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Up: Measurement of optical seeing


3 Results

Fifteen successful balloon launches were performed between June 20 and August 18, 1995, during the polar night. Each balloon payload contained our microthermal sensors, as well as a Vaisala radiosonde which supplied the required pressure and temperature measurements. In addition, the launches were timed to coincide with weather balloon flights, from which we were able to obtain wind velocity profiles.

The sampling rate of the radiosondes resulted in a vertical resolution of approximately 5-6 m. The mean seeing results were obtained by constructing a set of average $C_{\rm N}^{2}$ values at standard altitudes, in 5 m steps, interpolating between the nearest raw data points on either side of each standard level. The average seeing produced by any layer of the atmosphere may then be calculated simply by varying the limits of the integral in Eq. (3). Inspection of the raw data indicated that these altitude increments were small enough for linear interpolation to be an accurate approximation to the $C_{\rm N}^{2}$ profile. Unless otherwise stated, all calculations are performed using a wavelength of 0.5 $\mu$m and zenith angle $\gamma=0^\circ$.

Due to the difficulty of the launch procedure in polar winter conditions, the tether length between balloon and sonde at launch was only 10-20 m for most flights, with a reel attached to gradually pay out a further 30 m during the early part of the ascent. It is possible that the turbulent wake of the balloon had a minor effect on the data before the tether rolled out to its full extent ($\sim$50 m), especially in regions of low wind speed (i.e. when the balloon ascends almost vertically above the sonde), and hence the stated values of the seeing should be considered as upper limits.

\epsfbox{}\end{figure} Figure 1: Average $C_{\rm N}^{2}$ profile up to a height of 70 m, calculated from the 15 balloon sondes. Included are the two methods used to determine the lower altitude limit of the data, and extrapolate down to the surface. The mean $C_{\rm N}^{2}$ measurements from the 27 m-high tower (Marks et al. 1981) are indicated by the triangles, with extrapolations from 0-7 m and from 27-35 m shown by the dashed lines. The dotted line shows the average values obtained by editing the individual $C_{\rm N}^{2}$ profiles in the 0-40 m range, with reference to the corresponding wind and temperature profiles

In addition, the first 5-10 s of each flight's data were contaminated by large temperature fluctuations associated with the launch procedure, and it was expected that the seeing contribution from the lowest 30-50 m would be greatly overestimated due to this effect. Two methods were used to try to estimate as accurately as possible the $C_{\rm N}^{2}$ profile in this region. The first was to examine the raw data for individual flights in detail, with reference to the temperature and wind velocity gradients (see Sect. 3.4), and estimate the correct $C_{\rm N}^{2}$ values for each flight, in the lowest 50 m. The second method involved using the 1994 study of lower-boundary layer turbulence (Marks et al. 1996), from which we have long-term average $C_{\rm N}^{2}$ values up to a height of 27 m. Comparing this with the corresponding average radiosonde data clearly indicated the lower limit of validity of the balloon data, which could then be interpolated down to ground level using the 1994 values. The results from both of these analyses are shown in Fig. 1, together with the unmodified average $C_{\rm N}^{2}$ profile. It is clear that the radiosonde data is valid upward from around 40 m. Below this level, the two methods described provide very consistent estimates of the average $C_{\rm N}^{2}$ values.

A further difficulty was that most of the balloons reached an altitude of only 12-15 km, rather than the usual 25+ km, due to the reduced strength of the balloon material at very low temperatures. Thus any turbulence above 15 km was not measured. However, due to the very low air pressure, the optical turbulence at this altitude is generally extremely low, and the $C_{\rm N}^{2}$ measurements invariably dropped to around the $10^{-18}-10^{-19}~{\rm m}^{-2/3}$ level by the end of each flight. This trend continued in the one flight that reached an altitude of >20 km. Integrating up to 25 km using an artificial $C_{\rm N}^{2}$ profile based on weather balloon pressure and temperature data from the NOAA weather balloons (see Eq. 2) indicated that the unsampled region of the atmosphere contributed less than $0.01\hbox{$^{\prime\prime}$}$ to the seeing.

3.1 Summary of results

The seeing measurements from the 15 flights are summarised in Table 1. The weather observer's notes from the time of each launch indicate that 10 of the 15 flights took place in clear conditions, with some scattered cloud present on the other 5 days. The mean total integrated seeing was measured to be 1.86 $\pm$ 0.02$\hbox{$^{\prime\prime}$}$. The quoted uncertainty represents the slight discrepancy between the results from the two methods (described above) used to estimate the contribution from 0-40 m. The average free atmosphere contribution of 0.37$\hbox{$^{\prime\prime}$}$ (corresponding to r0=27.2 cm) represents only $\sim$7% of the integrated optical turbulence ($\int C_{\rm N}^{2}(h){\rm d}h$).

