1. Introduction

The tropopause is one of the basic features of the earth's atmosphere. It separates the troposphere, which is marked by a relatively low static stability, from the stably stratified stratosphere. Besides the stratification, there are several other atmospheric properties in which the stratosphere differs significantly from the troposphere, for example, moisture and the ozone concentration. Hence, it is not surprising that the tropopause has received increasing interest during the last two or three decades. A major part of the literature deals with exchange processes through the tropopause (e.g., Shapiro 1980; Wirth 1995) or attempts to estimate the amount of the mass exchange through the tropopause (e.g., Holton 1990; Ebel et al. 1996). The importance of this mass exchange lies in its impact on atmospheric chemistry. For example, stratospheric ozone chemistry involves many trace constituents whose sources are in the troposphere.

The literature on the tropopause itself concentrates mainly on the tropical tropopause and, especially, on its temperature. Since the upward branch of the Brewer–Dobson circulation is located in the Tropics, the tropical tropopause temperature controls the stratospheric water vapor mixing ratio. However, the mean tropical tropopause temperature is still too high to account for the observed extreme dryness of the stratosphere. According to Newell and Gould-Stewart (1981), Indonesia is the only region where the tropopause is really cold enough. Therefore, they have suggested that most of the tropical upwelling occurs in that region (see also Frederick and Douglass 1983). Another interesting feature of the tropical tropopause is its annual cycle that is related to the annual cycle of the stratospheric meridional circulation (Yulaeva et al. 1994; Reid and Gage 1996). A first climatology of the tropical tropopause has been presented by Highwood and Hoskins (1998).

Comparatively little work has been done on the extratropical tropopause. Although Appenzeller et al. (1996) pointed out that a significant amount of stratosphere–troposphere exchange may occur due to the annual cycle of the mean tropopause pressure, there appears to be only one global tropopause climatology (Hoinka 1998, hereafter H98; Hoinka 1999). Moreover, these studies did not focus on the annual cycle of the tropopause. Hoinka considered only seasonal means of summer and winter, which may be too coarse to resolve the annual cycle. In fact, the study of Highwood et al. (2000, hereafter HHB), who investigated the Arctic tropopause in more detail, suggests a double wave with maxima of the tropopause pressure in spring and autumn and minima in summer and winter. However, detailed studies of the tropopause in the remaining extratropical regions are still missing. In particular, the Antarctic tropopause deserves further research because of the difficulties in determining it in winter. As has already been recognized by Court (1942), the tropopause is very indistinct in Antarctic winter so that it is questionable whether the common thermal criterion is applicable in this case. The same question may be posed on the Arctic winter tropopause although HHB state that its determination with the thermal criterion is unproblematic. A detailed investigation of the sharpness of the polar tropopause and a comparison between different tropopause criteria are needed to answer these questions.

The main goal of this paper is to fill these gaps in the knowledge of the polar tropopause. Moreover, the study is extended to the subpolar regions in order to capture the transition between the polar regions and middle latitudes. The data analysis is mainly based on the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA) data for the period 1979–93, which have already been used by H98. Compared with the original ECMWF analysis data, the ERA dataset has the advantage to constitute a homogeneous dataset (see H98 for a more thorough discussion). New algorithms are used to determine both the thermal and the dynamical tropopause from this dataset. They have been validated against a 5-yr set of radiosonde data for both polar regions. In order to extend this validation to the dynamical tropopause, an additional algorithm has been developed for the determination of the dynamical tropopause from the radiosonde data. It uses interpolated vorticity fields from the ERA data because the density of radiosonde stations is too low in the polar regions to compute the vorticity from the radiosonde wind data. Since the thermal tropopause criterion has been found to be inadequate for Antarctic winter, the dynamical criterion is taken as standard in this paper. One section will be devoted to the comparison between the thermal and the dynamical criterion. For tropopause pressure and temperature, the discussion is restricted the ERA-derived fields. However, the radiosonde data are used to evaluate the sharpness of the tropopause because the vertical resolution of the ERA data is too coarse for this purpose.

The outline of this paper is as follows. A brief description of the datasets is given in section 2. Section 3 presents the tropopause criteria and their application to the data. The validation of the new algorithms is described in section 4. In section 5, climatological fields of tropopause pressure and tropopause temperature are presented. The annual cycle of the tropopause pressure is discussed in more detail in section 6. Section 7 gives a comparison between the thermal and the dynamical tropopause and an analysis of the differences between them. The sharpness of the tropopause, that is, the amount of change in the vertical temperature gradient across the tropopause, is considered in section 8. Finally, a summary of the main results is given in section 9. Some details of the new algorithms are presented in appendixes A–C.

