Atmospheric turbulence causes laser intensity fluctuation, beam drift, and beam spreading, which necessitates the determination of its intensity. Refractive index structure constant (Cn2) profile and atmospheric coherence length (r0) are usually used to describe the atmospheric turbulence in the whole layer. The Cn2 profile in the whole layer is difficult to measure in real time economically in some cases, and researchers estimate atmospheric turbulence in different ways. Cn2 profile can be estimated using conventional meteorological parameters or artificial neural networks. Nevertheless, such methods either perform poorly in real time or require a considerable amount of measured data. An atmospheric coherence length monitor is usually employed to measure atmospheric coherence length and the isoplanatic angle, which can be further used for the real-time inversion of Cn2 profile. However, this instrument is easily affected by bad weather because it needs to track stars continuously. The study proposes a method to estimate the whole-layer atmospheric optical turbulence with multi-source measurement data from the microwave radiometer, wind profiler radar, meteorological sensor, micro-thermometer, and radiosonde. Being real-time and weather-proof, the proposed method is effective in engineering applications.

Specifically, a real-time atmospheric parameter profile is constructed with multi-source measurement data from the microwave radiometer, wind profiler radar, meteorological sensor, and radiosonde. Real-time ground-based data and radiosonde data are spliced together in accordance with the coefficients of correction at different heights. Then, this study distinguishes the atmospheric stratification state and calculates boundary layer height according to the distribution characteristics of the potential temperature gradient with the data from the microwave radiometer. After that, the Cn2 profile in the boundary layer is estimated by applying the exponential decline model, using real-time data from the micro-thermometer. The exponential decline index is -3/4 during the daytime and -2/3 at night. The Cn2 profile in the free atmosphere is estimated by employing the Dewan outer-scale model, using the previously constructed real-time atmospheric parameter profile. Furthermore, the Cn2 profiles in the two layers are spliced together to estimate r0 according to the integral relationship between the two layers. Finally, the estimated r0 is compared with the value measured by the atmospheric coherence length monitor.

The calculated boundary layer height varies from hundreds of meters at night to more than three thousand meters in the afternoon, and it is based on the previously constructed real-time atmospheric parameter profile data from August 3 to August 5 (Fig. 2). The estimated Cn2 profiles in the boundary layer and free atmosphere are spliced together, and the results show that Cn2 decreases with fluctuations, as altitude increases from ground level to 25 km. The order of magnitude of the estimated Cn2 decreases from 10^-15 to 10^-19 at night and in the morning and from 10^-14 to 10^-19 during the daytime (Fig. 3). The estimated r0 has the same order of magnitude and daily variation trend as those of the measured values. The consistency between them is fair in unstable atmospheric stratification but poor in the case of stable and near-neutral atmospheric stratifications (Fig. 4). The deviation is maximum in near-neutral atmospheric stratification, when the atmospheric turbulence near the ground is weak (Fig. 5). The root-mean-square error (RMSE) between the estimated r0 and the measured r0 is 2.988 in unstable atmosphere stratification, 6.858 in near-neutral atmospheric stratification, and 5.088 in stable atmosphere stratification. The correlation in unstable atmospheric stratification is much better than that in stable or near-neutral atmospheric stratifications (Table 2). In addition, the estimated r0 in the two component layers is compared with that in the whole layer obtained by applying the Dewan model. The RMSE between the estimated r0 and the measured r0 shows that the estimated r0 in the whole layer is slightly more consistent than that in the two component layers. Nevertheless, the standard deviation shows that the estimated r0 in the two component layers is much less fluctuant than that in the whole layer (Fig. 7). The deviation of the estimated r0 from the measured r0 is caused by several reasons. First, the atmospheric turbulence model has a technical route different from that of instrument measurement. Second, the applicability of the atmospheric turbulence model is doubtful in the sense that the similarity theory of turbulence is probably false in stable or near-neutral atmospheric stratification. Last but not least, data fusion and processing may also cause estimation errors.

Multi-source atmospheric measurement data are used to estimate Cn2 profile and r0 in real time. The results show that the estimated r0 has the same order of magnitude and daily variation trend as those of the measured r0. Moreover, the RMSE is minimum in unstable atmospheric stratification and maximum in stable atmospheric stratification, and the correlation in unstable atmospheric stratification is better than that in stable or near-neutral atmospheric stratification. Analysis proves that the whole-layer atmospheric optical turbulence can be estimated in real time by estimating the Cn2 profile in the two component layers with multi-source measurement data. The proposed method provides better real-time performance in estimating the whole-layer atmospheric optical turbulence and can validate instrument measurement in some cases. Therefore, it has great engineering application significance. Since the key to this method is to estimate the Cn2 profile in the boundary layer accurately, modifying the atmospheric turbulence model for the boundary layer is important for improving estimation accuracy.