Editorial Type:
Article
Article Type:
Research Article

Simple Nonparametric Techniques for Exploring Changing Probability Distributions of Weather

Christopher A. T. Ferro Department of Meteorology, University of Reading, Reading, United Kingdom

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Abdelwaheb Hannachi Department of Meteorology, University of Reading, Reading, United Kingdom

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David B. Stephenson Department of Meteorology, University of Reading, Reading, United Kingdom

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Print Publication:
01 Nov 2005
DOI:
https://doi.org/10.1175/JCLI3518.1
Page(s):
4344–4354
Restricted access

Abstract

Anthropogenic influences are expected to cause the probability distribution of weather variables to change in nontrivial ways. This study presents simple nonparametric methods for exploring and comparing differences in pairs of probability distribution functions. The methods are based on quantiles and allow changes in all parts of the probability distribution to be investigated, including the extreme tails. Adjusted quantiles are used to investigate whether changes are simply due to shifts in location (e.g., mean) and/or scale (e.g., variance). Sampling uncertainty in the quantile differences is assessed using simultaneous confidence intervals calculated using a bootstrap resampling method that takes account of serial (intraseasonal) dependency. The methods are simple enough to be used on large gridded datasets. They are demonstrated here by exploring the changes between European regional climate model simulations of daily minimum temperature and precipitation totals for winters in 1961–90 and 2071–2100. Projected changes in daily precipitation are generally found to be well described by simple increases in scale, whereas minimum temperature exhibits changes in both location and scale.

Corresponding author address: C. Ferro, Department of Meteorology, University of Reading, Earley Gate, P.O. Box 243, Reading RG6 6BB, United Kingdom. Email: c.a.t.ferro@reading.ac.uk

Abstract

Anthropogenic influences are expected to cause the probability distribution of weather variables to change in nontrivial ways. This study presents simple nonparametric methods for exploring and comparing differences in pairs of probability distribution functions. The methods are based on quantiles and allow changes in all parts of the probability distribution to be investigated, including the extreme tails. Adjusted quantiles are used to investigate whether changes are simply due to shifts in location (e.g., mean) and/or scale (e.g., variance). Sampling uncertainty in the quantile differences is assessed using simultaneous confidence intervals calculated using a bootstrap resampling method that takes account of serial (intraseasonal) dependency. The methods are simple enough to be used on large gridded datasets. They are demonstrated here by exploring the changes between European regional climate model simulations of daily minimum temperature and precipitation totals for winters in 1961–90 and 2071–2100. Projected changes in daily precipitation are generally found to be well described by simple increases in scale, whereas minimum temperature exhibits changes in both location and scale.

Corresponding author address: C. Ferro, Department of Meteorology, University of Reading, Earley Gate, P.O. Box 243, Reading RG6 6BB, United Kingdom. Email: c.a.t.ferro@reading.ac.uk

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