Measurements of vertical eddy diffusivity across the tropopause using radio acoustic sounding system (RASS)



[1] A four day high temporal resolution MU radar RASS data set was obtained under light wind conditions in August 1995, enabling retrieval of virtual temperatures up to 20 km. This provided a unique opportunity to study the vertical eddy diffusivity K across the tropopause using RASS Brunt-Väisälä frequency N and radar spectral width. Co-located six hourly radiosondes enabled calculation of K using radiosonde N and radar spectral width. RASS K decreased across the WMO tropopause, from (0.39 ± 0.05) m2s−1 in the uppermost kilometre of the troposphere to (0.27 ± 0.03) m2s−1 in the lowermost kilometre of the stratosphere. The equivalent radiosonde K were (0.43 ± 0.06) m2s−1 and (0.31 ± 0.07) m2s−1 respectively. The WMO tropopause seems to provide a better definition than the cold-point tropopause in separating the stratosphere from the troposphere when considering the mixing of minor constituents.

1. Introduction

[2] Exchange of air and minor constituents between the troposphere and stratosphere occurs via a variety of processes and on different scales. Convection acts to enhance mixing in the Upper Troposphere and Lower Stratosphere (UTLS) region in both the tropics [Pfister et al., 1986; Sherwood and Dessler, 2001] and in the mid-latitudes [Dessler and Sherwood, 2004]. Turbulent mixing of air within tropopause folds also acts to move air between the two regions in the mid-latitudes [Shapiro, 1980]. Transport and horizontal mixing between the upper troposphere and the lowermost stratosphere (below 380 K potential temperature) occurs at a much faster rate than mixing between the lowermost stratosphere and the rest of the stratosphere [Holton et al., 1995].

[3] Turbulent diffusion is another mechanism for troposphere/stratosphere exchange but acts on the small scale [Holton et al., 1995]. Accurate measurements of the vertical eddy diffusivity K are important to incorporate correctly into models as it determines the vertical distribution of minor constituents. Measurements of diffusion across the tropopause are particularly important, given that this forms the boundary between the troposphere (where minor atmospheric constituents are often generated) and the very stable stratospheric region.

[4] Previous campaign-based techniques for calculating K have used data obtained from aircraft [Pavelin et al., 2002; Whiteway et al., 2003] and high-resolution balloons [Gavrilov et al., 2005]. VHF radar observations combined with standard 12-hourly radiosonde data resulted in the construction of multi-year climatologies of K below 20 km at various sites [Fukao et al., 1994; Nastrom and Eaton, 1997; Rao et al., 2001; Nastrom and Eaton, 2005]. In the climatological analyses, smaller K were observed in the stratosphere than in the troposphere, with a gradual decrease in K with height. An approximate formula for calculating the vertical eddy diffusivity K (m2s−1) using a combination of radar and radiosonde data is given by [Fukao et al., 1994]:

equation image

where σt is the radar half-power half-width turbulent spectral width (ms−1). N is the Brunt-Väisälä frequency (rads−1) which was previously usually obtained from radiosonde data. Effects due to beam and wind shear broadening were removed from the observed spectral width in order to obtain σt [Hocking, 1985]. Equation (1) is appropriate for homogeneous turbulence [Fukao et al., 1994] and is used here to allow direct comparison with previous climatological work. Other multiplicative factors such as 0.05 [Whiteway et al., 2003] or 0.24 [Weinstock, 1978] have also been used or derived theoretically depending upon different assumptions. Thus, it should be noted that all of these techniques for calculating K are only approximate.

[5] The atmosphere varies on time scales shorter than 12 hours so higher frequency fluctuations could not be considered when constructing radar climatologies of K. Radio Acoustic Sounding System (RASS) offers the ability to sample the virtual temperature Tv, from which N is calculated, with a temporal resolution of a few minutes. However, RASS is generally only possible on a campaign basis and previously, height limitations have restricted turbulence analyses to the troposphere only [Alexander et al., 2007].

