Mark J Woodhouse | University of Bristol (original) (raw)
Papers by Mark J Woodhouse
Royal Society Open Science
The SARS-CoV-2 epidemic has impacted children's education, with schools required to implement... more The SARS-CoV-2 epidemic has impacted children's education, with schools required to implement infection control measures that have led to periods of absence and classroom closures. We developed an agent-based epidemiological model of SARS-CoV-2 transmission in a school classroom that allows us to quantify projected infection patterns within primary school classrooms, and related uncertainties. Our approach is based on a contact model constructed using random networks, informed by structured expert judgement. The effectiveness of mitigation strategies in suppressing infection outbreaks and limiting pupil absence are considered. COVID-19 infections in primary schools in England in autumn 2020 were re-examined and the model was then used to estimate infection levels in autumn 2021, as the Delta variant was emerging and it was thought likely that school transmission would play a major role in an incipient new wave of the epidemic. Our results were in good agreement with available da...
EGU General Assembly Conference Abstracts, Apr 1, 2016
EGU General Assembly Conference Abstracts, Apr 1, 2017
Royal Society Open Science, 2021
Drawing on risk methods from volcano crises, we developed a rapid COVID-19 infection model for th... more Drawing on risk methods from volcano crises, we developed a rapid COVID-19 infection model for the partial return of pupils to primary schools in England in June and July 2020, and a full return in September 2020. The model handles uncertainties in key parameters, using a stochastic re-sampling technique, allowing us to evaluate infection levels as a function of COVID-19 prevalence and projected pupil and staff headcounts. Assuming average national adult prevalence, for the first scenario (as at 1 June 2020) we found that between 178 and 924 [90% CI] schools would have at least one infected individual, out of 16 769 primary schools in total. For the second return (July), our estimate ranged between 336 (2%) and 1873 (11%) infected schools. For a full return in September 2020, our projected range was 661 (4%) to 3310 (20%) infected schools, assuming the same prevalence as for 5 June. If national prevalence fell to one-quarter of that, the projected September range would decrease to b...
Journal of Fluid Mechanics
It is increasingly common for models of shallow-layer overland flows to include equations for the... more It is increasingly common for models of shallow-layer overland flows to include equations for the evolution of the underlying bed (morphodynamics) and the motion of an associated sedimentary phase. We investigate the linear stability properties of these systems in considerable generality. Naive formulations of the morphodynamics, featuring exchange of sediment between a well-mixed suspended load and the bed, lead to mathematically ill-posed governing equations. This is traced to a singularity in the linearised system at Froude number Fr = 1 that causes unbounded unstable growth of short-wavelength disturbances. The inclusion of neglected physical processes can restore well posedness. Turbulent momentum diffusion (eddy viscosity) and a suitably parametrised bed load sediment transport are shown separately to be sufficient in this regard. However, we demonstrate that such models typically inherit an associated instability that is absent from non-morphodynamic settings. Implications of our analyses are considered for simple generic closures, including a drag law that switches between fluid and granular behaviour, depending on the sediment concentration. Steady morphodynamic flows bifurcate into two states: dilute flows, which are stable at low Fr, and concentrated flows which are always unstable to disturbances in concentration. By computing the growth rates of linear modes across a wide region of parameter space, we examine in detail the effects of specific model parameters including the choices of sediment erodibility, eddy viscosity and bed load flux. These analyses may be used to inform the ongoing development of operational models in engineering and geosciences.
![Research paper thumbnail of plumes: a comparison of plume properties predicted by an integral plume model to observations of volcanic lightning during the 2010 eruption of Eyjafjallajökull, Iceland. Bulletin of Volcanology, 76(8), [828]](https://attachments.academia-assets.com/89640409/thumbnails/1.jpg)
](Observations of volcanic lightning made using a lightning mapping array during the 2010 eruption ... more Observations of volcanic lightning made using a lightning mapping array during the 2010 eruption of Eyjafjallajökull allow the trajectory and growth of the volcanic plume to be determined. The lightning observations are compared with predictions of an integral model of volcanic plumes that includes descriptions of the interaction with wind and the effects of moisture. We show that the trajectory predicted by the integral model closely matches the observational data and the model well describes the growth of the plume downwind of the vent. Analysis of the lightning signals reveals information on the dominant charge structure within the volcanic plume. During the Eyjafjallajökull eruption both monopole and dipole charge structures were observed in the plume. By using the integral plume model, we propose the varying charge structure is connected to the availability of condensed water and low temperatures at high altitudes in the plume, suggesting ice formation may have contributed to t...
