Corresponding author: C. O. Ao, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr., M/S 138-308, Pasadena, CA 91109, USA. (firstname.lastname@example.org)
 GPS radio occultation data collected over the period 2002–2011 were analyzed to examine the possible expansion of the tropical belt due to climate change. By the use of high vertical-resolution temperature profiles, monthly averages of the lapse rate tropopause were obtained and used to derive a decade-long time series of the tropical edge latitude (TEL) in each hemisphere and its linear trends. Two different TEL criteria were examined. Our analysis shows that a statistically significant widening trend of ≈1° latitude/decade was found in the Northern Hemisphere (NH) by either criterion. This contrasts strongly with the Southern Hemisphere (SH), where no statistically significant trends were found. Comparison with ECMWF reanalysis shows good agreement, but the agreement is worse over SH. Substantial differences in seasonal trends were found between NH and SH, with the latter showing strong widening in the austral summer countered by contraction over the austral winter and spring.
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 The tropics is characterized by the Hadley circulation where moist air ascends near the equator and dry air descends in the subtropics. Thus, the latitudes corresponding to the descending branch of the Hadley circulation in each hemisphere can be viewed as the boundaries of the tropics. Since the Hadley circulation is not directly observable from current measurements, other physical indicators that are known to exhibit strong changes in the tropical and extratropical regions have been used to define the tropical boundaries. This includes the tropopause height, jet stream locations, ozone, precipitation/evaporation, and outgoing longwave radiation. Recent observation and modeling studies looking into such metrics have shown some evidence that the width of the tropics has been expanding in the past few decades as a result of climate change [Seidel et al., 2008; Davis and Rosenlof, 2012, and references therein]. Even a small widening of the tropics would have significant societal implications since the poleward shift of the jet streams and subtropical dry zones directly affect weather and precipitation patterns. However, the reported widening rates (0.25°–3.0° latitude per decade) and their statistical significance vary substantially depending on the metrics used to define the tropical boundaries as well as the data used to obtain them [Davis and Rosenlof, 2012, hereafter DR12]. While a careful reexamination of the various tropical edge diagnostics by DR12 reduces the higher range of widening rates to about 1.5°, the spread is still uncomfortably large. Furthermore, many of the existing studies rely on products from the reanalyses, which have unknown time-varying biases. Accurate global measurements are sorely needed to help reduce the uncertainty in the estimates of tropical widening.
 One approach toward defining the width of the tropical belt is to use the latitudinal distribution of the thermal or lapse rate tropopause (LRT) height. This definition exploits the fact that the LRT height in the tropics has large values exceeding 15 km, while in the extratropics, the LRT height is closer to 10–12 km. This approach was first investigated by Seidel and Randel  using radiosonde data and reanalyses. Birner  then presented a detailed sensitivity analysis of tropopause-based approach and suggested more refined and robust algorithms for defining the tropical width. Similar tropopause-based algorithms were presented by DR12, which differed from Birner  in that the mean LRT heights were used instead of their frequency of occurrence. Both Birner  and DR12 propose subjective and objective definitions for computing the tropical boundaries. In subjective definitions, a height value that represents departure from the tropics must be specified. In objective definitions, the criteria are derived based on the latitudinal gradient of the LRT height or distribution. The results from Birner  and DR12 show that the tropical widening rate is sensitive to the definition used and that the different reanalyses gave inconsistent answers.
 Global Positioning System radio occultations (GPSROs) provide arguably the best remote sensing measurements of the thermal structure of the tropopause region and have been used to study the climatology, variability, and trend of the tropopause [Son et al., 2011, and references therein]. Among the most salient features of GPSRO are their accuracy of 0.2–0.5 K in measuring temperature in the upper troposphere/lower stratosphere region, vertical resolution of 200 m, self-calibrating nature, and near-uniform global coverage [Kursinski et al., 1997; Ho et al., 2012]. These features make GPSRO especially suitable to examine the possible widening of the tropical belt through the use of tropopause height.
 In contrast to traditional satellite sounders, GPSRO has a relatively recent history. Continuous coverage has been available only since 2001 with the launch of the German CHAMP (Challenging Minisatellite Payload) mission which collected about 150 soundings per day from 2001–2008 [Wickert et al., 2001]. CHAMP was then followed by the Taiwan/US FORMOSAT-3/COSMIC (Constellation Observing System for Meteorology, Ionosphere, and Climate) mission (2006–present), a constellation of six satellites, which collects about 1500 profiles per day [Anthes et al., 2008]. In this paper, we utilize 10 years of GPSRO temperature profiles collected from these two missions spanning the period January 2002–December 2011 to study the annual and seasonal trends of the tropical boundaries as defined by the LRT height. We will adopt both the subjective and objective criteria introduced by DR12. For comparison, we will also apply similar processing on temperature profiles from the ECMWF (European Centre for Medium-Range Weather Forecasts) Re-Analysis interim (ERA-int). In addition, we will discuss how the uncertainty in the measurements from sampling and vertical resolution affect the trend estimations.