Table 1: Summary of integrated seeing and boundary layer data, from 16 balloon launches between 20 June and 18 August 1995. The "free atmosphere'' refers to the entire atmosphere excluding the boundary layer. Values are quoted for a wavelength of 0.5 $\mu$m

Measurement & Mean & Std.~D...
 ...) & 220 & 70 & 190 & 165 & 120 & 275 \\ \noalign{\smallskip}

The range of total seeing values is very large ($\sigma=0.75\hbox{$^{\prime\prime}$}$), and sub-arcsecond seeing was measured from ground level in 3 of the 15 flights. The free atmosphere contribution, on the other hand, was relatively constant throughout the season ($\sigma=0.07\hbox{$^{\prime\prime}$}$), which indicates that the variability is largely due to fluctuations in boundary layer turbulence. Figure 2 shows the statistical distribution of total and free atmosphere integrated seeing results. The intense and highly variable boundary layer signal agrees with the results of the 1994 experiment (Marks et al. 1996), where the seeing contribution from just the lowest 27 m was measured to be 0.64$\hbox{$^{\prime\prime}$}$, $\sigma=0.40\hbox{$^{\prime\prime}$}$.

The height of the boundary layer is 220 m on average. The upper limit of the boundary layer was defined as the lowest height, h0, at which successive calculations of the integrated seeing (Eqs. (3)-(4)) varied according to:

\varepsilon_{h_{0}+1}^{\infty} - \varepsilon_{h_{0}}^{\infty} \leq 
where the sub- and super-scripts refer to the limits of the integration in Eq. (3). In all cases, this corresponded closely to the limit of the steeply increasing section of the temperature profile, although the temperature inversion occasionally continued more weakly for a further 100 m or so.

It is worth noting the wavelength dependence of $\varepsilon$:from Eqs. (3-4), $\varepsilon \propto \lambda^{-1/5}$, and so, for example, at a wavelength of 2.4 $\mu$m, the corresponding values are $1.36\hbox{$^{\prime\prime}$}$ for the full atmosphere and $0.27\hbox{$^{\prime\prime}$}$ for the free atmosphere. This particular wavelength is of significance since it is in the so-called "cosmological window'': a waveband corresponding to a natural minimum in airglow emission, and at which the sky brightness due to thermal emission at the South Pole is a factor of 10-100 lower than at any other ground-based site (Ashley et al. 1996).

3.2 Comparison with H-DIMM observations

A modified version of a differential image motion monitor, known as an "H- DIMM'' (Bally et al. 1996) was also in place at the South Pole during 1995. This instrument consisted of a 60 cm telescope with a multiple-aperture mask, and is essentially similar in principle to the standard DIMM as described by Sarazin & Roddier (1996).

Seeing measurements were taken by the H-DIMM near-simultaneously with a microthermal balloon flight on 5 occasions during the season. The results are compared in Fig. 3. The correlation between the two experiments is reasonably good for three of the flights, while for the other two, the microthermal data gives a significantly lower value for the FWHM seeing than does the H-DIMM. These discrepancies are most probably due to serious disturbances in the H-DIMM images caused by internal heaters being inadvertently left on during many of the observations, a problem which was not noticed until after the completion of the experiment. These distortions were thought to be largely confined to one particular region of the image data, which was removed during the reduction process. However, it is possible that some effect of this heating was present across the rest of the image, which may have artificially elevated the derived seeing. A small residual effect of this nature would be most noticeable at times of relatively low atmospheric seeing, as was the case for the two observations in question.

\end{figure} Figure 2: Seeing data statistics for the 15 balloon sondes launched in 1995: a) total (from ground level), b) free atmosphere

\epsfbox{}\end{figure} Figure 3: Comparison of H-DIMM (triangles) and microthermal (crosses) seeing measurements on the five occasions that the two experiments were performed simultaneously, from 23 June to 21 July, 1995. The error bars derive from the uncertainty in the $C_{\rm N}^{2}$ values from 0-40 m

3.3 Individual flight characteristics; relation of boundary layer seeing to atmospheric parameters

The vertical profile of the optical turbulence at the South Pole is markedly different from that measured using similar techniques at other sites around the world. Figure 4 is a plot of $C_{\rm N}^{2}$ vs. altitude for three of the balloon launches, and illustrates the conditions typically observed. Potential temperature[*] and wind velocity gradients are also included in the boundary layer profiles (Figs. 4a,c,e). Note that different scales are used on the $C_{\rm N}^{2}$ axes for the three boundary layer plots.

