Supplementary Material In the following, the relevant data sets and test results, together with the corresponding figures, are shown for each volcano, together with a short comment on the volcano characteristics and the fit quality. The names adopted for the repose time fit parameters are exponential distribution: Weibull distribution: log-logistic distribution: Tupungatito year VEI year VEI year VEI Tupungatito Volcano is located in the high Andes east of Chile's capital 1829 2 1925 2 1961 2 Santiago, which is inhabited by six million people and by far Chile's 1835 2? 1946 2 1964 2 most important industrial and commercial centre. The volcano built up 1861 2 1958 2 1968 2 since Pleistocene times in the Nevado Sin Nombre Caldera (Siebert and 1889 2 1959 2 1980 2 Simkin, 2002), its recent activity consists of 18 smaller historical 1897 2 1959 2 1986 1 eruptions, which produced a total erupted volume of about 6 km³ 1901 2 1960 2 1987 2 (Sruoga et al., 1993). 1907 2 2 fit A t k d x0 p ²/DoF R KS-diff. AICc exp. 15.17±0.36 10.57±0.39 0.384 0.978 0.097 14.0 16± 0 9.97±0.27 0.442 0.974 0.095 14.0 WB 15.37±0.98 0.0970 0.9297 0.364 0.975 0.108 15.1 ±0.009 ±0.092 16± 0 0.1023 0.8811 0.356 0.975 0.126 13.3 ±0.003 ±0.039 log 15.04±0.51 6.881 1.494 0.445 0.976 0.134 17.1 ±0.470 ±0.097 16± 0 6.140 1.385 0.479 0.973 0.177 16.5 ±0.247 ±0.072 KS-threshold: 0.328 all fits pass the K-S-test The difference in AICc for fixed vs. fit A is minor for all distribution functions. The Weibull and exponential function give a slightly better fit than the log-logistic function, but the difference in AICc is not marked enough to significantly prefer these models. T [years] Exp_var Exp_const WB_var WB_const Log_var Log_const 0 0.0 0.0 0.0 0.0 0.0 0.0 1 9.0 9.5 8.2 7.8 5.5 5.1 2 17.2 18.2 15.7 15.0 10.6 9.9 5 37.7 39.4 34.6 33.3 23.3 21.9 10 61.2 63.3 57.0 55.1 38.9 36.8 20 84.9 86.5 81.1 79.2 58.1 55.3 50 99.1 99.3 98.3 97.7 80.6 78.1 100 100.0 100.0 100.0 99.9 91.0 89.3 200 100.0 100.0 100.0 100.0 96.3 95.3 500 100.0 100.0 100.0 100.0 99.0 98.5 1000 100.0 100.0 100.0 100.0 99.6 99.4 Maipo year VEI year VEI The ideally-shaped stratocone of Maipo Volcano is nested in the ~18 km diameter Diamante Caldera km that formed 450 ka BP (Sruoga et al., 2005). Seven historical 1826 2 1869 2 eruptions of VEI = 2 occurred over the past 200 years. Despite its location in the 1829 2? 1905 2 wider Santiago region (Región Metropolitana), the volcano and its surroundings are 1831 2 1908 2 developed for rustic tourism and therefore frequently visited. 1833 2 1912 2? 2 fit A t k d x0 p ²/DoF R KS-diff. AICc exp. 4.121±0.437 27.02±5.61 1.069 0.378 0.483 4.8 7± 0 11.41±1.33 1.797 0.076 0.609 22.8 WB fit cannot be performed 7± 0 0.1140 0.3281 0.550 0.503 0.388 -20.9 ±0.020 ±0.062 log 7.392±0.696 2.684 0.5523 0.491 0.722 0.342 -22.7 ±1.173 ±0.093 7± 0 3.190 0.5622 0.482 0.719 0.367 -24.7 ±0.807 ±0.091 KS-threshold: 0.486 all fits pass the KS-test except the exponential function for fixed A The Weibull function cannot be fit stably when A is a free parameter. In the case of the exponential, the AICc for fixed A is much worse than for variable A. For the log-logistic distribution, this difference is not so pronounced, but the fit is somewhat better for fixed A. The AICc of the exponential function (both for fit and variable A) is significantly worse than for the Weibull and log-logistic function, indicating that the exponential function provides a less satistfactory fit to the data. The log-logistic distribution performs better than the Weibull, which is still considerably better than the exponential distribution. T [years] Exp_var Exp_const WB_const Log_var Log_const 0 0 0 0 0 0 1 3.63 8.39 0.73 0.49 0.50 2 7.14 16.08 1.46 0.98 0.99 5 16.90 35.48 3.57 2.39 2.42 10 30.94 58.37 6.90 4.62 4.67 20 52.30 82.67 12.95 8.68 8.76 50 84.29 98.75 27.36 18.36 18.54 100 97.53 99.98 43.61 29.45 29.74 200 99.94 100 62.17 42.72 43.12 500 100 100 83.27 60.14 60.63 1000 100 100 93.07 71.10 71.61 Planchón-Peteroa year VEI year VEI year VEI Planchón-Peteroa is a compound volcanic edifice, where several interlaced 1660 >=3 1878 2 1960 1 calderas host the three volcanic centres Planchón, Peteroa, and Azufre, the 1751 2 1889 2 1962 1 latter of which collapsed at about 11.5 ka BP (Tormey et al., 1995). The 1762 4 1937 2 1967 1? largest historical eruption (VEI = 4) occurred in 1762, thereafter the volcano 1835 2 1938 2 1991 2 calmed to a series of smaller eruptions of VEI = 2, while the most recent eruptions during the past fifty years only reached a VEI of 1. The volcanic 1837 2 1959 1 1998 1 complex is flanked by a border crossing road to Argentina. 