Resistant, Robust and Non-Parametric Techniques for the Analysis of Climate Data: Theory and Examples, Including Applications to Historical Radiosonde Station Data

Basic traditional parametric statistical techniques are used widely in climatic studies for characterizing the level (central tendency) and variability of variables, assessing linear relationships (including trends), detection of climate change, quality control and assessment, identification of extreme events, etc. These techniques may involve estimation of parameters such as the mean (a measure of location), variance (a measure of scale) and correlation/regression coefficients (measures of linear association); in addition, it is often desirable to estimate the statistical significance of the difference between estimates of the mean from two different samples as well as the significance of estimated measures of association. The validity of these estimates is based on underlying assumptions that sometimes are not met by real climate data. Two of these assumptions are addressed here: normality and homogeneity (and as a special case statistical stationarity); in particular, contamination from a relatively few ‘outlying values’ may greatly distort the estimates. Sometimes these common techniques are used in order to identify outliers; ironically they may fail because of the presence of the outliers! Alternative techniques drawn from the fields of resistant, robust and non-parametric statistics are usually much less affected by the presence of ‘outliers’ and other forms of non-normality. Some of the theoretical basis for the alternative techniques is presented as motivation for their use and to provide quantitative measures for their performance as compared with the traditional techniques that they may replace. Although this work is by no means exhaustive, typically a couple of suitable alternatives are presented for each of the common statistical quantities/tests mentioned above. All of the technical details needed to apply these techniques are presented in an extensive appendix. With regard to the issue of homogeneity of the climate record, a powerful non-parametric technique is introduced for the objective identification of ‘change-points’ (discontinuities) in the mean. These may arise either naturally (abrupt climate change) or as the result of errors or changes in instruments, recording practices, data transmission, processing, etc. The change-point test is able to identify multiple discontinuities and requires no ‘metadata’ or comparison with neighbouring stations; these are important considerations because instrumental changes are not always documented and, particularly with regard to radiosonde observations, suitable neighbouring stations for ‘buddy checks’ may not exist. However, when such auxiliary information is available it may be used as independent confirmation of the artificial nature of the discontinuities. The application and practical advantages of these alternative techniques are demonstrated using primarily actual radiosonde station data and in a few cases using some simulated (artificial) data as well. The ease with which suitable examples were obtained from the radiosonde archive begs for serious consideration of these techniques in the analysis of climate data.