Title: Determining the refractive index structure constant using high-resolution radiosonde data




НазваниеTitle: Determining the refractive index structure constant using high-resolution radiosonde data
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1.2 Estimating Turbulence


Turbulence in terms of Cn2 and CT2 has been estimated by many authors employing a multitude of techniques. To estimate vertical profiles the techniques are mainly those that use radar, thermosondes and radiosondes.


1.2.1 Radar

Radar can measure the refractive index structure function because Cn2 is proportional to the radar reflectivity, Ottersten [1969].




(4)


where η is the radar reflectivity and λ is the radar wavelength. A review of radar-based measurements of Cn2 is beyond the scope of this paper. Excellent reviews of the technique may be found in VanZandt et al [1978], Rao et al [1997] and Rao et al [2001].

The second advantage of the radar technique is its capability to acquire data in a systematic and continuous manner. This capability has yielded the insight that the conditional probability distribution of Cn2 (conditioned to the presence of turbulence) is log-normal at all heights and times, Wheelon [2001] and Nastrom et al [1986].

Unfortunately many authors, when publishing measurements of Cn2 have done so in the form of averages (seasonal, monthly or diurnal means) with little information on the probability distribution of the measurements, Ghosh et al [2001], Rao et al [2001]. Often it is also not clear whether the means obtained refer only to turbulent events, well above the minimum Cn2 detectable by the radar, or if these means are for all measurements. The data in this form is difficult to use in any applications that require statistical information such as those in radio-wave propagation where an outage probability needs to be estimated.

Under an experimental point of view the radar has the disadvantage that it is an expensive instrument to acquire and to operate. This is the reason why there are not many around the globe when compared with for instance radiosondes.


1.2.2 Thermosondes

Instrumented balloons carrying pairs of sensors at a given distance (e.g. 1 meter apart) have provided very high quality profile data.

The technique derives the one-dimensional structure function directly from differential measurement at the two sensors, Bufton et al [1972], Barlettti et al [1976] and Coulman [1973]





(5)


where T is the variable measured (usually temperature), r the distance between sensors. Local isotropy and homogeneity is assumed to derive Cn2.


This is a very powerful technique with vertical resolutions that, in principle, may be better than those achievable by radar.

The disadvantage of this technique is that it requires specially purpose built equipment and is limited to specific measurement campaigns. No systematic data is available as it is more expensive than radar.


1.2.3 Radiosondes

Standard meteorological radiosondes have been used to derive Cn2 , Warnock & VanZandt [1985], VanZandt et al [1978] and Vasseur [1999]. Radiosonde launches are generally carried out at synoptic times (0, 6, 12 and 18 UTC) across the globe. In more than 700 sites launches are carried out twice a day and in more than 300, four times a day. These measurements are carried out as part of the global meteorological network coordinated by the World Meteorological Organization.

Radiosondes measure all atmospheric variables of interest (pressure, humidity and temperature as well as wind speed and direction) across the full vertical profile however only measurements at standard and significant pressure levels are stored and archived.

These archived measurements have typical resolutions from 100 to 1000 meters, which are much bigger than the typical outer scales of turbulence. These resolutions are not sufficient to characterise turbulence, which in general occurs in relatively thin layers, and as a consequence, assumptions on the occurrence of turbulent layers are necessary to derive Cn2. Therefore probability distributions for wind shear, buoyancy and the outer scale of turbulence have to be assumed.

The advantage of these data is that it is easily available and covering a wide range of climates over long periods of time (some datasets cover more than 20 years).

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