2 Polar Research Institute of China, Shanghai200136, China;
3 University of Scienceand Technology of China, Hefei 230026,China;
4 Science Island Branch of GraduateSchool, University of Science and Technologyof China, Hefei 230031, China
1 Introduction The main effects on the performance of ground-based astronomical telescopes are sky background,transmittance,and optical turbulence and so on[1,2]. Atmospheric turbulence is the major reason for the serious decline of imaging quality of the astronomical optical telescope. Random refractive index fluctuations associated mainly with temperature fluctuations are called optical turbulence. Thesky background and transmittance limit telescope sensitivity,and optical turbulence limits resolution. Given theinfluence of atmospheric turbulence on astronomical parameters,seeing is not only one of the importantfactors in site location decision-making but is also a major measurement parameter. It is an important indicator in evaluating astronomical site quality. Turbulentintensity in the near-surfacelayer and its rate of decrease with height are closely related to the qualityof potential sites. Quoted fromPant’s measurement result in Devasthal,seeing of the near-surface 6-12 m layer is 1.28′′,but it is down sharply to 0.32′′ in the 12-18 m layer. In the circumstance where boundarylayer and free atmosphere turbulence at candidate astronomical sites are equivalent,as an indicator of seeing,one must compare turbulent intensity of the surface layer and rate of decrease with height to quantify which site is the best for astronomical applications.
Continuous observationof atmospheric optical turbulence of the surface layer is usually achieved using a meteorological mast equipped with several-layer micro-thermometers. Because dust readily causes probe contamination and strong wind,insects and other factors damage the probe,the micro-thermometer probes need regular replacement and cannot be used in unattended operation in adverseenvironments. We have proposed measuring the refractiveindex structure constant Cn with a single-point temperature structure function method,involving analysis of temperature fluctuation time-series data from an ultrasonic anemometer[4,5]. This method was coded into the dataacquisition system of a mobile atmospheric parameter measuring system[6,7],so Cn could be measuredin real time. This instrument was installed at Antarctic Taishan Station by the 30th Chinese National Antarctic Research Expedition (CHINARE) team for astronomical site testing. Major stations thatare currently used for astronomical observation in the Antarctic are Amundsen-Scott at the South Pole,Concordia at Dome C,Kunlun at Dome A,and Fuji at Dome F. At the SouthPole,the mean visual seeing,measured by 15 balloon flights in 1997,was 1.86′′,of which the free atmosphere component was only 0.37′′. At Dome C,the summer site testingmedian seeing based on a DifferentialImage Motion Monitor (DIMM) was 0.54′′. In 2004,by combining free- atmosphere Cn2 values determined by the Multi-Aperture Scintillation Sensorwith surface boundary layer turbulence determined by Sonic Detection and Ranging,atmospheric seeing above 30 m was 0.27′′. In 2005 seeing,isoplanatic angle and coherenttime above 30 m based on in situ balloon measurementwas 0.36′′,4.6′′,and 7.9 ms,respectively. In this paper,we analyze turbulence data obtained by a mobile atmospheric parameteracquisition system at Antarctic Taishan Station,and compare several methods of optical turbulence measurement. We found a value of Cn2 derived from a structure function analysis previously proposed with a sonic anemometer was different from that of micro-thermometer measured. Thus,a new method to measure Cn2 with a temperature spectrum analysis is proposed.. Cn2 data derived from an ultrasonic anemometer with the new method and micro-thermometer were mainly the same in magnitude and trend.2 Introduction to measurement system The Antarctic mobile atmospheric parametermeasurement systemincludes a CR5000 data logger,CSAT3 three- dimensional ultrasonic anemometer,micro-thermometer,temperature and relative humidity probe,wind monitor,485 communication module,power module,and a 3-m tower. Two levels of air temperature,relative humidity and wind speed,and one level of air pressure,surface temperature,atmospheric optical turbulence intensity and other atmospheric parameters can be measured. Taishan Station is located in Princess ElizabethLand between the Chinese Antarctic Zhongshan and Kunlun stations,76°58’E,73°51’S,at altitude 2621 m. Figure 1 shows the mobile atmospheric parameter measurement system at Chinese AntarcticTaishan Station. The site testingexperiments were carried out during the 30th CHINARE. Part of the data from 30 December 2013,when the system was installed,to 10 February 2014,when the expeditionstaff returned,were analyzed here. 3 Measurement methods of Cn2 For Kolmogorov turbulence,the refractive index structure constant and the temperature structure constant are defined as
where and denote the position vector,r is the magnitude of ,angle bracketsrepresent the ensemble average,and l0 and L0 are the inner and outer scales of the optical turbulence,respectively. For visible and near-infrared light,the refractiveindex fluctuation is mainly caused by temperature fluctuation. Conversion of CT2 to Cn2,depends on local pressureand temperature,and it is customary to use the following equation:
where T is air temperature (K) and P is air pressure(hPa). Therefore,Cn2 can be calculatedthrough Equations (2) and (3) by measuringthe square and average of the temperature difference given by two sensors separated by a known distance r in the inertialregion. This is called the structure function method of temperature differences between two points.
