Using first differences to reduce inhomogeneity in radiosonde temperature datasets

The utility of a "first difference'' method for producing temporally homogeneous large-scale mean time series is assessed. Starting with monthly averages, the method involves dropping data around the time of suspected discontinuities and then calculating differences in temperature from one year to the next, resulting in a time series of year-to-year differences for each month at each station. These first difference time series are then combined to form large-scale means, and mean temperature time series are constructed from the first difference series. When applied to radiosonde temperature data, the method introduces random errors that decrease with the number of station time series used to create the large-scale time series and increase with the number of temporal gaps in the station time series. Root-mean-square errors for annual means of datasets produced with this method using over 500 stations are estimated at no more than 0.03 K, with errors in trends less than 0.02 K decade(-1) for 1960-97 at 500 mb. For a 50-station dataset, errors in trends in annual global means introduced by the first differencing procedure may be as large as 0.06 K decade(-1) (for six breaks per series), which is greater than the standard error of the trend. Although the first difference method offers significant resource and labor advantages over methods that attempt to adjust the data, it introduces an error in large-scale mean time series that may be unacceptable in some cases.