An ensemble of state-of-the-art ash dispersion models: towards probabilistic forecasts to increase the resilience of air traffic against volcanic eruptions

Abstract. High-quality volcanic ash forecasts are crucial to minimize the economic impact of volcanic hazards on air traffic. Decision-making is usually based on numerical dispersion modelling with only one model realization. Given the inherent uncertainty of such an approach, a multi-model multi-source term ensemble has been designed and evaluated for the Eyjafjallajökull eruption in May 2010. Its use for flight planning is discussed. Two multi-model ensembles were built: the first is based on the output of four dispersion models and their own implementation of ash ejection. All a priori model source terms were constrained by observational evidence of the volcanic ash cloud top as a function of time. The second ensemble is based on the same four dispersion models, which were run with three additional source terms: (i) a source term obtained from a model background constrained with satellite data (a posteriori source term), (ii) its lower-bound estimate and (iii) its upper-bound estimate. The a priori ensemble gives valuable information about the probability of ash dispersion during the early phase of the eruption, when observational evidence is limited. However, its evaluation with observational data reveals lower quality compared to the second ensemble. While the second ensemble ash column load and ash horizontal location compare well to satellite observations, 3D ash concentrations are negatively biased. This might be caused by the vertical distribution of ash, which is too much diluted in all model runs, probably due to defaults in the a posteriori source term and vertical transport and/or diffusion processes in all models. Relevant products for the air traffic management are horizontal maps of ash concentration quantiles (median, 75 %, 99 %) at a finely resolved flight level grid as well as cross sections. These maps enable cost-optimized consideration of volcanic hazards and could result in much fewer flight cancellations, reroutings and traffic flow congestions. In addition, they could be used for route optimization in the areas where ash does not pose a direct and urgent threat to aviation, including the aspect of aeroplane maintenance.

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A tailored multi-model ensemble for air traffic management: Demonstration and evaluation for the Eyjafjallajökull eruption in May 2010

10.5194/nhess-2021-96 ◽

2021 ◽

Author(s):

Matthieu Plu ◽

Barbara Scherllin-Pirscher ◽

Delia Arnold Arias ◽

Rocio Baro ◽

Guillaume Bigeard ◽

...

Keyword(s):

Traffic Management ◽

Volcanic Ash ◽

Source Term ◽

A Priori ◽

Air Traffic Management ◽

Observational Evidence ◽

Air Traffic ◽

A Posteriori ◽

Source Terms ◽

Dispersion Models

Abstract. High quality volcanic ash forecasts are crucial to minimize the economic impact of volcanic hazards on air traffic. Decision-making is usually based on numerical dispersion modeling with only one model realization. Given the inherent uncertainty of such approach, a multi-model multi-source term ensemble has been designed and evaluated for the Eyjafjallajökull eruption in May 2010. Its use for air traffic management is discussed. Two multi-model ensembles were built: the first is based on the output of four dispersion models and their own implementation of ash ejection. All a priori model source terms were constrained by observational evidence of the volcanic ash cloud top as a function of time. The second ensemble is based on the same four dispersion models, which were run with three additional source terms: (i) a source term obtained with background modeling constrained with satellite data (a posteriori source term), (ii) its lower bound estimate, and (iii) its upper bound estimate. The a priori ensemble gives valuable information about the probability of ash dispersion during the early phase of the eruption, when observational evidence is limited. However, its evaluation with observational data reveals lower quality compared to the second ensemble. While the second ensemble ash column load and ash horizontal location compare well to satellite observations, 3D ash concentrations are negatively biased. This might be caused by the vertical distribution of ash, which is too much diluted in all model runs, probably due to defaults in the a posteriori source term and vertical transport and/or diffusion processes in all models. Relevant products for the air traffic management are horizontal maps of ash concentration quantiles (median, 75 %, 99 %) at a fine-resolved flight level grid. These maps can be used for route optimization in the areas where ash does not pose a direct and urgent threat to aviation. Cost-optimized consideration of such hazards will result in much less impact on flight cancellations, reroutings, and traffic flow congestions.