The relationship between temperature and wire resistance is
Thus,the ΔR and ΔT relationship is
where R0 is the resistance at reference temperature T0 and α is the coefficient of thermal resistivity of the wires.
The two resistance sensors are legs of a Wheatstone bridge that generatesa voltage differenceΔV proportional to the temperature difference ΔT:
Here,C is the calibration coefficient.
The principle of micro-thermometer measurement is the same as in the last paragraph. Cn2 is deduced from a pair of horizontally separated micro-temperature probes. The frequencyresponse range of the micro-thermometer is 0.1- 30 Hz,and the standard deviation of minimum temperature fluctuation is < 0.002°C.
The triaxial ultrasonic anemometer measures temperature from transit times t1 and t2 measured along a known distance path of the anemometer’ probe. The speed of sound in moist air is a function of temperature and humidity. Sonic temperature Ts and air temperature T have the following relationship:
Here,t1 and t2 are the transittimes in seconds for sound pulses traveling in opposite directions along acoustic path length d,and Vn is the magnitudeof the horizontal wind vector normal to d. q is specifichumidity. In dry conditions,the diferenceof Ts and T is very small.
For the temperature fluctuation time series data measured by the ultrasonicanemometer,Taylor’s frozen turbulence hypothesis was used to convert a time series of a fluctuating quantity into a spatial series of fluctuations along the direction of the mean wind. Therefore,Cn is deduced via Equations (9) and (3) by measuringthe square and average of the temperaturedifference between two time points in the inertialregion. This method is known as single-point temperature structurefunction method.
where τ is the time interval,determined by the average wind speed and the known space length (typically 1 m).
CT2 can be determined by the one-dimensional temperature spectrumof the turbulence inertia region. For Kolmogorov turbulence,the one-dimensional temperature wave number spectrumΨT(k) is
where k is the wave number. For the power spectrum,temporal and spatial frequencies are related by . It is easy to show that the relationship between the temporal and spatial one-dimensional spectra is
We can write
This method is called the single-point temperature spectrum method.
More generally,the form of ΨT(f ) can be expressed as
Here,A is the coefficient related to the generalized temperature structure constant ,and α is the spectral power law of one dimension. On a logarithmic scale,Equation. 13 is written as
can be estimated via linear regression.4 Measurement results and discussion 4.1 Comparison of Cn2 between ultrasonic anemometer with single-point temperature structure function method and micro-thermometer Figure 2 is an example of derived from the ultrasonic anemometer with structurefunction analysis and those from micro-thermometer at Taishan Station on 6 January 2014. The samplingfrequency of the ultrasonic anemometer was 50 Hz and the average time for calculating Cn2 was 20 s. It is seen that Cn2 values from the ultrasonic anemometer are several times greater than those of the micro-thermometer,sometimes even one order of magnitude greater. The characteristic Cn2 diurnal cycle with minima near sunrise (about 0900) and sunset (about 1900) is not obvious.The other time data also have similarcharacteristics. No matter the order of magnitudeand trend of Cn2,the data measured with the single-point temperature structure function method cannot be used to explain the Cn2 characteristics at Taishan Station. However,although the order of magnitude of Cn2 measured by the two methods had a few differences from other field experiments[4,5,6,16],trends were basicallythe same,with a correlation coefficient > 0.9. 