1.The SARS-CoV-2 epidemic continues to have major impacts on children’s education, with schools r... more 1.The SARS-CoV-2 epidemic continues to have major impacts on children’s education, with schools required to implement infection control measures that have led to long periods of absence and classroom closures. We have developed an agent-based epidemiological model of SARS-CoV-2 transmission that allows us to quantify projected infection patterns within primary school classrooms, and related uncertainties; the basis of our approach is a contact model constructed using random networks, informed by structured expert judgement. The effectiveness of mitigation strategies are considered in terms of effectiveness at supressing infection outbreaks and limiting pupil absence. Covid-19 infections in schools in the UK in Autumn 2020 are re-examined and the model used for forecasting infection levels in autumn 2021, as the more infectious Delta-variant was emerging and school transmission thought likely to play a major role in an incipient new wave of the epidemic. Our results were in good agre...
Journal of Volcanology and Geothermal Research, 2018
Meaningful forecasting of the atmospheric concentration and ground accumulation of volcanic ash d... more Meaningful forecasting of the atmospheric concentration and ground accumulation of volcanic ash during explosive eruptions requires detailed knowledge of the eruption source parameters. However, due to the large uncertainties in observations and limitations of current models used to make inferences from these, monitoring an ongoing eruption and quantifying the mass eruption rate in realtime is a considerable challenge. Within the EU supersite project "FutureVolc", an integrated approach has been applied to develop a quasi-autonomous multi-parameter system, denoted "REFIR", for monitoring volcanic eruptions in Iceland and assessing the eruption mass flow rate by inverting the plume height information and taking account of these uncertainties. REFIR has the capability to ingest and process streaming plume-height data provided by a multitude of ground based sensors, including C-and X-band radars and web-cam based plume height tracking systems. These observational data are used with a suite of plume models that also consider the current wind and other atmospheric conditions, providing statistically assessed best estimates of plume height and mass eruption rate. Provided instrumental data is available, near real-time estimates are obtained (the delay corresponding to the scan rate of data-providing instruments, presently of the order of minutes). Using the Hekla 2000, and Eyjafjallajökull 2010 eruptions in Iceland, the potential of REFIR is demonstrated and discussed through application to three scenarios. The system has been developed to provide maximum flexibility. A setup script assists the user in adapting to local conditions, allowing implementation of REFIR for any volcanic eruption site worldwide. REFIR is designed to be easily upgradable, allowing future extension of monitoring networks, learning from new events, and incorporation of new technologies and model improvements. This article gives an overview of the basic structure, models implemented, functionalities and the computational techniques of REFIR.
Journal of Fluid Mechanics, 2018
The unsteady ascent of a buoyant, turbulent line plume through a quiescent, uniform environment i... more The unsteady ascent of a buoyant, turbulent line plume through a quiescent, uniform environment is modelled in terms of the width-averaged vertical velocity and density deficit. It is demonstrated that for a well-posed, linearly stable model, account must be made for the horizontal variation of the velocity and the density deficit; in particular the variance of the velocity field and the covariance of the density deficit and velocity fields, represented through shape factors, must exceed threshold values, and that models based upon ‘top-hat’ distributions in which the dependent fields are piecewise constant are ill-posed. Numerical solutions of the nonlinear governing equations are computed to reveal that the transient response of the system to an instantaneous change in buoyancy flux at the source may be captured through new similarity solutions, the form of which depend upon both the ratio of the old to new buoyancy fluxes and the shape factors.
