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Abstract
The vertical distributions of optical turbulence ($C_{n}^2$ profiles) are a major factor in defining the capabilities of ground-based telescopes and interferometers. As site-testing campaigns are extremely expensive and instruments only provide the local atmospheric parameter, atmospheric modeling might represent an advance prediction result in astronomical sites. The key meteorological parameters and the integrated astroclimatic parameters (Fried parameter r0, seeing ɛ, isoplanatic angle θAO and wavefront coherence time τAO) related to the $C_{n}^2$ profiles above the Tibetan Plateau are investigated for astronomical applications by using the Weather Research and Forecasting (WRF) model. Radiosonde measurements from a field campaign at Lhasa station above the Tibetan Plateau are used to quantify the ability of this model. The results show that the $C_{n}^2$ profile decreases rapidly in the surface layer, increasing with height from the boundary layer to low stratosphere, and decreases gradually in the high free atmosphere. From the whole campaign measurements above the Tibetan Plateau, the mean r0 is 8.64 cm, the mean ɛ is 1.55′′, the mean θAO is 0.42′′ and the mean τAO is 1.89 ms, and the comparison with the other world’s leading observatory sites have been presented. In addition, such as the bias and the root-mean-squared error are used to quantify the performance of the WRF model. In spite of the model performance in reconstructing the meteorological parameters is reasonable in general, the uncertainty in quantifying the $C_{n}^2$ profiles and the integrated parameters are not negligible in some cases. The main results of this study tell us that the WRF model could provide a useful resource to design, monitor the performance of, and even optimize the operation of sophisticated Adaptive Optics (AO) systems.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The intensity of optical turbulence is usually described by the refractive index structure constant ($C_{n}^2$) [1], and the crucial role of optical turbulence in ground-based astronomy telescopes was recognized a long time ago. Nowadays, it is possible to improve the optical turbulence effect with AO systems. AO systems require a knowledge of the meteorological parameters and $C_{n}^2$ vertical profiles as well as the overall integrated parameters ($r_0$, $\varepsilon$, $\theta _{\textrm {AO}}$ and $\tau _{\textrm {AO}}$) [2–7], and these parameters are considered the main turbulence parameters in astronomy that directly influence the imaging resolution. Thus, it is desirable to have reliable statistics of these turbulence parameters for one site in order to operate ground-based facilities and AO systems.
The optical turbulence cannot be assumed constant, since it varies with height. There was a fairly recent experiment that measure the optical turbulence in the first few meters above ground level using a system containing eight resistance thermometer devices, in which the measurements were made flying this system under a tethered balloon [8]. In many cases, it is impractical and expensive to deploy instrumentation to directly measure $C_{n}^2$ profiles for many climates and seasons, a less expensive and convenient way to obtain the characteristics of $C_{n}^2$ parameters can be achieved by using a mesoscale atmospheric model. The Mesoscale non-hydrostatic model (Meso-NH) model has been proven to be reliable in reconstructing 3D maps of $C_{n}^2$ [9,10] and has been statistically validated above mid-latitude astronomical sites [11,12]. The first comparison of the atmosphere parameters using the monthly median of the analyses from the European Centre for Medium-Range Weather Forecasts (ECMWF) above South Pole, Dome C and Dome A has been performed, and the result shows that the thermodynamic instability conditions above Dome C are worse than those predicted above South Pole and Dome A [13]. More recently, the validation of the Meso-NH model with the support of measurements has been done above Dome C, and model results match measurements well [14,15]. An later study has been done to two other potential astronomical sites in Antarctica (Dome A and South Pole) to investigate the ability of the Meso-NH model, jointly with the Astro-Meso-NH package to discriminate atmospheric turbulence conditions, and it is evident that three sites have different characteristics as regards the seeing and the surface layer thickness [16]. The problem of modeling “seeing” using the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5) model and the preliminary results from a validation study have been investigated [17–19], furthermore, an operational prediction system where the $C_{n}^2$ or seeing algorithm is implemented within Weather Research and Forecasting (WRF) model has been used to provide the guidance for a short-term weather forecasts and optical turbulence at Mauna Kea Weather Center (MKWC, see online at MKWC) [20]. In order to evaluate the performance of Meso-NH model in forecasting the optical turbulence parameters, the simulation results related to a rich statistical sample of nights uniformly distributed with different years have been compared to the measurements above the European Southern Observatory (ESO) sites of the Very Large Telescope (VLT) and the European Extremely Large Telescope (E-ELT), and they got the conclusion that the model provides a not negligible positive impact on the service mode of top-class telescopes and ELTs [21,22].
