Effect of data spatial vertical resolution on the estimation of vertical profiles of the refractive index structure constant.

The vertical profile of optical turbulence is a key factor in the performance design of astronomical telescopes and adaptive optics instruments. As site-testing campaigns are extremely expensive, the selection of appropriate spatial resolution data and estimation methods is extremely important. This study investigated the effect of using different methods (Dewan, HMNSP99, Thorpe method) to estimate the refractive index structure constant (C n2) using different resolution data (5 m, 25 m, ERA5 data) in Huaihua, Hunan. Compared with Dewan, HMNSP99 for estimating C n2 using 5 m and 25 m resolution data, the Thorpe method almost always shows the best performance, with RXY above 0.75 and lower RMSE and MRE between estimated and measured C n2. The results of C n2 estimation using HMNSP99 at different resolution data varied widely, indicating that HMNSP99 is more sensitive to the data resolution and the temperature gradient is more sensitive to the resolution. Using ERA5 data, the two methods of estimating C n2 using Dewan and HMNSP99 have close results. It indicates that the wind shear is the main factor when the spatial resolution of the data is reduced to a certain degree, and the contribution of temperature gradient is small in the high altitude turbulence.

Estimation and characterization of atmospheric turbulence in the free atmosphere above the Tibetan Plateau using the Thorpe method.

Understanding turbulence in the free atmosphere is important for analyzing atmospheric pollution, forecasting weather, and light transmission. In this paper, we have tried to estimate the atmospheric refractive index structure constant C n2, the turbulent dissipation rate ε, and the turbulent diffusion coefficient K simultaneously during the experiment time over Lhasa, using the sounding data coupled with the Thorpe method. The result shows that the C n2 estimation gives a better performance with the correlation coefficients and the average relative error when compared with C n2 estimated by Dewan and HMNSP99. Besides this, the measured and estimated C n2, estimated ε, and K all show larger values in the troposphere, especially near the tropopause. It is worth noting that C n2 and ε are similar in terms of height distribution. These attempts at estimation all suggest that the Thorpe method can be used to estimate the intensity of turbulence in the free atmosphere over Lhasa.

Model for estimating the astronomical seeing at Dome A, Antarctica.

A model for estimating astronomical seeing at Kunlun Station (Dome A, Antarctica) is proposed. This model is based on the Tatarskii equation, using the wind shear and temperature gradient as inputs, and a seeing model depending directly on the weather data is provided. The seeing and near-ground weather data to build and validate the proposed seeing model were measured at Dome A during the summer of 2019. Two calculation methods were tested from the measured weather data relating the wind shear and temperature gradient to a combination of the two levels for the boundary layer. Both methods performed well, with correlation coefficients higher than 0.77. The model can capture the main seeing trends in which the seeing becomes small when weak wind speed and strong temperature inversion occur inside the boundary layer.

Reliable model to estimate the profile of the refractive index structure parameter (Cn2) and integrated astroclimatic parameters in the atmosphere.

Based on the statistical study of meteorological balloons equipped with thermosondes, a new model that estimates the profile of the refractive index structure constant (Cn2) is proposed. Utilizing temperature, pressure, and wind shear as inputs, this new approach can estimate vertical profiles of Cn2 with 100 m vertical resolution. We used four outer scale models (Thorpe, HMNSP99, Dewan, and our proposed model) on data acquired from Rongcheng (Shandong Peninsula) and Maoming (Guangdong Province) to estimate the Cn2 profiles and compared the results with the measured Cn2 profile. The proposed method outperformed the other three models, yielding an estimation profile that matched well with the measured median Cn2 profiles, with an average relative error generally less than 3.5% and a mean correlation coefficient larger than 0.72 in Maoming, an average relative error generally less than 3.4% and a mean correlation coefficient larger than 0.84 in Rongcheng. The proposed outer scale model also shows good performance in estimating integrated atmospheric parameters.

Simple method to estimate the optical turbulence over snow and ice.

A simple physics-based method for estimating optical turbulence (Cn2) within the surface layer over snow and ice is proposed, using the Tatarski equation with an improved outer scale model. This improved outer scale model mainly requires the calculation of the wind shear and temperature gradients. Based on the measurements from a mobile polar atmospheric parameter measurement system at the Antarctic Taishan Station in 2014, Cn2 was estimated using two methods: the Tatarski equation and the Monin-Obukhov similarity (MOS) theory. Compared with 16 days of measurements from a micro-thermometer, the correlation coefficient of log10(Cn2) estimated by the Tatarski equation is 0.72, which is a slightly more accurate Cn2 variation in trend and magnitude than the MOS theory. The results suggest that this simple method has potential value for the forecasting applications of optical turbulence.

Estimation of behavior of optical turbulence during summer in the surface layer above the Antarctic Plateau using the Polar WRF model.

An optical turbulence ($C_n^2$) was found to be concentrated predominantly in the thin surface layer (SL) above the Antarctic Plateau. We present an estimation of the behavior of the SL $C_n^2$ during the summer time over the entire Antarctic Plateau, using the polar-optimized version of the Weather Research and Forecast model (Polar WRF) coupled with the Monin-Obukhov similarity theory. The results show that the $C_n^2$ is affected by the sunlight direction and terrain height. The $C_n^2$ minimum occurs sometime around the morning and evening transitions, when the condition of neutral stability is achieved inside the SL. These $C_n^2$ minima may be attributed to the relatively weaker thermal convection resulting from a small temperature difference. The simulated $C_n^2$ data coincide well with the measurements taken at the Antarctic Taishan Station using a micro-thermometer and sonic anemometer; the data are also in agreement with the seeing values obtained from a differential image motion monitor. In addition, the Polar WRF captured the $C_n^2$ minimum more precisely compared to the standard WRF.

New $\text{C}_{n}

It is worth highlighting that, for the first time to the best of our knowledge, vertical profiles of atmospheric parameters and $C_n^2$ were measured at Lhasa, south of the Tibetan Plateau, using balloon-borne radiosondes. Based on the measurements, two new statistical models (Lhasa HMN and Lhasa Dewan) for estimating turbulence strength are proposed. Attention has been paid to evaluate the reliability of the two models to reconstruct vertical profiles of $C_n^2$ from a statistical perspective. The statistical analyses presenting the Lhasa HMN model are accompanied with lower bias, root mean square error (RMSE), and bias-corrected RMSE ($\sigma$) than those of the Lhasa Dewan model, which implies the Lhasa HMN model can better reveal the nature of turbulence characteristics of Lhasa influenced by unique local weather conditions. In addition, the comparison between the Lhasa HMN model and measurements in calculating integrated astroclimatic parameters is carried out, and the result suggests that the performance of the Lhasa HMN model is reliable and satisfactory. The new reliable $C_n^2$ model offers new insight into the characteristics of optical turbulence at Lhasa and provides support for pursuing astronomical site selection in the Tibetan Plateau.