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Determination of time- and height-resolved volcanic ash emissions and their use for quantitative ash dispersion modeling: the 2010 Eyjafjallajökull eruption

Atmospheric Chemistry and Physics ◽

10.5194/acp-11-4333-2011 ◽

2011 ◽

Vol 11 (9) ◽

pp. 4333-4351 ◽

Cited By ~ 242

Author(s):

A. Stohl ◽

A. J. Prata ◽

S. Eckhardt ◽

L. Clarisse ◽

A. Durant ◽

...

Keyword(s):

Volcanic Ash ◽

Dispersion Model ◽

A Priori ◽

Volcanic Eruptions ◽

General Nature ◽

Aviation Industry ◽

Dispersion Modeling ◽

Source Information ◽

European Area ◽

Ash Dispersion

Abstract. The April–May, 2010 volcanic eruptions of Eyjafjallajökull, Iceland caused significant economic and social disruption in Europe whilst state of the art measurements and ash dispersion forecasts were heavily criticized by the aviation industry. Here we demonstrate for the first time that large improvements can be made in quantitative predictions of the fate of volcanic ash emissions, by using an inversion scheme that couples a priori source information and the output of a Lagrangian dispersion model with satellite data to estimate the volcanic ash source strength as a function of altitude and time. From the inversion, we obtain a total fine ash emission of the eruption of 8.3 ± 4.2 Tg for particles in the size range of 2.8–28 μm diameter. We evaluate the results of our model results with a posteriori ash emissions using independent ground-based, airborne and space-borne measurements both in case studies and statistically. Subsequently, we estimate the area over Europe affected by volcanic ash above certain concentration thresholds relevant for the aviation industry. We find that during three episodes in April and May, volcanic ash concentrations at some altitude in the atmosphere exceeded the limits for the "Normal" flying zone in up to 14 % (6–16 %), 2 % (1–3 %) and 7 % (4–11 %), respectively, of the European area. For a limit of 2 mg m−3 only two episodes with fractions of 1.5 % (0.2–2.8 %) and 0.9 % (0.1–1.6 %) occurred, while the current "No-Fly" zone criterion of 4 mg m−3 was rarely exceeded. Our results have important ramifications for determining air space closures and for real-time quantitative estimations of ash concentrations. Furthermore, the general nature of our method yields better constraints on the distribution and fate of volcanic ash in the Earth system.

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Uncertainty assessment and applicability of an inversion method for volcanic ash forecasting

10.5194/acp-2016-1075 ◽

2017 ◽

Cited By ~ 1

Author(s):

Birthe Marie Steensen ◽

Arve Kylling ◽

Nina Iren Kristiansen ◽

Michael Schulz

Keyword(s):