Meteorological Applications, 2016
The spread of a dense gas in the atmosphere is a phenomenon that occurs widely with natural (and ... more The spread of a dense gas in the atmosphere is a phenomenon that occurs widely with natural (and anthropogenic) causes and is often associated with high impact and hazardous events. In this study a method of simulating the spread of dense gases in a numerical weather prediction model is presented. This approach has the advantage that dense gases can be simulated in regions of complex terrain using realistic forcings (in terms of both the driving meteorological fields and the representation of surface characteristics). The model formulation is tested against semi-idealized gravity-current-type experiments and similar modelling studies. As an example application, the Lake Nyos disaster of 1986, where a dense CO 2 cloud spread through a mountainous region of Cameroon, is simulated. The predicted spread of CO 2 agrees (qualitatively) very well with the observations. The method provides a means of determining a potential 'safe height' above which simulated concentrations are not hazardous, and thus the height above which refuge should be taken during similar future events. The simulation demonstrates a novel application which can be rapidly applied to other scenarios.
Journal of Fluid Mechanics, 2016
We model the unsteady evolution of turbulent buoyant plumes following temporal changes to the sou... more We model the unsteady evolution of turbulent buoyant plumes following temporal changes to the source conditions. The integral model is derived from radial integration of the governing equations expressing the evolution of mass, axial momentum and buoyancy in the plume. The non-uniform radial profiles of the axial velocity and density deficit in the plume are explicitly captured by shape factors in the integral equations; the commonly assumed top-hat profiles lead to shape factors equal to unity. The resultant model for unsteady plumes is hyperbolic when the momentum shape factor, determined from the radial profile of the mean axial velocity in the plume, differs from unity. The solutions of the model when source conditions are maintained at constant values are shown to retain the form of the well-established steady plume solutions. We demonstrate through a linear stability analysis of these steady solutions that the inclusion of a momentum shape factor in the governing equations tha...
Atmospheric Chemistry and Physics, 2017
The separation of volcanic ash and sulfur dioxide (SO 2) gas is sometimes observed during volcani... more The separation of volcanic ash and sulfur dioxide (SO 2) gas is sometimes observed during volcanic eruptions. The exact conditions under which separation occurs are not fully understood but the phenomenon is of importance because of the effects volcanic emissions have on aviation, on the environment, and on the earth's radiation balance. The eruption of Grímsvötn, a subglacial volcano under the Vatnajökull glacier in Iceland during 21-28 May 2011 produced one of the most spectacular examples of ash and SO 2 separation, which led to errors in the forecasting of ash in the atmosphere over northern Europe. Satellite data from several sources coupled with meteorological wind data and photographic evidence suggest that the eruption column was unable to sustain itself, resulting in a large deposition of ash, which left a low-level ash-rich atmospheric plume moving southwards and then eastwards towards the southern Scandinavian coast and a high-level predominantly SO 2 plume travelling northwards and then spreading eastwards and westwards. Here we provide observational and modelling perspectives on the separation of ash and SO 2 and present quantitative estimates of the masses of ash and SO 2 that erupted, the directions of transport, and the likely impacts. We hypothesise that a partial column collapse or "sloughing" fed with ash from pyroclastic density currents (PDCs) occurred during the early stage of the eruption, leading to an ash-laden gravity intrusion that was swept southwards, separated from the main column. Our model suggests that water-mediated aggregation caused enhanced ash removal because of the plentiful supply of source water from melted glacial ice and from entrained atmospheric water. The analysis also suggests that ash and SO 2 should be treated with separate source terms, leading to improvements in forecasting the movement of both types of emissions.