Figure 4a-f: $C_{\rm N}^{2}$ vs. altitude: a-b) for 23/06/95, c-d) for 21/07/95, e-f) for 18/08/95. The boundary layer plots include potential temperature gradient, $\left\vert{\rm d}\theta/{\rm d}z\right\vert$ (dashed lines) and wind velocity gradient, $\left\vert{\rm d}\vec{U}/{\rm 
d}z\right\vert$ (dotted lines). The axes on the right of each plot show $\left\vert{\rm d}\theta/{\rm d}z\right\vert$, in units of $^{\circ}{\rm C/m}^{-1}$. Units for $\left\vert{\rm d}\vec{U}/{\rm 
d}z\right\vert$ are not shown; it is approximately equal to 0.5 (RHS axis scale) ${\rm m\, s}^{-1}$, offset by -0.05 for clarity

The boundary layer turbulence structure is quite complex, and contains several strong $C_{\rm N}^{2}$ peaks, generally occurring in layers around 10-20 m in thickness. The most intense of these are often concentrated in two regions; one close to the surface (up to 50-100 m), and another closer to the top of the inversion layer ($\sim$200 m). This feature is clearly evident in Figs. 4a,c, and was observed in many of the other flights. It corresponds to a "two-tiered'' temperature inversion, as indicated by the secondary rise in ${\rm d}\theta/{\rm d}z$ in each of these flights.

The layers of intense optical turbulence, and its overall rapid decrease with altitude, are strongly correlated with simultaneous sharp fluctuations in ${\rm d}\theta/{\rm d}z$ and $\left\vert{\rm d}\vec{U}/{\rm 
d}z\right\vert$, as can be seen clearly in the three flights shown. Figure 5 shows the average profiles of these quantities along with the $C_{\rm N}^{2}$ measurements. The mean temperature inversion magnitude is $\sim$25$^\circ$C. These observations agree with the known requirements for optical turbulence: the presence of both a significant temperature gradient and mechanical turbulence produced by wind shear. In other words, it is the combination of a strong temperature inversion and a wind velocity gradient which produces such a strong seeing contribution close to the surface, as can be seen clearly in Fig. 5.

The occurrence of sub-arcsecond seeing from ground level (observed on three occasions) tended to coincide with a shift in wind direction away from the bearing of the usual katabatic flow (between grid N and E) toward the SE quadrant, with a corresponding increase in surface level temperature and decrease in wind speed. The temperature during the best seeing conditions observed ($0.8\hbox{$^{\prime\prime}$}$) was -42$^\circ$C, about 18$^\circ$C above average. These influxes of relatively warm air from the coast onto the plateau occur very occasionally throughout the winter. The markedly improved seeing that occurs during these events highlights the importance of the katabatic wind to the generation of optical turbulence in the boundary layer.

\epsfbox{}\end{figure} Figure 5: Average $C_{\rm N}^{2}$, $\left\vert{\rm d}\theta/{\rm d}z\right\vert$,and $\left\vert{\rm d}\vec{U}/{\rm 
d}z\right\vert$ profiles up to a height of 1 km above the surface. Wind velocity data were obtained from weather balloon launches performed almost simultaneously with our flights

Relatively poor seeing (> 2.5$\hbox{$^{\prime\prime}$}$), tended to occur during fairly typical wind and temperature conditions. However, the three worst boundary layer seeing measurements coincided with a very pronounced "double inversion'', as described previously, with very intense $C_{\rm N}^{2}$ peaks in the upper part of the boundary layer.

In all but one of the flights, the free atmosphere turbulence was very weak, with the strongest peaks usually around two orders of magnitude weaker than those measured in the boundary layer. There was very little tropopause instability observed in any of the data, with occasional layers of increased optical turbulence not restricted to any particular region of the atmosphere.

The conditions for wind-generated turbulence are often defined in terms of the Richardson number:

R_{\rm i} & = & \frac{g}{\theta}\frac{\left({\rm d}\theta/{\rm ...
 ... d}\vec{U}/{\rm d}z\right)^{2}}\nonumber\\  & < & \frac{1}{4}\cdot\end{eqnarray}
Equation (5) is usually stated as the criterion for the development of turbulence. This inequality was calculated for all flights, and observed to be consistent with the $C_{\rm N}^{2}$ measurements in the lower part of the boundary layer as a whole. However, it did not appear to describe very well the intense individual turbulent layers, which often coincided with large positive values of ${\rm d}\theta/{\rm d}z$. In the free atmosphere, the occasional layers of relatively large $C_{\rm N}^{2}$ were often associated with dips in $R_{\rm i}$ below the critical value of 1/4, as shown in the example of Fig. 6. Any features not coinciding with a decrease in $R_{\rm i}$ generally occurred in thin layers with a sharp rise in $\theta$ of up to $1-2^{\circ}$C.