Satellite Data ◽

Volcanic Ash ◽

A Priori ◽

A Priori Estimate ◽

Satellite Observations ◽

Inversion Method ◽

A Posteriori ◽

Priori Estimate ◽

Satellite Retrieval ◽

Emission Estimate

Abstract. Significant improvements in the way we can observe and model volcanic ash clouds have been obtained since the 2010 Eyjafjallajökull eruption. One major development has been data assimilation techniques, which aim to bring models in closer agreement to satellite observations and reducing the uncertainties for the ash emission estimate. Still, questions remains to which degree the forecasting capabilities are improved by inclusion of such techniques are and how these improvements depend on the data input. This study exploits how different satellite data and different uncertainty assumptions of the satellite and a priori emissions affect the calculated volcanic ash emission estimate, which is computed by an inversion method that couples the satellite and a priori emissions with dispersion model data. Two major ash episodes over four days in April and May of the 2010 Eyjafjallajökull eruption are studied. Specifically, inversion calculations are done for four different satellite data sets with different size distribution assumptions in the retrieval. A reference satellite data set is chosen and the range between the minimum and maximum 4 day average load of hourly retrieved ash is 121 % in April and 148 % in May, compared to the reference. The corresponding a posteriori maximum and minimum emission sum found for these four satellite retrievals range from 26 % and 47 % of the a posteriori reference estimate for the same two periods. Varying the assumptions made in the satellite retrieval therefore translates into uncertainties in the calculated emissions and the modelled ash column loads. By further exploring the weighting of uncertainties connected to a priori emissions and the other-than-size uncertainties in the satellite data, the uncertainty in the a priori estimate is found to have an order of magnitude more impact on the a posteriori solution compared to the other-than-size uncertainties in the satellite. Part of this is explained by a too high a priori estimate used in this study that is reduced by around half in the a posteriori reference estimate. Setting large uncertainties connected to both a priori and satellite input data is shown to compensate each other. Because of this an inversion based emission estimate in a forecasting setting needs well tested and considered assumptions on uncertainties for the a priori emission and satellite data. The quality of using the inversion in a forecasting environment is tested by adding gradually, with time, more observations to improve the estimated height versus time evolution of Eyjafjallajökull ash emissions. We show that the initially too high a priori emissions are reduced effectively when using just 12 hours of satellite observations. More satellite observations (> 12 h), in the Eyjafjallajökull case, place the volcanic injection at higher altitudes. Adding additional satellite observations (> 36 h) changes the a posteriori emissions to only a small extent for May and minimal for the April period, because the ash is dispersed and transported effectively out of the domain after 1–2 days. A best-guess emission estimate for the forecasting period was constructed by averaging the last 12 hours of the a posteriori emission. Using this emission for a forecast simulation performs better especially compared to model simulations with no further emissions over the forecast period in the case of a continued volcanic eruption activity. Because of undetected ash in the satellite retrieval and diffusion in the model, the forecast simulations generally contain more ash than the observed fields and the model ash is more spread out. Overall, using the a posteriori emissions in our model reduces the uncertainties connected to both the satellite observations and the a priori estimate to perform a more confident forecast in both amount of ash released and emission heights.

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Two fractional regularization methods for identifying the radiogenic source of the Helium production-diffusion equation

AIMS Mathematics ◽

10.3934/math.2021662 ◽

2021 ◽

Vol 6 (10) ◽

pp. 11425-11448

Author(s):

Xuemin Xue ◽

◽

Xiangtuan Xiong ◽

Yuanxiang Zhang ◽

Keyword(s):

Diffusion Equation ◽

Source Term ◽

Regularization Parameter ◽

A Priori ◽

Regularization Methods ◽

A Posteriori ◽

Parameter Choice ◽

Ill Posed ◽

Parameter Choice Rules ◽

Regularized Solution

<abstract><p>The predication of the helium diffusion concentration as a function of a source term in diffusion equation is an ill-posed problem. This is called inverse radiogenic source problem. Although some classical regularization methods have been considered for this problem, we propose two new fractional regularization methods for the purpose of reducing the over-smoothing of the classical regularized solution. The corresponding error estimates are proved under the a-priori and the a-posteriori regularization parameter choice rules. Some numerical examples are shown to display the necessarity of the methods.</p></abstract>

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Determination of time- and height-resolved volcanic ash emissions for quantitative ash dispersion modeling: the 2010 Eyjafjallajökull eruption

Atmospheric Chemistry and Physics Discussions ◽

10.5194/acpd-11-5541-2011 ◽

2011 ◽

Vol 11 (2) ◽

pp. 5541-5588 ◽

Cited By ~ 19

Author(s):

A. Stohl ◽

A. J. Prata ◽

S. Eckhardt ◽

L. Clarisse ◽

A. Durant ◽

...

Keyword(s):

