Statistical methods for interpreting Monte Carlo ensemble forecasts

Tellus, Series A: Dynamic Meteorology and Oceanography

Volumn 52, Issue 3, 2000, Pages 300-322

  Stephenson, David B ^a,c   Doblas Reyes, Francisco J ^b  

^a MÉTÉO FRANCE   (France)

^b INSTITUTO NACIONAL DE TÉCNICA AEROESPACIAL   (Spain)

^c UNIVERSITY OF READING   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ENSEMBLE FORECASTING; ENTROPY; MONTE CARLO ANALYSIS; STATISTICAL ANALYSIS; WEATHER FORECASTING;

EID: 0034098639     PISSN: 02806495     EISSN: None     Source Type: Journal    
DOI: 10.3402/tellusa.v52i3.12267     Document Type: Article

References (62)

1. Anderson, J. L. 1997. The impact of dynamical constraints on the selection of initial conditions for ensemble predictions: low-order perfect model results. Mon. Wea. Rev. 125, 2969-2083.
2. Atger, F. 1999. Tubing: an alternative to clustering for the classification of ensemble forecasts. Weather and Forecasting 14, 741-757.
3. Barkmeijer, J. 1996. Constructing fast-growing perturbations for the nonlinear regime. J. Atmos. Sci. 53, 2838-2851.
4. Barkmeijer, J., Buizza, R. and Palmer, T. N. 1999. 3D-Var Hessian singular vectors and their potential use in the ECMWF ensemble prediction system. Quart. J. Roy. Met. Soc. 125, 2333-2351.
5. Barkmeijer, J., Gijzen, Van M. and Bouttier, F. 1998. Singular vectors and estimates of the analysis error covariance metric Quart. J. Roy. Met. Soc. 124, 1695-1713.
6. Brankovic, C. and Palmer, T. N. 1997. Atmospheric seasonal predictability and estimates of ensemble size Mon. Wea. Rev. 125, 859-874.
7. Brankovic, C., Palmer, T. N., Molteni, F., Tibaldi, S. and Cubasch, U. 1990. Extended-range predictions with ECMWF models: time-lagged ensemble forecasting. Quart. J. Roy. Met. Soc. 116, 867-912.
8. Buizza, R. 1994. Sensitivity of optimal unstable structures. Quart. J. Roy. Met. Soc. 120, 429-451.
9. Buizza, R. 1997. Potential forecast skill of ensemble prediction and spread and skill distributions of the ECMWF ensemble prediction system. Mon. Wea. Rev. 125, 99-119.
10. Buizza, R., Gelaro, R., Molteni, F. and Palmer, T. N. 1997. The impact of increased resolution on predictability studies with singular vectors. Quart. J. Roy. Met. Soc. 123, 1007-1033.
11. Buizza, R. and Palmer, T. N. 1995. The singular-vector structure of the atmospheric global circulation. J. Atmos. Sci. 52, 1434-1456.
12. Buizza, R. , Petroliagis, T., Palmer, T. N., Barkmeijer, J., Hamrud, M., Hollingsworth, A., Simmons, A. and Wedi, N. 1998. Impact of model resolution and ensemble size on the performance of an ensemble prediction system. Quart. J. Roy. Met. Soc. 124, 1935-1960.
13. Burgers, G. and Stephenson, D. B. 1999. The "Normality" of El Niño. Geophys. Res. Letters 26, 1027-1030.
14. Carnevale, G. F. 1982. Statistical features of the evolution of two-dimensional turbulence. J. Fluid. Mech. 122, 143-153.
15. Carnevale, G. F., Frisch, U. and Salmon, R. 1981. H theorems in statistical fluid dynamics. J. Phys. A 14, 1701-1718.
16. Carnevale, G. F. and Holloway, G. 1982. Information decay and the predictability of turbulent flows. J. Fluid. Mech. 116, 115-121.
17. Charney, J. G., Fjörtoft, R. and von Neumann, J. 1950. Numerical integration of the barotropic vorticity equation. Tellus 2, 237-254.
18. Cox, T. F. and Cox, M. A. A. 1994. Multidimensional scaling. Chapman and Hall, London.
19. Ehrendorfer, M. 1994. The Liouville equation and its potential usefulness for the prediction of forecast skill. Part I: Theory. Mon. Wea. Rev. 122, 703-713.
20. Ehrendorfer, M. and Tribbia, J. J. 1997. Optimal prediction of forecast error covariances through singular vectors. J. Atmos. Sci. 54, 286-313.
21. Epstein, E. S. 1969a The role of initial uncertainties in prediction. J. Appl. Meteor. 8, 190-198.
22. Epstein, E. S. 1969b. Stochastic dynamic prediction. Tellus 21, 739-759.
23. Hadamard, J. 1898. Les surfaces a courbures opposées et leurs lignes géodesiques. J. Math. Pure et Appl. 4, 27-73.
24. Hamill, T. M. and Colucci, S. J. 1998 Evaluation of Eta-RSM ensemble probabilistic precipitation forecasts. Mon. Wea. Rev. 126, 711-724.
25. Houtekamer, P. L. and Derome, J. 1995. Methods for ensemble prediction. Mon. Wea. Rev. 123, 2181-2196.
26. Houtekamer, P. L., Lefaivre, L., Derome, J., Ritchie, H. and Mitchell, H. L. 1996. A system simulation approach to ensemble prediction. Mon. Wea. Rev. 124, 1225-1242.
27. Landau, L. D. and Lifshitz, E. M. 1980. Statistical physics. Butterworth Heinemann, 3rd edition, vol. 5.
