Browsing by Subject "convection-diffusion"

The quantification of carbon dioxide emissions pose a significant and multi-faceted problem for the atmospheric sciences as a part of the research regarding global warming and greenhouse gases. Emissions originating from point sources, referred to as plumes, can be simulated using mathematical and physical models, such as a convection-diffusion plume model and a Gaussian plume model. The convection-diffusion model is based on the convection-diffusion partial differential equation describing mass transfer in diffusion and convection fields. The Gaussian model is a special case or a solution for the general convection-diffusion equation when assumptions of homogeneous wind field, relatively small diffusion and time independence are made. Both of these models are used for simulating the plumes in order to find out the emission rate for the plume source. An equation for solving the emission rate can be formulated as an inverse problem written as y=F(x)+ε where y is the observed data, F is the plume model, ε is the noise term and x is an unknown vector of parameters, including the emission rate, which needs to be solved. For an ill-posed inverse problem, where F is not well behaved, the solution does not exist, but a minimum norm solution can be found. That is, the solution is a vector x which minimizes a chosen norm function, referred to as a loss function. This thesis focuses on the convection-diffusion and Gaussian plume models, and studies both the difference and the sensibility of these models. Additionally, this thesis investigates three different approaches for optimizing loss functions: the optimal estimation for linear model, Levenberg–Marquardt algorithm for non-linear model and adaptive Metropolis algorithm. A goodness of different fits can be quantified by comparing values of the root mean square errors; the better fit the smaller value the root mean square error has. A plume inversion program has been implemented in Python programming language using the version 3.9.11 to test the implemented models and different algorithms. Assessing the parameters' effect on the estimated emission rate is done by performing sensitivity tests for simulated data. The plume inversion program is also applied for the satellite data and the validity of the results is considered. Finally, other more advanced plume models and improvements for the implementation will be discussed.