[6] In this paper we present an analysis of K obtained from the first RASS campaign to measure high temporal resolution Tv in the UTLS region. Ks obtained using six-hourly co-located radiosonde Ns data are also presented.

2. Data Sets

[7] Wind and temperature data were recorded up to 20 km with the MU-RASS in Shigaraki, Japan (location 34.85°N, 136.10°E, 370 m MSL) for four days during summer, 2–6 August 1995. During one cycle of data collection, two Doppler wind and three RASS observations were made. These were combined to give a temporal resolution of 3.6 minutes. The spectral width σt was recorded at the same time as the Doppler wind measurements. In the UTLS region, σt was (0.6 ± 0.2) ms−1. Full technical details of the MU-RASS experimental parameters are given by Furumoto and Tsuda [2001]. The mean winds during the campaign were light and are shown in Figure 1a. The amplitude of the zonal wind did not exceed 7 ms−1, while the meridional wind amplitude was always less than 9 ms−1. The low wind speeds meant that effects due to beam broadening were small. The mean temperature profile is displayed in Figure 1b, where a mean cold point tropopause at (17.7 ± 0.5) km is visible.

Figure 1.

Mean wind profile during the campaign: (a) u (solid line), v (dashed line), and (b) the mean temperature.

[8] Radiosondes were launched every six hours from the MU radar site during the campaign. The radiosondes took approximately 70 minutes to ascend to 20 km. In order to compare radiosonde Ks with the RASS K, only RASS N and radar σt obtained less than 70 minutes after each radiosonde launch were used when constructing the median profiles. Data obtained from nine of the 17 radiosonde launches were used for comparisons with the RASS. The majority of these were launched during the second half of the campaign, on 4 August or 5 August, when RASS acoustic echoes were consistently obtained up to 20 km.

3. Results

[9] The median radiosonde Ns are shown in Figure 2a along with the median RASS N. The median is used instead of the mean in order to minimise effects of any outlying data. The campaign mean cold-point tropopause is (1.0 ± 0.6) km higher than the WMO tropopause. The WMO definition states that the tropopause occurs at the lowest altitude where the lapse rate decreases to 2 Kkm−1 or less and the average lapse rate at levels within 2 km above the tropopause does not exceed 2 Kkm−1. As a result of gravity wave activity, the region between the WMO and cold-point tropopauses showed sharp decreases in Ns and N. This is a result of a region of low stability which was present during radiosonde launches 9 and 10. The data are replotted in Figure 2b relative to the tropopause heights. Small differences outside uncertainties are noted, but the profiles are in general agreement. The decrease of N at ∼17 km observed in Figure 2a is not clearly apparent in Figure 2b because the tropopause height varied. The frequency occurrence distribution of N is not Gaussian because N can only be positive. The non-Gaussian distribution was mainly observed in the 11–14 km region. Therefore the standard errors in Figure 2 are not uniformly distributed around the median.

Figure 2.

(a) Comparison between the campaign averaged radiosonde derived N (red line) and RASS derived N (black line). The horizontal black, red, and green dashed lines mark the median RASS WMO tropopause, radiosonde WMO tropopause, and RASS cold point tropopause, respectively. (b) Median N values plotted relative to the median tropopauses. Red shows the radiosonde derived N, black the RASS derived N, and green the RASS cold-point tropopause relative N. Uncertainty bars are discussed in the text.

3.1. The 3.6 Minute RASS K

[10] Values of N obtained from the entire 3.6 minute temporal resolution RASS data set are used to calculate K, which is shown in Figure 3. Large K occurred in the unstable region below 14 km, due to periods of low or negative N2. Directly below the RASS WMO tropopause height, K often exceeded 1.0 m2s−1, while in the lower stratosphere, K was usually less than 0.5 m2s−1. A sharp decrease in K occurred at the tropopause which was primarily due to the increased N. Several discontinuities in the tropopause height are also visible, for example at 1000 LT 3 August and 0000 LT 5 August.

Figure 3.