In recent years, ground-based observation has been looking towards the Tibetan Plateau, especially its the highest plateau (an average elevation that exceeds 4500 m, and sometimes called “the roof of the world”) in the world with an area of 2.5 million km$^{2}$ (spans approximately 1000 km from north to south and 2800 km from east to west) and the region hosts unique weather regimes and natural phenomena. In this study, we try a first attempt to quantify the characteristics of atmospheric turbulence above the Tibetan Plateau, and we intend to investigate the performance of the WRF model above Tibetan Plateau, including the comparison between model and measurements.
This paper is broken down as follows: Section 2 gives a brief overview of balloon-borne measurement and the WRF model configuration, Section 3 describes the $C_{n}^2$ estimation model and the $C_{n}^2$ integrated parameter. Section 4 presents the results of meteorological parameters (wind speed and temperature) and $C_n^2$ deduced from the WRF model and radiosonde measurement. In addition, some statistical operators are used to assess the accuracy of the WRF model. Finally, conclusions are drawn in Section 5.
2. Measurement and WRF model configuration
2.1 Radiosonde measurement
The Tibetan Plateau (TP hereafter) climates have considerable spatial variation that are dry climates in the west and northwest influenced by west wind and wet climates in the southeast influenced by Indian monsoon [23]. Annual precipitation varies from 420 mm to 580 mm, while average air temperature varies from 4.5 $^\circ$C to 7 $^\circ$C. As “the global water tower”, TP is the main pathway for water vapor cross-tropopause transport, which exerts a major influence on the energy balance of the earth-atmosphere system [24,25]. Also, the TP is one of the most sensitive regions to global climate change, and the climate warming has increased the temperature over the TP by more than 0.25 $^\circ$C per decade. Literature indicate that the recent warming over the TP begin early and appear intense with respect to the global warming compared with its neighboring areas or the same latitudinal zone [26,27]. Lhasa radiosonde station (29.667 $^\circ$N, 91.133 $^\circ$E, at altitude 3648 m) is located in the TP, its position and height distributions are shown in Fig. 1 in which the black point stands for the Lhasa radiosonde station. Lhasa is located in the middle of the Tibetan Plateau, on the north side of the Himalayas, at an altitude of 3650 m, and it is located in the valley plain in the middle of the Lhasa River which flows into the Brahmaputra. Lhasa has sunny weather throughout the year, with little rainfall, no severe cold in winter, and no extreme heat in summer. The annual sunshine time is more than 3,000 hours, which is known as the “sunlight city”.
Fig. 1. The topographical distributions map of Tibetan Plateau, and the black point represents Lhasa radiosonde station which is the center grid of the WRF model domain.
The values of refractive index structure constant ($C_{n}^2$ [m$^{-2/3}$]) measured by micro-thermometers are deduced from a pair of horizontally separated micro-temperature probe wires. For visible and near-infrared wavelengths, the refractive index fluctuation is mainly caused by temperature fluctuation [28], and $C_{n}^2$ is related to the corresponding temperature structure constant ($C_T^2$), as follows
where $T$ is air temperature (K) and $P$ is air pressure (hPa). $C_T^2$ is defined as the constant of proportionality in the inertial subrange form of the temperature structure function $D_T(r)$. In the inertial subrange of atmospheric turbulence [29], temperature structure parameter $C_T^2$ is given by the Kolmogorov form as belowThe device used for balloon-borne micro-thermometers measurements employed the platinum wire sensor with a 10 $\mu$m diameter. The sensors were mounted 1 m apart in a horizontal plane. A styrofoam box lined with polyurethane insulation housed the signal processing electronics and batteries and provided support for the thermal sensors. The platinum wire has a linear resistance-temperature coefficient, and it responds to an increase in atmospheric temperature with an increase in resistance. The two sensors are legs of a Wheatstone bridge, and the resistance of sensors is very nearly proportional to temperature and thus temperature change is sensed as an imbalance voltage of Wheatstone bridge. This voltage was then amplified, bandpass filtered, and synchronously detected. The noise level of sensors and the electronic processing of signals corresponded to a temperature difference of 0.002 K [30,31]. The micro-thermometer provides $C_T^2$ values by measuring the mean square temperature fluctuations and thus the $C_n^2$ values can be acquired.
