NOAA Logo National  Environmental Satellite, Data, and Information Service. National Climatic Data Center National Climatic Data Center, U.S. Department of Commerce
Radiosonde Atmospheric Temperature Products for Assessing Climate


First Differencing

For RATPAC-A, the first difference ("FD") procedure (Peterson et al. 1998) was used to update the Lanzante et al. (2003; hereafter LKS) data. As discussed in more detail in Free et al. (2004), this method is designed to reduce inhomogeneities in large-scale mean time series without making adjustments to the individual time series. The method involves taking the difference in temperature between one time step and the next (the "first difference"), then computing large-scale means of the FD series, and finally reconstructing large-scale temperature series from the FD series (see Appendix of Free et al. (2005) for details). By omitting portions of the station time series around the times of known changes in instruments or procedures, an attempt is made to eliminate the effect of inhomogeneities due to such changes. However, the method introduces a random error that increases with the number of time gaps in the data and with decreasing number of stations, so that results are limited to large-scale means. Although this method does not use neighbor stations as reference series in the usual sense, it does in effect rely on other stations in a region to supply information about temperature change at times of metadata events at an affected station, and so does not adjust individual stations independently.

The method was applied to IGRA monthly means starting in 1996. Before 1996, the RATPAC-A time series is the mean of the ("LIBCON") adjusted LKS station data, without use of FD. Note that the "LIBCON" subset, one of several available versions of the LKS adjusted data, was used since it is the version preferred by the LKS authors. Although the LKS dataset runs through 1997, IGRA data was substituted for 1996 and 1997 because the short record left after the adjustments makes LKS adjustments in 1996 and 1997 less reliable than those at earlier times. (The LKS approach requires several years of data both before and after a possible inhomogeneity to make the best adjustment.)

Starting in 1995, we deleted six months of data from the IGRA monthly means before and after each metadata event for any station having a relevant event documented by a report from the country in which the station was located. Some events were considered relevant only for certain stations and levels. For example, a change in reporting practices affecting temperatures below -90°C was considered relevant only for stations and levels where temperatures near that cutoff were reported. Data were also deleted at times in 1996 and 1997 where LKS had made adjustments or had deleted data due to homogeneity concerns. Despite recent efforts by NCDC to update the station histories, useful metadata after 1995 was available for just 38 of the 85 stations. Based on this metadata, cuts were made at a total of 29 stations. The series were then combined using the method described in more detail in the Appendix of Free et al. (2005).

Spatial Averaging

In an effort to obtain spatially unbiased large-scale means, we compensate for uneven longitudinal distribution of stations by creating regional means before averaging data into zonal bands. Each 30-degree zonal band was divided into three longitudinal regions of 120 degrees each: 30W to 90E, 90E to 150 W and 150 W to 30W. Hemispheric (0-90 degrees), tropical (30S-30N) and extratropical (30-90 degrees) means were calculated from these zonal means, areally weighted using the cosine of the latitude of the midpoint of the zone, and the global mean was the average of the hemispheric means. To facilitate comparison with other datasets, time series for the region from 20N to 20 S are also provided.

Endpoint Outlier Trimming

An endpoint outlier trimming procedure was used to reduce the random errors introduced by the FD procedure. As described in Peterson et al. (1998) and Free et al. (2004), this procedure removes data exceeding a prescribed multiple of the standard deviation of the original time series if the data fall at the end of a data segment (immediately before or after a gap). If a larger multiple is used as a cutoff, fewer data points are removed than with a smaller multiple.Results from the FD procedure are sensitive to the choice of this multiple, or trim factor (Free et al. 2005). For the reasons outlined in that paper, we chose a factor equal to one standard deviation from the mean.


In another effort to reduce random errors, before making cuts at the times of metadata events, data gaps of less than four months were filled using linear interpolation between months of data. This interpolation was used only at stations that were to be cut due to metadata events. The mean number of months of data added by interpolation to these 38 stations was about 6 per station.
top of page icon


Free M., D.J. Seidel, J.K. Angell, J. Lanzante, I. Durre and T.C. Peterson (2005) Radiosonde Atmospheric Temperature Products for Assessing Climate (RATPAC): A new dataset of large-area anomaly time series, J. Geophys. Res., 10.1029/2005JD006169.

Free, M., J.K. Angell, I. Durre, J. Lanzante, T.C. Peterson and D.J. Seidel(2004), Using first differences to reduce inhomogeneity in radiosonde temperature datasets, J. Climate, 21, 4171-4179.

Lanzante, J.R., S.A. Klein, and D.J. Seidel (2003), Temporal homogenization of monthly radiosonde temperature data. Part I: Methodology, J. Climate, 16, 224-240.

Peterson, T.C., T.R. Karl, P.F. Jamason, R. Knight, and D.R. Easterling (1998), First difference method: Maximizing station density for the calculation of long-term global temperature change, J. Geophys. Res., 103, 25,967-25,974.

top of page icon
Created by
Downloaded Friday, 24-Oct-2014 12:23:23 EDT
Last Updated Wednesday, 20-Aug-2008 12:11:36 EDT by
Please see the NCDC Contact Page if you have questions or comments.