Statistical Downscaling of Extreme Precipitation Events Using Censored Quantile Regression

P. Friederichs Meteorological Institute, University of Bonn, Bonn, Germany

Search for other papers by P. Friederichs in
Current site
Google Scholar
PubMed
Close
and
A. Hense Meteorological Institute, University of Bonn, Bonn, Germany

Search for other papers by A. Hense in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

A statistical downscaling approach for extremes using censored quantile regression is presented. Conditional quantiles of station data (e.g., daily precipitation sums) in Germany are estimated by means of the large-scale circulation as represented by the NCEP reanalysis data. It is shown that a mixed discrete–continuous response variable, such as a daily precipitation sum, can be statistically modeled by a censored variable. Furthermore, a conditional quantile skill score is formulated to assess the relative gain of a quantile forecast compared with a reference forecast. Just like multiple regression for expectation values, quantile regression provides a tool to formulate a model output statistics system for extremal quantiles.

Corresponding author address: P. Friederichs, Meteorological Institute, University of Bonn, Auf dem Hügel 20, 53121 Bonn, Germany. Email: pfried@uni-bonn.de

Abstract

A statistical downscaling approach for extremes using censored quantile regression is presented. Conditional quantiles of station data (e.g., daily precipitation sums) in Germany are estimated by means of the large-scale circulation as represented by the NCEP reanalysis data. It is shown that a mixed discrete–continuous response variable, such as a daily precipitation sum, can be statistically modeled by a censored variable. Furthermore, a conditional quantile skill score is formulated to assess the relative gain of a quantile forecast compared with a reference forecast. Just like multiple regression for expectation values, quantile regression provides a tool to formulate a model output statistics system for extremal quantiles.

Corresponding author address: P. Friederichs, Meteorological Institute, University of Bonn, Auf dem Hügel 20, 53121 Bonn, Germany. Email: pfried@uni-bonn.de

Save
  • Bremnes, J. B., 2004a: Probabilistic forecasts of precipitation in terms of quantiles using NWP model output. Mon. Wea. Rev., 132 , 338347.

    • Search Google Scholar
    • Export Citation
  • Bremnes, J. B., 2004b: Probabilistic wind power forecasts using local quantile regression. Wind Energy, 7 , 4754.

  • Brier, G. W., 1950: Verification of forecasts expressed in terms of probability. Mon. Wea. Rev., 78 , 13.

  • Caspary, H. J., 1996: Recent winter floods in Germany caused by changes in the atmospheric circulation across Europe. Phys. Chem. Earth, 20 , 459462.

    • Search Google Scholar
    • Export Citation
  • Chernozhukov, V., and H. Hong, 2002: Three-step censored quantile regression, with an application to extramarital affairs. J. Amer. Stat. Assoc., 97 , 872882.

    • Search Google Scholar
    • Export Citation
  • Efron, B., and R. J. Tibshirani, 1993: An Introduction to the Bootstrap. Chapman and Hall, 436 pp.

  • Engel, H., N. Busch, K. Wilke, P. Krahe, H-G. Mendel, H. Giebel, and C. Zieger, 1994: The 1993/94 flood in the Rhine basin. Federal Institute of Hydrology, BfG Rep. 0833.

  • Fahrmeir, L., and G. Tutz, 1994: Multivariate Statistical Modelling Based on Generalized Linear Models. Springer-Verlag, 425 pp.

  • Fitzenberger, B., 1997: A guide to censored quantile regressions. Robust Inference, G. S. Maddala and C. R. Rao, Eds., Vol. 15, Handbook of Statistics, Elsevier Science, 405–437.

    • Search Google Scholar
    • Export Citation
  • Gneiting, T., and A. E. Raftery, 2005: Strictly proper scoring rules, prediction, and estimation. University of Washington Tech. Rep. 463R, 38 pp. [Available online at http://www.stat.washington.edu/www/research/reports/2004/tr463R.pdf.].

  • Jolliffe, I. T., and D. B. Stephenson, 2003: Forecast Verification: A Practitioner’s Guide in Atmospheric Science. Wiley, 240 pp.

  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437471.

  • Klein Tank, A. M. G., and Coauthors, 2002: Daily dataset of 20th-century surface air temperature and precipitation series for the European Climate Assessment. Int. J. Climatol., 22 , 14411453.

    • Search Google Scholar
    • Export Citation
  • Koenker, R., 2005: Quantile Regression. Econometric Society Monographs, Vol. 38, Cambridge University Press, 349 pp.

  • Koenker, R., and B. Bassett, 1978: Regression quantiles. Econometrica, 46 , 3349.

  • Koenker, R., and F. Schorfheide, 1994: Quantile spline models for global temperature change. Climatic Change, 28 , 395404.

  • Powell, J. L., 1986: Censored regression quantiles. J. Econom., 32 , 143155.

  • R Development Core Team, cited. 2003: R: A language and environment for statistical computing. [Available online at http://www.R-project.org].

  • Rudolf, B., and J. Rapp, 2003: The century flood of the River Elbe in August 2002: Synoptic weather development and climatological aspects. Quarterly Rep. 2 of the German NWP-System of the Deutscher Wetterdienst, Part 1, 8–23.

  • Schulze, N., 2004: Microeconometric, financial, and environmental analyses. Ph.D. Dissertation, Eberhard-Karls-Universität Tübingen, 157 pp.

  • Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences: An Introduction. International Geophysics Series, Vol. 59, Academic Press, 467 pp.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1292 317 19
PDF Downloads 941 193 15