\epsfbox{}\end{figure} Figure 6: A comparison of $C_{\rm N}^{2}$ and $R_{\rm i}$ profiles for 02/07/95. $1/R_{\rm i}$ is plotted to show more clearly the regions of instability: any peaks above the dashed line satisfy $R_{\rm i}<1/4$. The integrated seeing values calculated for this flight were: $\varepsilon_{\rm 
tot.}=0.83\hbox{$^{\prime\prime}$}$, $\varepsilon_{\rm FA}=0.41\hbox{$^{\prime\prime}$}$

Table 2: Comparison of seeing conditions at the South Pole and some of the world's major observatory sites. FA, BL and SL refer to the free atmosphere, boundary layer and surface layer, respectively

Site & Altitude & Total se...
 ... \cite[1994]{ver:tun2} \\ Canary Is. \\ \noalign{\smallskip}

Most of the free atmosphere seeing was caused by these turbulent layers. The flights where no sharp peaks in $C_{\rm N}^{2}$ were observed (6 out of 15, including Figs. 4b,f) gave $\varepsilon_{\rm FA}=0.23-0.26\hbox{$^{\prime\prime}$}$. Further analysis of the long-term meteorological records, with regard to the behaviour of $R_{\rm i}$ and ${\rm d}\theta/{\rm d}z$, will therefore be useful in determining the frequency of the best free atmosphere seeing conditions at the South Pole.

The $C_{\rm N}^{2}$ measurements are in broad agreement with acoustic soundings performed at the South Pole since 1975 (e.g. Neff 1981), as well as other analyses of the meteorological data (Schwerdtfeger 1984; Gillingham 1993). While the acoustic backscatter measurements of $C_{\rm N}^{2}$ had a lower vertical resolution than the microthermal balloon sondes, they did illustrate the same features, i.e. a complex turbulence structure, often split into two layers, extending up to an altitude of 200-300 m, with a sharply defined upper limit, and much weaker activity thereafter.

3.4 Comparison with other sites

In contrast to the conditions observed at the South Pole, while the $C_{\rm N}^{2}$ profiles measured at mid-latitude sites (e.g. Roddier et al. 1990; Vernin & Muñoz-Tuñón 1994) often show a significant boundary layer contribution to the overall seeing, it usually extends to at least 1-2 km above ground level, and is invariably of much lower intensity. In addition, upper atmosphere turbulence, arising from jet streams and temperature fluctuations in the tropopause, is often a major component of the seeing at these sites.

Table 3 summarises seeing measurements from some of the world's leading observatory sites. It can be seen quite clearly that the optical turbulence at the South Pole is concentrated much closer to the surface than at any of these sites. The free atmosphere contribution is comparable to or lower than the best quoted results from the other sites. It is important to note that the value of $0.37\hbox{$^{\prime\prime}$}$ is calculated upward from $\sim$200 m above the surface. The contribution from the atmosphere above 2000 m (the average boundary layer height at the mid-latitude sites of similar altitude) at the South Pole is $<0.3\hbox{$^{\prime\prime}$}$.

\epsfbox{}\end{figure} Figure 7: Seeing as a function of height of the telescope above the surface. The solid line represents average results from our launches at the South Pole, while the dashed line is a summary of a similar experiment performed at the ESO-VLT site at Cerro Paranal, northern Chile (Fuchs 1995) in May 1993, averaged over 13 flights
As a more direct comparison, Fig. 7 shows the derived seeing, averaged over the fifteen flights, as a function of the altitude at which a hypothetical telescope is placed. This plot is obtained by increasing the lower altitude limit of the integral in Eq. (3) in 5 m steps. The optical turbulence falls sharply up to an altitude of $\sim$120 m, and decreases more gradually up to 200 m, beyond which the very low remaining seeing contribution decreases smoothly with altitude.

The results of similar experiments (averaged over thirteen flights) performed at the ESO-VLT site at Cerro Paranal, Northern Chile (Fuchs 1995), are included in the same figure. The two data sets were analysed using the same method. It is clear that, while South Pole is an inferior site (in terms of seeing) from ground level, most of the image degradation occurs very close to the surface. The seeing is better than that measured at Paranal above an altitude of only $\sim$100 m. The free atmosphere contribution, i.e. above $\sim$250 m, is around 60% of the corresponding value calculated from the Paranal data.

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