tokens: experiments in Rongcheng, along with the measured median profiles, are shown in Fig. 4 . The performance for estimation by the Dewan outer scale is the worst among four models. The estimated by the Dewan model is much smaller than the measured value below 8 km, with an abrupt change occurring at 8 km, and much larger than the measured value above 8 km. For completeness, Appendix A discusses the individual profiles in Rongcheng. The HMNSP99 and Thorpe models have a similar performance for estimation below 12 km, and are consistent with the measured values in both change trend and magnitude. At high altitude, the two models deviate from the measured values by different degrees: a larger deviation above 12 km appeared for sounding experiments for the Thorpe model. The Sθ model has the best prediction results, and it is consistent with the observed median profile in variation trend and magnitude. The relative error profiles for the above four models are illustrated in Fig. 4(b) . The relative error can demonstrate the variation of the deviation between the estimated value and the measured value with altitude. The deviation between the Dewan model and the observed median turbulence is the largest, while that of the Sθ model is the smallest, for all altitudes. The HMNSP99 and Thorpe models have a similar performance in RE (relative error) below 10 km, while HMNSP99 has better results above 10 km. Figure 4. Evaluation of the estimated median profiles (Rongcheng): (a) comparison of the estimated median profiles using the Thorpe (red), HMNSP99 (blue), Dewan (purple) and Sθ (green) models, and the measured profiles (black); (b) relative error of the estimated median profiles. Table 4 presents the RMSE, R xy , and MRE for the estimations of median obtained from the considered four outer-scale models for balloon experiments. The RMSE and MRE of estimated by the Sθ model are better than those for the other three models. It is worth noting that the R xy values of Thorpe, HMNSP99 and Sθ exceed 0.9, which means that the three models may accurately reflect the variation trend of measured turbulence. For the median values, the correlation coefficient of the estimated by the Sθ scale was the highest of all four models. As shown in Table 4 , the average relative error of the median values was generally lower than 1.6%, which meets estimation accuracy requirements for . Table 4. Statistical analysis for the estimation of in Rongcheng using the four outer-scale models, given for median profile. The specific results of the integral statistics of each sounding balloon and median profiles for Rongcheng are tabulated in Table 5 . Clearly, the Sθ scale provides reliable results, close to observed values. As can be seen, our new outer-scale model gives reasonable results when calculating integrated atmospheric parameters. Table 5. Comparison of integrated atmospheric parameters obtained via values observed by meteorological balloons and estimated by the Sθ model
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