Ensemble forecasting at NMC and the breeding method
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Ensemble forecasting at NMC and the breeding method

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    The breeding method has been used to generate perturbations for ensemble forecasting at NMC since December 1992. At that time a single breeding cycle with a pair of bred forecasts was implemented. A combination of bred perturbations and lagged forecasts provided a daily set of 14 global forecasts valid to 10 days. In March 1994, the ensemble was expanded to 7 independent breeding cycles on the new Cray C90 supercomputer, and the forecasts extended to 16 days, This provides 46 independent global forecasts valid for two weeks every day. For efficient ensemble forecasting, the initial perturbations to the control analysis should adequately sample the space of possible analysis errors. We point out that the analysis cycle is like a breeding cycle: it acts as a nonlinear perturbation model upon the evolution of the real atmosphere. The perturbation (i.e., the analysis error), carried forward in the first guess forecasts, is "scaled down" at regular intervals by the use of observations. Because of this, growing errors associated with the evolving state of the atmosphere develop within the analysis cycle and dominate subsequent forecast error growth. The breeding method simulates the development of growing errors in the analysis cycle. A difference field between two nonlinear forecasts is carried forward (and scaled down at regular intervals) upon the evolving atmospheric analysis fields. By construction, the bred modes are superpositions of the leading local (time dependent) Lyapunov vectors (LLVs) of the atmosphere. An important property of the leading LLVs is that all random perturbations assume their structure after a transientperiod. When several independent breeding cycles are performed, the phases and amplitudes of individual (and regional) leading LLVs are random, which ensures quasi-orthogonality among the global bred modes from independent breeding cycles. Off-line experimental runs with a 10-member ensemble (5 independent breeding cycles) show that the ensemble mean is superior to an optimally smoothed control and to randomly generated ensemble forecasts, and compares favorably with the medium range double horizontal resolution control. Moreover, a potentially useful relationship between ensemble spread and forecast error is also found both in the spatial and time domain. The improvement in skill of 0.04-0.11 in AC in forecasts at and beyond 7 days, together with the potential for estimation of the skill, suggest that this system will be a useful operational forecast tool. The results and methodology discussed should be applicable to the new operational ensemble configuration; where 17 independent forecasts are performed every day. The two methods used so far to produce operational ensemble forecasts, i.e., breeding and the adjoint (or "optimal perturbations"). technique applied at ECMWF, have several significant differences, but they both attempt to estimate the subspace of fast growing perturbations. The bred modes are estimates of fastest sustainable growth and as such they represent probable growing analysis errors. The optimal perturbations, on the other hand, estimate vectors with fastest transient growth and are less likely to occur in analysis error fields. A major practical difference between the two methods for ensemble forecasting is that breeding is much simpler and far less expensive than the adjoint technique.
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    Zoltan Toth and Eugenia Kalnay.

    "April 7, 1995."

    Also available online in PDF via the NOAA Central Library.

    Includes bibliographical references (pages 25-28).

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