• AMS, 1968: Proceedings of the First Statistical Meteorology Conference. Amer. Meteor. Soc., 179 pp.

  • Bohm, D., 1957: Causality and Chance in Modern Physics. D. Van Nostrand, 170 pp.

  • Carlisle, R., 1974: College Credit through TV: Old Idea, New Dimensions. Great Plains National Instructional Television Library, 194 pp.

    • Search Google Scholar
    • Export Citation
  • Chandrasekhar, S., 1943: Stochastic problems in physics and astronomy. Rev. Mod. Phys., 15, 189.

  • Charney, J. G., 1948: On the scale of the atmospheric motions. Geofys. Publ., 17, 117.

  • Charney, J. G., , R. Fjørtoft & , and J. von Neumann, 1950: Numerical integration of the barotropic vorticity equation. Tellus, 2, 237254.

    • Search Google Scholar
    • Export Citation
  • Committee on Atmospheric Sciences, 1966: The feasibility of a global observation and analysis experiment. NAS–NRC Publ. 1290, 172 pp.

  • Dyson, F. J., 1988: Infinite in All Directions. Harper and Row, 319 pp.

  • Eady, E. T., 1948: The theory of development in dynamic meteorology. Ph. D. dissertation. Imperial College, 78 pp.

  • Eady, E. T., 1949: Long waves and cyclone waves. Tellus, 1, 3352.

  • Eady, E. T., 1951: The quantitative theory of cyclone development. Compendium of Meteorology, T. Malone, Ed., Amer. Meteor. Soc., 464469.

    • Search Google Scholar
    • Export Citation
  • Ehrendorfer, M., 1997: Predicting the uncertainty of numerical weather forecasts: A review. Meteor. Z., 6, 147 183.

  • Epstein, E. S., 1960: Large scale motion in the stratosphere. Ph.D. dissertation, Pennsylvania State University, 122 pp.

  • Epstein, E. S., 1968: On the correspondence between theory and practice in probability forecasts. Proc. First Statistical Meteorology Conf., Hartford, CT, Amer. Meteor. Soc., 142154.

    • Search Google Scholar
    • Export Citation
  • Epstein, E. S., 1969: Stochastic dynamic prediction. Tellus, 21, 739759.

  • Epstein, E. S., 1985: Statistical Inference and Prediction in Climatology: A Bayesian Approach. Meteor. Monogr., No. 42, Amer. Meteor. Soc., 199 pp.

    • Search Google Scholar
    • Export Citation
  • Epstein, E. S. & , and R. J. Fleming, 1971: Depicting stochastic dynamic forecasts. J. Atmos. Sci., 28, 500511.

  • Epstein, E. S. & , and E. J. Pitcher, 1972: Stochastic analysis of meteorological fields. J. Atmos. Sci., 29, 244257.

  • Epstein, E. S., , C. Osterberg & , and A. Adel, 1956: A new method for the determination of the vertical distribution of ozone from a ground station. J. Meteor., 13, 318334.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 1994: Sequential data assimilation with a non-linear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99, 10 14310 162.

    • Search Google Scholar
    • Export Citation
  • Fleming, R. J., 1970: The concepts and implications of stochastic dynamic prediction. Ph.D. dissertation, University of Michigan, 171 pp.

    • Search Google Scholar
    • Export Citation
  • Fleming, R. J., 1971a: On stochastic dynamic prediction: I. The energetics of uncertainty and the question of closure. Mon. Wea. Rev., 99, 851872.

    • Search Google Scholar
    • Export Citation
  • Fleming, R. J., 1971b: On stochastic dynamic prediction: II. Predictability and utility. Mon. Wea. Rev., 99, 927938.

  • Ford, K. W., 1963: The World of Elementary Particles. Blaisdell, 245 pp.

  • GARP, 1969: GARP topics. Bull. Amer. Meteor. Soc., 50, 136141.

  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.

  • Ginsberg, E. & , and D. Bray, 1953: The Uneducated. Columbia University Press, 246 pp.

  • Gleeson, T. A., 1966: A causal relation for probabilities in synoptic meteorology. J. Appl. Meteor., 5, 365368.

  • Gleeson, T. A., 1967: On theoretical limits of predictability. J. Appl. Meteor., 6, 355359.

  • Gleeson, T. A., 1968: A modern physical basis for meteorological prediction. Proc. First Statistical Meteorology Conf., Hartford, CT, Amer. Meteor. Soc., 110.

    • Search Google Scholar
    • Export Citation
  • Harper, K. C., 2012: Weather by the Numbers: The Genesis of Modern Meteorology. MIT Press, 308 pp.