For the past few years, ground-based optical observatory has been looking forwards to TP, especially its summits and considerable climates in the internal continental plateau. All 14 radiosonde balloons were launched at Lhasa radiosonde station, shown in Fig. 2, and quality checks were then applied to remove outliers arising for various reasons following to ensure high-quality data that would not contaminate the results.
Fig. 2. Left: balloon-borne micro-thermometers; Middle: the balloon-borne micro-thermometers measurements are launched at Lhasa radiosonde station; Right: balloon-borne micro-thermometers flying in the sky.
Excluding 5 radiosonde measurements that are abnormal due to various factors such as weather and damage caused by strong winds, the remaining 9 radiosonde measurements are effectively available. Horizontal wind speed (GPS wind measurement) and absolute temperature were measured with an accuracy of 0.5 m$\cdot$s$^{-1}$ and 0.2 K, respectively. The balloon-borne micro-thermometer measurements are carried out from 2018-08-08 to 2018-08-16. All atmospheric parameters were collected with a height resolution of 10 m (sampled at 2 s intervals), and the available radiosondes with each date and hour were listed in Table 1.
Table 1. List of the 9 available radiosonde measurements are launched at Lhasa station during August 2018.
2.2 WRF Model configuration
The WRF model is a state-of-the-art mesoscale atmospheric model used for both professional forecasting and atmospheric research. It is developed by the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR) of the United States. In this study, the model is initialized with the Final Operational Global Analysis (FNL) data (at $1^\circ \times 1^\circ$ horizontal resolution) which are released every 6 h interval from the Website. In this work, the grid-nesting techniques (the horizontal resolution of the innermost domain is 500 m) consisting of using different embedded domains which extend on smaller and smaller surfaces with increasing horizontal resolution but with the same vertical grid (72 vertical levels, from 3.7 km up to 30.1 km above sea level) have been used. It is evident that the higher the model vertical levels mean the higher the computing effort. Thus, the model configuration selected should be suitable to perform $C_{n}^2$ estimates using a relative low computing effort. In general, three embedded domains where the horizontal resolution of the innermost domain is 500 m are used to obtain the meteorological parameters and the relevant parameters related to optical turbulence [21,22,32]. With reference to the previous research experience (Masciadri and Lascaux), we used a two-way grid-nesting because this has the advantage of taking into account the feedback between each couple of father and son domains. This configuration allows the largest domain covers an 1500 km by 1500 km area at a 12.5 km horizontal grid resolution. The embedded domains nest down to the innermost domain 500 m for the location of balloon-borne micro-thermometer measurements at Lhasa radiosonde station. The WRF model basic simulation parameters configurations are listed in Table 2.
Table 2. WRF model grid-nesting configuration. The second column is the number of horizontal grid points, the third column is the horizontal resolution and the fourth column is the horizontal surface covered by the WRF model domain.
Many of atmospheric parameters exported by the WRF model depend upon the parameterization schemes that have been chosen for the simulation, most of which are self-explanatory, but some require additional explanation. The main physical schemes are listed in Table 3, and the parameterization schemes are explained in User’s Guide [33] as follows:
- 1. The model employs WRF Single-Moment 5 class (WSM-5) scheme used in the micro-physics process which is a slightly more sophisticated version of WSM-3 (contains three kinds of water materials: water vapor, cloud water or cloud ice, rainwater or snow).
