No abstract

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 fo...

26. We chose these values of the target factors to produce our final results because we have concluded that they are the most likely to be free of errors. They are calculated from oceanic observations to reduce errors from uncorrected diurnal variations, and we use unweighted MSU channel 2 data (T2 in SOM) to avoid additional noise due to the differencing procedure used to calculate TLT. The values of the intersatellite offsets needed to be recalculated to remove obvious intersatellite differences. In the supporting online material, we discuss the impact of using different data subsets to determine the target factors. This information is used to help determine the structural uncertainty. 27. We obtain this estimate of the tropical TLT trend when we recalculate the intersatellite offsets to optimize them for tropical data. If this reoptimization is not performed, as it is not in producing maps such as those shown in Fig. 3, we obtain a smaller trend value of 0. The month-to-month variability of tropical temperatures is larger in the troposphere than at Earth's surface. This amplification behavior is similar in a range of observations and climate model simulations and is consistent with basic theory. On multidecadal time scales, tropospheric amplification of surface warming is a robust feature of model simulations, but it occurs in only one observational data set. Other observations show weak, or even negative, amplification. These results suggest either that different physical mechanisms control amplification processes on monthly and decadal time scales, and models fail to capture such behavior; or (more plausibly) that residual errors in several observational data sets used here affect their representation of long-term trends.Tropospheric warming is a robust feature of climate model simulations that include historical increases in greenhouse gases (1-3). Maximum warming is predicted to occur in the middle and upper tropical troposphere. Atmospheric temperature measurements from radiosondes also show warming of the tropical troposphere since the early 1960s (4-7), consistent with model results (8). The observed tropical warming is partly due to a step-like change in the late 1970s (5, 6). Considerable attention has focused on the shorter record of satellite-based atmospheric temperature measurements (1979 to present). In both models and observations, the tropical surface warms over this period. Simulated surface warming is amplified in the tropical troposphere, corresponding to a decrease in lapse rate (2,3,9). In contrast, a number of radiosonde and satellite data sets suggest that the tropical troposphere has warmed less than the surface, or even cooled, which would correspond to an increase in lapse rate (4)(5)(6)(7)(8)(9)(10)(11)(12).This discrepancy may be an artifact of residual inhomogeneities in the observations (13)(14)(15)(16)(17)(18)(19). Creating homogeneous climate records requires the identification and removal of nonclimatic influences from data that were primarily collected for weather forecasting...