Estimating probabilities of occurrence related to impacts on glacial lakes from large rock-ice avalanches&#160;
Authors: Haeberli Wilfried , Allen Simon , Frey Holger 
Published: March 2022

&lt;p&gt;Worst-case scenarios concerning volumes and hydrographs of sudden, far-reaching&amp;#160; impact/flood waves from existing and future glacial lakes are based on assumed impacts from large, high-energy rock- or rock/ice-avalanches. The probability of occurrence related to such events as a basis for quantitative hazard and risk assessment and intercomparison depends on their expected magnitude and frequency. Magnitude is given by the term &amp;#8220;large&amp;#8221;&amp;#160; - here defined as volumes of millions of m&lt;sup&gt;3&lt;/sup&gt; which enable near-instantaneous displacement of lake volumes in the order of millions to tens of millions of m&lt;sup&gt;3&lt;/sup&gt;. Quantitative determination of related frequencies, on the other hand, faces fundamental difficulties for a number of reasons. Rock-ice avalanches are non-repetitive events: Once an event has occurred it cannot occur again in the same way from the exact same site, because the unstable rock mass has definitely been removed from its detachment zone. Destabilisation processes which precede rock- or rock/ice avalanches are cumulative processes: Under conditions of continued global warming, future conditions are not only different from the past, but also from present-day situations. Scenarios of drastic and long-term future glacier vanishing and permafrost degradation/thaw must be taken into consideration, along with changes in atmospheric triggering conditions.&lt;/p&gt;&lt;p&gt;During the past years, first steps towards producing a useful statistical data basis have been achieved concerning regional developments in time of rock- and rock/ice avalanches for selected cold mountain areas of variable sizes. The existing statistical data bases together with indications about effects from warming trends can now be used to rougly determine event recurrence times per unit area of steep icy peaks. This, in turn, opens the possibility to quantitatively estimate expected probabilities of occurrence related to possible future extreme impacts on critical locations, such as involving glacial lakes and process cascades. In view of the still strongly limited statistical data and the complexity of the involved processes, only order-of-magnitude estimates can be achieved. A first preliminary analysis based on quantitative information from the European Alps and Glacier Bay National Park indicates event recurrence times of about 10&lt;sup&gt;3&lt;/sup&gt; to 10&lt;sup&gt;4&lt;/sup&gt; years per km&lt;sup&gt;2&lt;/sup&gt; of steep icy peaks with an increase of about a factor of 5 as documented for the Alps during the past few decades. Applying these results to the slopes in the catchment of three glacial lakes of high practical interest provides probabilities of ocurrence per year of 0.01 to 0.001 for Laguna Palcacocha (Cordillera Blanca, Peru), 0.1 to 0.01 for Lower Barun Lake (Nepal Himalaya) and 0.1 to 0.01 for the system of lakes which is likely to form during the coming decades at Great Aletsch glacier (Swiss Alps) where presently no lake exists.&lt;/p&gt;&lt;p&gt;Such first estimates indicate important possibilities for quantitative hazard and risk assessments but need further improvement by systematic data collection about large catastrophic mass flows in cold mountains and by analysing the key environmental factors in a more differentiated way.&lt;/p&gt;