  • Hirschberg, P. A., and Coauthors, 2011: A weather and climate enterprise strategic implementation plan for generating and communicating forecast uncertainty information. Bull. Amer. Meteor. Soc., 92, 16511666.

    • Search Google Scholar
    • Export Citation
  • Kraichnan, R. H., 1964: Kolmogorov's hypothesis and Eulerian turbulence theory. Phys. Fluids, 7, 17231734.

  • Kraichnan, R. H., 1970: Instability in fully developed turbulence. Phys. Fluids, 13, 569575.

  • Kurihara, Y., 1970: A statistical-dynamical model of the general circulation of the atmosphere. J. Atmos. Sci., 27, 847870.

  • Leith, C. E., 1974: Theoretical skill of Monte Carlo forecasts. Mon. Wea. Rev., 102, 409418.

  • Leith, C. E., 1997: Oral history interview. Interview by P. Edwards, 2 July 1997, Stanford University. [Available from Center for the History of Physics, American Institute of Physics, College Park, MD 20740.]

    • Search Google Scholar
    • Export Citation
  • Leith, C. E. & , and R. H. Kraichnan, 1972: Predictability of turbulent flows. J. Atmos. Sci., 29, 10411058.

  • Lewis, J. M., 1998: Clarifying the dynamics of the general circulation: Phillips's 1956 experiment. Bull. Amer. Meteor. Soc., 79, 3960.

    • Search Google Scholar
    • Export Citation
  • Lewis, J. M., 2005: Roots of ensemble forecasting. Mon. Wea. Rev., 133, 18651885.

  • Lewis, J. M., 2008: Smagorinsky's GFDL: Building the team. Bull. Amer. Meteor. Soc., 89, 13391353.

  • Lorenz, E. N., 1948: A method of applying the hydrodynamic and thermodynamic equations to atmospheric models. D.Sc. dissertation, Massachusetts Institute of Technology, 133 pp.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1953: The interaction between a mean flow and random disturbances. Tellus, 5, 246250.

  • Lorenz, E. N., 1960: Maximum simplification of the dynamic equations. Tellus, 12, 243254.

  • Lorenz, E. N., 1962: The statistical prediction of solutions of dynamical equations. Proc. Int. Symp. on Numerical Weather Prediction, Tokyo, Japan, Meteorological Society of Japan, 629634.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130141.

  • Lorenz, E. N., 1965: On the possible reasons for long-term period fluctuations of the general circulation. Proc. WMOIUGG Symp. on Research and Development Aspects of Long-Range Forecasting, Boulder, CO, World Meteorological Organization, 207219.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1966: Atmospheric predictability. Advances in Numerical Weather Prediction, Travelers Research Center, 3438.

  • Lorenz, E. N., 1968: On the range of atmospheric predictability. Proc. First Statistical Meteorology Conf., Hartford, CT, Amer. Meteor. Soc., 1119.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1982: Atmospheric predictability experiments with a large numerical model. Tellus, 34, 505513.

  • Lynch, P., 2006: The Emergence of Numerical Weather Prediction: Richardson's Dream. Cambridge University Press, 279 pp.

  • Metropolis, N. & , and S. Ulam, 1949: The Monte Carlo method. J. Amer. Stat. Assoc., 44, 335341.

  • Mosteller, F., , R. Rourke & , and G. Thomas, 1961: Probability and Statistics. Addison-Wesley, 395 pp.

  • Murphy, A. H. & , and E. S. Epstein, 1967a: Verification of probabilistic predictions: A brief review. J. Appl. Meteor., 6, 748755.

  • Murphy, A. H. & , and E. S. Epstein, 1967b: A note on probability forecasts and “hedging.” J. Appl. Meteor., 6, 10021004.

  • Oort, A., 1964: On estimates of the atmospheric energy cycle. Mon. Wea. Rev., 92, 483493.

  • Opsteegh, J. D. & , and H. M. Van den Dool, 1980: Seasonal differences in the stationary response of a linearized primitive equation model: Prospects for long-range weather forecasting? J. Atmos. Sci., 37, 21692185.

    • Search Google Scholar
    • Export Citation
  • Panofsky, W., 2007: Panofsky on Physics, Politics, and Peace: Pief Remembers. Springer, 191 pp.

  • Pitcher, E. J., 1974: Stochastic dynamic prediction using atmospheric data. Ph.D. dissertation, University of Michigan, 154 pp.

  • Pitcher, E. J., 1977: Application of stochastic dynamic prediction to real data. J. Atmos. Sci., 34, 321.

  • Platzman, G. W., 1964: An exact integral of complete spectral equations for unsteady one-dimensional flow. Tellus, 16, 422431.

  • Platzman, G. W., 1967: A retrospective view of Richardson's book on weather prediction. Bull. Amer. Meteor. Soc., 48, 514550.