2. Datasets

In the present study, we use the model-level ERA data on the latitude–longitude grid. Compared to the standard pressure-level data, which are also available from the ECMWF, the model-level data have approximately twice as many levels (31 instead of 15) and, therefore, a better vertical resolution. This is especially valid in the tropopause region, so that the model-level data are certainly more appropriate for the determination of the tropopause. In addition, the smoothing of the meteorological fields inherent in the interpolation from the model levels to the standard pressure levels probably would further deteriorate the quality of the ERA-derived tropopauses. The horizontal resolution of the data is 1.125° × 1.125°, corresponding to their spectral resolution of T106.

The radiosonde data used in this study cover the regions poleward of 55°N and 50°S, respectively, and the time period from 1989 to 1993. The locations of the radiosonde stations are displayed in Fig. 1. The data have been provided by the German Weather Service (Deutscher Wetterdienst, DWD). According to the standard World Meteorological Organization (WMO) TEMP format, this dataset includes explicitly reported thermal tropopauses (see below). Since the radiosonde data had not been checked for coding or measurement errors, some simple quality checks were applied. The reported tropopauses were checked for consistency with the sounding, and the soundings were checked for strongly overadiabatic temperature gradients. If overadiabatic gradients could be eliminated by removing a single data point, this point was assumed to be a coding error and was removed. However, if a sounding contained more than two errors, the whole sounding was not taken into account. If the reported tropopause was inconsistent with the WMO criterion, the tropopause was calculated directly from the sounding. Finally, the 500- and 100-hPa temperatures were checked against the respective values interpolated from the ERA data. Since the majority of data points was less than 3 K apart, differences of more than 4 K were taken as an indication that the sounding had been eliminated during the data assimilation cycle at the ECMWF.

The data analysis reported in this paper is restricted to 1200 UTC. A preliminary analysis of the radiosonde data had shown that the diurnal cycle of the tropopause pressure is negligible.

3. Tropopause criteria

b. Dynamical tropopause

An alternative to the thermal criterion, based on potential vorticity (PV), was first proposed by Reed (1955). The hydrostatic form of the PV in height coordinates is given by

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where ρ is the density, f is the Coriolis parameter, k is the unit vector in the vertical, v = (u, υ) is the horizontal wind vector, and θ is the potential temperature. In contrast to the vertical temperature gradient, P is materially conserved for adiabatic motions. Therefore, it can be argued that P is more appropriate to divide stratospheric air from tropospheric air than ∂T/∂z, especially in cyclogenetically active regions.

From Eq. (1), it is clear that the stratosphere is marked by higher absolute PV values than the troposphere, the sign of the PV being positive in the Northern Hemisphere (NH) and negative in the Southern Hemisphere (SH). In the following, only the NH case is considered. Using the PV unit (PVU), which is defined as 1 PVU = 10⁻⁶ K m² kg⁻¹ s⁻¹, tropospheric air can be characterized by PV values of ≲1 PVU, while stratospheric air typically has P ≳ 5 PVU. Thus, the PV threshold used as tropopause definition must be somewhere in between these values. However, there is still no generally accepted value. The WMO (1986) suggested a threshold of 1.6 PVU, but most authors use values between 2 and 3.5 PVU. A comparison between the thermal tropopause and the dynamical tropopause with threshold values ranging between 1 and 5 PVU was performed by Hoerling et al. (1991). They found that the pressure of the dynamical tropopause is systematically higher than that of the thermal tropopause for values less than 3 PVU while it is systematically lower for values greater than 4 PVU. The best agreement was found for a threshold value of 3.5 PVU. Therefore, Hoerling et al. suggested this value to delineate the dynamical tropopause.

One may argue against this method of determining an “optimal” threshold for the PV tropopause that the thermal criterion is itself—at least to a certain extent—arbitrary and, therefore, not a suitable reference. Moreover, the thermal criterion is not able to characterize air masses because the vertical temperature gradient is not a conserved quantity. There are, however, other arguments to use a higher value than 1.6 PVU, especially in the polar regions. First, our data analysis revealed that the 1.6 PVU surface frequently descends below the 700-hPa level in polar winter. Under very strong cyclonic influence, it is even possible that the 1.6 PVU surface intersects the ground. Second, the comparison between radiosonde-derived tropopauses and ERA-derived tropopauses (see next section) showed that the correlation between them is much worse for 1.6 PVU than for 3.5 PVU, indicating that a threshold of 1.6 PVU does not yield well-defined, reproducible results. Third, there are too many cases where the 1.6 PVU criterion, applied to the radiosonde data, detects multiple tropopauses. Certainly, some of them can be interpreted as tropopause folds, but the percentage of multiple tropopauses (up to 70% in winter) is more than an order of magnitude larger than the percentage of tropopause folds found in previous studies (e.g., van Haver et al. 1996). All this suggests that 1.6 PVU is not an appropriate tropopause criterion at least at higher latitudes. A higher value or a latitude-dependent value that is higher at polar latitudes is needed to separate stratospheric air from tropospheric air.

