*4.1. Validation*

Proper validation should be based on the comparison between the prediction results and the actual characteristics affected by future rockfalls [16,35]. The selection of approaches depends on the characteristics of dataset. In this study, the space partition to separate our rockfall inventory into two groups was chosen since information was lacking related to the time of the 235 historical rockfalls (Figure 8). To validate the prediction result, the rockfall inventory was partitioned into two groups. One group was used for prediction (Figure 1a) and the other was used for validation (Figure 1b).

**Figure 8.** The validation of the prediction result obtained by using one group of historical rockfalls separated by the space partition (Figure 1a).

The first group with 118 historical rockfalls (Figure 1a) was adopted to calculate the rock mass strength and build the R–S relationship curve. According to the fitting result of the selected 118 rockfall sources, the minimum and maximum rock mass cohesions (*c*) are 28 and 230 kPa, respectively, and both internal friction angles (*ϕ*) are 22◦. To present a common case of application, we used the mean value of the upper envelope and the lower envelope to build the R–S relationship curve in this paper. Based on the procedure of our approach (Figure 3), the rockfall source areas were obtained. The second group with 117 historical rockfalls (Figure 1b) was used to validate the prediction result (Figure 8). The validation result demonstrated that 117 historical rockfalls occupy 71.92% of the rockfall source areas in the validation area predicted by our new approach, which proves to be a good prediction.

Besides, the prediction result was validated with field work. Most of the rockfall source areas identified by our approach are distributed on slopes with high relief and steep terrain. This is consistent with the observation of rockfall distribution on the maps of DEM and hillshade (Figure 8). Most of the historical rockfall deposits are distributed at the foot of the slopes with identified rockfall source areas, proving that the identified rockfall source areas are distributed rockfalls that occurred in the past, and that unstable slopes are prone to rockfall in the future [19].

#### *4.2. Uncertainty Analysis*

An accurate calculation of rock mass strength parameters is the fundamental work in our new proposed approach. For example, for a slope with a specific relief (H) and slope angle (*β*), the bigger the rock mass strength estimated, the higher the value of the limit relief (Hc) calculated by Equation (1), and hence the bigger the difference between Hc and H. For the stability of the slope, more stable (i.e., the lower rockfall susceptibility) slopes were predicted. In other words, if the rock mass strength parameters are overestimated, the slope would be prone to rockfall with an incorrect prediction of low susceptibility. In our new approach, the more accurate estimated rock mass strength parameters will greatly improve the accuracy of the R–S relationship curve, and hence the prediction results of rockfall source areas. However, it is very difficult to quantitatively estimate the rock mass strength at the landscape. An in situ test is recognized as one of the most reliable

methods to obtain rock mass strength [10,20], which proves to be very difficult to carry out in high mountain areas. In this paper, the back analysis for rock mass strength using historical rockfalls based on the Culmann model is adopted, whose accuracy depends on the reliability of the identification, the boundary of historical rockfalls, and the uncertainty in fitting the data.

According to the procedure of our approach and the sketch in Figure 3, the specific area (A) is also important in affecting the accuracy of the prediction result. For example, if a smaller area than the real one was defined to search the potential rockfall source areas, a lower relief (H) than the real value of a potential source area would be obtained. For the same slope angle and corresponding estimated Hc, the area would mistakenly be regarded as more stable (Figure 3) than its real stability state. In this paper, the mean area of historical rockfalls is defined as the specific area (A) for searching the potential rockfall source areas. The definition of the parameter could be further studied in the future.

The resolution of DEM plays an important role in controlling the accuracy of the result [5] because it is the basic data in almost every data process of our new approach. The higher the resolution of the DEM, the higher the accuracy of the values of the relief and slope angles of historical rockfalls and the potential rockfall source areas. However, it is not easy to acquire a high-quality DEM in a large study area currently.

#### **5. Conclusions**

The main type of rock mass failure in the Wolong area of Tibet is rockfall. Using data from helicopter-based remote sensing imagery, a DEM with 10 m resolution of the study area, images from Google Earth, and field work, a rockfall inventory including 235 rockfalls scars on bedrocks and 109 rockfall deposits was prepared. According to the statistical results, the relief of historical rockfalls is mainly distributed between 40 and 130 m, the slope angle is generally larger than 45◦, and the area of each historical rockfall scar is generally less than 9000 m2. A clear inverse relationship between the relief and slope angles of historical rockfalls enabled us to calculate the rock mass strength at the landscape scale base on the Culmann model, obtaining the minimum and maximum rock mass cohesions (*c*) in the study area from 28 to 270 kPa, respectively, and the internal friction angle of 23◦.

Required by the actual needs of identification on high and steep slopes, this paper proposes a new approach using the relief–slope angle relationship to identify the rockfall source areas controlled by the rock mass strength on a regional scale. Based on historical rockfalls and a high-resolution DEM, we obtained the parameters used in our proposed approach. By applying our approach, the potential rockfall source areas in the study area were identified and further zoned into three susceptibility classes that could be used as a reference for the study of regional rockfall susceptibility assessment. According to the results, rockfall source areas within the high susceptibility class are mainly distributed on the slopes with the angles of 60–66◦, those of medium susceptibility are distributed on the slopes with the angles of 54–61◦, and those of low susceptibility are distributed on the slopes with the angles of 46–55◦.

By the space partition and the field work, our prediction result was validated. Most of the rockfall source areas (i.e., 71.92%) identified in the validation area are occupied by actual historical rockfalls, which proves the accurate prediction ability of our approach. The locations of the rockfall source areas obtained in this paper could provide reference for actual rockfall disaster prevention and mitigation in the study area. Our proposed approach could be used to identify the rockfall source areas in the regional areas that are not accessible. In the paper, the dominant uncertainty is derived from the process of calculating the rock mass strength parameters, the process of defining the specific area (A) that is used for searching the rockfall source areas, and the resolution of the DEM. Many more studies estimating the rock mass strength at the landscape scale and defining the specific area (A) are necessary in the future.

**Author Contributions:** Conceptualization, X.W.; methodology X.W., H.L.; formal analysis, H.L., J.S.; writing—original draft preparation, X.W., H.L.; writing—review and editing, X.W.; visualization, H.L.; supervision, X.W.; project administration, J.S.; funding acquisition, X.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Second Tibetan Plateau Scientific Expedition and Research Program (STEP) (Grant No. 2019QZKK0904), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA23090402), the Application of Synthetic Aperture Radar-Based Geological Hazard Analysis Technology on the Strategic Electricity Transmission Passage of Sichuan-Tibet Plateau (Grant No. 52199918000C).

**Acknowledgments:** We thank the program research group of the State Grid Corporation of China for providing the 10 m resolution topographic DEM data.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

#### **References**