Journal of Geophysical Research: Solid Earth, 2013
Estimates of volcanic source mass flux, currently deduced from observations of plume height, are ... more Estimates of volcanic source mass flux, currently deduced from observations of plume height, are crucial for ash dispersion models for aviation and population hazard. This study addresses the role of the atmospheric wind in determining the height at which volcanic plumes spread in the atmosphere and the relationship between source mass flux and plume height in a wind field. We present a predictive model of volcanic plumes that describes the bending over of the plume trajectory in a crosswind and show that model predictions are in accord with a dataset of historic eruptions if the profile of atmospheric wind shear is described. The wind restricts the rise height of volcanic plumes such that obtaining equivalent rise heights for a plume in a windy environment would require an order of magnitude increase in the source mass flux over a plume in a quiescent environment. Our model calculations are used to calibrate a semi-empirical relationship between the plume height and the source mass flux that explicitly includes the atmospheric wind speed. We demonstrate that the model can account for the variations in plume height observed during the first explosive phase of the 2010 Eyjafjallajökull eruption using independently measured wind speeds and show that changes in the observed plume height are better explained by changing meteorology than abrupt changes in the source mass flux. This study shows that unless the wind is properly accounted for, estimates of the source mass flux during an explosive eruption are likely to be very significant underpredictions of the volcanic source conditions.
Frontiers in Earth Science, 2017
Journal of Volcanology and Geothermal Research, 2016
Integral models of volcanic plumes allow predictions of plume dynamics to be made and the rapid e... more Integral models of volcanic plumes allow predictions of plume dynamics to be made and the rapid estimation of volcanic source conditions from observations of the plume height by model inversion. Here we introduce PlumeRise, an integral model of volcanic plumes that incorporates a description of the state of the atmosphere, includes the effects of wind and the phase change of water, and has been developed as a freely available web-based tool. The model can be used to estimate the height of a volcanic plume when the source conditions are specified, or to infer the strength of the source from an observed plume height through a model inversion. The predictions of the volcanic plume dynamics produced by the model are analysed in four case studies in which the atmospheric conditions and the strength of the source are varied. A global sensitivity analysis of the model to a selection of model inputs is performed and the results are analysed using parallel coordinate plots for visualisation and variance-based sensitivity indices to quantify the sensitivity of model outputs. We find that if the atmospheric conditions do not vary widely then there is a small set of model inputs that strongly influence the model predictions. When estimating the height of the plume, the source mass flux has a controlling influence on the model prediction, while variations in the plume height strongly effect the inferred value of the source mass flux when performing inversion studies. The values taken for the entrainment coefficients have a particularly important effect on the quantitative predictions. The dependencies of the model outputs to variations in the inputs are discussed and compared to simple algebraic expressions that relate source conditions to the height of the plume.
Bulletin of Volcanology, 2015
Mathematical models of natural processes can be used as inversion tools to predict unobserved pro... more Mathematical models of natural processes can be used as inversion tools to predict unobserved properties from measured quantities. Uncertainty in observations and model formulation impact on the efficacy of inverse modelling. We present a general methodology, history matching, that can be used to investigate the effect of observational and model uncertainty on inverse modelling studies. We demonstrate history matching on an integral model of volcanic plumes that is used to estimate source conditions from observations of the rise height of plumes during the eruptions of Eyjafjallajökull, Iceland, in 2010 and Grímsvötn, Iceland, in 2011. Sources of uncertainty are identified and quantified, and propagated through the integral plume model. A preliminary sensitivity analysis is performed to identify the uncertain model parameters that strongly influence model predictions. Model predictions are assessed against observations through an implausibility measure that rules out model inputs that are considered implausible given the quantified uncertainty. We demonstrate that the source mass flux at the volcano can be estimated from plume height observations, but the magmatic temperature, exit velocity and exsolved gas mass fraction cannot be accurately determined. Uncertainty in plume height observations and Editorial responsibility: C. Bonadonna
Journal of Fluid Mechanics, 2015
Volcanic eruptions commonly produce buoyant ash-laden plumes that rise through the stratified atm... more Volcanic eruptions commonly produce buoyant ash-laden plumes that rise through the stratified atmosphere. On reaching their level of neutral buoyancy, these plumes cease rising and transition to horizontally spreading intrusions. Such intrusions occur widely in density-stratified fluid environments, and in this paper we develop a shallow-layer model that governs their motion. We couple this dynamical model to a model for particle transport and sedimentation, to predict both the time-dependent distribution of ash within volcanic intrusions and the flux of ash that falls towards the ground. In an otherwise quiescent atmosphere, the intrusions spread axisymmetrically. We find that the buoyancy-inertial scalings previously identified for continuously supplied axisymmetric intrusions are not realised by solutions of the governing equations. By calculating asymptotic solutions to our model we show that the flow is not self-similar, but is instead time-dependent only in a narrow region at ...
