# A Probabilistic Forecast Algorithm of Nonconvective Turbulence over the Tibetan Plateau
## 4 Turbulence Probability Index  
The aggregation methods for turbulence indices have been mentioned in many studies [11; 12; 13; 16]. In general, the indices are normalized and given different weights according to the turbulence forecast accuracy, and then a deterministic forecast for the turbulence intensity is made. [PERSON] et al. [17] employed a multidiagnostic approach to account for potential uncertainties in their first attempt at producing probabilistic forecasts of turbulence. They developed an ensemble of turbulence diagnostics that provided a percentage agreement on the likelihood of exceeding a specific EDR threshold. In Section 3.1, we did not normalize or map the turbulence indices to EDR but instead calculated the threshold values for each turbulence index. Considering this approach, utilizing a probabilistic method for ensembles would be more practical. Therefore, referring to [PERSON]'s approach [17], a turbulence probability index was defined by aggregating the 17 turbulence indices in this study. The probability index (PI) of a turbulence event with a certain intensity at a given grid point is defined as follows:  
\[\text{PI}=\sum_{i=1}^{n}s_{i}/n \tag{1}\]  
where \(n\) is the number of turbulence indices and \(s_{i}\) is recorded as 1 when the turbulence index \"\(i\)\" hits a certain intensity of turbulence and otherwise is recorded as 0. A higher probability index means that turbulence with a threshold intensity will more likely occur. Previous studies evaluated the forecasting capabilities of turbulence diagnostics for turbulence events based on observations, such as PIREPs (pilot reports) [12; 16; 17; 29; 30]. Unfortunately, for this study, we were unable to obtain observational data due to a lack of co-operation with the civil aviation department. As an alternative, we selected three turbulence events that occurred on the Chengdu-Lhasa route on 26 February 2006, 23 October 2009 [22], and 11 February 2023 ([[https://www.dimsumdaily.hk/china-west-air-flight-heading-towards-chongqing-plummets-suddenly-during-turbulence-many-passengers-scream-incessantly/](https://www.dimsumdaily.hk/china-west-air-flight-heading-towards-chongqing-plummets-suddenly-during-turbulence-many-passengers-scream-incessantly/)]([https://www.dimsumdaily.hk/china-west-air-flight-heading-towards-chongqing-plummets-suddenly-during-turbulence-many-passengers-scream-incessantly/](https://www.dimsumdaily.hk/china-west-air-flight-heading-towards-chongqing-plummets-suddenly-during-turbulence-many-passengers-scream-incessantly/)), accessed on 5 March 2023), between 0600-0800 UTC for analysis. The Chengdu-Lhasa route is a plateau route located between 91-104\({}^{\circ}\) E and 29-31\({}^{\circ}\) N, with a total length of 1250 km. The black box in Figure 3 represents the range of the route, and the black dashed line represents the route itself. We compared the timing, location, and probability index (PI) calculation results of three turbulence events on the Chengdu-Lhasa route. Figure 3 shows the PI distribution calculated using 17 turbulence indices during these three turbulence events. Since we do not have observational data to support the correction algorithm for the turbulence intensity description, it is difficult to verify the correctness of the turbulence intensity description. Therefore, we focused on whether the PI could reflect the turbulence events and used light or greater PI values. During these periods, the turbulence index on the route reached above 0.8, indicating a high probability of turbulence occurrence (Figure 3a-f). This to some extent demonstrates the validity of the turbulence index used in this paper to represent turbulence. Furthermore, we removed the MWT indices and only used 11 CAT indices to calculate the turbulence probability index (PICAT). Figure 4 shows the PICAT results of the three turbulence events. We found that using only the CAT index is not sufficient to accurately capture turbulence events. The PICAT result of the 2023 event is similar to the PI result (Figures 3f and 4c).