Following Hoerling et al. (1991) and H98, a constant value of 3.5 PVU is used in this paper to define the dynamical tropopause. According to Grewe and Dameris (1996), a constant threshold value is more appropriate than a latitude-dependent value if the attention is restricted to polar latitudes. The algorithm to determine the PV tropopause from the ERA data is quite similar to that used for the thermal tropopause. First, the PV according to Eq. (1) is calculated between each two adjacent model levels and assigned to intermediate levels. Then, the level where the threshold value is met is determined, and the tropopause height is calculated under the assumption that the PV varies linearly with height in the tropopause region. Tropopause pressure and temperature are determined as for the thermal tropopause. The detailed description of this algorithm and the algorithm for the calculation of the dynamical tropopause from the radiosonde data are given in appendixes B and C, respectively. In addition, an empirical correction of the ERA-derived pressure of the dynamical tropopause is described that has been used to minimize systematical errors (appendix B).

It should be noted that a thickness criterion similar to the second part of the thermal WMO criterion has been introduced into the PV criterion. It requires that the mean potential vorticity between the tropopause and all levels within 2 km above the tropopause remains above 3.5 PVU. A thickness criterion like this has proved to be very important when calculating the dynamical tropopause from radiosonde data because thin layers of enhanced stability (e.g., subsidence inversions) may otherwise be misinterpreted as the tropopause. However, it may be omitted when using the ERA data except in Antarctic winter, which means that it is not as important as in the thermal tropopause case. Nevertheless, we suggest to incorporate some kind of thickness criterion into the definition of the dynamical tropopause so as to reduce the sensitivity to the vertical resolution of the data. Otherwise, higher-resolution datasets, which will presumably become available during the next years, may not yield reproducible dynamical tropopauses.

4. Validation of the ERA-derived tropopauses

For the last five years of the ECMWF reanalysis period, that is, 1989–93, all available radiosonde data poleward of 55°N and 50°S, respectively, (see Fig. 1) have been evaluated in order to validate the tropopauses derived from the ERA data. To compare the different datasets, the ERA tropopause fields are first interpolated linearly to the locations of the radiosonde stations. Then, the data are averaged over months and certain geographical areas. In the Northern Hemisphere, two latitude belts (55°–65°N, 65°–90°N) and four longitude sectors (45°W–45°E, 45°–135°E, 135°E–135°W, 135°–45°W) are distinguished. The longitude sectors are chosen such that regions with similar tropopause properties are put together (cf. Figs. 3–6). In the SH, the sparse density of radiosonde stations allows only for a subdivision into two regions, namely 50°–55°S and 62°–90°S (Antarctica).¹ The number of data points per month and region typically ranges between 1000 and 3500 in the NH regions and between 900 and 1200 in Antarctica. The lowest numbers (∼500) are found at 50°–55°S where there are only four radiosonde stations.

For each of these regions, the monthly mean tropopause pressure, its standard deviation, and the correlation coefficient between ERA- and radiosonde-derived tropopause pressures are computed. The two latter quantities are considered in order to show that the skill of the ERA-derived tropopauses is not restricted to monthly means. Annual mean statistics for these quantities are summarized in Table 1. Moreover, monthly mean tropopause temperatures are compared. Since the differences between the ERA-derived tropopauses and the radiosonde-derived tropopauses are quite similar in most of the regions defined above (see Table 1), only three regions will be discussed in detail. These are 45°W–45°E, >65°N (northern Atlantic and Europe), 55°–65°N, 135°E–135°W (eastern Siberia and Alaska) and <62°S (Antarctica). This selection is sufficient to resolve meridional differences in the Arctic as well as interhemispheric differences.

b. Tropopause pressure, standard deviation

The standard deviation of the tropopause pressure can be taken as a measure for the synoptic-scale variability of the tropopause. In the present analysis, it is computed according to

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The summation extends over all data points (radiosonde stations or interpolated ERA values) of one region, one month, and the period 1989–93. Typical values of σ_pTP (dynamical tropopause) are 30–40 hPa in Arctic summer, 40–50 hPa in Arctic winter, 25–35 hPa in Antarctic summer, and 30–40 hPa in Antarctic winter. In the storm track regions, σ_pTP reaches 55–65 hPa in winter and spring (cf. H98). The thermal tropopause generally exhibits 3–6 hPa lower σ_pTP values than the dynamical tropopause except for Antarctic winter where thermal σ_pTP is about 5 hPa larger.