Royal Society Open Science
The SARS-CoV-2 epidemic has impacted children's education, with schools required to implement... more The SARS-CoV-2 epidemic has impacted children's education, with schools required to implement infection control measures that have led to periods of absence and classroom closures. We developed an agent-based epidemiological model of SARS-CoV-2 transmission in a school classroom that allows us to quantify projected infection patterns within primary school classrooms, and related uncertainties. Our approach is based on a contact model constructed using random networks, informed by structured expert judgement. The effectiveness of mitigation strategies in suppressing infection outbreaks and limiting pupil absence are considered. COVID-19 infections in primary schools in England in autumn 2020 were re-examined and the model was then used to estimate infection levels in autumn 2021, as the Delta variant was emerging and it was thought likely that school transmission would play a major role in an incipient new wave of the epidemic. Our results were in good agreement with available da...
EGU General Assembly Conference Abstracts, Apr 1, 2016
EGU General Assembly Conference Abstracts, Apr 1, 2017
Royal Society Open Science, 2021
Drawing on risk methods from volcano crises, we developed a rapid COVID-19 infection model for th... more Drawing on risk methods from volcano crises, we developed a rapid COVID-19 infection model for the partial return of pupils to primary schools in England in June and July 2020, and a full return in September 2020. The model handles uncertainties in key parameters, using a stochastic re-sampling technique, allowing us to evaluate infection levels as a function of COVID-19 prevalence and projected pupil and staff headcounts. Assuming average national adult prevalence, for the first scenario (as at 1 June 2020) we found that between 178 and 924 [90% CI] schools would have at least one infected individual, out of 16 769 primary schools in total. For the second return (July), our estimate ranged between 336 (2%) and 1873 (11%) infected schools. For a full return in September 2020, our projected range was 661 (4%) to 3310 (20%) infected schools, assuming the same prevalence as for 5 June. If national prevalence fell to one-quarter of that, the projected September range would decrease to b...
Journal of Fluid Mechanics
It is increasingly common for models of shallow-layer overland flows to include equations for the... more It is increasingly common for models of shallow-layer overland flows to include equations for the evolution of the underlying bed (morphodynamics) and the motion of an associated sedimentary phase. We investigate the linear stability properties of these systems in considerable generality. Naive formulations of the morphodynamics, featuring exchange of sediment between a well-mixed suspended load and the bed, lead to mathematically ill-posed governing equations. This is traced to a singularity in the linearised system at Froude number Fr = 1 that causes unbounded unstable growth of short-wavelength disturbances. The inclusion of neglected physical processes can restore well posedness. Turbulent momentum diffusion (eddy viscosity) and a suitably parametrised bed load sediment transport are shown separately to be sufficient in this regard. However, we demonstrate that such models typically inherit an associated instability that is absent from non-morphodynamic settings. Implications of our analyses are considered for simple generic closures, including a drag law that switches between fluid and granular behaviour, depending on the sediment concentration. Steady morphodynamic flows bifurcate into two states: dilute flows, which are stable at low Fr, and concentrated flows which are always unstable to disturbances in concentration. By computing the growth rates of linear modes across a wide region of parameter space, we examine in detail the effects of specific model parameters including the choices of sediment erodibility, eddy viscosity and bed load flux. These analyses may be used to inform the ongoing development of operational models in engineering and geosciences.
Observations of volcanic lightning made using a lightning mapping array during the 2010 eruption ... more Observations of volcanic lightning made using a lightning mapping array during the 2010 eruption of Eyjafjallajökull allow the trajectory and growth of the volcanic plume to be determined. The lightning observations are compared with predictions of an integral model of volcanic plumes that includes descriptions of the interaction with wind and the effects of moisture. We show that the trajectory predicted by the integral model closely matches the observational data and the model well describes the growth of the plume downwind of the vent. Analysis of the lightning signals reveals information on the dominant charge structure within the volcanic plume. During the Eyjafjallajökull eruption both monopole and dipole charge structures were observed in the plume. By using the integral plume model, we propose the varying charge structure is connected to the availability of condensed water and low temperatures at high altitudes in the plume, suggesting ice formation may have contributed to t...