  • Platzman, G. W., 1979: The ENIAC computations of 1950: Gateway to numerical weather prediction. Bull. Amer. Meteor. Soc., 60, 302312.

    • Search Google Scholar
    • Export Citation
  • Poincaré, H., 1952: Science and Hypothesis. Dover, 244 pp.

  • Richardson, L. F., 1922: Weather Prediction by Numerical Process. Cambridge University Press, 236 pp.

  • Savage, L., 1954: The Foundations of Statistics. John Wiley & Sons, 294 pp.

  • Simmons, A. & , and A. Hollingsworth, 2002: Some aspects of the improvements in skill of numerical weather prediction. Quart. J. Roy. Meteor. Soc., 128, 647677.

    • Search Google Scholar
    • Export Citation
  • Smagorinsky, J., 1983: The beginnings of numerical weather prediction and general circulation modeling: Early recollections. Advances in Geophysics, Vol. 25, Academic Press, 337.

    • Search Google Scholar
    • Export Citation
  • Thompson, P. D., 1983: A history of numerical weather prediction in the United States. Bull. Amer. Meteor. Soc., 64, 755769.

  • Wax, N., 1954: Selected Papers on Noise and Stochastic Processes. Dover, 337 pp.

  • Wheeler, J. A. & , and K. W. Ford, 1998: Geons, Black Holes, & Quantum Foam: A Life in Physics. W. W. Norton, 380 pp.

  • Wiin-Nielsen, A., 1991: The birth of numerical weather prediction. Tellus, 43, 3652.

  • WMO, 1965: WMO-IUGG Symposium on Research and Development Aspects of Long-Range Forecasting, Boulder, CO. World Meteorological Organization Tech. Note 66, 345 pp.

    • Search Google Scholar
    • Export Citation
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Edward Epstein's Stochastic–Dynamic Approach to Ensemble Weather Prediction

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  • 1 National Severe Storms Laboratory, Norman, Oklahoma, and Desert Research Institute, Reno, Nevada
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In the late 1960s, well before the availability of computer power to produce ensemble weather forecasts, Edward Epstein (1931–2008) developed a stochastic–dynamic prediction (SDP) method for calculating the temporal evolution of mean value, variance, and covariance of the model variables: the statistical moments of a time-varying probability density function that define an ensemble forecast. This statistical–dynamical approach to ensemble forecasting is an alternative to the Monte Carlo formulation that is currently used in operations. The stages of Epstein's career that led to his development of this methodology are presented with the benefit of his oral history and supporting documentation that describes the retreat of strict deterministic weather forecasting. The important follow-on research by two of Epstein's protégés, Rex Fleming and Eric Pitcher, is also presented.

A low-order nonlinear dynamical system is used to discuss the rudiments of SDP and Monte Carlo and to compare these approximate methods with the exact solution found by solving Liouville's equation. Graphical results from these various methods of solution are found in the main body of the paper while mathematical development is contained in an online supplement. The paper ends with a discussion of SDP's strengths and weaknesses and its possible future as an operational and research tool in probabilistic–dynamic weather prediction.

CORRESPONDING AUTHOR: J. M. Lewis, National Severe Storms Laboratory, Norman, OK 73072, E-mail: jlewis@dri.edu

A supplement to this article is available online (10.1175/BAMS-D-13-00036.2)

In the late 1960s, well before the availability of computer power to produce ensemble weather forecasts, Edward Epstein (1931–2008) developed a stochastic–dynamic prediction (SDP) method for calculating the temporal evolution of mean value, variance, and covariance of the model variables: the statistical moments of a time-varying probability density function that define an ensemble forecast. This statistical–dynamical approach to ensemble forecasting is an alternative to the Monte Carlo formulation that is currently used in operations. The stages of Epstein's career that led to his development of this methodology are presented with the benefit of his oral history and supporting documentation that describes the retreat of strict deterministic weather forecasting. The important follow-on research by two of Epstein's protégés, Rex Fleming and Eric Pitcher, is also presented.

A low-order nonlinear dynamical system is used to discuss the rudiments of SDP and Monte Carlo and to compare these approximate methods with the exact solution found by solving Liouville's equation. Graphical results from these various methods of solution are found in the main body of the paper while mathematical development is contained in an online supplement. The paper ends with a discussion of SDP's strengths and weaknesses and its possible future as an operational and research tool in probabilistic–dynamic weather prediction.

CORRESPONDING AUTHOR: J. M. Lewis, National Severe Storms Laboratory, Norman, OK 73072, E-mail: jlewis@dri.edu

A supplement to this article is available online (10.1175/BAMS-D-13-00036.2)

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