© D. Andre Erasmus, 1988 and 1996
ABSTRACT: Large aperture, advanced technology telescopes constitute major financial investments. Optimizing the image quality on these telescopes is critically dependent upon atmospheric effects. These effects occur in the atmospheric boundary layer, in and around telescope domes, and in the free atmosphere. Telescope dome effects may be minimized by engineering efforts. Atmospheric effects, however, cannot be changed, but they may be quantified and/or forecasted. There is growing evidence that microphysical processes occurring in the atmosphere (viz., variations in atmospheric refractive index caused by high-frequency temperature fluctuations), which cause degradation of image quality, are related to ambient meteorological conditions. The existence and nature of some of these relationships are known but further research on this topic is needed. This information would be the basis for the development of seeing-quality forecasts and would also improve procedures for telescope site selection.
TABLE OF CONTENTS
1. Introduction
The larger a telescope's aperture, the greater the degradation of image quality due to atmospheric effects will be. For many applications in astronomy, therefore, excellent seeing is just as important as having a large telescope aperture. The key to predicting limitations on image quality due to atmospheric effects is understanding the relationship between the microphysical atmospheric processes that determine the seeing quality and ambient meteorological conditions. This is because ambient meteorological parameters are more readily measured than microscale variables. In addition, these data are archived, thus making available a large data base from which conclusions about the observing conditions at various sites may be deduced. Finally, an understanding of the relationship between seeing quality and meteorological conditions is a prerequisite to the possible development of seeing quality forecasts.
Atmospheric turbulence that degrades observing quality occurs in three main regions within the telescope viewing path, each of which is associated with different mechanisms of turbulence generation. These regions are the atmospheric boundary layer, the free atmosphere and the area in and around the telescope dome. Reducing the detrimental effects of telescope domes is related to the design and thermal characteristics of the telescope structure. It is therefore largely an engineering problem. Thus the main limitation on image quality is atmosphere effects, a factor that cannot be altered. There are, however, temporal variations in the effects of the atmosphere that are closely related to the movement and intensity variations of weather systems at various scales. It may be possible, therefore, to take advantage of periods of excellent seeing quality by forecasting the seeing conditions.
There is, therefore, a two-fold benefit to be derived from an understanding of the relationship between seeing quality and meteorological conditions:
i) An understanding of the relationship between seeing quality and meteorological conditions would permit the use of existing meteorological data in the selection of new observatory sites. The use of these data would enable the compilation of reliable long-term statistics on observing conditions and would reduce the need for additional data collection in the site selection process.
ii) If the seeing quality can be linked to meteorological parameters, then data collected by existing weather station networks and by weather satellites could be used to forecast seeing quality on an operational basis. Such forecasts would improve the efficiency with which telescope facilities are used, since they would provide advanced notice of good seeing quality, allowing adequate time for changes in telescope instrumentation so that the greatest benefit can be derived from the seeing conditions.
It is clear, therefore, why Coulman (1985) identifies "relating seeing quality to larger scale meteorological conditions" as the most important, outstanding problem in the field of astronomical seeing.
Erasmus (1986), has provided a subjective discussion on relationships between astronomical observing quality and meteorological conditions at the Mauna Kea Observatory. Observing conditions are affected by cloud cover, atmospheric humidity, and high-frequency temperature fluctuations associated with atmospheric turbulence. It is the last mentioned factor that is responsible for the degradation in image quality that astronomers identify as poor seeing quality. This effect may occur on both spectroscopic and photometric nights.
Different meteorological processes are responsible for generating turbulence in the boundary layer and free atmosphere respectively. In the boundary layer, local scale phenomena determine turbulence intensity, whereas in the free atmosphere, synoptic scale conditions are connected with turbulence generation. The approach to establishing the connection between microscale turbulence and ambient conditions is therefore strongly dependent on the relative contributions to the image quality degradation from the boundary layer and the free atmosphere.
The physical relationship between atmospheric turbulence and seeing quality has been reviewed in detail by Roddier (1981) and Coulman (1985). When a plane wave of light with uniform amplitude propagates through a refractively nonuniform medium such as the atmosphere, it exhibits amplitude and phase fluctuations. When such a wave front is focused, the resulting image varies in intensity, sharpness, and position. These variations are commonly referred to as scintillation, image blurring, and image motion, respectively.
In turbulent flows, there is a range of eddy sizes that are large enough to avoid dissipation by friction and yet are too small to be imparting kinetic energy to the flow, called the inertial subrange. At separations (r) of the order of inertial subrange scales, the temperature structure coefficient (CT2) in a locally isotropic field has the form:
CT2 = [T (x) - T (x +r)]2 /r2/3 (1)
where 0.1m <~ r <~ 1.0m is the separation vector and T is temperature. Seeing quality is therefore related to high-frequency temperature fluctuations associated with atmospheric turbulence.