1.The SARS-CoV-2 epidemic continues to have major impacts on children’s education, with schools r... more 1.The SARS-CoV-2 epidemic continues to have major impacts on children’s education, with schools required to implement infection control measures that have led to long periods of absence and classroom closures. We have developed an agent-based epidemiological model of SARS-CoV-2 transmission that allows us to quantify projected infection patterns within primary school classrooms, and related uncertainties; the basis of our approach is a contact model constructed using random networks, informed by structured expert judgement. The effectiveness of mitigation strategies are considered in terms of effectiveness at supressing infection outbreaks and limiting pupil absence. Covid-19 infections in schools in the UK in Autumn 2020 are re-examined and the model used for forecasting infection levels in autumn 2021, as the more infectious Delta-variant was emerging and school transmission thought likely to play a major role in an incipient new wave of the epidemic. Our results were in good agre...
Journal of Volcanology and Geothermal Research, 2018
Meaningful forecasting of the atmospheric concentration and ground accumulation of volcanic ash d... more Meaningful forecasting of the atmospheric concentration and ground accumulation of volcanic ash during explosive eruptions requires detailed knowledge of the eruption source parameters. However, due to the large uncertainties in observations and limitations of current models used to make inferences from these, monitoring an ongoing eruption and quantifying the mass eruption rate in realtime is a considerable challenge. Within the EU supersite project "FutureVolc", an integrated approach has been applied to develop a quasi-autonomous multi-parameter system, denoted "REFIR", for monitoring volcanic eruptions in Iceland and assessing the eruption mass flow rate by inverting the plume height information and taking account of these uncertainties. REFIR has the capability to ingest and process streaming plume-height data provided by a multitude of ground based sensors, including C-and X-band radars and web-cam based plume height tracking systems. These observational data are used with a suite of plume models that also consider the current wind and other atmospheric conditions, providing statistically assessed best estimates of plume height and mass eruption rate. Provided instrumental data is available, near real-time estimates are obtained (the delay corresponding to the scan rate of data-providing instruments, presently of the order of minutes). Using the Hekla 2000, and Eyjafjallajökull 2010 eruptions in Iceland, the potential of REFIR is demonstrated and discussed through application to three scenarios. The system has been developed to provide maximum flexibility. A setup script assists the user in adapting to local conditions, allowing implementation of REFIR for any volcanic eruption site worldwide. REFIR is designed to be easily upgradable, allowing future extension of monitoring networks, learning from new events, and incorporation of new technologies and model improvements. This article gives an overview of the basic structure, models implemented, functionalities and the computational techniques of REFIR.
Journal of Fluid Mechanics, 2018
The unsteady ascent of a buoyant, turbulent line plume through a quiescent, uniform environment i... more The unsteady ascent of a buoyant, turbulent line plume through a quiescent, uniform environment is modelled in terms of the width-averaged vertical velocity and density deficit. It is demonstrated that for a well-posed, linearly stable model, account must be made for the horizontal variation of the velocity and the density deficit; in particular the variance of the velocity field and the covariance of the density deficit and velocity fields, represented through shape factors, must exceed threshold values, and that models based upon ‘top-hat’ distributions in which the dependent fields are piecewise constant are ill-posed. Numerical solutions of the nonlinear governing equations are computed to reveal that the transient response of the system to an instantaneous change in buoyancy flux at the source may be captured through new similarity solutions, the form of which depend upon both the ratio of the old to new buoyancy fluxes and the shape factors.