Volcanic Ash ◽

Size Range ◽

Dispersion Model ◽

A Priori ◽

Volcanic Eruptions ◽

General Nature ◽

Aviation Industry ◽

Dispersion Modeling ◽

Source Information ◽

Ash Dispersion

Abstract. The April–May 2010 volcanic eruptions of Eyjafjallajökull, Iceland caused significant economic and social disruption in Europe whilst state of the art measurements and ash dispersion forecasts were heavily criticized by the aviation industry. Here we demonstrate for the first time that dramatic improvements can be made in quantitative predictions of the fate of volcanic ash emissions, by using an inversion scheme that couples a priori source information and the output of a Lagrangian dispersion model with satellite data to estimate the volcanic ash source strength as a function of altitude and time. From the inversion, we obtain a total fine ash emission of the eruption of 8.3 ± 4.2 Tg for particles in the size range of 2.8–28 μm diameter and extrapolate this to a total ash emission of 11.9 ± 5.9 Tg for the size range of 0.25–250 μm. We evaluate the results of our a posteriori model using independent ground-based, airborne and space-borne measurements both in case studies and statistically. Subsequently, we estimate the area over Europe affected by volcanic ash above certain concentration thresholds relevant for the aviation industry. We find that during three episodes in April and May, volcanic ash concentrations at some altitude in the atmosphere exceeded the limits for the "normal" flying zone in up to 14% (6–16%), 2% (1–3%) and 7% (4–11%), respectively, of the European area. For a limit of 2 mg m−3 only two episodes with fractions of 1.5% (0.2–2.8%) and 0.9% (0.1–1.6%) occurred, while the current "no-fly" zone criterion of 4 mg m−3 was rarely exceeded. Our results have important ramifications for determining air space closures and for real-time quantitative estimations of ash concentrations. Furthermore, the general nature of our method yields better constraints on the distribution and fate of volcanic ash in the Earth system.

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Modelling the volcanic ash plume from Eyjafjallajökull eruption (May 2010) over Europe: evaluation of the benefit of source term improvements and of the assimilation of aerosol measurements

10.5194/nhess-2021-97 ◽

2021 ◽

Author(s):

Matthieu Plu ◽

Guillaume Bigeard ◽

Bojan Sič ◽

Emanuele Emili ◽

Luca Bugliaro ◽

...

Keyword(s):

Volcanic Ash ◽

Source Term ◽

Sensitivity Study ◽

Numerical Dispersion ◽

Dispersion Models ◽

Horizontal Dispersion ◽

Realistic Representation ◽

Ash Plume ◽

Ground Based Lidar ◽

The Vertical Distribution

Abstract. Numerical dispersion models are used operationally worldwide to mitigate the effect of volcanic ash on aviation. In order to improve the representation of the horizontal dispersion of ash plumes and of the 3D concentration of ash, a study was conducted using the MOCAGE model during the EUNADICS-AV project. Source term modelling and assimilation of different data were investigated. A sensitivity study to source term formulation showed that a resolved source term, using the FPLUME plume-rise model in MOCAGE, instead of a parameterised source term, induces a more realistic representation of the horizontal dispersion of the ash plume. The FPLUME simulation provides more concentrated and focused ash concentrations in the horizontal and the vertical dimensions than the other source term. The assimilation of MODIS Aerosol Optical Depth has an impact on the horizontal dispersion the plume, but this effect is rather low and local, compared to source term improvement. More promising results are obtained with the continuous assimilation of ground-based lidar profiles, which improves the vertical distribution of ash and helps to reach realistic values of ash concentrations. The improvement can remain several hours after and several hundred kilometers away downstream to the assimilated profiles.

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Data insertion in volcanic ash cloud forecasting

Annals of Geophysics ◽

10.4401/ag-6624 ◽

2015 ◽

Vol 57 ◽

Author(s):

Kate Louise Wilkins ◽

Shona Mackie ◽

Matthew Watson ◽

Helen N. Webster ◽

David J. Thomson ◽

...

Keyword(s):

Volcanic Ash ◽

Source Term ◽

Meteorological Data ◽

Satellite Observations ◽

Civil Aviation ◽

Operational Model ◽

Volcanic Source ◽

Insertion Method ◽

Volcanic Ash Cloud ◽

Ash Dispersion

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>During the eruption of Eyjafjallajökull in April and May 2010, the London Volcanic Ash Advisory Centre demonstrated the importance of infrared (IR) satellite imagery for monitoring volcanic ash and validating the Met Office operational model, NAME. This model is used to forecast ash dispersion and forms much of the basis of the advice given to civil aviation. NAME requires a source term describing the properties of the eruption plume at the volcanic source. Elements of the source term are often highly uncertain and significant effort has therefore been invested into the use of satellite observations of ash clouds to constrain them. This paper presents a data insertion method, where satellite observations of downwind ash clouds are used to create effective ‘virtual sources’ far from the vent. Uncertainty in the model output is known to increase over the duration of a model run, as inaccuracies in the source term, meteorological data and the parameterizations of the modelled processes accumulate. This new technique, where the dis- persion model (DM) is ‘reinitialized’ part-way through a run, could go some way to addressing this. </span></p></div></div></div>