Comparing σ_pTP obtained from radiosonde and ERA data (Fig. 2b), one finds that the synoptic-scale variability of the tropopause is slightly underestimated in the ERA data. This underestimation is more pronounced for the thermal tropopause (thin lines) than for the dynamical tropopauses (bold lines). In the Arctic regions, σ^ERA_pTP − σ^raso_pTP-differences found for the thermal tropopause range between −4 hPa in summer and −9 hPa in winter. In the Antarctic, the summer difference is again −4 hPa, but it is close to zero in winter. However, the good coincidence in winter must be considered as fortuitous because of the low correlation between ERA and radiosonde tropopauses (see below). Table 1 shows that the underestimation of σ_pTP for the dynamical tropopause is very similar in all parts of the north polar region. In the Southern Hemisphere, there appears to be no systematical underestimation at all, but this result should be taken with care due to the extreme sparsity of data. Nevertheless, we can conclude that the dependence of σ_pTP on the dataset in insignificant compared to observed values. This is particularly valid for dynamical tropopauses.

c. Tropopause pressure, correlation coefficients

To assess the degree of coincidence between radiosonde-derived tropopauses and ERA-derived tropopauses, the correlation coefficient

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is computed. Summation is again over one region, one month, and the 5-yr period 1989–93. Some examples are given in Fig. 2c, and annual mean values are again summarized in Table 1. In general, it can be stated that PV tropopauses (bold lines) show better correlations than thermal tropopauses (thin lines), especially in winter.

The thermal tropopauses show correlation coefficients between 0.90 and 0.93 in Arctic summer and between 0.81 and 0.89 in Arctic winter, the lowest values occurring in the region >65°N/45°–135°E (not shown). In the Antarctic, r_TP varies between 0.87 in summer and 0.62 in winter. In the annual mean, r_TP ranges between 0.89 and 0.92 in the Northern Hemisphere while a value of only 0.78 is found for Antarctica. The annual cycle of r_TP can be partly explained by the annual cycle of tropopause sharpness (see sections 7 and 8). Due to the low tropopause sharpness typical for winter, little differences between ERA and radiosonde temperature profiles may induce large differences in the tropopause pressure diagnosed by the thermal criterion. This is especially true in Antarctic winter where there are many cases without a well-defined thermal tropopause (section 7).

The r_TP values found for the PV tropopause vary between 0.91 and 0.94 in Arctic winter and between 0.94 and 0.96 in Arctic summer. In the Antarctic, r_TP ranges between 0.86 in winter and 0.92 in summer. The annual mean values are near 0.9 in Antarctica and between 0.93 and 0.95 in the remaining regions. Especially in winter, these values are appreciably better than those obtained for the thermal tropopause. A simple explanation for this can be found in the fact that PV tropopauses are by definition sharper than thermal tropopauses. In an atmosphere with a constant vertical temperature gradient, the PV increases with height proportional to p^−(1+κ) [see Eq. (C1)]. Therefore, the uncertainty in determining the tropopause induced by a given uncertainty in the data is far lower for the PV definition than for the thermal definition. In some sense, the PV definition may be regarded as numerically more stable than the thermal one. It should be noted that the use of the ERA vorticity data for the calculation of p^raso_TP (see appendix C) cannot be made responsible for the high r_TP values obtained here. Although the relative vorticity is a very important factor, the radiosonde-derived PV tropopauses turned out to coincide with a significant level (i.e., with a change in the vertical temperature gradient) in most cases. Therefore, they would not depend very sensitively on the vorticity data used for their computation.

5. Tropopause pressure and temperature

In this section, climatological fields of tropopause pressure and temperature in the polar regions are presented by means of polar stereographic charts. All fields are monthly means and refer to the dynamical tropopause (3.5 PVU) and the period 1979–93. Unlike H98 and HHB, who showed seasonal means, we decided to present monthly means in order to avoid excessive smoothing. It will turn out that this is particularly necessary to capture the tropopause temperature minimum in Arctic winter. In order to resolve the annual cycle as well as possible (see below), four months are shown for each hemisphere. These are January, April, July (NH)/August (SH), and October. The August is chosen instead of July in the Antarctic because the extreme values of tropopause pressure and temperature are reached in August there (see section 6). The annual means of the tropopause pressure for both polar regions have already been shown in H98.

