The radiosonde data used in this study were downloaded from CDAAC (https://rda.ucar.edu/datasets/ds351.0/). The data include the temperature, pressure, and moisture profiles generated from the original radiosonde data in the NCAR data archive (http://rda.ucar.edu/datasets/ds351.0), which provides global radiosonde data with the detailed instrument type.

There are more than 1100 radiosonde stations globally. Figure 1 depicts the geophysical locations for all RAOB data from June 2006 to April 2014. These include Vaisala RS80, RS90, RS92, AVK-MRZ (and other Russian sondes), VIZ-B2, Sippican MARK II A, Shanghai (from China), and Meisei (Japan). Table 1 summarizes the availability for different instrument types. In total, 17 different types of radiosonde systems were used. The solar absorptivity (α) and sensor infrared emissivity (ε) for the corresponding thermocap and thermistor for different instrument types are also summarized in Table 1. Most of the radiosonde data are collected twice per day.

Because the Vaisala RS80 sensor was never changed and should be the same for all RS80 models and the software uses the same radiation correction table that should not show any differences, we do not further separate Vaisala RS80 sensors (i.e., ID = 37, 52, 61, and 67). For the same reason, all RS92 sensors (ID = 79, 80, 81) are summarized together and all Russian sensors (ID = 27, 75, 88, 89, 58) are summarized as AVK sonde (see Table 2 and Sect. 3.1).

The reprocessed COSMIC (Version 2013.3520) and Metop-A/GRAS (Version 2016.0120) dry temperature profiles downloaded from UCAR CDAAC (http://cdaac-www.cosmic.ucar.edu/cdaac/products.html) are used in this study. With six GPS receivers on board six LEO satellites, COSMIC produced about 1000 to 2500 RO profiles per day for the launch in April 2006 through 2014 (the number has been declining since 2014 as the satellites have aged beyond their design lifetime of 5 years). With one receiver, Metop-A/GRAS produced about 600 RO profiles per day. The detailed inversion procedures of COSMIC Version 2013.3520 and Metop-A Version 2016.0120 are summarized at http://cdaac-www.cosmic.ucar.edu/cdaac/doc/documents/Sokolovskiy_newroam.pdf. The general description of CDAAC inversion procedures is described in Kuo et al. (2004) and Ho et al. (2009a, 2012). In a neutral atmosphere, the refractivity (N) is related to pressure (P in hPa), temperature (T in K), and the water vapor pressure (e in hPa) according to Smith and Weintraub (1953): N=77.6PT+3.73×105eT2. Because moisture in the upper troposphere and stratosphere is negligible, the dry temperature is nearly equal to the actual temperature (Ware et al., 1996). In this study, we use RO dry temperature from 200 to 20 hPa to quantify the temperature biases for different sensor types.

The RO atmPrf data from COSMIC and Metop-A/GRAS were first interpolated to the mandatory pressure level of the radiosondes (i.e., 200, 150, 100, 50, and 20 hPa). To account for the possible temporal and spatial mismatches between RO data and RAOBs, the RO data within 2 h and 300 km of the radiosonde data were collected for different RAOB instrument types. These matching criteria are similar to the criteria used by He et al. (2009). However, in contrast to He et al. (2009), positions of RO measurements at the corresponding heights are used in the RAOB–RO ensembles. We compute temperature differences between RO atmPrf and the corresponding RAOB pairs in the same pressure level i using the equation ΔTi,j=1n×∑s=1s=nTRAOBi,j,s-TRO(i,j,s)}, where j is the index for 18 instrument type listed in Table 1, and s is the index for all the matched pairs for each of 17 instrument types.

