Editorial Type:
Article
Article Type:
Research Article

The Impact of Dynamical Constraints on the Selection of Initial Conditions for Ensemble Predictions: Low-Order Perfect Model Results

Jeffrey L. Anderson Geophysical Fluid Dynamics Laboratory, Princeton University, Princeton, New Jersey

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Print Publication:
01 Nov 1997
DOI:
https://doi.org/10.1175/1520-0493(1997)125<2969:TIODCO>2.0.CO;2
Page(s):
2969–2983
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Abstract

A number of operational atmospheric prediction centers now produce ensemble forecasts of the atmosphere. Because of the high-dimensional phase spaces associated 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 Centers for Environmental 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 systems and a prescribed observational 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.

Corresponding author address: Dr. Jeffrey L. Anderson, GFDL, Princeton University, P.O. Box 308, Princeton, NJ 08540.

Abstract

A number of operational atmospheric prediction centers now produce ensemble forecasts of the atmosphere. Because of the high-dimensional phase spaces associated 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 Centers for Environmental 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 systems and a prescribed observational 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.

Corresponding author address: Dr. Jeffrey L. Anderson, GFDL, Princeton University, P.O. Box 308, Princeton, NJ 08540.

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  • Anderson, J. L., 1996a: Selection of initial conditions for ensemble forecasts in a simple perfect model framework. J. Atmos. Sci.,53, 22–36.

  • ——, 1996b: A method for producing and evaluating probabilistic forecasts from ensemble model integrations. J. Climate,9, 1518–1530.

  • Barker, T. W., 1991: The relationship between spread and forecast error in extended range forecasts. J. Climate,4, 733–742.

  • Barkmeijer, J., 1993: Local skill prediction for the ECMWF model using adjoint techniques. Mon. Wea. Rev.,121, 1262–1268.

  • Brankovic, C., T. N. Palmer, F. Molteni, S. Tibaldi, and U. Cubasch, 1990: Extended-range predictions with ECMWF models: Time-lagged ensemble forecasting. Quart. J. Roy. Meteor. Soc.,116, 867–912.

  • Brooks, H. E., M. S. Tracton, D. J. Stensrud, G. DiMego, and Z. Toth, 1995: Short-range ensemble forecasting: Report from a workshop, 25–27 July 1994. Bull. Amer. Meteor. Soc.,76, 1617–1624.

  • Buizza, R., 1995: Optimal perturbation time evolution and senstivity of ensemble prediction to perturbation amplitude. Quart. J. Roy. Meteor. Soc.,121, 1705–1738.

  • ——, and T. N. Palmer, 1995: The singular-vector structure of the atmospheric global circulation. J. Atmos. Sci.,52, 1434–1456.

  • ——, J. Tribbia, F. Molteni, and T. Palmer, 1993: Computation of optimal unstable structures for a numerical weather prediction model. Tellus,45A, 388–407.

  • Cheng, X., and J. M. Wallace, 1993: Cluster analysis of the Northern Hemisphere wintertime 500-hPa height field: Spatial patterns. J. Atmos. Sci.,50, 2674–2696.

  • Cramer, H., 1966: Mathematical Methods of Statistics. Princeton University Press, 575 pp.

  • Ehrendorfer, M., and J. J. Tribbia, 1997: Optimal prediction of forecast error covariances through singularvectors. J. Atmos. Sci.,54, 286–313.

  • Epstein, E. S., 1969: Stochasticdynamic prediction. Tellus,21, 739–759.

  • Errico, R. M., and T. Vukicevic, 1992: Sensitivity analysis using an adjoint of the PSU–NCAR mesoscale model. Mon. Wea. Rev.,120, 1644–1660.

  • ——, ——, and K. Raeder, 1993: Examination of the accuracy of a tangent linear model. Tellus,45A, 462–477.

  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res.,99, 10143–10162.

  • Farrell, B., 1990: Small error dynamics and the predictability of atmospheric flows. J. Atmos. Sci.,47, 2191–2199.

  • Gleeson, T. A., 1970: Statistical-dynamical prediction. J. Appl. Meteor.,9, 333–344.

  • Harrison, M. S. J., D. S. Richardson, K. Robertson, and A. Woodcock, 1995: Medium-range ensembles using both the ECMSF T63 and unified models—An initial report. UKMO Tech. Rep. 153, 25 pp. [Available from U.K. Meteorological Office, London Road, Bracknell, Berkshire RGIZ 2SZ, U.K.].