1860 2 As Planchón-Peteroa fails the test for independence, the analysis is repeated for eruptions after the year 1835. Still, the independence of successive eruptions cannot be ascertained, as the correlation coefficient points to a significant correlation (95% level of significance). Planchón-Peteroa is therefore excluded from the following analyses. Quizapu-Cerro Azul Historical eruptions of Cerro Azul took place through the parasite vent of Quizapu on its northern flank. The volcano is part of the larger Cerro Azul - Descabezado Grande - Resolana volcanic complex, year VEI characterised by several major stratovolcanoes and numerous small vents (Hildreth and Drake, 1992). 1846 2 Quizapu has produced one strong eruption in historical times, which is listed on the GVP-webpage as 1903 2 beginning in 1916 and lasting till 1932, although the major 9.5 km3 Plinian explosion took place in 1932. 1906 2 The influence of the exact onset date of this eruption on the statistical analysis is minor in this case, 1907 2 because it only switches the order of two repose times of 1-2 years and 16-17 years, respectively, which would rather smoothen the cumulative frequency plot and strengthen the stationary property of the data 1912 2 set. Since this VEI = 5+ eruption did not occur at the beginning of the eruption record but interspersed in 1913 2? a time interval with VEI = 2 eruptions, the record is considered to be complete and reliable. The VEI 5+ 1914 3 eruption followed the second strongest eruption of VEI = 3, suggesting that the volcano was 1916 5+ experiencing an episode of particularly fierce activity. The region around the volcano is intensely used: 1933 2 Major hydroelectrical power plants are constructed in the valley downstream of the volcano; several 1949 2? precious natural reserves attract a large number of tourists. Having been an ordinary border crossing to Argentina for a long time, the road connecting the Chilean metropole Talca with the Argentinian city of 1967 2? Malargüe via the Paso Pehuenche is currently upgraded and paved to become a major international hub. 2 fit A t k d x0 p ²/DoF R KS-diff. AICc exp. 7.264±0.36 15.36±1.12 0.552 0.853 0.323 34.4 10± 0 10.34±0.63 0.961 0.740 0.248 55.8 WB 8.316±1.20 0.08587 0.6569 0.344 0.874 0.181 24.6 ±0.0228 ±0.1106 10± 0 0.12336 0.5407 0.345 0.871 0.276 23.0 ±0.0083 ±0.0330 log 9.297±0.57 4.900 0.9772 0.394 0.897 0.175 27.3 ±0.818 ±0.0773 10± 0 4.058 0.9199 0.395 0.895 0.216 25.7 ±0.377 ±0.0594 KS-threshold: 0.410 all fits pass the KS-test The AICc is comparable for fixed vs. fit A in case of the Weibull and log-logistic distribution, but considerably worse for the exponential distribution. The exponential gives a less satisfactory fit that the Weibull; the log-logistic distribution, while not giving as good a fit as the Weibull distribution, still performs satisfactorily. T [years] Exp_var Exp_const WB_var WB_const Log_var Log_const 0 0.0 0.0 0.0 0.0 0.0 0.0 1 6.3 9.2 3.6 3.1 2.0 1.9 2 12.2 17.6 7.0 6.0 4.0 3.8 5 27.8 38.3 16.3 14.2 9.4 8.9 10 47.8 62.0 29.5 25.8 17.1 16.3 20 72.8 85.5 49.2 43.5 29.2 27.8 50 96.1 99.2 79.1 72.3 50.6 48.6 100 99.9 100.0 94.2 89.7 67.1 64.9 200 100.0 100.0 99.3 97.9 80.2 78.2 500 100.0 100.0 100.0 99.9 90.9 89.5 1000 100.0 100.0 100.0 100.0 95.2 94.2 Nevados de Chillán year VEI year VEI year VEI A series of major vents are aligned in an NNW-SSE trending direction at 1650 3? 1883 2? 1927 2? Nevados de Chillán, accompanied by several satellite vents (Dixon et al., 1999).