Meteorological Applications, 2016
The spread of a dense gas in the atmosphere is a phenomenon that occurs widely with natural (and ... more The spread of a dense gas in the atmosphere is a phenomenon that occurs widely with natural (and anthropogenic) causes and is often associated with high impact and hazardous events. In this study a method of simulating the spread of dense gases in a numerical weather prediction model is presented. This approach has the advantage that dense gases can be simulated in regions of complex terrain using realistic forcings (in terms of both the driving meteorological fields and the representation of surface characteristics). The model formulation is tested against semi-idealized gravity-current-type experiments and similar modelling studies. As an example application, the Lake Nyos disaster of 1986, where a dense CO 2 cloud spread through a mountainous region of Cameroon, is simulated. The predicted spread of CO 2 agrees (qualitatively) very well with the observations. The method provides a means of determining a potential 'safe height' above which simulated concentrations are not hazardous, and thus the height above which refuge should be taken during similar future events. The simulation demonstrates a novel application which can be rapidly applied to other scenarios.
Journal of Fluid Mechanics, 2016
We model the unsteady evolution of turbulent buoyant plumes following temporal changes to the sou... more We model the unsteady evolution of turbulent buoyant plumes following temporal changes to the source conditions. The integral model is derived from radial integration of the governing equations expressing the evolution of mass, axial momentum and buoyancy in the plume. The non-uniform radial profiles of the axial velocity and density deficit in the plume are explicitly captured by shape factors in the integral equations; the commonly assumed top-hat profiles lead to shape factors equal to unity. The resultant model for unsteady plumes is hyperbolic when the momentum shape factor, determined from the radial profile of the mean axial velocity in the plume, differs from unity. The solutions of the model when source conditions are maintained at constant values are shown to retain the form of the well-established steady plume solutions. We demonstrate through a linear stability analysis of these steady solutions that the inclusion of a momentum shape factor in the governing equations tha...
Atmospheric Chemistry and Physics, 2017
The separation of volcanic ash and sulfur dioxide (SO 2) gas is sometimes observed during volcani... more The separation of volcanic ash and sulfur dioxide (SO 2) gas is sometimes observed during volcanic eruptions. The exact conditions under which separation occurs are not fully understood but the phenomenon is of importance because of the effects volcanic emissions have on aviation, on the environment, and on the earth's radiation balance. The eruption of Grímsvötn, a subglacial volcano under the Vatnajökull glacier in Iceland during 21-28 May 2011 produced one of the most spectacular examples of ash and SO 2 separation, which led to errors in the forecasting of ash in the atmosphere over northern Europe. Satellite data from several sources coupled with meteorological wind data and photographic evidence suggest that the eruption column was unable to sustain itself, resulting in a large deposition of ash, which left a low-level ash-rich atmospheric plume moving southwards and then eastwards towards the southern Scandinavian coast and a high-level predominantly SO 2 plume travelling northwards and then spreading eastwards and westwards. Here we provide observational and modelling perspectives on the separation of ash and SO 2 and present quantitative estimates of the masses of ash and SO 2 that erupted, the directions of transport, and the likely impacts. We hypothesise that a partial column collapse or "sloughing" fed with ash from pyroclastic density currents (PDCs) occurred during the early stage of the eruption, leading to an ash-laden gravity intrusion that was swept southwards, separated from the main column. Our model suggests that water-mediated aggregation caused enhanced ash removal because of the plentiful supply of source water from melted glacial ice and from entrained atmospheric water. The analysis also suggests that ash and SO 2 should be treated with separate source terms, leading to improvements in forecasting the movement of both types of emissions.
Journal of Geophysical Research: Solid Earth, 2013
Estimates of volcanic source mass flux, currently deduced from observations of plume height, are ... more Estimates of volcanic source mass flux, currently deduced from observations of plume height, are crucial for ash dispersion models for aviation and population hazard. This study addresses the role of the atmospheric wind in determining the height at which volcanic plumes spread in the atmosphere and the relationship between source mass flux and plume height in a wind field. We present a predictive model of volcanic plumes that describes the bending over of the plume trajectory in a crosswind and show that model predictions are in accord with a dataset of historic eruptions if the profile of atmospheric wind shear is described. The wind restricts the rise height of volcanic plumes such that obtaining equivalent rise heights for a plume in a windy environment would require an order of magnitude increase in the source mass flux over a plume in a quiescent environment. Our model calculations are used to calibrate a semi-empirical relationship between the plume height and the source mass flux that explicitly includes the atmospheric wind speed. We demonstrate that the model can account for the variations in plume height observed during the first explosive phase of the 2010 Eyjafjallajökull eruption using independently measured wind speeds and show that changes in the observed plume height are better explained by changing meteorology than abrupt changes in the source mass flux. This study shows that unless the wind is properly accounted for, estimates of the source mass flux during an explosive eruption are likely to be very significant underpredictions of the volcanic source conditions.