6. The annual cycle of the tropopause

It can be inferred from Figs. 3 and 5 that the annual cycles of polar tropopause pressure can be classified into three different patterns. A single wave with highest tropopause pressure in winter and lowest in summer is typical for the midlatitudes and for the subpolar parts of eastern Siberia and North America. Northern Europe, western Siberia, and, generally, high Arctic latitudes exhibit a double wave with pressure maxima in spring and autumn and pressure minima in summer and winter. Finally, a single wave with maximum tropopause pressure in summer and minimum pressure in winter is found over the whole of Antarctica, with the amplitude increasing toward the South Pole. Transition zones without a distinct annual cycle are located in the southern midlatitudes around 50°S and in the subpolar parts of Europe.

Typical examples for the three patterns are displayed in Fig. 7a. The largest amplitude is found over central Antarctica with a maximum–minimum difference of about 100 hPa. Note that the extrema are attained in February and August–September. The single waves found in the subpolar parts of eastern Siberia and Canada–Alaska have a maximum–minimum difference of about 50 hPa, half as much as in central Antarctica. The summer minimum is attained in July–August, and the winter maximum is quite broad, especially in eastern Siberia where the tropopause pressure is almost constant between November and March. Even lower pressure amplitudes (∼30–40 hPa) are found at high northern latitudes where a double wave prevails. The primary pressure maximum is generally found in April in these regions, and the primary minimum is reached in July or August except for the region >80°N (Fig. 7b) where the tropopause pressure is lowest in December and January. The difference between the secondary maximum, which is attained in October or November, and the local minimum in January is generally weak. The transition from the single wave in subpolar regions to the double wave at high latitudes is demonstrated in Fig. 7b. While there are little differences in winter, the tropopause pressure increases in spring at high latitudes while it decreases in subpolar regions. In summer, a strong meridional gradient is evident, which has already been mentioned in the discussion of Fig. 3.

The tropopause temperature curves for the regions displayed in Fig. 7a are given in Fig. 7c. It is clearly evident that the regions with similar pressure patterns have also similar tropopause temperatures. The subpolar regions with a single pressure wave are marked with an almost constant tropopause temperature, the summer–winter difference amounting to only 3 K. At high northern latitudes, a temperature amplitude of 11–13 K is found, and an impressive value of 23 K is attained over central Antarctica. Note that the temperature minimum is reached in January in the Arctic while it is reached in August in the Antarctic. As mentioned above, these differences can be traced back to the differences in dynamical heating of the stratosphere.

In the following, it will be shown that the annual cycles of the tropopause pressure are closely related to the temperature difference between the midtroposphere and the lower stratosphere. Suppose, for example, that the surface temperature and the tropospheric temperature gradient are given and that the temperature of the stratosphere varies. Then, a cold stratosphere will be associated with a high tropopause (low tropopause pressure), and a warm stratosphere will correspond to a low tropopause (high tropopause pressure). A similar argument has already been proposed by Möller (1938). Of course, tropospheric temperatures are not constant throughout the year, but in a more general sense, one may expect that the tropopause pressure varies with the temperature difference between the midtroposphere and the lower stratosphere, for example, between 500 and 100 hPa. A large (small) temperature difference is then expected to be associated with a low (high) tropopause pressure.

Comparison of Figs. 7 and 8 reveals that this is indeed the case. In subpolar eastern Siberia (55°–60°N, 140°E–160°W; Fig. 8a), the 100-hPa temperature (T₁₀₀) is almost constant throughout the year while the 500-hPa temperature (T₅₀₀) has a distinct summer maximum. Therefore, T₅₀₀ − T₁₀₀ is larger in summer than in winter, corresponding to a tropopause pressure minimum in summer and a maximum in winter. Interestingly, this relation even holds for the months of November until March where both the tropopause pressure and T₅₀₀ − T₁₀₀ are almost constant. Over central Antarctica (Fig. 8c), the temperature amplitude is much larger in 100 hPa than in 500 hPa, yielding a maximum of T₅₀₀ − T₁₀₀ in August and a minimum in February. As the tropopause pressure extrema are attained in August (min) and in February (max), expectations are again met. Finally, northwestern Siberia (70°–80°N, 40°–100°E; Fig. 8b) is to be considered. Although the temperature ranges in 500 and 100 hPa have similar amplitudes, they are by no means parallel. In 500 hPa, there is a broad temperature minimum in winter and a sharp maximum in summer. On the other hand, a sharp minimum in winter and a broad maximum in summer are found in 100 hPa. As a result, T₅₀₀ − T₁₀₀ attains two maxima in January and July and two minima in April and October, again fitting the tropopause pressure extrema.