- 2. The long wave radiation uses the Rapid Radiative Transfer Model (RRTM) scheme which accounts for multiple bands and microphysics species.
- 3. The shortwave radiation uses Goddard scheme, two-stream multi-band scheme with ozone from climatology and cloud effects.
- 4. The surface exchanges are computed using the Eta similarity scheme which is based on Monin-Obukhov similarity with Zilitinkevich thermal roughness length.
- 5. The land surface uses Noah land surface model, which contains the unified NCEP/NCAR/AFWA scheme with soil temperature and moisture in four layers, fractional snow cover and frozen soil physics.
- 6. The planetary boundary layer uses Mellor-Yamada Janjik (MYJ) scheme which may be used to forecast the turbulent energy.
Table 3. Main physical schemes configuration.
Because of the WRF model each run is time-consuming and costs huge computational resource, the WRF model output result at 10 minutes intervals owing to the configuration limitation. In order to validate the results between the WRF model and measurement, it requires the measurement results are matched up with model outputs at the corresponding time period. The simulations start at 00:00 UTC of the measurement date and last in total 24 hours.
3. Methodology
3.1 $C_{n}^2$ estimation model
Optical turbulence profile ($C_{n}^2$ profile) from the ground to 20 or 30 km is needed to ascertain the effects of turbulence on laser beam propagation in the atmosphere. Such optical turbulence effect could then be used for assigning design parameters for AO systems which can greatly reduce the effect of turbulence. Optical turbulence profile estimation models are used to convert standard meteorological data into $C_{n}^2$ vertical profiles, and the Dewan $C_{n}^2$ profile model has been used for various research involving optical propagation during the past several years [41]. Also, it is being used to forecast optical seeing conditions for ground-based telescopes at Mauna Kea Observatories on the island of Hawaii by converting standard Numerical Weather Prediction (NWP) forecast model outputs into $C_{n}^2$ vertical profiles. The Dewan $C_{n}^2$ profile model uses the Tatarski model for estimating $C_{n}^2$ profile as below
whereThe Dewan model provides useful $C_{n}^2$ vertical profiles in the upper troposphere and stratosphere, though there is certainly a need for improvement at these altitudes. The modified-Dewan $C_{n}^2$ model described in this study is developed and tested at the Air Force Research Laboratory (AFRL) Holloman Spring 1998 and Holloman Spring 1999 thermosonde campaigns (New Mexico). Based on the statistical relationships, wind shear ($S$) and temperature lapse rate ($\frac {{\textrm d}T}{{\textrm d}h}$) which have an important influence on the generation and development of $C_{n}^2$, are added to the $L_0$ model [42]. Therefore, the outer scales $L_0$ model takes $S$ and $\frac {{\textrm d}T}{{\textrm d}h}$ as two independent variable functions, which can be expressed as
3.2 $C_{n}^2$ integrated parameter
The Fried parameter $r_0$, seeing $\varepsilon$, isoplanatic angle $\theta _{\textrm {AO}}$ and wavefront coherence time $\tau _{\textrm {AO}}$ are the important parameters for the design and optimization of AO system, and these parameters are derived from $C_{n}^2$ and wind speed vertical profiles. The Fried parameter, also known as the coherence length, characterizes the equivalent aperture of a telescope whose resolution is no longer affected by atmospheric optical turbulence. The $\varepsilon$ is defined as the full width at half maximum of a star image on the focal surface of a large-aperture telescope. The $\theta _{\textrm {AO}}$ is defined as the maximum angular distance between two star images with approximate wavefronts at the entrance pupil of the telescope. The $\tau _{\textrm {AO}}$ indicates how long the wavefront remains coherent which is often used in specification of adaptive optics control systems. These $r_0$, $\varepsilon$, $\theta _{\textrm {AO}}$ and $\tau _{\textrm {AO}}$ parameters are defined as
4. Results
4.1 Vertical profiles
The first thing to notice is the meteorological parameters from measurements and the WRF model. Figure 3 shows the vertical profiles of temperature from the WRF model and 9 separate flights radiosondes at Lhasa station above the Tibetan Plateau. The temperature goes from around -80 $^\circ$C to 25 $^\circ$C, this is in agreement with the minimum and maximum model values. Considering the entire free atmosphere, the temperature profiles reconstructed by the WRF model are close to the ones obtained with the radiosondes, which shows the WRF model values are coherent with the measurements.
