WU Xiaoqing, TIAN Qiguo, JIANG Peng, CHAI Bo, QING Chun,CAI Jun, JIN Xinmiao & ZHOU Hongyan,

1 Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Science, Key Laboratory of Atmospheric Composition and Optical Radiation, Chinese Academy of Science, Hefei 230031, China;

2 Polar Research Institute of China, Shanghai 200136, China;

3 University of Science and Technology of China, Hefei 230026, China;

4 Science Island Branch of Graduate School, University of Science and Technology of 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 ぼuctuations are called optical turbulence.The sky background and transmittance limit telescope sensitivity, and optical turbulence limits resolution. Given the influence of atmospheric turbulence on astronomical parameters, seeing is not only one of the important factors in site location decision-making but is also a major measurement parameter. It is an important indicator in evaluating astronomical site quality. Turbulent intensity in the near-surface layer and its rate of decrease with height are closely related to the quality of potential sites. Quoted from Pant’s measurement result in Devasthal[3], 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 boundary layer 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 observation of 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 adverse environments. We have proposed measuring the refractive index structure constantCn2with 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 data acquisition system of a mobile atmospheric parameter measuring system[6-7], soCn2could be measured in 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 that are 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 South Pole, the mean visual seeing, measured by 15 balloon flights in 1997, was 1.86′′, of which the free atmosphere component was only 0.37′′[8]. At Dome C, the summer site testing median seeing based on a Differential Image Motion Monitor (DIMM) was 0.54′′[9]. In 2004, by combining freeatmosphereCn2values determined by the Multi-Aperture Scintillation Sensor[10]with surface boundary layer turbulence determined by Sonic Detection and Ranging, atmospheric seeing above 30 m was 0.27′′. In 2005 seeing, isoplanatic angle and coherent time above 30 m based onin situballoon measurement[11]was 0.36′′, 4.6′′, and 7.9 ms, respectively. In this paper, we analyze turbulence data obtained by a mobile atmospheric parameter acquisition system at Antarctic Taishan Station, and compare several methods of optical turbulence measurement. We found a value ofCn2derived from a structure function analysis previously proposed with a sonic anemometer was different from that of microthermometer measured. Thus, a new method to measureCn2with a temperature spectrum analysis is proposed.Cn2data 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 parameter measurement system[6]includes a CR5000 data logger, CSAT3 threedimensional 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 Elizabeth Land 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 Antarctic Taishan Station. The site testing experiments 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 expedition staff returned, were analyzed here.

Figure 1 Mobile atmospheric parameters measurement system installed at Antarctic Taishan Station.

3 Measurement methods of Cn2

For Kolmogorov turbulence, the refractive index structure constant and the temperature structure constant are defined as[11]

whereTis air temperature (K) andPis air pressure (hPa).Therefore,C2ncan be calculated through Equations (2) and(3) by measuring the square and average of the temperature difference given by two sensors separated by a known distancerin the inertial region. This is called the structure function method of temperature differences between two points.

The relationship between temperature and wire resistance is

Thus, the ΔRand ΔTrelationship is

whereis the resistance at reference temperatureT0andαis the coefficient of thermal resistivity of the wires.

The two resistance sensors are legs of a Wheatstone bridge that generates a voltage difference ΔVproportional to the temperature difference ΔT:

Here,Cis the calibration coefficient.

The principle of micro-thermometer measurement is the same as in the last paragraph.Cn2is deduced from a pair of horizontally separated micro-temperature probes. The frequency response range of the micro-thermometer is 0.1–30 Hz, and the standard deviation of minimum temperatureぼuctuation is ＜ 0.002°C[13].

The triaxial ultrasonic anemometer measures temperature from transit timest1andt2measured along a known distance path of the anemometer’ probe. The speed of sound in moist air is a function of temperature and humidity. Sonic temperatureTsand air temperatureThave the following relationship[14]:

Here,t1andt2are the transit times in seconds for sound pulses traveling in opposite directions along acoustic path lengthd, andVnis the magnitude of the horizontal wind vector normal tod.qis specific humidity. In dry conditions,the diference ofTsandTis very small.

