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In recent years, there has been a growing interest in ensemble approaches for modelling the atmospheric transport of volcanic aerosol, ash, and lapilli (tephra). The development of such techniques enables the exploration of novel methods for incorporating real observations into tephra dispersal models. However, traditional data assimilation algorithms, including ensemble Kalman filter (EnKF) methods, can yield suboptimal state estimates for positive-definite variables such as those related to volcanic aerosols and tephra deposits. This study proposes two new ensemble-based data assimilation techniques for semi-positive-definite variables with highly skewed uncertainty distributions, including aerosol concentrations and tephra deposit mass loading: the Gaussian with non-negative constraints (GNC) and gamma inverse-gamma (GIG) methods. The proposed methods are applied to reconstruct the tephra fallout deposit resulting from the 2015 Calbuco eruption using an ensemble of 256 runs performed with the FALL3D dispersal model. An assessment of the methodologies is conducted considering two independent datasets of deposit thickness measurements: an assimilation dataset and a validation dataset. Different evaluation metrics (e.g. RMSE, MBE, and SMAPE) are computed for the validation dataset, and the results are compared to two references: the ensemble prior mean and the EnKF analysis. Results show that the assimilation leads to a significant improvement over the first-guess results obtained from the simple ensemble forecast. The evidence from this study suggests that the GNC method was the most skilful approach and represents a promising alternative for assimilation of volcanic fallout data. The spatial distributions of the tephra fallout deposit thickness and volume according to the GNC analysis are in good agreement with estimations based on field measurements and isopach maps reported in previous studies. On the other hand, although it is an interesting approach, the GIG method failed to improve the EnKF analysis. [ABSTRACT FROM AUTHOR]

In recent years, there has been a growing interest in ensemble approaches for modelling volcanic plumes. The development of such techniques enables the exploration of novel methods for incorporating real observations into tephra dispersal models. However, traditional data assimilation algorithms, including ensemble Kalman filter methods, can yield suboptimal state estimates for positive-definite variables such as volcanic aerosols and tephra deposits. This study proposes two new ensemble-based data assimilation techniques for semi-positive-definite variables with highly skewed uncertainty distributions, including aerosol concentrations and tephra deposit mass loading. The proposed methods are applied to reconstruct the tephra fallout deposit resulting from the 2015 Calbuco eruption using an ensemble of 256 runs performed with the FALL3D dispersal model. Two datasets of deposit thickness measurements are considered: an assimilation dataset including 161 observations, and a validation dataset for an independent assessment of the methods. Results show that the assimilation leads to a significant improvement over the first-guess results, obtained from the simple ensemble forecast. The spatial distribution of the tephra fallout deposit thickness and the ashfall volume according to the analyses are in good agreement with estimations based on field measurements and isopach maps reported in previous studies. Both assimilation methods show a similar performance in terms of evaluation metrics and spatial distribution of the deposit. Finally, the potential application of the methodologies for the improvement of ash-cloud forecasts produced for operational models is also discussed. [ABSTRACT FROM AUTHOR]

Modelling atmospheric dispersal of volcanic ash and aerosols is becoming increasingly valuable for assessing the potential impacts of explosive volcanic eruptions on buildings, air quality, and aviation. Management of volcanic risk and reduction of aviation impacts can strongly benefit from quantitative forecasting of volcanic ash. However, an accurate prediction of volcanic aerosol concentrations using numerical modelling relies on proper estimations of multiple model parameters which are prone to errors. Uncertainties in key parameters such as eruption column height and physical properties of particles or meteorological fields represent a major source of error affecting the forecast quality. The availability of near-real-time geostationary satellite observations with high spatial and temporal resolutions provides the opportunity to improve forecasts in an operational context by incorporating observations into numerical models. Specifically, ensemble-based filters aim at converting a prior ensemble of system states into an analysis ensemble by assimilating a set of noisy observations. Previous studies dealing with volcanic ash transport have demonstrated that a significant improvement of forecast skill can be achieved by this approach. In this work, we present a new implementation of an ensemble-based data assimilation (DA) method coupling the FALL3D dispersal model and the Parallel Data Assimilation Framework (PDAF). The FALL3D+PDAF system runs in parallel, supports online-coupled DA, and can be efficiently integrated into operational workflows by exploiting high-performance computing (HPC) resources. Two numerical experiments are considered: (i) a twin experiment using an incomplete dataset of synthetic observations of volcanic ash and (ii) an experiment based on the 2019 Raikoke eruption using real observations of SO2 mass loading. An ensemble-based Kalman filtering technique based on the local ensemble transform Kalman filter (LETKF) is used to assimilate satellite-retrieved data of column mass loading. We show that this procedure may lead to nonphysical solutions and, consequently, conclude that LETKF is not the best approach for the assimilation of volcanic aerosols. However, we find that a truncated state constructed from the LETKF solution approaches the real solution after a few assimilation cycles, yielding a dramatic improvement of forecast quality when compared to simulations without assimilation. [ABSTRACT FROM AUTHOR]

Quantitative volcanic ash cloud forecasts are prone to uncertainties coming from the source term quantification (e.g., the eruption strength or vertical distribution of the emitted particles), with consequent implications for an operational ash impact assessment. We present an ensemble-based data assimilation and forecast system for volcanic ash dispersal and deposition aimed at reducing uncertainties related to eruption source parameters. The FALL3D atmospheric dispersal model is coupled with the ensemble transform Kalman filter (ETKF) data assimilation technique by combining ash mass loading observations with ash dispersal simulations in order to obtain a better joint estimation of the 3-D ash concentration and source parameters. The ETKF–FALL3D data assimilation system is evaluated by performing observing system simulation experiments (OSSEs) in which synthetic observations of fine ash mass loadings are assimilated. The evaluation of the ETKF–FALL3D system, considering reference states of steady and time-varying eruption source parameters, shows that the assimilation process gives both better estimations of ash concentration and time-dependent optimized values of eruption source parameters. The joint estimation of concentrations and source parameters leads to a better analysis and forecast of the 3-D ash concentrations. The results show the potential of the methodology to improve volcanic ash cloud forecasts in operational contexts. [ABSTRACT FROM AUTHOR]

Quantitative volcanic ash cloud forecasts are prone to uncertainties coming from the source term quantification (e.g. eruption strength or vertical distribution of the emitted particles), with consequent implications on operational ash impact assessment. We present an ensemble-based data assimilation and forecast system for volcanic ash dispersal and deposition aimed at reducing uncertainties related to eruption source parameters. The FALL3D atmospheric dispersal model is coupled with the Ensemble Transform Kalman Filter (ETKF) data assimilation technique by combining ash mass loading observations with ash dispersal simulations in order to obtain a better joint estimation of 3D ash concentration and source parameters. The ETKF-FALL3D data assimilation system is evaluated performing Observation System Simulation Experiments (OSSE) in which synthetic observations of fine ash mass loadings are assimilated. The evaluation of the ETKF-FALL3D system considering reference states of steady and time-varying eruption source parameters shows that the assimilation process gives both better estimations of ash concentration and time-dependent optimized values of eruption source parameters. The joint estimation of concentrations and source parameters leads to a better analysis and forecast of the 3D ash concentrations. Results show the potential of the methodology to improve volcanic ash cloud forecasts in operational contexts. [ABSTRACT FROM AUTHOR]