This excellent correlation between T₅₀₀ − T₁₀₀ and the tropopause pressure can be used to identify one important mechanism influencing the location of the polar tropopause. Comparing the temperature curves displayed in Fig. 8, one finds that it is primarily the T₁₀₀ cycle that exhibits large regional differences. Simulations with a radiative-convective model, which will be reported in a separate paper, indicate that these differences are mainly due to differences in the dynamical heating of the lower stratosphere. This suggests that the dynamical heating, which is related to the stratospheric meridional circulation (see section 5b), is one of the factors determining the height of the polar tropopause. Some evidence for the influence of dynamical heating can also be gained directly from the data. A comparison of winters, in which a major stratospheric warming occurred, with cold winters (with respect to the lower stratosphere), provides a way to isolate the effects of dynamical heating. Using the statistics of Naujokat and Labitzke (1993) and half-monthly means of T₁₀₀ from the ERA data, a class of seven major warming-influenced half months and a class of fourteen half months marked with a strong, cold polar vortex have been defined. The major warming class comprises the first half of February 1981 and 1991, January and the first half of February 1985, the second half of December 1987 and the first half of January 1988. The differences between the two classes (warm–cold) are displayed in Fig. 9. As can be seen in Fig. 9a, the T₁₀₀ differences reach up to 17 K near the pole. The corresponding tropopause pressure differences are shown in Fig. 9b. Over a large fraction of the Arctic, values between 30 and 50 hPa are found, emphasizing the large influence dynamical heating can have. Of course, this behavior is consistent with the simple geometric consideration given above that a warm stratosphere should be associated with high tropopause pressure. It should be noted that the differences shown in Fig. 9b are highly significant. The standard deviation of monthly mean tropopause pressures from year to year, computed as

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where p^M_TPy is the monthly mean tropopause pressure of a single year and p^M_TP is the monthly mean pressure of all years (as displayed in Figs. 3 and 5), ranges between 15 and 20 hPa in Arctic winter (not shown). Thus, the two classes defined above are about two standard deviations apart.

7. Comparison between thermal and dynamical tropopause

All results presented in the preceding two sections refer to the dynamical (3.5 PVU) tropopause. In this section, the differences between the thermal and the dynamical tropopause are discussed. Generally, it can be stated that both tropopause definitions yield similar results except for winter. In Arctic winter, differences are weak over eastern Siberia and Canada only. However, the thermal tropopause pressure is 10–20 hPa lower than the dynamical one over northern Europe and western Siberia, that is, in the polar vortex region. This confirms that the differences between our January tropopause pressure field and the DJF field presented by HHB are primarily due to the different tropopause criteria. Even stronger differences are found in Antarctic winter and Antarctic spring. In August, the thermal tropopause pressure is below 170 hPa over central Antarctica (Fig. 10a), corresponding to a thermal–dynamical difference of more than 60 hPa (Fig. 10b).

A closer investigation reveals that these large differences are primarily due to a too low static stability in the lower stratosphere. It has been found that the mean vertical temperature gradient in the Antarctic lower stratosphere is below −1.0 K km⁻¹ between June and October. In July and August, it is even below −1.5 K km⁻¹. Thus, it is not surprising that the application of the thermal criterion is problematic in Antarctic winter. More precisely, it depends on synoptic-scale conditions whether the thermal criterion yields a meaningful tropopause or not. As can easily be reproduced with the technique of PV inversion, a thin, very stable layer is typically present above upper-tropospheric anticyclones, while the lower stratosphere is less stable than in its background state within and above cutoff lows (e.g., Hoskins et al. 1985). In anticyclonic cases, it can therefore be expected that both tropopause criteria yield the same results, but in cyclonic cases, the thermal criterion may diagnose a substantially lower tropopause pressure than the dynamical one.

In order to illustrate this point, a PV inversion has been performed for a cyclonic disturbance embedded in background conditions typical for Antarctic winter [see Wirth (2000) for a description of the algorithm]. Tropospheric and stratospheric temperature gradients are assumed to be −6.5 and −1.0 K km⁻¹, respectively, and the cyclone is prescribed as a cos²-shaped displacement of the tropopause with a radius of 500 km and a peak displacement of 3 km. Axisymmetry and gradient wind balance are assumed for the inversion. The result is displayed in Fig. 11. While the dynamical tropopause, denoted by the lower boundary of the gray-shaded area, is displaced downward in the cyclone, the thermal tropopause, denoted by the thick solid line, is displaced upward. Due to the cyclone-induced destabilization of the lower stratosphere, the thermal criterion is not met at the height of the dynamical tropopause but several kilometers higher up. In the cyclone center, thermal and dynamical tropopauses are 6 km apart.

