Bayesian inference and wind field statistical modeling applied to multiple source estimation

We present a methodology to identify multiple pollutant sources in the atmosphere that combines a data-driven dispersion model with Bayesian inference and uncertainty quantification. The dispersion model accounts for a realistic wind field based on the output of a multivariate dynamic linear model (DLM), estimated from measured wind components time series. The forward problem solution, described by an adjoint transient advection-diffusion partial differential equation, is then obtained using an appropriately stabilized finite element formulation. The Bayesian inference tool accounts for uncertainty in the concentration data and automatically states the balance between the prior and the likelihood. The source parameters are estimated by a Metropolis in Gibbs Monte Carlo Markov chain (MCMC) algorithm with adaptive steps. The MCMC algorithm is initialized with a maximum a posteriori estimator obtained with particle swarm optimization to accelerate convergence. Finally, the proposed methodology seems to outperform inversion techniques from previous works.

On the role of financial support programs in mitigating the SARS-CoV-2 spread in Brazil

BACKGROUND

During 2020, there were no effective treatments or vaccines against SARS-CoV-2. The most common disease contention measures were social distance (social isolation), the use of face masks and lockdowns. In the beginning, numerous countries have succeeded to control and reduce COVID-19 infections at a high economic cost. Thus, to alleviate such side effects, many countries have implemented socioeconomic programs to fund individuals that lost their jobs and to help endangered businesses to survive.

METHODS

We assess the role of a socioeconomic program, so-called "Auxilio Emergencial" (AE), during 2020 as a measure to mitigate the Coronavirus Disease 2019 (COVID-19) outbreak in Brazil. For each Brazilian State, we estimate the time-dependent reproduction number from daily reports of COVID-19 infections and deaths using a Susceptible-Exposed-Infected-Recovered-like (SEIR-like) model. Then, we analyse the correlations between the reproduction number, the amount of individuals receiving governmental aid, and the index of social isolation based on mobile phone information.

RESULTS

We observed significant positive correlation values between the average values by the AE and median values of an index accounting for individual mobility. We also observed significantly negative correlation values between the reproduction number and this index on individual mobility. Using the simulations of a susceptible-exposed-infected-removed-like model, if the AE was not operational during the first wave of COVID-19 infections, the accumulated number of infections and deaths could be 6.5 (90% CI: 1.3-21) and 7.9 (90% CI: 1.5-23) times higher, respectively, in comparison with the actual implementation of AE.

CONCLUSIONS

Our results suggest that the AE implemented in Brazil had a significant influence on social isolation by allowing those in need to stay at home, which would reduce the expected numbers of infections and deaths.

Uncertainty quantification and atmospheric source estimation with a discrepancy-based and a state-dependent adaptative MCMC

We address the source characterization of atmospheric releases using adaptive strategies in Bayesian inference in combination with the numerical solution of the dispersion problem by a stabilized finite element method and uncertainty quantification in the measurements. The adaptive techniques accelerate the convergence of Monte Carlo Markov Chain (MCMC) algorithms, leading to accurate reconstructions of the source parameters. Such accuracy is illustrated by the comparison with results from previous works. Moreover, the technique used to simulate the corresponding dispersion problem allowed us to introduce relevant meteorological information. The uncertainty quantification also improves the quality of reconstructions. Numerical examples using data from the Copenhagen experimental campaign illustrate the effectiveness of the proposed methodology. We found errors in reconstructions ranging from 0.11% to 8.67% of the size of the search region, which is similar to results found in previous works using deterministic techniques, with comparable computational time.

Source characterization of airborne pollutant emissions by hybrid metaheuristic/gradient-based optimization techniques

We propose a methodology to estimate single and multiple emission sources of atmospheric contaminants. It combines hybrid metaheuristic/gradient-descent optimization techniques and Tikhonov-type regularization. The dispersion problem is solved by the Galerkin/Least-squares finite element formulation, which allows more realistic modeling. The accuracy of the proposed inversion model is tested under different contexts with experimental data. To identify single and multiple emissions, we use experimental field data. We consider different configurations for both the Tikhonov-type functional and optimization techniques. Several single and composite data misfit functions are tested. We also use a discrepancy-based choice rule for the regularization parameter. The resulting inversion tool is highly versatile and presents accurate results under different contexts with a competitive computational cost.