  • Hollingsworth, A., 1980: An experiment in Monte Carlo forecasting procedure. Proc. ECMWF Workshop on Stochastic Dynamic Forecasting, Reading, United Kingdom, ECMWF, 65–85.

  • Houtekamer, P. L., 1993: Global and local skill forecasts. Mon. Wea. Rev.,121, 1834–1846.

  • ——, 1995: The construction of optimal perturbations. Mon. Wea. Rev.,123, 2888–2898.

  • ——, and J. Derome, 1994: Prediction experiments with two-member ensembles. Mon. Wea. Rev.,122, 2179–2191.

  • ——, and ——, 1995: Methods for ensemble prediction. Mon. Wea. Rev.,123, 2181–2196.

  • ——, L. Lefaivre, J. Derome, H. Ritchie, and H. L. Mitchell, 1996: A system simulation approach to ensemble prediction. Mon. Wea. Rev.,124, 1225–1242.

  • Kalnay, E., and A. Dalcher, 1987: Forecasting forecast skill. Mon. Wea. Rev.,115, 349–356.

  • Leith, C. E., 1974: Theoretical skill of Monte Carlo forecasts. Mon. Wea. Rev.,102, 409–418.

  • Leonardo, A., 1995: Numerical studies on the Lorenz-84 atmospheric model. Department of Mathematics Tech. Rep., 49 pp. [Available from Dept. of Mathematics, Utrecht University, Box 80010, Utrecht 3508 TA, the Netherlands.].

  • Lonnberg, P., and A. Hollingsworth, 1986: The statistical structure of short-range forecast errors as determined from radiosonde data. Part II: The covariance of height and wind errors. Tellus,38A, 137–161.

  • Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci.,20, 130–141.

  • ——, 1984: Irregularity: A fundamental property of the atmosphere. Tellus,36A, 98–110.

  • ——, and V. Krishnamurthy, 1987: On the nonexistence of a slow manifold. J. Atmos. Sci.,44, 2940–2950.

  • Molteni, F., and S. Tibaldi, 1990: Regimes in the wintertime circulation over the northern extratropics. II: Consequences for dynamical predictability. Quart. J. Roy. Meteor. Soc.,116, 1263–1288.

  • ——, and T. N. Palmer, 1991: A real-time scheme for the prediction offorecast skill. Mon. Wea. Rev.,119, 1088–1097.

  • ——, R. Buizza, T. N. Palmer, and T. Petroliagis, 1996: The ECMWF ensemble prediction system: Methodology and validation. Quart. J. Roy Meteor. Soc.,122, 73–120.

  • Mureau, R., F. Molteni, and T. N. Palmer, 1993: Ensemble prediction using dynamically-conditioned perturbations. Quart. J. Roy. Meteor. Soc.,119, 299–323.

  • Palmer, T. N., 1993: Extended-range atmospheric prediction and the Lorenz model. Bull. Amer. Meteor. Soc.,74, 49–66.

  • ——, F. Molteni, R. Mureau, R. Buizza, P. Chapelet, and J. Tribbia, 1993: Ensemble prediction. Proc. ECMWF Seminar, Vol. 1, Reading, United Kingdom, ECMWF, 21–66.

  • Parrish, D. F., and J. C. Derber, 1992: The National Meteorological Center’s spectral statistical-interpolation analysis system. Mon. Wea. Rev.,120, 1747–1763.

  • Tracton, S., and E. Kalnay, 1993: Operational ensemble forecasting at NMC: Practical aspects. Wea. Forecasting,8, 379–398.

  • Toth, Z., and E. Kalnay, 1993: Ensemble forecasting at NMC: The generation of perturbations. Bull. Amer. Meteor. Soc.,74, 2317–2330.

  • ——, and ——, 1996: Ensemble forecasting at NMC and the breeding method. NMC Office Note 407, 58 pp. [Available from NOAA/NWS/NCEP/EMC, 5200 Auth Road, Camp Springs, MD 20746.].

  • Vukicevic, T., 1991: Nonlinear and linear evolution of initial forecast errors. Mon. Wea. Rev.,119, 1602–1611.

  • ——, and K. Raeder, 1995: Use of an adjoint model for finding triggers for alpine lee cyclogenesis. Mon. Wea. Rev.,123, 800–816.

  • Wobus, R. L., and E. Kalnay, 1995: Three years of operational prediction of forecast skill at NMC. Mon. Wea. Rev.,123, 2132–2148.

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