For the temperature fluctuation time series data measured by the ultrasonic anemometer, Taylor’s frozen turbulence hypothesis was used to convert a time series of aぼuctuating quantity into a spatial series of ぼuctuations along the direction of the mean wind. Therefore,is deduced via Equations (9) and (3) by measuring the square and average of the temperature difference between two time points in the inertial region. This method is known as single-point temperature structure function method.

whereτis the time interval, determined by the average wind speed and the known space length (typically 1 m).

can be determined by the one-dimensional temperature spectrum of the turbulence inertia region. For Kolmogorov turbulence, the one-dimensional temperature wave number spectrumΨT(k) is wherekis the wave number. For the power spectrum,temporal and spatial frequencies are related byk. 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 ofcan be expressed as

Here,Ais the coefficient related to the generalized temperature structure constantandαis 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 structure function analysis and those from micro-thermometer at Taishan Station on 6 January 2014.The sampling frequency of the ultrasonic anemometer was 50 Hz and the average time for calculatingCn2was 20 s. It is seen thatvalues from the ultrasonic anemometer are several times greater than those of the micro-thermometer,sometimes even one order of magnitude greater. The characteristicdiurnal cycle with minima near sunrise(about 0900) and sunset (about 1900) is not obvious. The other time data also have similar characteristics. No matter the order of magnitude and trend ofthe data measured with the single-point temperature structure function method cannot be used to explain thecharacteristics at Taishan Station. However, although the order of magnitude ofCn2measured by the two methods had a few differences from other field experiments[4-6,16], trends were basically the same,with a correlation coefficient ＞ 0.9.

4.2 Comparison of Cn2 between ultrasonic anemometer with single-point temperature spectrum method and micro-thermometer

Figure 2 Comparison of Cn2 derived from ultrasonic anemometers with structure function analysis and those from micro-thermometer.

Using Equations (10)–(12) we measuredCn2by the single-point temperature spectrum 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 medianCT2of a set of values in the inertial region was calculated by the formula (12),Cn2was obtained. Figure 3 is a comparison ofCn2values derived from the ultrasonic anemometers with spectrum analysis and micro-thermometer, using Figure 2 dataset. In comparison with Figure 2,Cn2values derived from the ultrasonic anemometer with spectrum analysis are closer to those from the micro-thermometer.The former was smoother than 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 measuringCn2from ultrasonic anemometer instead 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 comparison ofCn2values from spectrum analysis of sonic anemometer data and microthermometer data from 11 January through 2 February 2014.In this dataset, under various meteorological conditions and regardless of day or night, the comparison was satisfactory.

Figure 3 Comparison of Cn2 derived from ultrasonic anemometers with spectrum analysis and micro-thermometer.

Figure 4 Comparison of Cn2 derived from ultrasonic anemometers with spectrum analysis and micro-thermometer during field experiment.

Figure 5 Comparison of Cn2 frequency distribution derived from ultrasonic anemometer with spectrum analysis and micro-thermometer during field experiment.

Figure 5 compares aCn2frequency distribution from spectrum analysis with the sonic anemometer and microthermometer data on 30 December 2013 to 10 February 2014. Sample numbers were 3446 and 59175, respectively.Table 1 is aCn2frequency distribution from the microthermometer and anemometer in 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, theCn2frequency 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.

At Taishan Station, the difference ofCn2measured by the single-point temperature structure function method and the sonic anemometer and micro-thermometer is very large. Thismay be related with factors such as spectral characteristics,turbulent multi-scale spatial and temporal structure, and whether the Taylor assumption is valid. A similar result was found in reference[17]. In that work, an aero thermal series from a cold wire probe mounted on an aircraft was analyzed.CT2from the structure function sometimes agreed well with spectral analysis, but sometimes the difference was very large, five times larger than the spectrum analysis results. The author believed that the large differences were in the regionsαwhere 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 thatCT2must be obtained via the single-point temperature structure function method under the Taylor assumption. To discover whyCn2values from the ultrasonic anemometer were several times larger than those of the micro-thermometer at Taishan Station,it is necessary to determine the power frequency distribution of the temperature spectrum during an experiment. Figure 6 is the frequency distribution of the power law of a onedimensional spectrum. The frequency forα＜?1 was 36.2%,and that forα＞?1 was 63.8%. That is, there is nearly twothirds 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[4-6,15]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.

Table 1Cn2 frequency distribution derived from spectrum analysis of sonic anemometer and micro-thermometer data

5 Conclusions

Atmospheric parameters at Taishan Station from 30 December 2013 through 10 February 2014 were obtained by a mobile measuring system, and these data were analyzed.Cn2derived from the single-point temperature spectrum method with the sonic anemometers and micro-thermometer was compared. In the range ?15 ＜ lg(Cn2) ＜ ?13.8, the frequencies of both were 78%. Frequencies for lg(Cn2) ＞?13.8 were 1.7% and 6.9%, respectively, and for lg(Cn2) ＜?15 they were 20.3% and 14.8%. Compared with the microthermometer, results ofCn2measured by the ultrasonic anemometer from the spectrum analysis method were satisfactory in magnitude and trend.

Figure 6 Frequency distribution of power law of one-dimensional spectrum.

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