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## Publicatie

# Lagrangian Dispersion Modeling in a Horizontally Homogeneous Meteorology for Efficient Data Assimilation Design

### Boek - Dissertatie

Atmospheric dispersion models have become a standard support tool in emergency preparedness and response systems that assess the impact on health and environment of a hazardous plume in the atmosphere. Especially in the near-field range, the evolution of a plume can be challenging to predict due to a complex site geometry. A wide range of dispersion models exists, from simple Gaussian models to the more complex computational fluid dynamics-based models. The models mainly differ in the amount of detail by which terrain configurations (buildings, vegetation, etc.) and meteorology (wind field, turbulent diffusivity, etc.) are represented. First-order Lagrangian stochastic (LS) dispersion models offer a good trade-off between improved physical descriptions and computational complexity, notably in the near-field range. This is a desirable model property for use in emergency response systems, which is the framework that the current work aims to contribute to. Therefore, the focus lies on the Langevin model, a widely used first-order LS model. Model inversion is an indispensable tool in emergency situations since it allows to estimate sensitive model parameters from tracer measurements if no other data are available. In case of the Langevin model, however, this requires dealing with a six-dimensional phase space, which is computationally burdensome. An efficient data assimilation method for model inversion of the Langevin model in horizontally homogeneous meteorological conditions is presented. Moreover, dispersion models, which are coupled to an ambient-gamma dose rate model, are validated in the near-field range with routine Ar-41 releases from a nuclear research reactor, which is of particular interest for radiological emergency events.One of the major uncertainties in dispersion simulations at the near-field range is the representation of terrain effects. The first part of the current work focuses at quantifying this type of uncertainty for dose rate predictions over a homogeneous forest cover. At the Belgian reactor BR1, situated in a forested environment, ambient gamma dose rate data from routine Ar-41 releases are available in the first 300 m from the release point. A forest parameterization is developed that meets the site-specific needs, and integrated in different dispersion models. Using different terrain roughness parameterizations, three types of dispersion models are compared: a Langevin model, an advection--diffusion model and a Gaussian plume model as a special case of the previous one. It has been found that all models are biased up to a factor of four, partly due to an uncertain source strength. The dose rate uncertainty due to the model choice is a factor of 2.2 for a stack release and a factor of 14 for a ground release.In the second part of the current work, a data assimilation method embedded in a Bayesian inference framework is developed for model inversion of the Langevin model in horizontally homogeneous meteorological conditions. Firstly, a kernel density estimator for the concentration field is presented that is a variation on the classical kernel smoother. Moreover, this estimator is rigorously derived for the Langevin equation using path integral theory. It simply consists of the product between a Gaussian kernel and a 1D kernel smoother. The special feature of this path integral-based (PI) estimator is that a 3D concentration field is estimated with the faster convergence rate of a 1D kernel smoother, i.e., 4/5 instead of 4/7 that applies to a 3D kernel smoother. Its numerical convergence rate and efficiency is compared with that of a 3D kernel smoother. The convergence study shows that the PI estimator has a superior convergence rate with an efficiency, in mean integrated squared error sense, comparable with the one of the optimal 3D Epanechnikov kernel. Secondly, it is shown that the PI estimator allows for an easy derivation of kernel estimators for the first and second-order sensitivities of the concentration field. Besides that these estimators inherit the improved convergence rate of 4/5, only a single forward run of the dispersion model is required to evaluate all the sensitivities. However, the choice of control variables is limited to parameters describing dispersion in the horizontal directions and the source term. The advantage of the PI estimator over a 3D kernel smoother is that more model parameters are eligible as control variable with the presented methodology. It is shown that the data assimilation method is capable of recovering the input parameters of forward simulations with high accuracy, which shows the proper functioning of the method. Finally, the data assimilation method is demonstrated on the well-known Project Prairie Grass data set.

Toegankelijkheid:Embargoed