial conditions are chosen. For instance, the European Centre for Medium-Range Weather Forecasts uses singular vectors of the forecast model and the National Center for Envionmental Prediction use the "breeding cycle" to determine a limited set of directions in phase space that are sampled by the ensemble forecast. The use of dynamical constraints on the selection of initial conditions for ensemble forecasts is examined in a perfect model study using a pair of three-variable dynamical system and a prescribed pbservational error distribution. For these systems, one can establish that the direct use of dynamical constraints has no impact on the error of the ensemble mean forecast and a negative impact on forecasts of higher-moment quantities such as forecast spread. Simple examples are presented to show that this is not a result of the use of low-order dynamical systems but is instead related to the fundamental nature of the dynamics of these particular low-order systems themselves. Unless operational prediction models have fundamentally different dynamics, this study suggests that the use of dynamically constrained ensembles may not be justified. Further studies with more realistic prediction models are needed to evaluate this possibility.