Beyond the Average: Computation of Vertical Profiles in Dilute Pyroclastic Density Currents and Their Use in Shallow‐Water Models

Abstract Pyroclastic density currents (PDCs) present significant hazards due to their high temperatures and dynamic pressures. Accurate estimation of dynamic pressure, vital for assessing potential damage, requires knowledge of the vertical variations of velocity and particle concentration within the PDC, particularly in the first few meters of the flow above the ground. Existing approaches to dynamic pressure calculations used in hazard assessment are often based on average values for velocity and particle volume fraction. These average values may misrepresent the flow dynamics, especially near the base of the flow where the gradients of flow variables are larger. Here, we present a new, physically based approach that allows for the calculation of the vertical profiles of velocity and concentration from a combination of depth‐averaged values for these properties and non‐dimensional flow parameters. Finally, we demonstrate the use of these profiles within an existing shallow‐water model and show its potential applications toward probabilistic hazard assessment.