The methods to obtain atmospheric refractive index structure constant $(C_n^2)$ by instrument measurement are limited spatially and temporally and they are more difficult and expensive over the ocean. It is useful to forecast $C_n^2$ effectively from Weather Research and Forecasting Model (WRF) outputs. This paper introduces a method that WRF Model is used to forecast the routine meteorological parameters firstly, and then $C_n^2$ is calculated based on these parameters by the Bulk model from the Monin-Obukhov similarity theory (MOST) over the ocean near-surface. The corresponding $C_n^2$ values measured by the micro-thermometer which is placed on the ship are compared with the ones forecasted by WRF model to determine how this method performs. The result shows that the forecasted $C_n^2$ is consistent with the measured $C_n^2$ in trend and the order of magnitude as a whole, as well as the correlation coefficient is up to 77.57%. This method can forecast some essential aspects of $C_n^2$ and almost always captures the correct magnitude of $C_n^2$, which experiences fluctuations of two orders of magnitude. Thus, it seems to be a feasible and meaningful method that using WRF model to forecast near-surface $C_n^2$ value over the ocean.

It is worth highlighting that, for the first time to the best of our knowledge, vertical profiles of atmospheric parameters and 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 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 () 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 model offers new insight into the characteristics of optical turbulence at Lhasa and provides support for pursuing astronomical site selection in the Tibetan Plateau.

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.

The vertical profile of $C_n^2$ is the main factor for accurate astronomical observation and laser communication, however, hardware-based instruments and associated data are not widely available due to logistical and financial issues. In this article, we developed an indirect method, a hybrid network structure which is a combination of the backpropagation neural network and the simulated annealing algorithm, to fit the vertical profile of $C_n^2$. Radiosonde measurements from a field campaign over the Tibetan Plateau at Dachaidan (37.7○N, 95.3○E, 3180 m ASL) were performed in 2020 August to estimate the accuracy of our model, during which a balloon-borne portable turbulence meteorological radiosonde was used to measure the atmospheric optical profiles. Besides, the integrated astronomical parameters (the coherence length r0, seeing ε0, isoplanatic angle θ0, and the wavefront coherence time τ0), derived from $C_n^2$ and wind-speed vertical profiles, are investigated for astronomical applications using the proposed model. In addition, quantitative evaluations such as the correlation coefficient, the root mean squared error, and the systematic bias are used to quantify the performance of our model. More interesting, this model is found to outperform a widely used external scale model for the prevalent atmospheric conditions and shows better correlation and reliable estimates.

The vertical distributions of atmospheric turbulence (⁠|$C_n^2$|⁠) are key factors in determining the performance of ground-based telescopes and interferometers. As site-testing campaigns are extremely expensive, atmospheric modelling may represent the estimated results of astronomical sites. We propose a new outer-scale model to estimate refractive index structure constant (⁠|$C_n^2$|⁠) profiles containing potential temperature and wind shear. The integrated astroclimatic parameters (Fried parameter r₀, seeing ε, isoplanatic angle θ₀, and coherence time τ₀) can also be calculated using this outer-scale model. Radiosonde measurements from a filed campaign at Tibet (Lhasa) and Rongcheng (Shandong) are utilized to quantify the performance of this model. Compared with the Dewan model, HMNSP99 model and Thorpe model, the new model gives better results as a profile and an astroclimatic parameter estimator. Compared with the measured median profile, the correlation coefficient reaches 0.88 in Lhasa and 0.87 in Rongcheng.

In Antarctica, excellent astronomical observing conditions have been measured at Dome A during night-time (or polar winter). This study investigates the performance of the Polar-optimized version of the Weather Research and Forecasting (Polar WRF, PWRF hereafter) for simulating the night-time astronomical seeing at Dome A. The seeing values were estimated by a seeing model, which used the PWRF-simulated wind speed and temperature as inputs. Furthermore, three methods to obtain the boundary layer height in the seeing model have been examined. The estimated seeing agrees well with 50-d measurements from the KunLun Differential Image Motion Monitor at Dome A during the night-time of 2019; the correlation coefficients range from 0.62 to 0.71. The PWRF-simulated meteorological parameters indicate that low wind speed and strong temperature inversion (when a large gradient Richardson number always occurs) near the ground can lead to good seeing condition. The results suggest that the PWRF model could be a reliable tool for scheduling observational astronomy at Dome A during night-time.