Fig. 3. The vertical profiles of temperature from the WRF model and the radiosonde at Lhasa station above the Tibetan Plateau.
Figure 4 shows the vertical profiles of wind speed from the WRF model and radiosonde. There are significant differences in wind speed trend with several types distinguishable, while in some case the wind speed reconstructed by the WRF model is slightly larger than the one measured by radiosonde. Obviously, the wind speed increases with height, and the maximum wind speed reaches 25 m$\cdot$s$^{-1}$. The weak upper wind demonstrates the well the conditions suitable for adaptive optics observations for future ground-based optical and infrared telescopes.
Figure 5 shows the $C_n^2$ vertical profiles from the WRF model and radiosonde, and some evidence can be found for the variations of the optical turbulence strength. It is found that the $C_{n}^2$ vertical distribution decreases sharply in the surface layer as well as increase with height from the boundary layer to low stratosphere, and decreases gradually in the free atmosphere. In the free atmosphere, the $C_{n}^2$ values are near the order of 10$^{-17}$ m$^{-2/3}$, and in the boundary layer the $C_{n}^2$ values are in the order of 10$^{-16}$ m$^{-2/3}$. Moreover, it is well visible that the $C_n^2$ values simulated by the WRF model to be about twice as large measured by the radiosonde measurement. The differences between the WRF model and measurement are relatively minor from the ground up to around 13 km above ground level, and somewhat more pronounced above 13 km.
Almost all of the WRF model and the measurement results show peaks that correspond to the tropopause, and the measurements indicate that $C_n^2$ in the daytime was more intense than that in the nighttime periods. As can be seen in Fig. 5, there is one point which needs attention that measurement number 7 (launchings date 2018-08-14 22:53) showed $C_n^2$ measurement weakest, which is noteworthy since the local time for measurement 7 is further past sunset than the other measurements that were taken during evening hours. However, this radiosonde measurement was released late at night (22:53 Local time), and whether the atmosphere is quieter during sounding is a possible factor.
In addition, the high variance may be attributed to a wider variety of atmospheric conditions included in the Tibetan Plateau, and the cloud broke the sky conditions is also a factor that cannot be ignored. Although the $C_n^2$ profiles obtained by the WRF model is accordance with the variation law of $C_n^2$ in the atmosphere, there are still some room to improve.
4.2 Overall model performances
The statistical operators the bias and the root-mean-squared error (RMSE) are used to assess the accuracy of the WRF model [43]. Bias and RMSE are defined as
where $X_i$ are the individual measured values, $Y_i$ are the individual values simulated by the WRF model at the same height and $N$ is the number of samples for a couple ($X_i$, $Y_i$) at the same height. $\overline X_i$ and $\overline Y_i$ stand for the average value of measured and the WRF model parameters, respectively. From the bias and the RMSE, it is possible to get the bias-corrected RMSE ($\sigma$) as below which represents the intrinsic uncertainty not affected by the bias, and it provides fundamental information on the systematic and statistical uncertainties. The statistical analysis results between the estimated and measured values are shown in Fig. 6.Fig. 6. First, second and third rows: the bias, the RMSE, and the bias-corrected RMSE ($\sigma$) of temperature, wind speed and $C_{n}^2$. In the bottom row, the lines represent the average of of temperature, wind speed and $C_{n}^2$ between the WRF model and the radiosonde.
