Towards non-linear inverse problem for atmospheric source term determination

2020 ◽  
Author(s):  
Ondřej Tichý ◽  
Václav Šmídl
Keyword(s):  
Inverse Problem ◽  
Source Term ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Problem Formulation ◽  
Tracer Experiment ◽  
Parametric Perturbation ◽  
Case Scenario ◽  
Linear Inverse Problem ◽  
Non Linear

<div>The basic linear inverse problem of atmospheric release can be formulated as <strong>y</strong> = M <strong>x</strong> + <strong>e</strong> , where <strong>y</strong> is the measurement vector which is typically in the form of gamma dose rates or concentrations, M is the source-receptor-sensitivity (SRS) matrix, <strong>x</strong> is the unknown source term to be estimated, and <strong>e</strong> is the model residue. The SRS matrix M is computed using an atmospheric transport model coupled with meteorological reanalyses. The inverse problem is typically ill-conditioned due to number of uncertainties, hence, the estimation of the source term is not straightforward and additional information, e.g. in the form of regularization or the prior source term, is often needed. Besides, traditional techniques rely on assumption that the SRS matrix is correct which is not realistic due to the number of approximations made during its computation. Therefore, we propose relaxation of the inverse model using introduction of the term Δ<sub>M</sub> such as <strong>y</strong> = ( M+ Δ<sub>M</sub> ) <strong>x</strong> + <strong>e</strong> leading to non-linear inverse problem formulation, where Δ<sub>M</sub> can be, as an example, parametric perturbation of the SRS matrix M in the spatial or temporal domain. We estimate parameters of this perturbation together with solving the inverse problem using variational Bayes procedure. The method will be validated on synthetic dataset as well as demonstrated on real case scenario such as the controlled tracer experiment ETEX or episode of ruthenium-106 release over the Europe on the fall of 2017.</div>

scholarly journals A tuning-free method for the linear inverse problem and its application to source term determination

2016 ◽  
Author(s):  
Ondřej Tichý ◽  
Václav Šmídl ◽  
Radek Hofman ◽  
Andreas Stohl
Keyword(s):  
Inverse Problem ◽  
Maximum Likelihood ◽  
Source Term ◽  
Transport Model ◽  
State Of The Art ◽  
Atmospheric Transport ◽  
Estimation Procedure ◽  
Tracer Experiment ◽  
Tuning Parameters ◽  
Ill Posed

Abstract. Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g. concentrations or deposition values) as a product of the source-receptor sensitivity (SRS) matrix obtained from an atmospheric transport model multiplied by the unknown source term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation allows to estimate also all tuning parameters from the measurements. The estimation procedure is based on the Variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to estimate also all tuning parameters from the observations. The proposed algorithm is tested and compared with the state-of-the-art method on data from the European Tracer Experiment (ETEX) where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.

scholarly journals LS-APC v1.0: a tuning-free method for the linear inverse problem and its application to source-term determination

2016 ◽  
Vol 9 (11) ◽  
pp. 4297-4311 ◽  
Author(s):  
Ondřej Tichý ◽  
Václav Šmídl ◽  
Radek Hofman ◽  
Andreas Stohl
Keyword(s):  
Inverse Problem ◽  
Maximum Likelihood ◽  
Source Term ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Estimation Procedure ◽  
Tracer Experiment ◽  
Tuning Parameters ◽  
Current State ◽  
Ill Posed

Abstract. Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g., concentrations or deposition values) as a product of the source-receptor sensitivity (SRS) matrix obtained from an atmospheric transport model multiplied by the unknown source-term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation also allows estimation of all tuning parameters from the measurements. The estimation procedure is based on the variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to also estimate all tuning parameters from the observations. The proposed algorithm is tested and compared with the standard methods on data from the European Tracer Experiment (ETEX) where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.

scholarly journals On the tuning of atmospheric inverse methods: comparisons with the European Tracer Experiment (ETEX) and Chernobyl datasets using the atmospheric transport model FLEXPART

2020 ◽  
Vol 13 (12) ◽  
pp. 5917-5934
Author(s):  
Ondřej Tichý ◽  
Lukáš Ulrych ◽  
Václav Šmídl ◽  
Nikolaos Evangeliou ◽  
Andreas Stohl
Keyword(s):  
Source Term ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Optimization Procedure ◽  
Sensitivity Study ◽  
Tracer Experiment ◽  
Additional Information ◽  
Regularization Parameters ◽  
Ill Posed ◽  
The Difference

Abstract. Estimation of the temporal profile of an atmospheric release, also called the source term, is an important problem in environmental sciences. The problem can be formalized as a linear inverse problem wherein the unknown source term is optimized to minimize the difference between the measurements and the corresponding model predictions. The problem is typically ill-posed due to low sensor coverage of a release and due to uncertainties, e.g., in measurements or atmospheric transport modeling; hence, all state-of-the-art methods are based on some form of regularization of the problem using additional information. We consider two kinds of additional information: the prior source term, also known as the first guess, and regularization parameters for the shape of the source term. While the first guess is based on information independent of the measurements, such as the physics of the potential release or previous estimations, the regularization parameters are often selected by the designers of the optimization procedure. In this paper, we provide a sensitivity study of two inverse methodologies on the choice of the prior source term and regularization parameters of the methods. The sensitivity is studied in two cases: data from the European Tracer Experiment (ETEX) using FLEXPART v8.1 and the caesium-134 and caesium-137 dataset from the Chernobyl accident using FLEXPART v10.3.

