## 4 Results  
Examples of the PDC invasion maps for the different scenarios and vent positions are reported in Figures 3 and 4. In scenario 1, these maps show that the PDC invasion area is partly controlled by the presence of the caldera rim (Figure 3). In particular, PDC are confined within the caldera for vents located in the inner side of the caldera (vents 1 and 6). PDC invasion area of vent 2, which is located within the caldera but close to a zone where the rim is interrupted and the caldera is open toward the north, many covers the valley located in the northern flank of the volcano and, with a less extension, the caldera floor. The PDC invasion areas related to vents 3 and 7, both located outside caldera, mainly cover the flanks of the volcano, and, in a lesser amount, the inner caldera floor. The distance covered by PDCs in scenario 1 does not exceed about 7 km from the respective vent. This result is consistent with that obtained from TITAND2 simulations by [PERSON] et al. [60] from six vents with a similar position with respect to the caldera rim and column height of 2-5 km. As concerns scenario 2, the PDC invasion area mainly affects the flanks of the volcano and, depending on the vent position, covers different sectors of the volcano (Figure 3). The caldera floor is always covered by the PDCs. The maximum runout distance from the runs with the smaller \(\Delta\)H/L value is in the order of 16-20 km, depending on the vent position. The distance from the runs with the larger \(\Delta\)H/L does not exceed 10 km (Figure 3). The results of scenario 3 show that the distance variesfrom 28 to 37 km for the smallest \(\Delta\)H/L value, whereas it is in the order of 12-15 km for the largest \(\Delta\)H/L. In scenario 3 runs, significant effects of the vent position on the PDC dispersion areas are lacking. In scenario 4, the distance of PDCs determined for the smaller \(\Delta\)H/L is of  
Figure 4: Top: examples of EC simulations in scenario 3 (column height = 20 km) from different vents (white number in the panel) and three selected \(\Delta\)H/L values. Bottom: examples of simulations in scenario 4 (column height = 30 km) from different vents (white number in the panel) and three selected \(\Delta\)H/L values. 80-85 km (Figure 4), a value corresponding to the maximum distance of 83 km measured in the field for the pumice-rich PDCs of the Millennium eruption [51; 61]. The maximum distance travelled by PDCs from the runswith the smallest \(\Delta\)H/L is between 35 and 40 km from the vent. The probability (\(p\)) invasion maps are shown in Figures 5-8. As expected, the more relevant feature of resulting probability maps is that the area of invasion and \(p\) increases with Ht. Low \(p\)-values (\(\leq\)0.5) and a dependence of invasion probability map from the vent location may be recognized in scenario 1 (Figure 5). For higher Ht (Scenarios 2-4; Figures 6-8), the probabilities of invasion reach 1 in the proximal and medial zones around the caldera area; \(p\) decreases with the distance rather symmetrically around the caldera showing less dependence on vent location with respect to scenario 1. In this latter scenario, the larger \(p\)-values may be found within the caldera and in the northern valley, where the caldera rim is breached (Figure 5). Figure 5: Probability map of invasion by PDCs in scenario 1 (Ht = 3 km) (spatial probability scale at the bottom) superimposed to the China-North Korea infrastructural network; the inset includes a detail of the caldera area. Different types of morphological settings like valleys and walls (caldera rim) influence the deposition and the mobility of PDCs. In scenario 1, only the top of the volcano is potentially affected by PDCs. The area covered by PDC includes the more elevated portion of the Changbaishan Natural Reserve and the road leading to the top of the volcano. In scenario 2, the area with \(p\geq 0.5\) characterizes the caldera and the upper, outer flanks of the volcano (Figure 6).