Different physics but similar dependence of runout distance with discharge rate: the duality of pyroclastic density currents

We address emplacement mechanisms of pyroclastic density currents (PDCs) through relationships between their runout distance and mass discharge rate of their parent eruptions. Assuming axisymmetric propagation typical of dilute currents that are little controlled by topography, we apply a simple method to estimate the runout distance of concentrated PDCs channelized in valleys. With these data, the runout distance of concentrated currents varies, as for their dilute counterparts, with the discharge rate to the power ~ 0.5, the latter being the consequence of radial propagation of the currents. This simple dependence between runout distance and discharge rate is both surprising and remarkable considering the fundamentally different natures of dilute or concentrated PDCs, which are governed by complex physics involving many parameters. This dependence further suggests that particle settling velocity, which controls the rate of decrease of the flow mass, has a second-order effect on the runout distance. We argue that the hindered settling model established for particle suspensions in a static fluid is relevant for estimating the settling velocity of particles in concentrated PDCs. Settling velocities of ~ 0.1 to 10 cm/s calculated for some natural examples correspond to deposit aggradation rates of the same order. These rates imply timescales of deposit formation significantly shorter than flow durations in some cases, suggesting that onset of deposition occurs at late stages of emplacement.