Vertical eddy diffusivity K in the UTLS region, with missing data marked white. RASS derived WMO tropopause heights are indicated by the red crosses. Lettering is referred to in the text.

[11] Layered structures in K are evident which sometimes persisted for at least a day. Changes in the magnitude of K were often apparent on time scales of about one hour. As an example, in Figure 3, the label (a) shows that around 0000 LT 4 August inside the enhanced layer at 16 km, K varied from 0.3 – 1.2 m2s−1. Further short period fluctuations are visible in the lower stratosphere, for example at the label (b) in Figure 3, where K varied from 0.1 – 0.8 m2s−1. It is possible that these high frequency fluctuations in K may be due to errors in the RASS Tv retrieval. However, in most instances the RASS tropopause does not show large variations in height at high frequency. It would appear then that these high frequency K fluctuations are real, but are clearly embedded in larger scale structures, which often persisted on the order of one day.

3.2. Campaign Average K

[12] While previous seasonal or multi-year analyses also showed general decreases of K in the UTLS, it is possible that the magnitude of the decrease across the tropopause was under-represented due to the low time resolution of radiosondes used to derive N [Fukao et al., 1994; Nastrom and Eaton, 1997]. The presence of co-located radiosonde data provided a unique opportunity to examine the differences between RASS K and radiosonde Ks. From Equation (1), the only difference between these methods is in N since both RASS and radiosonde require the use of the MU radar's σt. Radiosonde Ns values were interpolated to the radar altitudes before using the radar's 70-minute averaged σt to calculate Ks.

[13] Figure 4a shows the height relative median K profiles calculated with data from radiosondes and RASS. The rate of decrease of K and Ks in the lower stratosphere was much less than in the upper troposphere, as previously reported [Fukao et al., 1994]. The two curves show close agreement at most altitudes. In the UTLS region, small discrepancies between the RASS K and radiosonde Ks are observed at 17 km and above 19.5 km.

Figure 4.

(a) Campaign averaged radiosonde derived Ks using Ns (red line) and the RASS derived K using N (black line) and (b) relative to the tropopauses. Colouring and labelling are the same as Figure 2. Uncertainty bars mark the standard error (which is the standard deviation divided by the square root of the number of points) at each height.

[14] The height relative profiles do not reveal the full details of the decrease of K across the tropopause because the tropopause height is not constant. Therefore, the campaign median K profiles are replotted relative to each median tropopause height in Figure 4b. Within uncertainties, the two RASS profiles were consistent except from −1 km to 0 km, where the WMO tropopause relative RASS K were (0.39 ± 0.05) m2s−1 and the cold-point tropopause relative RASS K were (0.30 ± 0.03) m2s−1. This difference is attributed to the fact that the cold-point tropopause is (1.0 ± 0.6) km higher than the WMO tropopause and therefore includes air that has a lower K. The WMO tropopause relative RASS K showed a significant decrease at the tropopause boundary from (0.39 ± 0.05) m2s−1 in the uppermost kilometre of the troposphere to (0.27 ± 0.03) m2s−1 in the lowermost kilometre of the stratosphere.

[15] The radiosonde WMO tropopause relative Ks profile is also marked and showed a similar trend to the RASS WMO K profiles. Note the large Ks in the uppermost kilometre of the troposphere, where it was (0.46 ± 0.06) m2s−1, before decreasing to (0.31 ± 0.07) m2s−1 in the lowermost kilometre of the stratosphere. The RASS and radiosonde K showed overall agreement within uncertainties, although at certain heights there were small differences.

4. Discussion

[16] Previous measurements of UTLS K have shown a wide degree of variability, which may be due to different measurement techniques and atmospheric conditions. Fukao et al. [1994] calculated the seasonal median K from 1986 to 1988 at the MU radar site using standard 12 hourly radiosonde data to obtain Ns. Their results showed that above 18 km, K ∼0.3 m2s−1. The climatological measurements of K made by Fukao et al. [1994] are the same as those observed with the MU-RASS in this study. In the UTLS at two locations in the United States, K ∼0.4 – 0.5 m2s−1 [Nastrom and Eaton, 1997, 2005] thus in the upper troposphere, the high-resolution MU-RASS K also agreed. The MU-RASS K at 20 km was (0.23 ± 0.04) m2s−1, which was twice that obtained in India by Rao et al. [2001], where in summer K at 20 km was about 0.1 m2s−1.