The bias contains information on systematic errors, and the RMSE contains information on the statistical errors plus the systematic errors. In detail, observations and the WRF model profiles have been interpolated on a 100-m vertical grid, and then the average, the bias and the RMSE have been computed for each interpolated level to the resulting profiles. Figure 6 shows the bias, the RMSE and the average vertical profiles for temperature, wind speed and $C_n^2$ from the WRF model and the radiosonde measurement. For the temperature vertical profiles, the bias about 2 $^\circ$C from the ground up to around 24 km above ground level. Above 24 km, where the temperature slope is steeper, and the bias can reach up to 4 $^\circ$C. For wind speed, the value of bias is less than 3 m$\cdot$s$^{-1}$ at all altitudes, and the value of bias is the largest near 3 or 20 km altitude. From the ground to 17 km, the RMSE value is near 3 m$\cdot$s$^{-1}$, and the value of RMSE becomes larger above 17 km. Therefore, the WRF model values are coherent with the radiosonde measurements well.
As can be seen in Fig. 6, there is a not negligible problem that $C_n^2$ values have relatively large drift compared with radiosondes above 14 km or under 4 km. Even though the research on $C_n^2$ simulation is a continuous development and there is always room for improvement, in this preliminary study, we have made important progress in the estimation of $C_n^2$ profile. More and more observatories are interested in this kind of application, so improving the performance of the WRF model simulation is becoming more and more important.
4.3 Integrated parameters
The integrated parameters ($r_0$, $\varepsilon$, $\theta _{\textrm {AO}}$ and $\tau _{\textrm {AO}}$) are considered the main turbulence parameters in astronomy that directly influence the achievable imaging resolution. In reality, it is desirable to have reliable statistics of these parameters for a given site in order to improve the performance of AO systems. Figure 7 show all the 9 available launchings of turbulence integrated on the whole atmosphere between the WRF model and radiosonde measurement. We observe that the $r_0$, the $\varepsilon$, the $\theta _{\textrm {AO}}$ and the $\tau _{\textrm {AO}}$ between the WRF model and the radiosonde measurement are in agreement with each other in trend and magnitude in general except for some cases.
Fig. 7. Scattered plot of the relevant integrated parameters ($r_0$, $\varepsilon$, $\theta _{\textrm {AO}}$ and $\tau _{\textrm {AO}}$) derived from $C_{n}^2$ profiles between the WRF model and the radiosonde measurement (wavelength 550 nm).
The comparison of the relevant integrated parameters derived from the $C_{n}^2$ profiles for astronomical applications between the WRF model and radiosonde observations are tabulated in Tables 4–5. The result in Table shows the ability of the WRF model in reconstructing the integrated parameters from the $C_{n}^2$ profile. The common commentary as expected is that the WRF model performances in reconstructing the $C_n^2$ parameters are not as good as in reconstructing the meteorological parameters. This is due to the fact that the turbulence is a random quantity. Therefore, it is difficult to describe optical turbulence numerically. However, despite these inherent difficulties, we will still see that the results we have achieved are impressive and, more importantly, provide potential value for the application of AO systems.
Table 4. Comparison of the integrated parameters ($r_0$, $\varepsilon$) for astronomical applications between the WRF model and the radiosonde ($\Delta$=Model-Measurement).
Table 5. Same as Table 3, but for $\theta _{\textrm {AO}}$ and $\tau _{\textrm {AO}}$.
However, taking into consideration of the WRF model performances in simulating values of $r_0$, $\varepsilon$, $\theta _{\textrm {AO}}$ and $\tau _{\textrm {AO}}$, the performances are reasonable. In the analysis we presented, it appears evident that the uncertainty in quantifying the integrated parameters with the WRF model is not negligible in some cases. It’s just a big difference from the radiosonde measurement results released at late night (22:53 Local time). As mentioned in Section 4.1, the atmosphere is actually relatively quiet during radiosonde measurement, which is a very likely factor.
