Ensemble Forecasting at NCEP and the Breeding Method

Zoltan Toth Environmental Modeling Center, National Centers for Environmental Prediction, Camp Springs, Maryland

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Eugenia Kalnay Environmental Modeling Center, National Centers for Environmental Prediction, Camp Springs, Maryland

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Abstract

The breeding method has been used to generate perturbations for ensemble forecasting at the National Centers for Environmental Prediction (formerly known as the National Meteorological Center) since December 1992. At that time a single breeding cycle with a pair of bred forecasts was implemented. In March 1994, the ensemble was expanded to seven independent breeding cycles on the Cray C90 supercomputer, and the forecasts were extended to 16 days. This provides 17 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. It is shown 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 vectors are superpositions of the leading local (time-dependent) Lyapunov vectors (LLVs) of the atmosphere. An important property is that all random perturbations assume the structure of the leading LLVs after a transient period, which for large-scale atmospheric processes is about 3 days. 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 vectors from independent breeding cycles.

Experimental runs with a 10-member ensemble (five 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 pattern anomaly correlation for forecasts at and beyond 7 days, together with the potential for estimation of the skill, indicate that this system is a useful operational forecast tool.

The two methods used so far to produce operational ensemble forecasts—that is, breeding and the adjoint (or “optimal perturbations”) technique applied at the European Centre for Medium-Range Weather Forecasts—have several significant differences, but they both attempt to estimate the subspace of fast growing perturbations. The bred vectors provide estimates of fastest sustainable growth and thus represent probable growing analysis errors. The optimal perturbations, on the other hand, estimate vectors with fastest transient growth in the future. A practical difference between the two methods for ensemble forecasting is that breeding is simpler and less expensive than the adjoint technique.

* Additional affiliation: General Sciences Corporation, Laurel, Maryland.

Corresponding author address: Dr. Zoltan Toth, Environmental Modeling Center, NCEP, 5200 Auth Rd., Rm. 204, Camp Springs, MD 20746.

Email: Zoltan.Toth@noaa.gov

Abstract

The breeding method has been used to generate perturbations for ensemble forecasting at the National Centers for Environmental Prediction (formerly known as the National Meteorological Center) since December 1992. At that time a single breeding cycle with a pair of bred forecasts was implemented. In March 1994, the ensemble was expanded to seven independent breeding cycles on the Cray C90 supercomputer, and the forecasts were extended to 16 days. This provides 17 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. It is shown 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 vectors are superpositions of the leading local (time-dependent) Lyapunov vectors (LLVs) of the atmosphere. An important property is that all random perturbations assume the structure of the leading LLVs after a transient period, which for large-scale atmospheric processes is about 3 days. 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 vectors from independent breeding cycles.

Experimental runs with a 10-member ensemble (five 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 pattern anomaly correlation for forecasts at and beyond 7 days, together with the potential for estimation of the skill, indicate that this system is a useful operational forecast tool.

The two methods used so far to produce operational ensemble forecasts—that is, breeding and the adjoint (or “optimal perturbations”) technique applied at the European Centre for Medium-Range Weather Forecasts—have several significant differences, but they both attempt to estimate the subspace of fast growing perturbations. The bred vectors provide estimates of fastest sustainable growth and thus represent probable growing analysis errors. The optimal perturbations, on the other hand, estimate vectors with fastest transient growth in the future. A practical difference between the two methods for ensemble forecasting is that breeding is simpler and less expensive than the adjoint technique.

* Additional affiliation: General Sciences Corporation, Laurel, Maryland.

Corresponding author address: Dr. Zoltan Toth, Environmental Modeling Center, NCEP, 5200 Auth Rd., Rm. 204, Camp Springs, MD 20746.

Email: Zoltan.Toth@noaa.gov

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