[17] The comparison between radiosonde Ks and RASS K undertaken here revealed some discrepancies between the two measurement techniques during this campaign period at a few heights within 1 km of the tropopause. Observations showed that K derived from RASS observations varied on time scales shorter than the six hourly radiosonde launches. The instantaneous sampling nature of radiosondes, as opposed to the 70 minute RASS averaging, may also contribute to the observed differences. Further away from the tropopause, the RASS and radiosonde N and K agreement was good. This can be explained by assuming that if high frequency (less than six hour) N are quasi-sinusoidal, the positive and negative small scale perturbations will approximately balance, resulting in similar RASS and radiosonde K.

[18] Nastrom and Eaton [1997, 2005] plotted seasonal changes in K relative to the radiosonde tropopause and showed a decrease in the lower stratosphere with smallest K in summer. However, the decrease at the tropopause boundary in all seasons observed by Nastrom and Eaton [1997, 2005] was not as large as that observed in the present study with the high resolution RASS data.

5. Summary and Conclusions

[19] The first high temporal resolution measurements of RASS in the UTLS region were used in order to study K across the tropopause. A large difference between RASS derived WMO tropopause relative and cold point tropopause relative K was observed, due to the cold point tropopause being (1.0 ± 0.6) km higher. The RASS WMO tropopause relative K decreased from (0.39 ± 0.05) m2s−1 in the 1 km below the tropopause to (0.27 ± 0.03) m2s−1 in the 1 km above. Results from the radiosonde Ks in the same regions relative to the radiosonde WMO tropopause heights were (0.43 ± 0.06) m2s−1 and (0.31 ± 0.07) m2s−1 respectively. The RASS and radiosonde results agree within uncertainties. Differences between RASS and radiosonde were observed at −0.5 km and +0.5 km. This was due to differences in N at these heights which may be a result of the instantaneous sampling nature of radiosonde measurements.

[20] K measured with the high-resolution RASS data were similar to that reported previously in climatological studies, where 12 hourly radiosonde data only were available. Sub diurnal scale discontinuities in the RASS WMO tropopause height were observed, which is where mixing, transport and leakage of air between troposphere and stratosphere is expected to occur.

[21] The results from this work showed the clearest separation of RASS tropospheric K and stratospheric K when the WMO tropopause height definition is used. It appears that the WMO definition of the tropopause is more useful when separating tropospheric and stratospheric air for purposes of studying K. The cold-point tropopause is more susceptible to gravity wave activity and therefore the campaign medians included air from both atmospheric regions, thus smoothing out the difference across that tropopause.

[22] The background wind conditions observed during the campaign are typical of Shigaraki during the summer months. It is probable that the values of K obtained here are typical representations of the UTLS region above Shigaraki during summer, especially given the general agreement with the MU radar climatology presented by Fukao et al. [1994]. It is also worth noting that the summertime troposphere structure above the MU radar, with its very high and cold tropopause, is similar in structure to that observed in the tropical regions. Large K may also exist in these regions, especially since summertime K is known to be dominated by convective processes [Nastrom and Eaton, 1997].


[23] This research was partially supported by the Kyoto University Active Geosphere Investigations for the 21st Century COE (KAGI21) grant 15216301, which was approved by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan and completed while one of the authors (SPA) was in receipt of a Japan Society for the Promotion of Sciences (JSPS) post-doctoral fellowship. The study was partially supported by grants-in-aid for scientific research 13136203 and 18340140. We thank T. Adachi and J. Furumoto for providing the data sets. We thank two anonymous reviewers whose valuable comments improved the manuscript.