 The rest of the paper is structured as follows: Section 2 describes the data and the methodology. In section 3, a time series of the tropical edge in each hemisphere is derived and analyzed by the approaches listed above. A conclusion is offered in section 4.
2 Data and Methodology
 The tropical edge latitude (TEL) will be estimated for each hemisphere separately using the monthly zonal average of LRT height ZLRT. Specifically, we will compute the TEL using two of the four LRT-based definitions introduced in DR12. The first is a subjective criterion in which the TEL is defined as the latitude at which the LRT height falls to 1.5 km below the tropical average (15°S–15°N) LRT height. The use of such a “relative-height” threshold criterion is preferable to using an absolute height criterion since it removes the effect of globally uniform changes in LRT height. The second is an “objective” criterion in which the TEL corresponds to the mean area-weighted latitude of the meridional gradient of the LRT height, i.e.,
where φ denotes latitude. This “mean” tropopause gradient definition is designed to provide a robust measure of the latitude where the LRT height changes most quickly from the tropics to the extratropics without the need to impose a subjective height threshold.
 In this study, we will be using the temperature profiles collected from CHAMP for the period of the January 2002–December 2006 and COSMIC for January 2007–December 2011. The temperature profiles were retrieved at Jet Propulsion Laboratory (JPL) and are accessible through http://genesis.jpl.nasa.gov [Hajj et al., 2002; Ho et al., 2012]. The LRT for each occultation is derived according to the World Meteorological Organization definition, which is the lowest level at which the temperature lapse rate decreases to 2 K/km or less, with the additional condition that the average lapse rate within this level and all higher levels within 2 km does not exceed 2 K/km. In addition, in order to eliminate outliers due to noisy temperature profiles, we limit the search for the tropopause to altitudes between 8–20 km. Once a tropopause height is derived, each occultation can be characterized by time, latitude, longitude, and ZLRT. Occultations are then grouped by monthly and 5° latitudinal bins, and the LRT heights are averaged over each bin. There are ≈100 (1000) observations per monthly bin for CHAMP (COSMIC). The average LRT height is assigned to the center latitude of each bin and linearly interpolated between bins to obtain a function of ZLRT versus latitude.
 For comparison, LRT heights are computed from ERA-int from 2002–2011 (0.75°×0.75° horizontal resolution and 4 times daily). To assess the sampling uncertainty from GPSRO, we also subsample ERA-int at the GPSRO times and locations and compute the monthly zonal averages based on the subsampled data. For simplicity, we will henceforth refer the full ERA-int simply as “ERA” and the subsampled ERA-int as “ERAs”. We note that ERA does not provide a completely independent data set from GPSRO since GPSRO bending angles were assimilated into ERA beginning in May 2001 [Poli et al., 2010; Dee et al., 2011].
 Since CHAMP has 10 times less profiles than COSMIC, it is important to consider how the limited sampling from GPSRO, especially during the CHAMP era, will affect the trend estimates. In addition, the computation of ZLRT is known to be sensitive to the vertical resolution of the temperature profile [Reichler et al., 2003; Seidel and Randel, 2006]. The temperature profiles retrieved at JPL have a vertical resolution of 200 m. However, models and reanalyses generally have much lower vertical resolution. In order to achieve a more consistent comparison between the different data sets, the radio occultation temperature profiles have been smoothed using cubic polynomial with a 1 km moving window. We note, however, that ZLRTcalculated with 200 m vertical resolution is systematically smaller than those calculated with 1 km vertical resolution by a mean (median) value of about 300 (100) m over 60°S–60°N. The sensitivity of the tropical widening rates on vertical resolution and sampling will be addressed in section 3.
3 Results and Discussions
 In this section, we present results on the decade-long variabilities of the TEL in each hemisphere by applying the subjective and objective definitions based on ZLRT as described in section 2. We will examine annual and seasonal trends and compare the results between GPSRO and ERA. In addition, we will discuss how sampling and vertical resolution affect trend estimations.
3.1 Subjective Criterion
 According to this criterion, the TEL in each hemisphere is defined to be the latitude where the tropopause height falls to 1.5 km below the tropical average (15°S–15°N) tropopause height. Figures 1a and 1b show the TEL for each month for the period January 2002–December 2011 derived from GPSRO (blue curve), ERAs (green curve), and ERA (red curve) for the Northern Hemisphere (NH) and Southern Hemisphere (SH), respectively. A poleward bias is evident in TEL derived from ERA relative to that of the GPSRO. The mean differences are 1.30°(0.83°) in NH and 1.39°(0.90°) in SH between ERA (ERAs) and GPSRO.