A similar behavior can be inferred from data. Figure 12 shows thermal and dynamical tropopause pressures obtained from the radiosondes of central Antarctica (South Pole, Vostok and Halley Base) for the months of July to October. They are displayed as a function of relative vorticity at PV-tropopause level, normalized with the sign of the Coriolis parameter so that positive values correspond to cyclonic influence. It can be seen that the PV tropopause pressure increases continuously with relative vorticity. This is consistent with other observations and theoretical considerations (e.g., Hoskins et al. 1985). However, the opposite is the case for the thermal tropopause. Apart from strong scattering, the thermal tropopause pressure tends to decrease with increasing cyclonic influence. For anticyclonic cases, there is a good correspondence between both tropopause criteria, but under cyclonic influence, the thermal tropopause is found to be up to 10 km above the dynamical tropopause.

Thus, it can be concluded that the thermal criterion is not appropriate for polar winter. Due to the low static stability of the lower stratosphere, the thermal criterion does not yield a physically meaningful tropopause under cyclonic influence. In many cases, the thermal tropopause corresponds to PV values of 10 PVU or more (not shown). Moreover, the thermal criterion is very sensitive to little changes in the temperature profile. As shown in Fig. 2c, the correspondence between radiosonde-derived tropopauses and ERA-derived tropopauses is far worse in Antarctic winter than anywhere else. Tests with a lower threshold value (e.g., −3 K km⁻¹) revealed some improvement in Antarctic winter, but severe problems occurred in Canadian and eastern Siberian winter where the vertical temperature gradient may be around −3 K km⁻¹ throughout the troposphere. Therefore, a modification of the thermal criterion cannot be regarded as meaningful. With a possible exception of conserved trace gases (e.g., ozone; see Bethan et al. 1996), there appears to be no alternative to the PV-based tropopause definition in polar winter.

8. The sharpness of the tropopause

Finally, the sharpness of the polar tropopause shall be investigated. According to Wirth (2000), the tropopause sharpness is defined as the change in vertical temperature gradient across the tropopause, that is,

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with Δz = 1 km, for example. Since both γ_+Δz = (T_TP+Δz − T_TP)/Δz and γ_−Δz = (T_TP − T_TP−Δz)/Δz exhibit distinct annual cycles and regional differences, these quantities will be discussed separately before combining them to yield the tropopause sharpness.

Since the vertical resolution of the ERA data is not sufficient to determine the tropopause sharpness, temperature gradients are taken exclusively from radiosonde data. Moreover, the investigation is restricted to the dynamical tropopause because the thermal criterion is not appropriate for polar winter (see above). As in section 4, certain geographical regions are put together to clarify the regional differences of tropopause sharpness. In the Northern Hemisphere, we consider four latitude belts (55°–60°N, 60°–65°N, 65°–70°N, and 70°–80°N) and seven longitude sections, two of which are discussed in the following (western Siberia; 40°–100°E and Alaska–Canada; 100°–160°W). In the SH, the sparsity of radiosonde stations allows only for a division into four regions, namely 50°–55°S, 62°–72°S, Antarctic coast <72°S, and central Antarctica.² Note that there are no stations between 55° and 62°S.

The mean vertical temperature gradients between the tropopause and 1 km above (γ₊₁) are displayed in Fig. 13. Generally, it can be stated that γ₊₁ is larger in summer than in winter and that the amplitude of this annual cycle increases toward the Poles. As for tropopause pressure and temperature, the largest annual cycle is found over central Antarctica where γ₊₁ exceeds +5 K km⁻¹ in summer and is close to −2 K km⁻¹, the threshold value of the thermal criterion, in winter. At high Arctic latitudes, summer values are close to Antarctic values while γ₊₁ hardly falls below 0 K km⁻¹ in winter. This is consistent with the fact that the thermal criterion does a better job in Arctic winter than in Antarctic winter. Moreover, distinct zonal differences are present in the Arctic winter. In the polar vortex region (Fig. 13a), γ₊₁ ranges between 0 and +1.0 K km⁻¹ while it ranges between +1.0 and +3.5 K km⁻¹ in the Aleutian high region (Fig. 13b). The remaining longitude sections range between these values, with eastern Siberia being close to Alaska, middle Siberia being close to western Siberia and Europe being about half way in between. In summer, zonal differences are weaker, but γ₊₁ is still larger over Canada and Alaska than over western Siberia. However, the remaining regions behave differently from winter. γ₊₁ is even larger in Europe than in Canada and is even lower in middle and eastern Siberia than in western Siberia. Finally, note the abrupt change between the region 50°–55°S and the Antarctic coast. Although there are very few radiosonde stations in the southern hemisphere, there is clear evidence that the meridional gradient of the annual γ₊₁-cycle is far stronger in the Antarctic than in the Arctic.

