• Anderson, T. W., 1984: An Introduction to Multivariate Statistics. 2d ed. Wiley, 675 pp.

  • Branstator, G., A. Mai, and D. Baumhefner, 1993: Identification of highly predictable flow element for spatial filtering of medium- and extended-range numerical forecasts. Mon. Wea. Rev.,121, 1786–1802.

  • Briggs, W. M., and R. A. Levine, 1996: Wavelets and field forecast verification. Cornell University Biometrics Unit Tech. Rep. BU 1318M, 461 pp. [Available from Biometrics Unit, Ithaca, NY 14583.].

  • Chao, B. F., and I. Naito, 1995: Wavelet analysis provides a new tool for studying Earth’s rotation. Eos,76, 161–165.

  • Chui, C. K., L. Montefusco, and L. Puccio, 1994: Wavelets: Theory, Algorithms, and Applications. Academic Press, 627 pp.

  • Daley, R., 1993: Atmospheric Data Analysis. Cambridge University Press, 457 pp.

  • Daubechies, I., 1992: Ten Lectures on Wavelets. SIAM, 357 pp.

  • DeVore, R. A., 1993: Adaptive wavelet bases for image compression. Wavelets, Images, and Surface Fitting, P. J. Laurent, A. Le Méhauté, and L. L. Shumaker, Eds., A. K. Peters, 197–219.

  • Donoho, D. L., 1992: De-noising by soft-thresholding. Tech. Rep. 409, 37 pp. [Available from Dept. of Statistics, Stanford University, Stanford, CA 94305.].

  • ——, and I. M. Johnstone, 1994: Ideal spatial adaptation by wavelet shrinkage. Biometrika,81, 425–455.

  • ——, and ——, 1995: Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Stat. Assoc.,90, 1200–1224.

  • ——, ——, G. Kerkyacharian, and D. Picard, 1995: Wavelet shrinkage: Asymptopia? J. Roy. Stat. Soc.,57, 301–369.

  • Gao, W., and B. L. Li, 1993: Wavelet analysis of coherent structures at the atmosphere–forest interface. J. Appl. Meteor.,32, 1717–1725.

  • Goel, P., and B. Vidakovic, 1995: Wavelet transformations as diversity enhancers. Discussion Paper 95-04, 21 pp. [Available from ISDS, Duke University, Durham, NC 27708.].

  • Golub, G. H., and C. F. van Loan, 1989: Matrix Computations. Johns Hopkins Press, 642 pp.

  • Hagelberg, C. R., and N. K. K. Gamage, 1994: Applications of structure preserving wavelet decompositions to intermittent turbulence: A case study. Wavelets in Geophysics, E. Foufoula-Georgiou and P. Kumar, Eds., Academic Press, 45–80.

  • Hancock, M. S., and J. R. Wallis, 1994: An approach to statistical spatial-temporal modeling of meteorological fields. J. Amer. Stat. Assoc.,89, 368–390.

  • Hoffman, R. N., Z. Liu, J. F. Louis, and C. Grassotti, 1995: Distortion representation of forecast errors. Mon. Wea. Rev.,123, 2758–2770.

  • Johnstone, I. M., and B. W. Silverman, 1995: Wavelet threshold estimators for data with correlated noise. Tech. Rep. 37 pp. [Available from Dept. of Statistics, Stanford University, Stanford, CA 94305.].

  • Katul, G., and B. Vidakovic, 1995: The partitioning of attached and detached eddy motion in the atmospheric surface layer using Lorentz wavelet filtering. Discussion Paper 95-05, 31 pp. [Available from ISDS, Duke University, Durham, NC 27708.].

  • Kumar, P., and E. Foufoula-Georgiou, 1993: A new look at rainfall fluctuations and scaling properties of spatial rainfall using orthogonal wavelets. J. Appl. Meteor.,32, 209–222.

  • ——, and ——, 1994: Wavelet analysis in geophysics: An introduction. Wavelets In Geophysics, E. Foufoula-Georgiou and P. Kumar, Eds., Academic Press, 1–43.

  • Lau, K. M., and H. Weng, 1995: Climate signal detection using wavelet transform: How to make a time series sing. Bull. Amer. Meteor. Soc.,76, 2391–2402.

  • Laurent, P. J., A. Le Méhauté, and L. L. Shumaker, 1993: Wavelets, Images, and Surface Fitting. A. K. Peters, 528 pp.

  • Livezey, R. E., J. D. Hoopingarner, and J. Huang, 1995: Verification of official monthly mean 700-hPa height forecasts: An update. Wea. Forecasting,10, 512–527.

  • Meyers, S. D., B. G. Kelly, and J. J. O’Brien, 1993: An introduction to wavelet analysis in oceanography and meteorology: With application to the dispersion of Yanai waves. Mon. Wea. Rev.,121, 2858–2866.