In addition, we compare the monthly mean temperature biases ΔTTime for the matched pairs at different geographical regions from ΔTTimel,m,k=TRAOBl,m,k-TRO(l,m,k), where l, m, and k are the indices of the month bin for each vertical grid, zone, and month for the whole time series (k=1 to 95), respectively, from June 2006 to April 2014. The geographical zones (m) are from USA (m=1), Australia (m=2), Germany (m=3), Canada (m=4), United Kingdom (m=5), Brazil (m=6), Russia (m = 7), China (m = 8), and Japan (m = 9). The standard deviation of the time series is also computed to indicate the variability of ΔTTime. In this study, daytime data are from SZA from 0 to 90∘ and nighttime data are from SZA from 90 to 180∘. The SZA is computed from the synoptic launch time and location of sonde station because the time and location of the sonde at different heights are not available.

In total, we have more than 600 000 RAOB–RO pairs. Using Eq. (2), we compute the temperature biases of radiosonde measurements for each individual sensor type. The mean temperature bias for ensembles of the RAOB–RO pairs from June 2006 to April 2014 for the layer between 200 and 20 hPa for different RAOB sensor types is summarized in Table 2. The standard deviations for each radiosonde type are also shown. The radiosonde temperature biases vary for different sensor types. All biases are less than 0.25 K except for AVK and VIZ-B2, which reach 0.66 and 0.71 K, respectively, during the day.

The solar radiation effect on sensors is the dominant error source of RAOB temperature biases (Luers et al., 1998; He et al., 2009). We assume that all operational data have a radiation correction already applied. The global temperature biases relative to the co-located RO temperature at 50 hPa for various radiosonde sensor types for daytime and nighttime are shown in Fig. 2. Only those stations containing more than 50 RAOB–RO pairs are plotted. Figure 2a shows biases for different sensor types, which vary with geographical region. Most of the sensor types contain positive temperature biases ranging from 0.1 to 0.6 K during the daytime. This bias during daytime may be a result of the residual error of the systematic radiation bias correction. Although we only include stations containing more than 50 RAOB–RO pairs, some level of heterogeneity (i.e., Fig. 2a over Brazil) may be due to low sample sizes. For example, stations with temperature biases larger than 0.5 K in eastern Brazil contain only about 60 RAOB–RO pairs. The cause of the heterogeneity in temperature bias between North and South China is not certain at this point.

The mean nighttime biases are very different from those in the daytime for the same sensors. Figure 2b shows that most of the sensor types show a cold bias at night except for Vaisala in South America, Australia, and Europe. The mean biases at night for the two sonde types with the largest warm bias at daytime (AVK and VIZ-B2) are equal to -0.06 and -0.42 K, respectively (Table 2). The scatter of ΔT is similar for all sonde types during the day and night with standard deviations between 1.50 and 1.71 K (Table 2).

The global mean ΔT for the Vaisala RS92 of 0.16 K during the comparison period is slightly larger than the temperature comparison between Vaisala RS92 and COSMIC in 2007 (Ho et al., 2010b) (∼ 0.01 K) and in He et al. (2009) (∼ 0.04 K from ∼ 200 to 50 hPa). This could be in part because more RS92–RO pairs from lower SZA regions (for example, from the Southern Hemisphere and near-tropics; see Sect. 3.2) are included after 2007 (see Sect. 4).

More than 50 % of RAOB data are from Vaisala sondes, from a number of different countries. In total, 267 597 RS92 (ID = 79, 80, 81) ensemble pairs are distributed in all latitudinal zones during the daytime. To quantify a possible residual radiation correction error for Vaisala RS92 measurements in the lower stratosphere, which may vary with SZA, we compare the mean temperature differences from 200 to 20 hPa for daytime and nighttime over different regions in Figs. 3 and 4, respectively.

Figure 3 indicates that RS92 measurements in different regions have a similar quality in terms of mean differences from RO with a small warm bias above 100 hPa, as well as similar standard deviations relative to the mean biases of approximately 1.5 K. Because some stations in the United States are only interested in the tropospheric profiles and use smaller balloons, fewer RS92–RO samples are available above 70 hPa compared to those in other countries.