The use of non-linear inverse problem and enthalpy method in GTAW process of aluminum

2015 ◽  
Vol 66 ◽  
pp. 114-121 ◽  
Author(s):  
Elisan dos Santos Magalhães ◽  
Solidônio Rodrigues de Carvalho ◽  
Ana Lúcia Fernandes de Lima E Silva ◽  
Sandro Metrevelle Marcondes Lima E Silva
Keyword(s):  
Inverse Problem ◽  
Linear Inverse Problem ◽  
Enthalpy Method ◽  
Non Linear ◽  
Gtaw Process

scholarly journals Iterative algorithms for a non-linear inverse problem in atmospheric lidar

2017 ◽  
Vol 33 (8) ◽  
pp. 085010
Author(s):  
Giulia Denevi ◽  
Sara Garbarino ◽  
Alberto Sorrentino
Keyword(s):  
Inverse Problem ◽  
Iterative Algorithms ◽  
Linear Inverse Problem ◽  
Non Linear

scholarly journals A discussion on the determination of atmospheric OH and its trends

2002 ◽  
Vol 2 (4) ◽  
pp. 1261-1286 ◽  
Author(s):  
P. Jöckel ◽  
C. A. M. Brenninkmeijer ◽  
P. J. Crutzen
Keyword(s):  
Atmospheric Chemistry ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Temporal Trends ◽  
Three Dimensional ◽  
Tracer Experiment ◽  
Global Average ◽  
Surface Sites ◽  
Radical Distribution ◽  
Tracer Distribution

Abstract. The global hydroxyl radical distribution largely determines the oxidation efficiency of the atmosphere and, together with their sources and atmospheric transport, the distributions and lifetimes of most trace gases. Because of the great importance of several of these gases for climate, ozone budget and OH itself, it is of fundamental importance to acquire knowledge about atmospheric OH and possible trends in its concentrations. In the past, average concentrations of OH and trends were largely derived using industrially produced CH3CCl3 as a chemical tracer. The analyses have given valuable, but also rather uncertain results. In this paper we describe an idealized computer aided tracer experiment which has as one of its goals to derive tracer concentration weighted, global average <k(OH)>, where he temporal and spatial OH distribution is prescribed and k is the reaction rate coefficient of OH with a hitherto never produced (Gedanken) tracer, which is injected at a number of surface sites in the atmosphere in well known amounts over a given time period. Using a three-dimensional (3D) time-dependent chemistry/transport model <k(OH)> can be accurately determined from the calculated 3-D tracer distribution. It is next explored how well <k(OH)> can be retrieved solely from tracer measurements at a limited number of surface sites. The results from this analysis are encouraging enough to actually think about the feasibility to carry out a global dedicated tracer experiment to derive <k(OH)> and its temporal trends. However, before that, we propose to test the methods which are used to derive <k(OH)>, so far largely using CH3CCl3, with an idealized tracer experiment, in which a global model is used to calculate the "Gedanken"  tracer distribution, representing the real 3-D world, from which we next derive <k(OH)>, using only the tracer information from a limited set of surface sites. We propose here that research groups which are, or will be, involved in global average OH studies to participate in such an inter-comparison of methods, organized and over-seen by a committee appointed by the International Global Atmospheric Chemistry (IGAC) program.

scholarly journals Real-time measurement of radionuclide concentrations and its impact on inverse modeling of <sup>106</sup>Ru release in the fall of 2017

2020 ◽  
Author(s):  
Ondřej Tichý ◽  
Miroslav Hýža ◽  
Václav Šmídl
Keyword(s):  
Real Time ◽  
Temporal Resolution ◽  
Inverse Modeling ◽  
Source Term ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Monitoring Data ◽  
The Real ◽  
Concentration Measurements ◽  
Atmospheric Transport Model

Abstract. Abstract Low concentrations of 106Ru were detected across Europe at the turn of September and October 2017. The origin of 106Ru has still not been confirmed; however, current studies agree that the release occurred probably near Mayak in the southern Urals. The source reconstructions are mostly based on an analysis of concentration measurements coupled with an atmospheric transport model. Since reasonable temporal resolution of concentration measurements is crucial for proper source term reconstruction, the standard one week sampling interval could be limiting. In this paper, we present an investigation of the usability of the newly developed AMARA and CEGAM real-time monitoring systems, which are based on the gamma-ray counting of aerosol filters. These high resolution data were used for inverse modeling of the 106Ru release. We perform backward runs of the Hysplit atmospheric transport model driven with meteorological data from the global forecast system (GFS) and we construct a source-receptor sensitivity (SRS) matrix for each grid cell of our domain. Then, we use our least-squares with adaptive prior covariance (LS-APC) method to estimate possible locations of the release and the source term of the release. On Czech monitoring data, the use of concentration measurements from the standard regime and from the real-time regime is compared and better source reconstruction for the real-time data is demonstrated in the sense of the location of the source and also the temporal resolution of the source. The estimated release location, Mayak, and the total estimated source term, 237 ± 107 TBq, are in agreement with previous studies. Finally, the results based on the Czech monitoring data are validated with the IAEA reported dataset with a much better spatial resolution, and the agreement between the IAEA dataset and our reconstruction is demonstrated.

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