28. Leith, C. E. 1971. Atmospheric predictability and two-dimensional turbulence. J. Atmos. Sci. 28, 145-161.
29. Leith, C. E. 1974. Theoretical skill of Monte Carlo forecasts. Mon. Wea. Rev. 102, 409-418.
30. Leith, C. E. and Kraichnan, R. H. 1972. Predictability of turbulent flows. J. Atmos. Sci. 29, 1041-1058.
31. Lorenz, E. N. 1963. Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130-141.
32. Lorenz, E. N. 1969a. The predictability of a flow which possesses many scales of motion. Tellus 21, 289-307.
33. Lorenz, E. N. 1969b. Three approaches to atmospheric predictability. Bulletin American Met. Soc. 50, 345-349.
34. Mardia, K. V. 1970. Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519-530.
35. Mardia, K. V. 1974. Applications of some measures of multivariate skewness and kurtosis in testing normality and robustness studies. Sankhyä. The Indian Journal of Statistics 36, 115-128.
36. Mardia, K. V., Kent, J. T. and Bibby, J. M. 1979. Multivariate analysis. Academic Press Limited, London.
37. Molteni, F., Buizza, R., Palmer, T. N. and Petroliagis, T. 1996. The ECMWF ensemble prediction system: methodology and validation. Quart. J. Roy. Met. Soc. 122, 73-119.
38. Murphy, J. M. 1988. The impact of ensemble forecasts on predictability. Quart. J. Roy. Met. Soc. 114, 463-493.
39. Poincaré, H. 1890. Sur les equations de la dynamique de le problème de trois corps. Acta Math. 13, 1-270.
40. Ruelle, D. 1989. Chaotic evolution and strange attractors. Cambridge University Press, Cambridge.
41. Selten, F. M. 1997. Baroclinic empirical orthogonal functions as basis functions in an atmospheric model. Mon. Wea. Rev. 54, 2100-2114.
42. Sivillo, J. K., Ahlquist, J. E. and Toth, Z. 1997. An ensemble forecasting primer. Weather and Forecasting 12, 809-818.
43. Skelly, W. C. and Henderson-Sellers, A. 1996. Grid box or grid point: what type of data do GCMs deliver to climate impacts researchers? Int. J. Climatol. 16, 1079-1086.
44. Smagorinsky, J. 1969. Problems and promises of deterministic extended range forecasting. Bulletin American Met. Soc. 50, 286-311.
45. Smith, L. A. 1996. Accountability and error in ensemble forecasting. In: Palmer, T. (ed.): Predictabilty, ECMWF November 1997 Workshop on Predictability, vol. 1, pp. 351-368. Reading, UK. ECMWF.
46. Smith, L. A. and Gilmour, I. 1997. Accountability and internal consistence in ensemble formation. In: Palmer, T. (ed.): Predictabilty, ECMWF November 1997 Workshop on Predictability, vol. 2, p.15. Reading, UK. ECMWF.
47. Stephenson, D. B., Rupa Kumar, K., Doblas-Reyes, F.-J., Royer, J.-F., Chauvin, F. and Pezzulli, S. 1999. Extreme daily rainfall events and their impact on ensemble forecasts of the Indian monsoon. Mon. Wea. Rev. 127, 1954-1966.
48. Stephenson, D. B. 1997. Correlation of spatial climate/ weather maps and the advantages of using the mahalanobis metric in predictions. Tellus 49A, 513-527.
49. Strang, G. 1988. Linear algebra and its applications. Harcourt Brace Jovanovich, Inc., 3rd edition.
50. Stroe, R. and Royer, J.-F. 1993. Comparison of different error growth formulas and predictability estimation in numerical extended-range forecasts. Ann. Geophysicae 11, 296-316.
51. Sutton, O. G. 1951. Mathematics and the future of meteorology. Weather 6, 291-296.
52. The Economist, 27 March 1999. Economics focus: À la mode. 350, 90.
53. Thompson, P. D. 1957. Uncertainty of initial state as a factor in the predictability of large scale atmospheric flow patterns. Tellus 9, 275-295.
54. Toth, Z. 1991. Circulation patterns in phase space: a multinormial distribution? Mon. Wea. Rev. 119, 1501-1511.
55. Toth, Z. 1995. Degrees of freedom in Northern Hemisphere circulation data. Tellus 47A, 457-472.
56. Toth, Z. and Kalnay, E. 1993. Ensemble forecasting at NMC: the generation of perturbations. Bull. Amer. Meteor. Soc. 74, 2317-2330.
57. Toth, Z. and Kalnay, E. 1997. Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Rev. 125, 3297-3319.
58. Toth, Z., Kalnay, E., Tracton, S. M., Wobus, R. and Irwin, J. 1997. A synoptic evaluation of the NCEP ensemble. Weather and Forecasting 12, 140-153.
59. Wallace, J. M., Cheng, X. and Sun, D. 1991. Does low-frequency atmospheric variability exhibit regime-like behavior? Tellus 43AB, 16-26.
60. Weinberg, S. 1972. Gravitation and cosmology. John Wiley & Sons, Inc.
61. Whitaker, J. S. and Loughe, A. F. 1998. The relationship between ensemble spread and ensemble mean skill. Mon. Wea. Rev. 126, 3292-3302.
62. Zwiers, F. W. 1996. Interannual variability and predictability in an ensemble of AMIP climate simulations conducted with the CCC GCM2. Climate Dynamics 12, 825-847.