Modeling Dispersion of Radionuclides in the Turbulent Atmosphere

Abstract

In an effort to understand the assumptions and approximations involved in the physics on which atmospheric transport modeling (ATM) relies, we derived from first principles the Lagrangian turbulent velocity drift-diffusion model used by codes such as FLEXPART and HYSPLIT. We showed that the drift-diffusion model is a Langevin model representing the equation of motion for Lagrangian fluid particles based on the turbulent Navier-Stokes equation. That is, the incompressible turbulent Navier-Stokes equation is cast into the form of a stochastic differential equation (SDE) called the Langevin equation which describes the turbulent velocity component of the Lagrangian particle trajectory. The drift coefficient depends on the Lagrangian time scale modeled using the Lagrangian velocity autocorrelation function, while the diffusion coefficient depends additionally on the Reynolds stress or velocity variance. This makes clear that the turbulent Navier-Stokes equation is the physical basis of the drift-diffusion model used by FLEXPART and HYSPLIT and shows what assumptions and approximations are made.

In contrast to particle-based methods of the Lagrangian models, the advection-diffusion (AD) equation physically represents a mass-conservation equation in a turbulent fluid and directly models the mean Eulerian concentration field by employing an eddy diffusivity hypothesis. The AD model is the basis for Gaussian plume model codes such as MACCS2 which use the Pasquill-Gifford semi-empirical turbulence model. We parametrically compared the FLEXPART drift-diffusion model to the Gaussian puff model using synthetic meteorological data, which showed significant discrepancies between the vertical or horizontal dispersion parameters for unstable or stable atmospheres, respectively. However, by modifying the FLEXPART turbulence model to simulate the Gaussian puff model dispersion parameters, we demonstrated much better agreement between the two models. On the other hand, the FLEXPART concentration profile dispersion generally agreed well with the Lagrangian particle ensemble dispersion, validating to some extent the relationship between the Lagrangian and Eulerian turbulence parameters.

In addition to the complexities associated with physically modeling turbulence, we have demonstrated uncertainties associated with dry deposition, particle size distributions, radioactive decay chains, different meteorological data sets, virtual particle numbers, and mesoscale velocity fluctuations. We have performed studies on: local (100 km radius) and global scales, large (Fukushima) and small (DPRK) radionuclide (RN) emission sources, and particulate (volcanic ash) and gaseous species (Xe). Volcanic ash particulate transport simulations showed that it is necessary to use large numbers of particles per emission source, that the dry deposition model significantly reduces predicted atmospheric concentrations and that this is more pronounced for larger particle sizes. When we examined the radioxenon emissions from the Fukushima Daiichi nuclear accident, we found that the meteorological data set chosen has a significant impact on the simulated RN concentrations at detectors as close as Takasaki, with variations up to four orders of magnitude. Additionally, our studies on DPRK weapons tests showed that the measured RN data is often very sparse and difficult to explain and attribute to a particular source.

These studies all demonstrated the many uncertainties and difficulties associated with ATM of RNs when comparing to real data. Thus, we show that ATMs should rely as closely as possible on the underlying physics for accurately modeling RN dispersion in the turbulent atmosphere. In particular, one should use turbulence models based closely on the turbulent Navier-Stokes equation, accurate and high resolution meteorological data, and physics-based deposition and transmutation models.