These high frequency temperature fluctuations produce variations in the refractive index of light in the atmosphere. The refractive index structure parameter (Cn2), which is a measure of the average variability of the refractive index of light in the atmosphere, is related to CT2 as follows:
Cn2 = CT2 [7.9x10-5P/T2]2 (2)
where P is the pressure in mb and T is the temperature in K.
The total effect of atmospheric turbulence is derived from the integral of Cn2 (z) for all atmospheric layers. The Fried parameter (ro) is a commonly used measure of the total image degradation due to atmospheric turbulence. It is related to Cn2 as follows:
ro = [ 0.06 w2 / Cn2 (z) dz ]3/5 (m)
where w is the optical wavelength (usually taken as 550 nm).
There are three main types of turbulent motion that affect image quality.
i) Turbulence in the free atmosphere: In the free atmosphere, microthermal activity is associated with strong wind speed and temperature gradients that generally occur in the vicinity of the upper tropospheric jet stream at an altitude of about 12 km.
ii) Turbulence in the atmospheric boundary layer: At the boundary between the atmosphere and the Earth's surface, frictional effects cause the atmospheric boundary layer flow to be turbulent. This region is also characterized by strong temperature gradients.
iii) Turbulence in and around the telescope dome: The telescope dome interacts with the boundary layer flow in a manner that enhances turbulence in and around the dome. The effects of the telescope dome on seeing quality are dependent largely on the design and thermal characteristics of the structure itself and not on the site at which the facility is located.
The effects of ground turbulence are strongly dependent on local variations in surface roughness, thermal forcing, and topography. These factors affect the local wind speed and temperature gradients which are directly related to turbulence generation via the Richardson number (Ri).
Ri = (g/T)[(dT/dz)DALR - dT/dz)] / (dV/dz)2 (4)
where (dT/dz)DALR is the dry adiabatic temperature lapse rate with height, dT/dz is the observed temperature lapse rate with height, g is gravitational acceleration, T is the mean temperature in the layer and dV/dz is the wind speed versus height gradient. Wyngaard et al. (1971) have developed a semiempirical theory relating CT2 to Ri in the surface boundary layer. The values of CT2 computed using their technique and those measured directly show remarkably good agreement. Thus the theoretical bases for relating CT2 to ambient parameters has been confirmed by observations.
Mahrt (1985) studied the structure of turbulence in a very stable boundary layer. He found that enhanced turbulence may occur at the top of the surface inversion layer where the nocturnal drainage flow interacts with the synoptic flow regime. This phenomenon usually occurs in the upper boundary layer at heights of 200-500 m above the surface. A stable drainage flow accompanied by a surface inversion layer does develop on the slopes of mountains at night so the interactions described by Mahrt (1985) may be occurring at observatory sites. In addition, mass continuity demands that the air removed from the summit at night by the drainage flow be replaced by enhanced subsidence above the mountain. This may produce adjacent layers of different potential temperatures (an inversion). If mixing occurs under these circumstances, microthermal activity may result. These two mechanisms may be responsible for turbulence generation in the layer between 30 m and 1000 m.
Free atmosphere effects are determined by synoptic scale meteorological systems. Since these systems are migratory or undergo temporal oscillations in intensity and have scales of between 500 and 5000 km, they induce changes in atmospheric conditions at a particular locality with a time scale of between 1 and 5 days. Available data on the latitudinal position and strength of the subtropical westerly jet stream at the longitude of Hawaii (Sadler, 1975), for example, indicates that the level of microthermal activity in the free atmosphere above Mauna Kea is highly variable since the jet stream occurs in a region of strong temperature and wind speed gradients, these variations are likely to be associated with changes in seeing quality.
Van Zandt et al (1978, 1981) have developed a model that simulates profiles of Cn2 (z) in the free atmosphere. Limited comparison of model simulations with observations (Green et al, 1984) have been made. Deviations between simulated and observed profiles of Cn2 (z) occurred in the lower troposphere due to high humidity and low static stability in the area where the observations were made. These conditions are not typical of the free atmosphere above observatory sites where the air is extemely dry and stable. Thus it is likely that the Van Zandt model can be used to quantify the contributions of free atmosphere turbulence to image quality degradation.
The discussion above shows that the theoretical basis for using meteorological parameters to quantify the effects of atmospheric turbulence on seeing quality exists. There is good reason to believe that seeing quality can be related to ambient meteorological conditions. Therefore the potential exists to use these data to quantify and possibly forecast seeing quality at telescope sites.
4. References
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Wyngaard, J. C., Ozumi, Y., and Collins, S. A. 1971: Behavior of refractive index structure parameter near the ground. J. Opt. Soc. Am. 61, 1636-1650.