It has been 10 years since the ash cloud from the eruption of Eyjafjallajökull caused unprecedented disruption to air traffic across Europe. During this event, the London Volcanic Ash Advisory Centre (VAAC) provided advice and guidance on the expected location of volcanic ash in the atmosphere using observations and the atmospheric dispersion model NAME (Numerical Atmospheric-Dispersion Modelling Environment). Rapid changes in regulatory response and procedures during the eruption introduced the requirement to also provide forecasts of ash concentrations, representing a step-change in the level of interrogation of the dispersion model output. Although disruptive, the longevity of the event afforded the scientific community the opportunity to observe and extensively study the transport and dispersion of a volcanic ash cloud. We present the development of the NAME atmospheric dispersion model and modifications to its application in the London VAAC forecasting system since 2010, based on the lessons learned. Our ability to represent both the vertical and horizontal transport of ash in the atmosphere and its removal have been improved through the introduction of new schemes to represent the sedimentation and wet deposition of volcanic ash, and updated schemes to represent deep moist atmospheric convection and parametrizations for plume spread due to unresolved mesoscale motions. A good simulation of the transport and dispersion of a volcanic ash cloud requires an accurate representation of the source and we have introduced more sophisticated approaches to representing the eruption source parameters, and their uncertainties, used to initialize NAME. Finally, upper air wind field data used by the dispersion model is now more accurate than it was in 2010. These developments have resulted in a more robust modelling system at the London VAAC, ready to provide forecasts and guidance during the next volcanic ash event.

We present a Bayesian inversion method for estimating volcanic ash emissions using satellite retrievals of ash column load and an atmospheric dispersion model. An a priori description of the emissions is used based on observations of the rise height of the volcanic plume and a stochastic model of the possible emissions. Satellite data are processed to give column loads where ash is detected and to give information on where we have high confidence that there is negligible ash. An atmospheric dispersion model is used to relate emissions and column loads. Gaussian distributions are assumed for the a priori emissions and for the errors in the satellite retrievals. The optimal emissions estimate is obtained by finding the peak of the a posteriori probability density under the constraint that the emissions are non-negative. We apply this inversion method within a framework designed for use during an eruption with the emission estimates (for any given emission time) being revised over time as more information becomes available. We demonstrate the approach for the 2010 Eyjafjallajökull and 2011 Grímsvötn eruptions. We apply the approach in two ways, using only the ash retrievals and using both the ash and clear sky retrievals. For Eyjafjallajökull we have compared with an independent dataset not used in the inversion and have found that the inversion-derived emissions lead to improved predictions.

Large explosive eruptions can result in the formation of an umbrella cloud which rapidly expands, spreading ash out radially from the volcano. The lateral spread by the intrusive gravity current dominates the transport of the ash cloud. Hence, to accurately forecast the transport of ash from large eruptions, lateral spread of umbrella clouds needs to be represented within volcanic ash transport and dispersion models. Here, we describe an umbrella cloud parameterisation which has been implemented into an operational Lagrangian model and consider how it may be used during an eruption when information concerning the eruption is limited and model runtime is key. We examine different relations for the volume flow rate into the umbrella, and the rate of spreading within the cloud. The scheme is validated against historic eruptions of differing scales (Pinatubo 1991, Kelud 2014, Calbuco 2015 and Eyjafjallajökull 2010) by comparing model predictions with satellite observations. Reasonable predictions of umbrella cloud spread are achieved using an estimated volume flow rate from the empirical equation by Bursik et al. and the observed eruption height. We show how model predictions can be refined during an ongoing eruption as further information and observations become available.

We present results for tetrad (four-particle) dispersion in homogeneous isotropic turbulence by means of a simple Lagrangian stochastic model with a focus on the inertial subrange. We show that for appropriate values of C ₀, the constant of proportionality in the second-order Lagrangian velocity structure function, the shape statistics agree well with equivalent results from a direct numerical simulation (DNS) of turbulence. Moreover, we show that the shape statistics are independent of C ₀ for a wide range of C ₀-values. We also show that the parameters which characterise the shape of the tetrads can be approximately related to appropriate ratios of the growth rates of the mean square separation, the mean square area and the mean square volume of the tetrads. By means of exit times, we are able to estimate the equivalent values for the DNS data. We also consider the statistics of four-point velocity differences (via a diffusion tensor) which agree well with the DNS. We show that the nature of the velocity field experienced by the tetrad varies significantly with C ₀.