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Uncertainty assessment and applicability of an inversion method for volcanic ash forecasting

Atmospheric Chemistry and Physics ◽

10.5194/acp-17-9205-2017 ◽

2017 ◽

Vol 17 (14) ◽

pp. 9205-9222 ◽

Cited By ~ 2

Author(s):

Birthe Marie Steensen ◽

Arve Kylling ◽

Nina Iren Kristiansen ◽

Michael Schulz

Keyword(s):

Satellite Data ◽

Volcanic Ash ◽

A Priori ◽

Satellite Observations ◽

Inversion Method ◽

A Posteriori ◽

Satellite Retrieval ◽

Mass Load ◽

Satellite Retrievals ◽

Emission Estimate

Abstract. Significant improvements in the way we can observe and model volcanic ash clouds have been obtained since the 2010 Eyjafjallajökull eruption. One major development has been the application of data assimilation techniques, which combine models and satellite observations such that an optimal understanding of ash clouds can be gained. Still, questions remain regarding the degree to which the forecasting capabilities are improved by inclusion of such techniques and how these improvements depend on the data input. This study explores how different satellite data and different uncertainty assumptions of the satellite and a priori emissions affect the calculated volcanic ash emission estimate, which is computed by an inversion method that couples the satellite retrievals and a priori emissions with dispersion model data. Two major ash episodes over 4 days in April and May of the 2010 Eyjafjallajökull eruption are studied. Specifically, inversion calculations are done for four different satellite data sets with different size distribution assumptions in the retrieval. A reference satellite data set is chosen, and the range between the minimum and maximum 4-day average load of hourly retrieved ash is 121 % in April and 148 % in May, compared to the reference. The corresponding a posteriori maximum and minimum emission sum found for these four satellite retrievals is 26 and 47 % of the a posteriori reference estimate for the same two periods, respectively. Varying the assumptions made in the satellite retrieval is seen to affect the a posteriori emissions and modelled ash column loads, and modelled column loads therefore have uncertainties connected to them depending on the uncertainty in the satellite retrieval. By further exploring our uncertainty estimates connected to a priori emissions and the mass load uncertainties in the satellite data, the uncertainty in the a priori estimate is found in this case to have an order-of-magnitude-greater impact on the a posteriori solution than the mass load uncertainties in the satellite. Part of this is explained by a too-high a priori estimate used in this study that is reduced by around half in the a posteriori reference estimate. Setting large uncertainties connected to both a priori and satellite mass load shows that they compensate each other, but the a priori uncertainty is found to be most sensitive. Because of this, an inversion-based emission estimate in a forecasting setting needs well-tested and well-considered assumptions on uncertainties for the a priori emission and satellite data. The quality of using the inversion in a forecasting environment is tested by adding gradually, with time, more observations to improve the estimated height versus time evolution of Eyjafjallajökull ash emissions. We show that the initially too-high a priori emissions are reduced effectively when using just 12 h of satellite observations. More satellite observations (> 12 h), in the Eyjafjallajökull case, place the volcanic injection at higher altitudes. Adding additional satellite observations (> 36 h) changes the a posteriori emissions to only a small extent for May and minimal for the April period, because the ash is dispersed and transported effectively out of the domain after 1–2 days. A best-guess emission estimate for the forecasting period was constructed by averaging the last 12 h of the a posteriori emission. Using this emission for a forecast simulation leads to better performance, especially compared to model simulations with no further emissions over the forecast period in the case of a continued volcanic eruption activity. Because of undetected ash in the satellite retrieval and diffusion in the model, the forecast simulations generally contain more ash than the observed fields, and the model ash is more spread out. Overall, using the a posteriori emissions in our model reduces the uncertainties in the ash plume forecast, because it corrects effectively for false-positive satellite retrievals, temporary gaps in observations, and false a priori emissions in the window of observation.

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