Statistical methods for interpreting Monte Carlo ensemble forecasts

David B. Stephenson; Francisco J. Doblas-Reyes

doi:10.3402/tellusa.v52i3.12267

Statistical methods for interpreting Monte Carlo ensemble forecasts

Tellus

Volume 52 (2000): Issue 3

By: David B. Stephenson and Francisco J. Doblas-Reyes

Open Access

|Jan 2000

Anderson , J. L . 1997 . The impact of dynamical con-straints on the selection of initial conditions for ensemble predictions: low-order perfect model results . Mon. Wea. Rev . 125 , 2969 – 2983 .
Search in Google Scholar Back to article
Atger , F . 1999 . Tubing: an alternative to clustering for the classification of ensemble forecasts . Weather and Forecasting 14 , 741 – 757 .
Search in Google Scholar Back to article
Barkmeijer , J . 1996 . Constructing fast-growing perturba-tions for the nonlinear regime. J. Atmos. Sc i . 53 , 2838 – 2851 .
Search in Google Scholar Back to article
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 .
Search in Google Scholar Back to article
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 .
Search in Google Scholar Back to article
Brankovic , C. and Palmer , T. N . 1997 . Atmospheric seasonal predictability and estimates of ensemble size Mon. Wea. Re v . 125 , 859 – 874 .
Search in Google Scholar Back to article
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 .
Search in Google Scholar Back to article
Buizza , R . 1994 . Sensitivity of optimal unstable struc-tures . Quart. J. Roy. Met. Soc . 120 , 429 – 451 .
Search in Google Scholar Back to article
Buizza , R . 1997 . Potential forecast skill of ensemble prediction and spread and skill distributions of the ECMWF ensemble prediction system. Mon. Wea. Re v . 125 , 99 – 119 .
Search in Google Scholar Back to article
Buizza , R. , Gelaro , R. , Molteni , F. and Palmer , T. N . 1997 . The impact of increased resolution on predictab-ility studies with singular vectors . Quart. J. Roy. Met. Soc . 123 , 1007 – 1033 .
Search in Google Scholar Back to article
Buizza , R. and Palmer , T. N . 1995 . The singular-vector structure of the atmospheric global circulation. J. Atmos. Sc i . 52 , 1434 – 1456 .
Search in Google Scholar Back to article
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 .
Search in Google Scholar Back to article
Burgers , G. and Stephenson , D. B . 1999 . The “Normal-ity” of El Nifio. Geophys. Res. Letters 26 , 1027 - 1030. Carnevale , G. F. 1982. Statistical features of the evolution of two-dimensional turbulence . J. Fluid. Mech . 122 , 143 – 153 .
Search in Google Scholar Back to article
Carnevale , G. F. , Frisch , U. and Salmon , R . 1981 . H theorems in statistical fluid dynamics . J. Phys. A 14 , 1701 – 1718 .
Search in Google Scholar Back to article
Carnevale , G. F. and Holloway , G . 1982 . Information decay and the predictability of turbulent flows . J. Fluid. Mech . 116 , 115 – 121 .
Search in Google Scholar Back to article
Charney , J. G. , Fjortoft , R. and von Neumann , J . 1950 . Numerical integration of the barotropic vorticity equation . Tellus 2 , 237 – 254 .
Search in Google Scholar Back to article
Cox , T. F. and Cox , M. A. A . 1994 . Multidimensional scaling . Chapman and Hall , London .
Search in Google Scholar Back to article
Ehrendorfer , M . 1994 . The Liouville equation and its potential usefulness for the prediction of forecast skill. Part I: Theory. Mon. Wea. Re v . 122 , 703 – 713 .
Search in Google Scholar Back to article
Ehrendorfer , M. and Tribbia , J. J . 1997 . Optimal predic-tion of forecast error covariances through singular vectors. J. Atmos. Sc i . 54 , 286 – 313 .
Search in Google Scholar Back to article
Epstein , E. S . 1969a The role of initial uncertainties in prediction . J. Appl. Meteor . 8 , 190 – 198 .
Search in Google Scholar Back to article
Epstein , E. S . 1969b . Stochastic dynamic predic-tion . Tellus 21 , 739 – 759 .
Search in Google Scholar Back to article
Hadamard , J . 1898 . Les surfaces a courbures opposées et leurs lignes géodesiques . J. Math. Pure et Appl . 4 , 27 – 73 .
Search in Google Scholar Back to article
Hamill , T. M. and Colucci , S. J . 1998 Evaluation of Eta-RSM ensemble probabilistic precipitation forecasts. Mon. Wea. Re v . 126 , 711 – 724 .
Search in Google Scholar Back to article
Houtekamer , P. L. and Derome , J . 1995 . Methods for ensemble prediction. Mon. Wea. Re v . 123 , 2181 – 2196 .
Search in Google Scholar Back to article
Houtekamer , P. L. , Lefaivre , L. , Derome , J. , Ritchie , H. and Mitchell , H. L . 1996 . A system simulation approach to ensemble prediction. Mon. Wea. Re v . 124 , 1225 – 1242 .
Search in Google Scholar Back to article
Landau , L. D. and Lifshitz , E. M . 1980 . Statistical physics . Butterworth Heinemann , 3rd edition , vol . 5 .
Search in Google Scholar Back to article
Leith , C. E . 1971 . Atmospheric predictability and two-dimensional turbulence. J. Atmos. Sc i . 28 , 145 – 161 .
Search in Google Scholar Back to article
Leith , C. E . 1974 . Theoretical skill of Monte Carlo forecasts. Mon. Wea. Re v . 102 , 409 – 418 .
Search in Google Scholar Back to article
Leith , C. E. and Kraichnan , R. H . 1972 . Predictability of turbulent flows. J. Atmos. Sc i . 29 , 1041 – 1058 .
Search in Google Scholar Back to article
