Quantifying changes and their uncertainties in probability distribution of climate variables using robust statistics

Abstract

Robust tools are presented in this manuscript to assess changes in probability density function (pdf) of climate variables. The approach is based on order statistics and aims at computing, along with their standard errors, changes in various quantiles and related statistics. The technique, which is nonparametric and simple to compute, is developed for both independent and dependent data. For autocorrelated data, serial correlation is addressed via Monte Carlo simulations using various autoregressive models. The ratio between the average standard errors, over several quantiles, of quantile estimates for correlated and independent data, is then computed. A simple scaling-law type relationship is found to hold between this ratio and the lag-1 autocorrelation. The approach has been applied to winter monthly Central England Temperature (CET) and North Atlantic Oscillation (NAO) time series from 1659 to 1999 to assess/quantify changes in various parameters of their pdf. For the CET, significant changes in median (or scale) and also in low and high quantiles are observed between various time slices, in particular between the pre- and post-industrial revolution. Observed changes in spread and also quartile skewness of the pdf, however, are not statistically significant (at 95% confidence level). For the NAO index we find mainly large significant changes in variance (or scale), yielding significant changes in low/high quantiles. Finally, the performance of the method compared to few conventional approaches is discussed.