The mean vertical temperature gradients between the tropopause and 1 km below (γ₋₁) show weaker annual cycles and regional differences than γ₊₁, but they are still worth to be discussed shortly. Some selected regions are displayed in Fig. 14. First, it may be noted that the annual cycle of γ₋₁ is weaker in the Antarctic than in the Arctic. This is also valid for the regions not shown here. In the Arctic, γ₋₁ is generally lower in summer than in winter, indicating that the troposphere is more stably stratified in winter. There are almost no regional differences in Arctic summer, γ₋₁ being very close to the standard atmosphere value of −6.5 K km⁻¹, but there are moderate differences in winter. The highest values (≈−4.5 K km⁻¹) are found in Canada–Alaska poleward of 70°N and in middle and eastern Siberia between 55° and 70°N. The lowest values (≈−5.7 K km⁻¹) are found in Europe (not shown).

It follows that the annual cycle and the regional differences of the tropopause sharpness (Fig. 15) arise primarily from γ₊₁. Consequently, the tropopause sharpness is substantially higher in summer than in winter with the amplitude increasing toward the Poles. The main effect of γ₋₁ is that the summer maximum of tropopause sharpness is slightly higher at high northern latitudes than over central Antarctica although the opposite is the case for γ₊₁. It should be mentioned that the synoptic-scale variability of tropopause sharpness is at least as large as its annual cycle. As mentioned in the previous section, the tropopause sharpness is much higher over upper-tropospheric anticyclones than within cutoff lows.

9. Summary

The polar and subpolar tropopause has been investigated using the ECMWF Reanalysis (ERA) data from 1979 to 1993 and radiosonde data from 1989 to 1993. Both the thermal and the dynamical (3.5 PVU) tropopause have been computed from each dataset. The tropopauses calculated from the radiosonde data have been used to validate the tropopauses calculated from the ERA data and to investigate the sharpness of the tropopause, which requires high vertical resolution. The validation revealed that the ERA data are suited very well for this study. The uncertainties in the determination of the tropopause pressure are negligible compared to typical regional differences, and the warm bias in the tropopause temperature arising from the low vertical resolution of the ERA data can be overcome by extrapolating the temperature gradient below or above the tropopause.

A central result from this study is that the annual cycle of polar tropopause pressure can be classified into three different patterns. A single wave with a tropopause pressure maximum in winter and a minimum in summer is found in the subpolar parts of eastern Siberia and North America. A double wave with pressure maxima in spring and autumn and minima in summer and winter is typical for northern Europe, western Siberia, and generally for high Arctic latitudes. Finally, Antarctica exhibits a reversed single wave with a pressure maximum in summer and a minimum in winter. Tropopause temperatures are generally highest in summer and lowest in winter, but the amplitude of their annual cycles shows large differences. It is lowest in those regions that exhibit the first pressure pattern (single pressure maximum in winter) and largest in the Antarctic. A comparison between the tropopause pressure and the temperatures in 500 and 100 hPa reveals that the tropopause pressure is closely related to the temperature difference between 500 and 100 hPa or, more generally, between the midtroposphere and the lower stratosphere. A large temperature difference then corresponds to a low tropopause pressure and a small temperature difference to a high tropopause pressure.

The differences between the thermal tropopause and the dynamical tropopause are weak except for polar winter. In Arctic winter, they are weak only in the Aleutian high region but moderate in the polar vortex region (Europe, western Siberia). The by far largest differences occur in Antarctic winter where the thermal tropopause pressure is about 60 hPa lower than the dynamical tropopause pressure. These differences can be traced back to the low static stability of the lower stratosphere in Antarctic winter. Since the mean vertical temperature gradient between the (dynamical) tropopause and the 100-hPa level is close to −2 K km⁻¹, that is, the threshold value of the thermal criterion, the thermal criterion is not appropriate for Antarctic winter.

A quantity that is closely related to the mean static stability of the lower stratosphere is the sharpness of the tropopause, that is, the change in vertical temperature gradient across the tropopause. Its annual cycle and its regional differences are primarily determined by the mean temperature gradient above the tropopause since it varies much more strongly than the gradient below the tropopause. Generally, the tropopause sharpness is higher in summer than in winter with the summer–winter difference increasing toward the Poles. In winter, the lowest tropopause sharpness is attained in the Antarctic, being accompanied with the failure of the thermal criterion. In the Arctic, the tropopause is sharper in the Aleutian high region than in the polar vortex region. The synoptic-scale variability of the tropopause sharpness will be addressed in detail in a future paper.