Lorenz , E. N . 1963 . Deterministic nonperiodic flow. J. Atmos. Sc i . 20 , 130 – 141 .
Search in Google Scholar Back to article
Lorenz , E. N . 1969a . The predictability of a flow which possesses many scales of motion. Tellus 21 , 289 - 307.
Search in Google Scholar Back to article
Lorenz , E. N. 1969b. Three approaches to atmospheric predictability. Bulletin American Met. Soc. 50 , 345 - 349.
Search in Google Scholar Back to article
Mardia , K. V. 1970. Measures of multivariate skewness and kurtosis with applications . Biometrika , 57 , 519 – 530 .
Search in Google Scholar Back to article
Mardia , K. V . 1974 . Applications of some measures of multivariate skewness and kurtosis in testing normal-ity and robustness studies . Sankhyti. The Indian Journal of Statistics 36 , 115 – 128 .
Search in Google Scholar Back to article
Mardia , K. V. , Kent , J. T. and Bibby , J. M . 1979 . Multi-variate analysis . Academic Press Limited , London .
Search in Google Scholar Back to article
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 .
Search in Google Scholar Back to article
Murphy , J. M . 1988 . The impact of ensemble forecasts on predictability . Quart. J. Roy. Met. Soc . 114 , 463 – 493 .
Search in Google Scholar Back to article
Poincaré , H . 1890 . Sur les equations de la dynamique dele probléme de trois corps . Acta Math . 13 , 1 – 270 .
Search in Google Scholar Back to article
Ruelle , D . 1989 . Chaotic evolution and strange attractors . Cambridge University Press , Cambridge .
Search in Google Scholar Back to article
Selten , F. M . 1997 . Baroclinic empirical orthogonal functions as basis functions in an atmospheric model. Mon. Wea. Re v . 54 , 2100 – 2114 .
Search in Google Scholar Back to article
Sivillo , J. K. , Ahlquist , J. E. and Toth , Z . 1997 . An ensemble forecasting primer . Weather and Forecasting 12 , 809 – 818 .
Search in Google Scholar Back to article
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 .
Search in Google Scholar Back to article
Smagorinsky , J . 1969 . Problems and promises of deter-ministic extended range forecasting . Bulletin American Met. Soc . 50 , 286 – 311 .
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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. Re v . 127 , 1954 – 1966 .
Search in Google Scholar Back to article
Stephenson , D. B . 1997 . Correlation of spatial climate/weather maps and the advantages of using the mahal-anobis metric in predictions . Tellus 49A , 513 – 527 .
Search in Google Scholar Back to article
Strang , G . 1988 . Linear algebra and its applications . Harcourt Brace Jovanovich, Inc., 3rd edition.
Search in Google Scholar Back to article
Stroe , R. and Royer , J.-F . 1993 . Comparison of different error growth formulas and predictability estimation in numerical extended-range forecasts . Ann. Geophys-icae 11 , 296 – 316 .
Search in Google Scholar Back to article
Sutton , O. G. 1951 . Mathematics and the future of met-eorology. Weather 6 , 291 – 296.
Search in Google Scholar Back to article
The Economist, 27 March 1999. Economics focus: ik la mode. 350,90.
Search in Google Scholar Back to article
Thompson , P. D . 1957 . Uncertainty of initial state as a factor in the predictability of large scale atmospheric flow patterns . Tellus 9 , 275 – 295 .
Search in Google Scholar Back to article
Toth , Z . 1991 . Circulation patterns in phase space: a multinormal distribution? Mon. Wea. Re v . 119 , 1501 – 1511 .
Search in Google Scholar Back to article
Toth , Z . 1995 . Degrees of freedom in Northern Hemi-sphere circulation data . Tellus 47A , 457 – 472 .
Search in Google Scholar Back to article
Toth , Z. and Kalnay , E . 1993 . Ensemble forecasting at NMC: the generation of perturbations . Bull. Amer. Meteor. Soc . 74 , 2317 – 2330 .
Search in Google Scholar Back to article
Toth , Z. and Kalnay , E . 1997 . Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Re v . 125 , 3297 – 3319 .
Search in Google Scholar Back to article
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 .
Search in Google Scholar Back to article
Wallace , J. M. , Cheng , X. and Sun , D . 1991 . Does low-frequency atmospheric variability exhibit regime-like behavior? Tellus 43AB , 16 - 26 .
Search in Google Scholar Back to article
Weinberg , S . 1972 . Gravitation and cosmology . John Wiley & Sons , Inc .
Search in Google Scholar Back to article
Whitaker , J. S. and Loughe , A. F . 1998 . The relationship between ensemble spread and ensemble mean skill. Mon. Wea. Re v . 126 , 3292 – 3302 .
Search in Google Scholar Back to article
Zwiers , F. W . 1996 . Interannual variability and predict-ability in an ensemble of AMIP climate simulations conducted with the CCC GCM2 . Climate Dynamics 12 , 825 – 847 .
Search in Google Scholar Back to article

Authors

Metrics

Articles in this issue

DOI: https://doi.org/10.3402/tellusa.v52i3.12267 | Journal eISSN: 3035-9554

Journal RSS Feed

Language: English

Page range: 300 - 322

Submitted on: Aug 10, 1998

Accepted on: Dec 6, 1999

Published on: Jan 1, 2000

Published by: Stockholm University Press

In partnership with: Paradigm Publishing Services

© 2000 David B. Stephenson, Francisco J. Doblas-Reyes, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 52 (2000): Issue 3