  • Miyakoda, K., G. D. Hembree, R. F. Strickler, and I. Shulman, 1972: Cumulative results of extended forecast experiments. Part I: Model performance for winter cases. Mon. Wea. Rev.,100, 836–854.

  • Murphy, A. H., 1991: Forecast verification: Its complexity and dimensionality. Mon. Wea. Rev.,119, 1590–1601.

  • ——, 1995: The coefficients of correlation and determination as measures of performance in forecast verification. Wea. Forecasting,10, 681–688.

  • ——, and R. L. Winkler, 1987: A general framework for forecast verification. Mon. Wea. Rev.,115, 1330–1338.

  • ——, and E. S. Epstein, 1989: Skill scores and correlation coefficients in model verification. Mon. Wea. Rev.,117, 572–581.

  • Nason, G. P., 1994: Wavelet regression by cross-validation. Tech. Rep. 447, 45 pp. [Available from Dept. of Statistics, Stanford University, Stanford, CA 94305.].

  • Perrie, W., and B. Toulany, 1989: Correlations of sea level pressure fields for objective analysis. Mon. Wea. Rev.,117, 572–581.

  • Persson, A., 1996: Forecast error and inconsistency in medium range weather prediction. Preprints, 13th Conf. on Probability and Statistics in the Atmospheric Sciences, San Francisco, CA, Amer. Meteor. Soc., 253–259.

  • Preisendorfer, R. W., 1988: Principal Component Analysis in Meteorology and Oceanography. Elsevier, 425 pp.

  • Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992: Numerical Recipes in C. 2d ed. Cambridge University Press, 994 pp.

  • Radok, U., and T. J. Brown, 1993: Anomaly correlation and an alternative: Partial correlation. Mon. Wea. Rev.,121, 1269–1271.

  • Saito, N., 1994: Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum description length comparison. Wavelets in Geophysics, E. Foufoula-Georgiou and P. Kumar, Eds., Academic Press, 299–324.

  • Serrano, E., R. Compagnucci, and M. Fabio, 1992: The use of wavelet transform for climatic estimates. Proc. Fifth Int. Meeting on Statistical Climatology, Toronto, Canada, AES, Environment Canada, 259–262.

  • Taylor, C. C., 1991: Measure of similarity between two images. Spatial Statistics and Imaging, A. Possolo, Ed., IMS Lecture Notes, Vol. 20, IMS, 382–391.

  • Van den Dool, H. M., and L. Rukhovets, 1994: On the weights for an ensemble-averaged 6–10-day forecast. Wea. Forecasting,9, 457–465.

  • Vidakovic, B., and P. Müller, 1994: Wavelets for kids. ISDS Discussion Paper 94-13, 26 pp. [Available from ISDS, Duke University, Durham, NC 27708.].

  • Weng, H., and K. M. Lau, 1994: Wavelets, period doubling, and time-frequency localization with application to organization of convection over the tropical Western Pacific. J. Atmos. Sci.,51, 2523–2541.

  • Wickerhauser, M. L., 1994: Comparison of picture compression methods: Wavelet, wavelet packet, and local cosine transform coding. Wavelets: Theory, Algorithms, and Applications, C. K. Chui, L. Montefusco, and L. Puccio, Eds., Academic Press, 585–621.

  • Wilks, D. S., 1995. Statistical Methods in the Atmospheric Sciences. Academic Press, 467 pp.

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Wavelets and Field Forecast Verification

William M. BriggsDepartment of Soil, Crop, and Atmospheric Sciences, Cornell University, Ithaca, New York

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Richard A. LevineDivision of Statistics, University of California at Davis, Davis, California

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Abstract

Current field forecast verification measures are inadequate, primarily because they compress the comparison between two complex spatial field processes into one number. Discrete wavelet transforms (DWTs) applied to analysis and contemporaneous forecast fields prove to be an insightful approach to verification problems. DWTs allow both filtering and compact physically interpretable partitioning of fields. These techniques are used to reduce or eliminate noise in the verification process and develop multivariate measures of field forecasting performance that are shown to improve upon existing verification procedures.

Corresponding author address: Dr. William M. Briggs, Dept. of Soil, Crop, and Atmospheric Sciences, Cornell University, 1123 Bradfield Hall, Ithaca, NY 14853-1901.

Email: wmb2@cornell.edu

Abstract

Current field forecast verification measures are inadequate, primarily because they compress the comparison between two complex spatial field processes into one number. Discrete wavelet transforms (DWTs) applied to analysis and contemporaneous forecast fields prove to be an insightful approach to verification problems. DWTs allow both filtering and compact physically interpretable partitioning of fields. These techniques are used to reduce or eliminate noise in the verification process and develop multivariate measures of field forecasting performance that are shown to improve upon existing verification procedures.

Corresponding author address: Dr. William M. Briggs, Dept. of Soil, Crop, and Atmospheric Sciences, Cornell University, 1123 Bradfield Hall, Ithaca, NY 14853-1901.

Email: wmb2@cornell.edu

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