## Section: New Results

### Inverse modeling

We continued research on inverse modelling techniques, with a focus on hyperparameter estimation when the statistics are non-Gaussian. We applied these methods to the estimation of the caesium-137 Fukushima source term using heterogenous datasets. We applied similar methods to the estimation of Volatile Organic Compounds (VOC) at the European scale by assimilation of the EMEP VOC observations over one year. We also studied the estimation of several hyperparameters in the context of CO${}_{2}$ flux inversions.

#### Estimation of the caesium-137 source term from the Fukushima Daiichi nuclear power plant using a consistent joint assimilation of air concentration and deposition observations

Participants : Victor Winiarek, Marc Bocquet, Nora Duhanyan [CEREA] , Yelva Roustan [CEREA] , Olivier Saunier [IRSN] , Anne Mathieu [IRSN] .

To estimate the amount of radionuclides and the temporal profile of the source term released in the atmosphere during the accident of the Fukushima Daiichi nuclear power plant in March 2011, inverse modeling techniques have been used and have proven their ability in this context. In a previous study, the lower bounds of the caesium-137 and iodine-131 source terms were estimated with such techniques, using activity concentration observations. The importance of an objective assessment of prior errors (the observation errors and the background errors) was emphasised for a reliable inversion. In such critical context where the meteorological conditions can make the source term partly unobservable and where only a few observations are available, such prior estimation techniques are mandatory, the retrieved source term being very sensitive to this estimation.

We propose to extend the use of these techniques to the estimation of prior errors when assimilating observations from several data sets [21] . The aim is to compute an estimate of the caesium-137 source term jointly using all available data about this radionuclide, such as activity concentrations in the air, but also daily fallout measurements and total cumulated fallout measurements. It is crucial to properly and simultaneously estimate the background errors and the prior errors relative to each data set. A proper estimation of prior errors is also a necessary condition to reliably estimate the a posteriori uncertainty of the estimated source term. Using such techniques, we retrieve a total released quantity of caesium-137 in the interval $11.6-19.3$ PBq with an estimated standard deviation range of $15-20\%$ depending on the method and the data sets. The “blind” time intervals of the source term have also been strongly mitigated compared to the first estimations with only activity concentration data.

#### An inverse modeling method to assess the source term of the Fukushima Nuclear Power Plant accident using gamma dose rate observations

Participants : Olivier Saunier [IRSN] , Anne Mathieu [IRSN] , Damien Didier [IRSN] , Maryline Tombette [IRSN] , Denis Quélo [IRSN] , Victor Winiarek, Marc Bocquet.

The Chernobyl nuclear accident, and more recently the Fukushima accident, highlighted that the largest source of error on consequences assessment is the source term, including the time evolution of the release rate and its distribution between radioisotopes. Inverse modeling methods, which combine environmental measurements and atmospheric dispersion models, have proven being efficient in assessing source term due to an accidental situation. Most existing approaches are designed to use air sampling measurements and some of them also use deposition measurements [21] . Some studies have been conceived to use dose rate measurements, but none of the developed methods were carried out to assess the complex source term of a real accident situation like the Fukushima accident. However, dose rate measurements are generated by the most widespread measurement system and, in the event of a nuclear accident, these data constitute the main source of measurements of the plume and radioactive fallout during releases. This study [18] , [23] proposes a method to use dose rate measurements as part of an inverse modeling approach to assess source terms. The method is proven efficient and reliable when applied to the accident at the Fukushima Daiichi Nuclear Power Plant (FD-NPP). The emissions for the eight main isotopes have been assessed. Accordingly, 105.9 PBq of ${}^{131}$I, 35.8 PBq of ${}^{132}$I, 15.5 PBq of ${}^{137}$Cs and 12,134 PBq of noble gases were released. The events at FD-NPP (such as venting, explosions, etc.) known to have caused atmospheric releases are well identified in the retrieved source term. The estimated source term is validated by comparing simulations of atmospheric dispersion and deposition with environmental observations. In total, it was found that for 80 % of the measurements, simulated and observed dose rates agreed within a factor of 2. Changes in dose rates over time have been overall properly reconstructed, especially in the most contaminated areas to the northwest and south of the FD-NPP. A comparison with observed atmospheric activity concentration and surface deposition shows that the emissions of caesiums and ${}^{131}$I are realistic but that ${}^{132}$I and ${}^{132}$Te are probably underestimated and noble gases are likely overestimated. Finally, an important outcome of this study is that the method proved to be perfectly suited to emergency management and could contribute to improve emergency response in the event of a nuclear accident.