Figure 4 depicts the mean RS92–RO temperature differences from 200 to 20 hPa for nighttime. The nighttime RS92 data over different regions show similar standard deviations of about 1.5 K compared to those at daytime. In most of the regions, the mean nighttime temperature biases are similar to those in the daytime results, with small (0.1–0.2 K) warm biases above 100 hPa. These residual nighttime warm biases are not seen in the RAOB–RO ensemble pairs for Sippican MARK, VIZ-B2, AVK, and Shanghai sondes (see Sect. 3.3). This 0.1–0.2 K warm bias for RS92 at night could be due to calibration of the RS92 temperature sensor (see Dirksen et al., 2014).

Because the quality of RO temperature is not affected by sunlight, the small but obvious geographic-dependent biases are most likely due to the residual radiation correction for RS92 and when and how different countries apply the radiation correction (see Sect. 4.1).

To consider a possible SZA dependence of the temperature bias due to residual radiation errors for Vaisala RS92, we bin the computed temperature differences in 5∘ bins at each of the RAOB mandatory pressure levels above 200 hPa using all the RAOB–RO ensembles. Figure 5 depicts the temperature biases at 50 hPa as function of SZA in six regions. Only those bins that contain more than 50 RAOB–RO pairs are included. Zero SZA is at noon and 90∘ SZA corresponds to sunrise or sunset. Figure 5 shows that the daily mean difference varies from 0.09 K (Canada) to 0.31 K (Brazil), with a slightly larger warm bias for low SZA (near noon) than that at higher SZA (late afternoon and in the night).

Unlike Vaisala sondes, which are distributed in almost all latitudinal zones, other sonde types are distributed mainly in the northern midlatitudes. Figure 6 depicts the mean temperature differences from 200 to 20 hPa in the daytime for Sippican, VIZ-B2, AVK, and Shanghai. The biases for VIZ-B2 and AVK-MRZ are positive everywhere above 200 hPa, with means of about 0.7 K. The biases are smaller for Sippican and Shanghai. These mean biases are similar to those from He et al. (2009). The small differences between these and He et al. (2009) results are likely due to the sampling differences between He et al. (2009) (August 2006 to February 2007, or 7 months) and this study (95 months).

Figure 7 depicts the mean temperature differences from 200 to 20 hPa in the nighttime also for Sippican, VIZ-B2, AVK-MRZ, and Shanghai. The nighttime biases are generally less than 0.1 K except from VIZ-B2 above 100 hPA where they exceed 0.5 K. The small positive values for VIZ-B2 and AVK-MRZ, which were present in the daytime (Fig. 6), are not present during the night (Fig. 7)

We also bin the temperature differences for these four sonde types in 5∘ SZA bins for each mandatory pressure levels above 200 hPa using all the RAOB–RO pairs from June 2006 to April 2014. Only those bins contain more than 50 RAOB–RO pairs are included. Figure 8 depicts the differences at 50 hPa as a function of SZA for Sippican MARK, VIZ-B2, AVK-MRZ, and Shanghai.

The VIZ-B2 sonde has a large warm bias (as high as 2.0 K) during daytime and a cold bias (as low as -1.0 K) at night. AVK has a bias from about 0.7 to 1.1 K in the daytime where its nighttime biases are close to zero. The mean biases for the Sippican and Shanghai sondes show less diurnal variation and are 0.08 and -0.17 K, respectively.

The Vaisala RS92 radiosonde was introduced in 2003 and is scheduled to be replaced by the Vaisala RS41 in 2017. Vaisala included a reinforcement of the RS92 sensor in 2007, which affected the radiation error. To account for this sensor update, the radiation correction tables were updated in 2011 (RSN2010, software version 3.64), which is used to replace the original radiation correction table. Between 200 and 20 hPa, the correction in RSN2010 is about 0.1 K larger than in RSN2005 (see http://www.vaisala.com/en/products/soundingsystemsandradiosondes/soundingdatacontinuity/RS92DataContinuity/Pages/revisedsolarradiationcorrectiontableRSN2010.aspx). It is likely that each country updated the correction table for their entire network. However, when exactly each country implemented these updated tables is unknown.