Table 6 summarises the measurements of $r_0$, $\varepsilon$, $\theta _{\textrm {AO}}$ and $\tau _{\textrm {AO}}$ from some of the world’s leading observatory sites. It would appear from the available data that any site that has an overall average $r_0$ of 10 cm or higher at a wavelength of 550 nm is very rare if not nonexistent. Generally, a good site has a thin surface boundary layer and there is a rapid return of optical turbulence to the altitude dependence associated with the surrounding lower elevations. It can be seen quite clearly that the mean $r_0$ is 8.64 cm, the mean $\varepsilon$ is 1.55$''$, the mean $\theta _{\textrm {AO}}$ is 0.42$''$ and the mean $\tau _{\textrm {AO}}$ is 1.89 ms, and the Tibetan Plateau is confirmed to be a potential astronomical observatory site.
Table 6. Summary of the astrophysical parameters above the Tibetan Plateau, and comparison with the other world’s major observatory sites.
Comparing the numbers in Table 6 the calculated isoplanatic angle for the Lhasa site is very small compared the numbers given for other sites in the world. In isoplanatic angle’s integral formula Eq. (9), a high weight function is included. According to the measurement results in different parts of the world, the turbulence intensity is generally characterized in most cases by gradually decreasing with increasing altitude. Even if a strong turbulence layer appears near the tropopause, it is usually weaker than near-surface turbulence. However, in the Lhasa area, it is almost gradually increasing from the boundary layer to the tropopause (except for 22:53 Local time sounding), and even the strong turbulence layer near the tropopause is stronger than the near-surface layer. These characteristics of turbulence intensity distribution with height may all be factors that cause the isoplanatic angle to be small.
5. Conclusions
In this paper, we presented the main results we obtained on the profiles of meteorological parameters and $C_n^2$ from a radiosonde field campaign at Lhasa station above the Tibetan Plateau. We analyzed the key meteorological parameters on which the $C_n^2$ depends (temperature and wind speed) and four main integrated astronomical parameters ($r_0$, $\varepsilon$, $\theta _{\textrm {AO}}$ and $\tau _{\textrm {AO}}$) that are fundamental information in the adaptive optics optimization and the planning of ground-based observations. Furthermore, we try to investigate the WRF model performances in reconstructing $C_n^2$ parameters, including the comparison with radiosonde measurement. The results we obtained on the radiosonde measurement and the WRF model are summarized in a nutshell.
The profiles of temperature and wind speed from the WRF model are in agreement with the measurements over the entire free atmosphere, and the temperature profiles reconstructed by the WRF model are as pronounced as the ones measured by radiosonde measurement. However, there are significant differences in wind vertical distributions. Although the $C_{n}^2$ profiles from the WRF model are closed to the radiosondes in general, there are still some deviations between the model and the measurements. As expected, the WRF model performances in simulating the $C_n^2$ are not as good as in simulating the meteorological parameters. This is due to the fact that the spatio-temporal scale of the optical turbulence disturbance is much smaller than the WRF model grid size, and also because the turbulence is a random quantity. Therefore, it is difficult to describe optical turbulence precisely numerically. However, the $C_n^2$ profiles and the integrated astronomical parameters obtained from the WRF model can provide a rough approximation of optical turbulence conditions above the Tibetan Plateau. All the integrated astronomical parameters from $C_{n}^2$ profiles on the whole atmosphere between the WRF model and the radiosonde measurement are reasonable in general, and the uncertainty in quantifying the integrated parameters with the WRF model is not negligible in some cases. However, despite these inherent difficulties, we will still see that the results we have achieved are impressive and, more importantly, provide potential value for the application of AO systems.
In future work, we intend to continue our studies on the $C_n^2$ estimation model in order to improve the WRF model simulation performances, and this is a research line that we will follow with attention. It is worth highlighting that these results were obtained for the first time above the Tibetan Plateau using a mesoscale model (WRF model). The main results of this study tell us that WRF model can provide useful information for designing, monitoring, and even optimizing the performance of sophisticated AO systems.
Funding
Strategic Priority Research Program of Chinese Academy of Sciences (XDA17010104); National Natural Science Foundation of China (91752103); Foundation of Key Laboratory of Science and Technology Innovation of Chinese Academy of Sciences (CXJJ-19S028).
Acknowledgments
The authors thank the National Centre for Atmospheric Research for access to their meteorological data sets.
Disclosures
The authors declare no conflicts of interest.
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