Tracking volcanic plume thermal evolution and eruption source unsteadiness in ground-based thermal imagery using spectral-clustering

Volcanic plumes typically have unsteady source conditions, where mass and heat fluxes from the vent evolve or fluctuate on time scales from seconds to hours. However, integral plume models routinely assume source conditions that are statistically stationary, and the degree to which source unsteadiness influences the mechanics of plume rise and air entrainment has not been established with quantitative predictions. We address this knowledge gap by examining eruptions with varying unsteady character at Sabancaya Volcano, Peru. We develop a novel tracking algorithm based on spectral clustering, which tracks the spatiotemporal evolution of coherent turbulent structures in plumes using ground-based, thermal infrared imagery. For turbulent structures tracked in time and space, we calculate the power law decay exponent of excess temperature with height. In general, more unsteady or transient events are characterized by power law exponents matching theoretical predictions for an instantaneous point release of buoyancy (i.e. a thermal), which evolve with sustained emissions to values consistent with steady plumes. Our results support previous findings from field evidence and laboratory experiments that entrainment and gravitational stability in unsteady volcanic plumes are inadequately captured by time-averaging or constant entrainment coefficients. We propose a quantitative definition for plume source unsteadiness which captures the timing and magnitude of source fluctuations on time scales that influence entrainment mechanics, and which provisionally predicts our observed differences in power law behavior. We argue for systematic experimental and numerical studies of the relationship between source unsteadiness and entrainment to develop unsteady entrainment parameterizations for integral plume models.