To identify possible RS92 temperature biases due to changes of the radiation correction table (i.e., RSN2010), we compare the mean ΔT from January 2007 to December 2010 to those from January 2011 to April 2014 over the United States, Australia, Germany, Canada, United Kingdom, and Brazil (Fig. 9a–f). There is no consistent pattern of differences in these two periods over the six regions, with mean differences ranging from -0.122 K (Australia) to 0.047 K (United States). The small differences in profile shapes and magnitudes are an indication of the magnitude of the uncertainty in RS92 temperatures due to differences in implementing the radiation correction tables.

The Deutscher Wetterdienst (DWD), Germany's Meteorological Service, implemented the updated radiation correction for the Vaisala RS92 in the spring of 2015 rather than in 2011 to avoid inconsistencies with corrections already implemented in their data assimilation system. This may in part explain the greater consistency of ΔTover Germany for these two time periods than over other countries.  This also indicates the importance of establishing traceability through careful documentation and metadata tracking, which is especially important for using radiosonde data in climate studies. The relatively small temperature difference between these two periods over the United States is most likely a statistical artifact due to the very small number of coincidences in this period.

In this section we look at time series and trends in the de-seasonalized radiosonde–RO temperature differences from 2006 to 2014 in order to determine the long-term stability of these differences. Ideally, if both radiosondes and RO were free of biases, the time series would be stable and show small differences near zero with small standard deviations and no trends. We choose 50 hPa for showing these time series because the biases tend to be larger at this level than at lower levels. We also computed time series for 150 hPa, but except for lower biases the results were similar to those at 50 hPa (not shown).

Figure 10 shows daytime and nighttime time series of monthly mean temperature biases at 50 hPa for Vaisala RS92 for the United States, Australia, Germany, Canada, United Kingdom, and Brazil. Table 3 summarized the mean and standard deviation of the monthly mean temperature differences for RS92 and RO at 50 hPa. Figure 10 indicates that there is little variation over time in the monthly mean temperature differences at 50 hPa in all six regions, with little difference between day and night values. The magnitudes of the mean biases range from -0.01 K for Canada to over 0.2 K in Australia, Germany, and Brazil. The standard deviations range from a low of 0.18 K (Australia, day) to a high of 0.46 K (United States, night). The small (less than 0.5 K) standard deviation for RS92 over daytime and nighttime over these six regions demonstrates the long-term stability of RS92 data.

Figure 11 shows the daytime and nighttime time series of monthly mean temperature biases for Sippican MARK IIA, VIZ-B2, AVK-MRZ, and Shanghai in northern hemispheric midlatitude (60–20∘ N) at 50 hPa and the results are summarized in Table 4. All daytime biases are below 0.25 K in magnitude, except for Russia (0.8 K) and VIS-B2 (0.87 K). The magnitudes of the mean nighttime biases are all less than 0.25 K except for VIS-B2, which is -0.56 K. The daytime biases for Russia and VIS-B2 contain obvious inter-seasonal variation.

Figure 12 shows daytime and nighttime time series of monthly mean de-seasonalized temperature biases at 50 hPa for Vaisala RS92 for the United States, Australia, Germany, Canada, United Kingdom, and Brazil. Table 3 summarizes the trends of the de-seasonalized temperature differences, and shows the de-seasonalized trends in RO temperatures for comparison. The root mean square (RMS) of the de-seasonalized time series (RMS of difference) in Table 3 indicates the trend uncertainty of the time series.

