Abstract:
The use of data analysis cooperatively with partial differential equations is a successful technique to estimate the main parameters of diverse phenomena in many fields (medicine, biology, ecology,...). In the area of ecology, analysis of historical climate change data that leads to global warming, necessitates an estimation of various atmospheric gas concentrations, primarily CO2. In the po- lar regions of Greenland (Denmark) and the southern Antarctic, it is possible to retrace the histories of several atmospheric gases over the last centuries using currently obtained data through the examination of the air volumes injected into the open porosity of the Firn (compacted snow).
This thesis uses powerful modern techniques of computational mathematics based on studying an appropriate inverse problem. It consists in starting with the direct problem, where we analyze and numerically simulate a time-dependent partial differential equation that models the Firn, given its diffusion coefficients. Once the direct problem is properly solved via a robust MATLAB software, one then looks at recovering the diffusion coefficient on the basis of current Firn mea- surements. Inverse techniques reduce to solving a minimization problem on a constrained set, solved also using efficient MATLAB toolboxes. Successful results obtained from numerical simulations conducted on the direct and inverse prob- lems validate the feasibility of this method to estimate Firn diffusion coefficients.