 Figures 1c and 1d show the deseasonalized TEL monthly anomalies after subtracting seasonal cycles derived independently for GPSRO, ERAs, and ERA (obtained by averaging the TEL for each month over the 10 year span). Linear regression on the GPSRO TEL anomalies shows a poleward trend of 1.08°±0.63°/decade in NH, where the “error bars” represent the 95% confidence interval (2σ). The confidence interval is calculated by taking into account the correlation in the time series based on the lag-1 autocorrelation of the regression residuals [Santer et al., 2000]. A smaller expanding trend of 0.66°±0.63°/decade is found in ERA, while ERAs yields a trend of 0.94°±0.65°/decade, which is very consistent with the GPSRO result. In SH, GPSRO differs more from ERA and ERAs. GPSRO shows a poleward trend of 0.54°±0.88°/decade, larger than both the ERA and ERAs trends (at −0.17°±1.01°/decade and 0.14°±0.93°/decade, respectively). Unlike the NH, none of the SH trends are statistically significant.
3.2 Objective Criterion
 Using equation (1) for the TEL, we arrive at Figure 2. The TEL from this criterion is more poleward than from the subjective criterion by about 2° in NH and 4° in SH, consistent with DR12. Relative to GPSRO, a poleward bias can again be seen from ERA, but it is smaller than the subjective criterion case: 0.67° (0.39°) for the ERA (ERAs) in NH and 0.76° (0.53°) in SH.
 Linear regression of the monthly anomalies again shows a clear poleward trend in NH, with 0.74°±0.46°/decade for GPSRO and 0.50°±0.55°/decade (0.64°±0.52°/decade) for the ERA (ERAs). In SH, GPSRO shows essentially no trend at 0.05°±0.70°/decade, while ERA-interim yields an equatorward trends (tropical contraction) of −0.52°±0.73°/decade for the full data set and −0.36°±0.75° for the subsampled data set, although none of these trends are statistically significant.
 The tropical widening trends from both criteria are summarized in Table 1. These results demonstrate that the tropical widening rate is sensitive to the criterion used to define the tropical edge, consistent with what was found in previous studies [Birner, 2010; DR12]. Overall, the objective criterion considered here yields smaller poleward expansion rates relative to the subjective criterion. Furthermore, the difference between the two criteria is larger in the SH than in the NH. This difference could be a consequence of the averaging nature of the objective criterion, which represents a more smeared out version of the tropical edges. When the entire width of the tropics (obtained by adding the NH TEL and SH TEL) is considered, the difference between the two criteria is further magnified, with the subjective criterion yields a trend of 1.95°±1.18°/decade while the objective criterion yields a trend of 0.76°±0.98°.
Table 1. Tropical Widening Rates From GPSRO, ERAs, and ERA and Their Differences (Degree Latitude per Decade)a
Error bars are 95% confidence intervals, with statistical significant trends shown in boldface.
 To better quantify the difference between GPSRO and ERA/ERAs, we construct the time series for the difference in monthly anomalies between each pair of the data sets. GPSRO-ERA yields the actual difference between the GPSRO and ERA data sets, while GPSRO-ERAs removes the effects from sampling, and ERAs-ERA provides a direct measure of the sampling difference. The inferred linear trends for all pairs are shown in Table 1. Overall, GPSRO yields more poleward expansion than ERA. The differences between GPSRO and ERA, which vary from ≈0.3°–0.7° per decade, are statistically significant across hemispheres and criteria except when the objective criterion is used for NH. When sampling is taken into account (GPSRO-ERAs), the differences between GPSRO and ERA are reduced, especially when the subjective criterion is used. Indeed, the ERAs-ERA trends show that the objective criterion is much less sensitive to sampling than the subjective criterion. However, significant trends in GPSRO-ERAs persist in SH under both criteria (0.4°/decade).
3.3 Seasonal Trends
 Besides the annual trends, we have also examined the trends in separate seasons and hemispheres. Figure 3 shows the estimated linear trends from GPSRO, ERAs, and ERA using both TEL criteria. The error bars represent 95% confidence intervals; however, they were computed here without adjusting for data correlation due to the smaller number of data points. Despite the larger uncertainties, the results reveal some striking seasonal differences between NH and SH trends. In NH, the tropics can be seen to be widening throughout the year, with the largest widening rate occurring in the boreal summer months (June-July-August (JJA)). In SH, the widening rate is especially large over the austral summer months (December-January-February (DJF)); however, the widening during DJF is largely countered by the contraction that occurs during JJA and September-October-November (SON). Consistent with annual trend results shown in Figures 1 and 2, the difference between the two TEL criteria is larger over the SH, especially over DJF and SON, where the widening and contraction rates are respectively largest.
