Astronomic Seeing



Good seeing:

The Physics of Seeing

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).

The Meteorology of Seeing

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.