The de-seasonalized temperature differences are computed from ΔTDeseasonl,m,k=TRAOBl,m,k-TTime‾(l,m,k′), where l, m, and k are the indices of the month bin for each layer, zone, and month for the whole time series (k=1 to 95), respectively, and k′ is the index of the month bin of the year (k=1 to 12). TTime‾ (l,m,k′) is the mean RO temperature co-located for different sensor types for each level (l), zone (m), and averaged over all available years for a particular month (k′). Note that because the period of available measurements for each of the sensor types is different, the months used to compute TTime¯ (l,m,k′) may vary for different sensor types.

Figure 12 indicates the de-seasonalized trends in daytime temperature differences for RS92 are within ±0.26 (K/5 yr). The greatest magnitudes of the trends are 0.23 and 0.26 K/5 yr over Canada and United Kingdom, respectively. These larger de-seasonalized trends may be a result of incomplete daytime radiation corrections applied in these regions in 2007–2010 and 2011–2014 (Fig. 9). The largest nighttime de-seasonalized trend is in the United States (-0.21 K/5 yr).

The de-seasonalized trends in RO temperatures are generally larger than those for the radiosonde–RO differences (Table 3). A maximum de-seasonalized trend of 1.14 K/5 yr is found for nighttime temperatures over the United Kingdom. A minimum de-seasonalized trend of -0.69 K/5 yr is found for daytime temperatures over Canada. Trends with magnitude greater than 0.5 K/5 yr are found over the United States, Germany, Canada, and the United Kingdom. The fact that these de-seasonalized trends in RO are significantly greater than the de-seasonalized trends in the differences suggests that they represent a physical signal in these regions. However, the time series is too short to represent a long-term climate signal; instead these likely represent real but short-term trends associated with natural variability. A long-term (de-seasonalized) trend in temperature at this level associated with global warming (stratospheric cooling) might be approximately -0.1 to -0.2 K decade-1 or -0.05 to -0.1 K/5 yr (Randel et al., 2016). Trends of the RS-92 minus RO differences reported in this paper for the Vaisala RS92 radiosonde at 50 hPa (Table 3) range from -0.21 K/5 yr (US, night) to 0.26 K/5 yr (United Kingdom, day), which are comparable to those reported by Randel et al. (2016).

We compare the global trend of radiosonde–RO temperature differences for the Vaisala and other radiosondes at 50 hPa in Table 4. The Vaisala RS92 biases are 0.22 (day) and 0.12 K (night). The trends in global de-seasonalized temperature differences for Vaisala RS92 for daytime and nighttime are equal to 0.07 and -0.09 K/5 yr, respectively. The 95 % confidence intervals for slopes are shown in the parentheses in Table 4. This indicates that although there might be a small residual radiation error for RS92, the trend in RS92 and RO temperature differences from June 2006 to April 2014 is within ±0.09 K/5 yr globally. These values are just above the 1σ calibration uncertainty estimated by Dirksen et al. (2014). This means that probably the stability of the calibration alone could explain most of this very small trend. It is also consistent with the change in radiation correction.

Figure 13 depicts the de-seasonalized temperature differences for Sippican MARK IIA, VIZ-B2, AVK-MRZ, and Shanghai in northern hemispheric midlatitude (60–20∘ N) at 50 hPa and the results are summarized in Table 4. The 95 % confidence intervals for slopes are shown in the parentheses in Table 4. The de-seasonalized trend of the daytime differences varies from -0.14 (Russia) to 0.47 K/5 yr (VIZ-B2). The magnitudes of the daytime trend of difference are less than 0.2 K/5 yr for all sensor types except for VIZ-B2 and Sippican, both of which exceed 0.4 K/5 yr. These are much larger than those of the Vaisala RS92 (0.07 K/5 yr).

The corresponding nighttime de-seasonalized trends in the biases vary from -0.35 (VIZ-B2) to 0.24 K/5 yr (Sippican). Again, these are much larger than those of Vaisala RS92 (-0.09 K/5 yr). Thus the VIZ-B2 sensor stands out as having larger biases and trends than do the other sensors.