4.2 Comparison of Cn2 between ultrasonic anemometer with single-point temperature spectrum method and micro-thermometer Using Equations (10)-(12) we measured Cn2 by the single-point temperaturespectrum method. Triaxial sonic anemometer sampling frequency was 50 Hz and the sampling period was 16.4 min. This yielded 49200 data points per run. A fast Fourier transform was carried out and the power spectrum of 25 Hz was obtained. The power spectrum was smoothed and combined with wind speed,and the approximate inertial range was determined. After the median CT2 of a set of values in the inertial region was calculated by the formula (12),Cn2 was obtained. Figure 3 is a comparison of Cn2 values derived from the ultrasonic anemometers with spectrumanalysis and micro-thermometer,using Figure 2 dataset. In comparison with Figure 2,Cn2 values derived from the ultrasonic anemometer with spectrum analysis are closer to those from the micro-thermometer. The former was smootherthan the latter,and was only sensitive over 2×10 -16m -2/3 ,but the micro-thermometer was sensitive about 2×10 -18m -2/3. To confirm the data reliability by ultrasonic anemometer at Taishan Station in an adverse environment,and the possibility of measuring Cn2 from ultrasonic anemometerinstead of micro-thermometer,we compared both instruments for long time. After abnormal data owing to the broken wire being eliminated,a 23-day dataset was used. Figure 4 is a comparisonof Cn2values from spectrumanalysis of sonic anemometer data and micro- thermometer data from 11January through 2 February2014. In this dataset,under various meteorological conditions and regardless of day or night,the comparison was satisfactory.
At Taishan Station,the difference of CT2 measured by the single-point temperature structure function method and the sonic anemometer and micro-thermometer is very large. This may be relatedwith factors such as spectral characteristics,turbulent multi-scalespatial and temporal structure,and whether the Taylor assumption is valid. A similarresult was found in reference. In that work,an aero thermal series from a cold wire probe mounted on an aircraft was analyzed.CT2 from the structurefunction sometimes agreed well with spectral analysis,but sometimes the difference was very large,fivetimes largerthan the spectrumanalysis results. The author believedthat the large differences were in the regions α where deviated from −5/3,so the structure function estimator was only valid for −3≤α<−1. For aero-thermal series data to be used in spectral analysis,it is speculated that Cn2 must be obtained via the single-point temperature structure function method under the Taylor assumption. To discoverwhy Cn2 values from the ultrasonic anemometer were several times larger than those of the micro-thermometer at Taishan Station,it is necessaryto determine the power frequency distribution of the temperature spectrum during an experiment. Figure 6 is the frequency distribution of the power law of a one- dimensional spectrum.The frequency for α< −1 was 36.2%,and that for α > −1 was 63.8%. That is,there is nearly two-thirds of spectral power outside the range −3≤α<−1,so we cannot use the single-point temperature structure function method to calculateCn2. In addition,during the Taishan Station experiment,average wind speed was 7.7 m·s-1,and the maximum was 16.3 m·s -1.Average wind speed from the literature[4,5,6,15] was not more than 3 m·s-1,so we should consider that this speed has an impact on the single-point measurement of temperature structure function method.
Figure 5 compares a Cn2 frequency distribution from spectrum analysis with the sonic anemometer and microthermometer data on 30 December 2013 to 10 February 2014. Sample numberswere 3446 and 59175,respectively. Table 1 is a Cn2 frequency distribution from the micro- thermometer and anemometerin three frequency ranges. In the −15<lg(Cn2)<−13.8 range,the frequencies of the two are both 78%. Frequencies in the lg(Cn2) > −13.8 range are 1.7% and 6.9%,respectively,and those in the lg(Cn2) < −15 range are 20.3% and 14.8%. During the experiment,78% optical turbulence at Taishan Station was concentrated in the range 10-15<Cn2<1.6×10-14. In this range,the Cn2 frequency distributions of both anemometer and micro-thermometer were consistent. Frequency statistics within the scope of strong and weak turbulence measured by the two instruments had a 6% difference. This may be attributable to smoothing,because the time for those statistics of the ultrasonic anemometer was 16.4 min whereas that for the microthermometer was only 20 s.
|Frequency distribution range||Micro-thermometer||Sonic anemometer|
|lg (Cn2) > -13.8||1.7%||6.9%|
|-15<lg (Cn2)< -13.8||78.0%||78.3%|
|lg (Cn2)< -15||20.3%||14.8%|
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