Frontiers in Earth Science, 2017
Journal of Volcanology and Geothermal Research, 2016
Integral models of volcanic plumes allow predictions of plume dynamics to be made and the rapid e... more Integral models of volcanic plumes allow predictions of plume dynamics to be made and the rapid estimation of volcanic source conditions from observations of the plume height by model inversion. Here we introduce PlumeRise, an integral model of volcanic plumes that incorporates a description of the state of the atmosphere, includes the effects of wind and the phase change of water, and has been developed as a freely available web-based tool. The model can be used to estimate the height of a volcanic plume when the source conditions are specified, or to infer the strength of the source from an observed plume height through a model inversion. The predictions of the volcanic plume dynamics produced by the model are analysed in four case studies in which the atmospheric conditions and the strength of the source are varied. A global sensitivity analysis of the model to a selection of model inputs is performed and the results are analysed using parallel coordinate plots for visualisation and variance-based sensitivity indices to quantify the sensitivity of model outputs. We find that if the atmospheric conditions do not vary widely then there is a small set of model inputs that strongly influence the model predictions. When estimating the height of the plume, the source mass flux has a controlling influence on the model prediction, while variations in the plume height strongly effect the inferred value of the source mass flux when performing inversion studies. The values taken for the entrainment coefficients have a particularly important effect on the quantitative predictions. The dependencies of the model outputs to variations in the inputs are discussed and compared to simple algebraic expressions that relate source conditions to the height of the plume.
Bulletin of Volcanology, 2015
Mathematical models of natural processes can be used as inversion tools to predict unobserved pro... more Mathematical models of natural processes can be used as inversion tools to predict unobserved properties from measured quantities. Uncertainty in observations and model formulation impact on the efficacy of inverse modelling. We present a general methodology, history matching, that can be used to investigate the effect of observational and model uncertainty on inverse modelling studies. We demonstrate history matching on an integral model of volcanic plumes that is used to estimate source conditions from observations of the rise height of plumes during the eruptions of Eyjafjallajökull, Iceland, in 2010 and Grímsvötn, Iceland, in 2011. Sources of uncertainty are identified and quantified, and propagated through the integral plume model. A preliminary sensitivity analysis is performed to identify the uncertain model parameters that strongly influence model predictions. Model predictions are assessed against observations through an implausibility measure that rules out model inputs that are considered implausible given the quantified uncertainty. We demonstrate that the source mass flux at the volcano can be estimated from plume height observations, but the magmatic temperature, exit velocity and exsolved gas mass fraction cannot be accurately determined. Uncertainty in plume height observations and Editorial responsibility: C. Bonadonna
Journal of Fluid Mechanics, 2015
Volcanic eruptions commonly produce buoyant ash-laden plumes that rise through the stratified atm... more Volcanic eruptions commonly produce buoyant ash-laden plumes that rise through the stratified atmosphere. On reaching their level of neutral buoyancy, these plumes cease rising and transition to horizontally spreading intrusions. Such intrusions occur widely in density-stratified fluid environments, and in this paper we develop a shallow-layer model that governs their motion. We couple this dynamical model to a model for particle transport and sedimentation, to predict both the time-dependent distribution of ash within volcanic intrusions and the flux of ash that falls towards the ground. In an otherwise quiescent atmosphere, the intrusions spread axisymmetrically. We find that the buoyancy-inertial scalings previously identified for continuously supplied axisymmetric intrusions are not realised by solutions of the governing equations. By calculating asymptotic solutions to our model we show that the flow is not self-similar, but is instead time-dependent only in a narrow region at ...