#### Estimation of volatile organic compound emissions for Europe using data assimilation

Participants : Mohammad Reza Koohkan, Marc Bocquet, Yelva Roustan [CEREA] , Yougseob Kim [CEREA] , Christian Seigneur [CEREA] .

The emissions of non-methane volatile organic compounds (VOCs) over western Europe for the year 2005 are estimated via inverse modeling by assimilation of in situ observations of concentration and they are subsequently compared to a standard emission inventory. The study [16] focuses on fifteen VOC species: five aromatics, six alkanes, two alkenes, one alkyne and one biogenic diene. The inversion relies on a validated fast adjoint of the chemical transport model used to simulate the fate and transport of these VOCs. The assimilated ground-based measurements over Europe are provided by the European Monitoring and Evaluation Programme (EMEP) network. The background emissions errors and the prior observational errors are estimated by maximum likelihood approaches. The positivity assumption on the VOC emission fluxes is pivotal for a successful inversion and this maximum likelihood approach consistently accounts for the positivity of the fluxes. For most species, the retrieved emissions lead to a significant reduction of the bias, which underlines the misfit between the standard inventories and the observed concentrations. The results are validated through a forecast test and a cross-validation test. An estimation of the posterior uncertainty is also provided. It is shown that the statistically consistent non-Gaussian approach, based on a reliable estimation of the errors, offers the best performance. The efficiency in correcting the inventory depends on the lifetime of the VOCs and the accuracy of the boundary conditions. In particular, it is shown that the use of in situ observations using a sparse monitoring network to estimate emissions of isoprene is inadequate because its short chemical lifetime significantly limits the spatial radius of influence of the monitoring data. For species with longer lifetime (a few days), successful, albeit partial, emission corrections can reach regions hundreds of kilometres away from the stations. Domainwide corrections of the emissions inventories of some VOCs are significant, with underestimations on the order of a factor of two for propane, ethane, ethylene and acetylene.

#### Hyperparameter estimation for uncertainty quantification in mesoscale carbon dioxide inversions

Participants : Lin Wu [LSCE, France] , Marc Bocquet, Frédéric Chevallier [LSCE, France] , Thomas Lauvaux [Department of Meteorology, Pennsylvania State University, USA] , Kenneth Davies [Department of Meteorology, Pennsylvania State University, USA] .

Uncertainty quantification is critical in the inversion of CO${}_{2}$ surface fluxes from atmospheric concentration measurements. We estimate the main hyperparameters of the error covariance matrices for a priori fluxes and CO${}_{2}$ concentrations, that is, the variances and the correlation lengths, using real, continuous hourly CO${}_{2}$ concentration data in the context of the Ring 2 experiment of the North American Carbon Program Mid Continent Intensive. Several criteria, namely maximum likelihood (ML), general cross-validation (GCV) and ${\chi}^{2}$ test are compared for the first time under a realistic setting in a mesoscale CO${}_{2}$ inversion. It is shown [22] that the optimal hyperparameters under the ML criterion assure perfect ${\chi}^{2}$ consistency of the inverted fluxes. Inversions using the ML error variances estimates rather than the prescribed default values are less weighted by the observations, because the default values underestimate the model-data mismatch error, which is assumed to be dominated by the atmospheric transport error. As for the spatial correlation length in prior flux errors, the Ring 2 network is sparse for GCV and this method fails to reach an optimum. In contrast, the ML estimate (e.g. an optimum of 20 km for the first week of June 2007) does not support long spatial correlations that are usually assumed in the default values.