Particle filter based volcanic ash emission inversion applied to a hypothetical sub-Plinian Eyjafjallajökull eruption using the chemical component of the Ensemble for Stochastic Integration of Atmospheric Simulations (ESIAS-chem) version 1.0

A particle filter based inversion system to derive time- and altitude-resolved volcanic ash emission fluxes along with its uncertainty is presented. For the underlying observation information only vertically integrated ash load data as provided by retrievals from nadir looking imagers mounted on geostationary satellites is assimilated. We aim to estimate the temporally varying emission profile with error margins, along with evidence of its dependencies on wind driven transport patterns within variable observation intervals. Thus, a variety of observation types, although not directly related to volcanic ash, can be utilized to constrain the probabilistic volcanic ash estimate. The system validation addresses the special challenge of ash cloud height analyses in case of observations restricted to bulk column mass loading information, mimicking the typical case of geostationary satellite data. The underlying method rests on a linear-combination of height-time emission finite elements of arbitrary resolution, each of which is assigned to a model run subject to ensemble-based space-time data assimilation. Employing a modular concept, this setup builds the Ensemble for Stochastic Integration of Atmospheric Simulations (ESIAS-chem) that comprises a particle smoother in combination with a discrete-grid ensemble extension of the Nelder-Mead minimization method. The ensemble version of the EURopean Air pollution Dispersion – Inverse Model (EURAD-IM) is integrated into ESIAS-chem but can be replaced by other models. The performance of ESIAS-chem is tested by identical twin experiments. The application of the inversion system to two notional sub-Plinian eruptions of the Eyjafjallajökull with strong ash emission changes with time and injection heights demonstrate the ability of ESIAS-chem to retrieve the volcanic ash emission fluxes from the assimilation of column mass loading data only. However, the analysed emission profiles strongly differ in their levels of accuracy depending of the strength of wind shear conditions. Under strong wind shear conditions at the volcano the temporal and vertical varying volcanic emissions are analyzed up to an error of only 10 % for the estimated emission fluxes. For weak wind shear conditions, however, analysis errors are larger and ESIAS-chem is less able to determine the ash emission flux variations. This situation, however, can be remedied by extending the assimilation window. In the performed test cases, the ensemble predicts the location of high volcanic ash column mass loading in the atmosphere with a very high probability of > 95 %. Additionally, the ensemble is able to provide a vertically resolved probability map of high volcanic ash concentrations to a high accuracy for both, high and weak wind shear conditions.

Study of Losses in the Production Line of a Large Footwear Company

The article analyzes the production loss, also referred to as reject, in the largest footwear producer of the World, the Alpargatas company. The article presents a discussion of the probabilistic modelling, the development of a stochastic model, that uses It\^{o} stochastic integration, based on temporal series provided by the company, and the identification of eventual solutions to the loss of production.