*3.2. Empirical Thresholds*

Among the 123 landslide events recorded in the study period, 51 events occurred within the first polygon Mananthavady, 36 events in the second polygon Vythiri, 15 events in the third polygon Ambalayavayal and 21 events within the last polygon, Kuppadi. As described earlier, four different approaches were used to define thresholds using the Frequentist method for the study area.

Using the frequentist approach, thresholds of several exceedance probabilities are defined for the study area (Figure 8a). Out of the 123 landslide events considered for the analysis, 5% of events are expected to fall below the T5 line, 2.5% below the T2.5 line and 1% events are below T1 line. No events are expected to fall below the threshold line of 0.05% exceedance probability for such a small dataset, which makes the line well below the possible critical conditions. All defined threshold lines are observed to follow this pattern.

For Wayanad district, new rainfall thresholds were defined for possible landslide initiation, based on the frequentist approach. All three regional scale thresholds are following the pattern as depicted in Figure 8a, in terms of percentage events below each threshold line. The merged thresholds have the highest slope of −0.24 but lesser intercept values than Imax thresholds. For Imax thresholds, the rainfall event with maximum average intensity among the four rain gauge stations was considered for analysis. In most of the cases, it was observed that the nearest rain gauge recorded the maximum average precipitation, and, in some cases, other rain gauges were chosen for analysis. Thus, the intercept of the threshold is slightly higher than that of merged data with a lesser slope. The peak I threshold follows a pattern which is different from the power-law form associated to intensity–duration thresholds as described in the work of Caine [24]: the resulting slope of the threshold is a positive value. The reason for this could be that in the meteo-climatic setting of the study area, the total duration (D) of the main event and the peak intensity registered in one of the sub-events are completely independent and the relationship among them leads to an equation form that does not follow the power-law form discovered by Caine. On the contrary, the longer the main rainfall event, the higher the possibility of more intense bursts of rain, hence the positive exponent of the power-law function reported in Figure 8d.

**Figure 8.** Regional scale intensity–duration thresholds established for Wayanad with different exceedance probabilities. (**a**) Critical rainfall conditions with different exceedance probabilities, (**b**) Average intensity vs duration (Merged), (**c**) Maximum average intensity vs duration (Imax), (**d**) Peak daily intensity vs duration (Peak I).

From Figure 9, it can be inferred that the rainfall conditions that triggered landslides in the four separate polygons are slightly different from each other. Polygon 1 (Manathavady) covers the maximum area and most of the landslide incidences are found to be located within the boundary. The rainfall parameters that triggered landslides in Polygon 1 and Polygon 2 are characterized by relatively higher intensity, and hence the slope of threshold curves is less than that of the merged data. These regions are affected by large flows as the high-altitude regions in the district falls within these polygons. In Polygon 3 (Ambalavayal), the number of events is the least and the observed events were the results of relatively higher intensity rainfalls. In Polygon 3 and Polygon 4 (Kuppadi), most of the incidences recorded were earth slides and cut slope failures. These polygons are at lesser elevations, with moderate to low dissected plateau geomorphological conditions, and the slope failures are induced by anthropogenic activities in the pursuit of infrastructure development. Since the number of events considered in each polygon is lower, the percentage distribution of landslides below each threshold line is slightly different from that shown in Figure 8a. For a better comparison of the threshold pattern, all thresholds were plotted on the same graph for all the four exceedance probabilities as shown in Figure 10. This helps for an easy comparison of the defined thresholds at each level of exceedance.

**Figure 9.** Local scale intensity–duration thresholds established for Wayanad with different exceedance probabilities. (**a**) Average intensity vs duration (R1), (**b**) Average Intensity vs Duration (R2), (**c**) Average Intensity vs Duration (R3), (**d**) Average Intensity vs Duration (R4).

From Figure 10, it can be observed that for all exceedance levels, the relative positions of all the defined thresholds follow a similar pattern. Peak I and R3 thresholds are much higher than all the other thresholds. At lesser durations, Peak I thresholds are observed to be lower than R3 and the reverse is observed during higher durations. R4 thresholds are the lowest in all cases, as the region is characterized by less intensity rainfalls. R2 thresholds are conservative at lesser durations, but as the duration increases, the threshold curve crossed merged, Imax and R1 thresholds. R1 thresholds are observed to be in close similarity with the Imax values as at some exceedance probabilities, R1 is higher than both Imax and merged thresholds and generally at higher durations, the threshold becomes more conservative. The Imax thresholds are always higher than that of the merged thresholds with similar values at low durations. The shift between the two threshold lines increases as the duration increases.

**Figure 10.** Comparison of different thresholds at (**a**) 5% exceedance probability (**b**) 2.5% exceedance probability (**c**) 1% exceedance probability (**d**) 0.05% exceedance probability.