3.4 Sensitivity to Vertical Resolution and Sampling
 As discussed in section 2, the derivation of monthly averaged ZLRT and consequently TEL depend on the vertical resolution of the temperature profiles. To quantify the trend sensitivity on vertical resolution, we repeat our analysis using the nonsmoothed temperature profiles with 200 m vertical resolution instead of 1 km considered thus far. Table 2 shows that the 200 m vertical resolution results yield slightly lower trends, but the differences between the vertical resolution considered are relatively small at ≈0.05° or less.
Table 2. Tropical Widening Rates From GPSRO for Different Vertical Resolution and Sampling Density (Degree Latitude per Decade)a
1 km, all cosmic
200 m, all cosmic
1 km, subset of cosmic
Error bars are 95% confidence intervals, with statistical significant trends shown in boldface.
 Another key uncertainty to consider is sampling density, especially during the CHAMP era (prior to 2007). The difference between ERA and ERAs as shown above provides some assurance that the effect of sparse CHAMP sampling on the trend estimations should be relatively minor. Here we provide a different measure of the sampling uncertainty through intentional degradation of COSMIC coverage starting 2007 by randomly selecting 4000 profiles per month to approximate the CHAMP coverage. Table 2 shows that the widening rates are slightly higher when the reduced COSMIC data are used. The effect is much larger under the subjective criterion (≈0.15°) than the objective criterion (≈0.05°).
 Understanding how the atmospheric circulation changes as a result of anthropogenic climate change is a fundamental scientific question with significant societal impact. To make substantial progress, there is a strong need for accurate and stable global observations. With sub-kilometer vertical resolution and 0.2–0.5 K accuracy in temperature in the upper troposphere and lower stratosphere, GPSRO measurements can be used effectively in monitoring changes associated with the thermal tropopause. The tropopause height has been used to infer the tropical boundaries and to monitor the possible change of the tropical width due to global warming. Previous studies primarily utilized reanalyses to examine this problem and found that widening rates calculated from different reanalyses were quite different.
 In this paper, we present the first trend results that are based entirely on global tropopause observations for the period of 2002–2011. Applying two different criteria for defining the tropical edge latitudes, we find statistically significant tropical expansion trend in the NH under either criterion of about 1° latitude/decade, while the SH exhibits no significant trend at all. In addition, we find rather different seasonal trends between the two hemispheres. While NH TEL expands throughout the year, SH TEL shows strong expansion in the austral summer which is opposed by contraction during austral winter and spring. The contraction during September–November is especially large under the objective criterion. Comparison with ERA shows that there are generally good agreement between GPSRO and ERA; however, the agreement is clearly worse over SH. These results are quite different from the trends shown in DR12 based on different reanalyses from 1979–2009.
 The hemispheric differences are intriguing and deserve further studies. Modeling studies have suggested that large ozone loss in Antarctica contributed strongly to the expansion of the tropical belt in SH during the austral summer [Son et al., 2010; Polvani et al., 2011], while the NH tropical expansion might be driven primarily by an increase of black carbon and tropospheric ozone [Allen et al., 2012]. But what causes the SH tropical contraction seen in June–August and September–November? Given the short time series considered here, it is possible that interannual variabilities such as El Niño–Southern Oscillation could have significant impacts on seasonal trend estimations.
 Though qualitatively similar, the two criteria considered for defining the TEL yield different trends, with the subjective criterion giving larger widening rates. The objective criterion is found to be less sensitive to changes in vertical resolution and sampling. However, even for the subjective criterion, the estimated trends are relatively robust with respect to vertical resolution and sampling.
 Finally, we note that other metrics not based on tropopause heights have recently been developed for the tropical boundaries that can be estimated from GPSRO measurements. In particular, GPSRO temperature and height data from COSMIC was used in a recent study [Davis and Birner, 2013] to study and validate new tropical edge metrics based on bulk tropospheric stability and geostrophic wind. These metrics were shown to be better correlated with the subtropical jet cores than the Hadley cell edges. Clearly, different tropical edge diagnostics are sensitive to different tropical and extratropical processes, and a multidiagnostic approach is essential in delineating the different processes and how they impact the trends and variabilities of the tropical boundaries.
 The research described in this paper was carried out at the Jet Propulsion Laboratory (JPL), California Institute of Technology, under a contract with the National Aeronautics and Space Administration. We thank the reviewers for insightful comments which have helped to improve the manuscript.
 The Editor thanks two anonymous reviewers for assistance in evaluating this manuscript.