Tropospheric aerosol detection over Southern Ireland using a backscatter Raman lidar

Lidar is an optical remote sensing instrument that can measure atmospheric parameters. A Raman lidar instrument (UCLID) was established at University College Cork to contribute to the European lidar network, EARLINET. System performance tests were carried out to ensure strict data quality assurance for submission to the EARLINET database. Procedures include: overlap correction, telecover test, Rayleigh test and zero bin test. Raman backscatter coefficients, extinction coefficients and lidar ratio were measured from April 2010 to May 2011 and February 2012 to June 2012. Statistical analysis of the profiles over these periods provided new information about the typical atmospheric scenarios over Southern Ireland in terms of aerosol load in the lower troposphere, the planetary boundary layer (PBL) height, aerosol optical density (AOD) at 532 nm and lidar ratio values. The arithmetic average of the PBL height was found to be 608 ± 138 m with a median of 615 m, while average AOD at 532 nm for clean marine air masses was 0.119 ± 0.023 and for polluted air masses was 0.170 ± 0.036. The lidar ratio showed a seasonal dependence with lower values found in winter and autumn (20 ± 5 sr) and higher during spring and winter (30 ± 12 sr). Detection of volcanic particles from the eruption of the volcano Eyjafjallajökull in Iceland was measured between 21 April and 7 May 2010. The backscatter coefficient of the ash layer varied between 2.5 Mm-1sr-1 and 3.5 Mm-1sr-1, and estimation of the AOD at 532 nm was found to be between 0.090 and 0.215. Several aerosol loads due to Saharan dust particles were detected in Spring 2011 and 2012. Lidar ratio of the dust layers were determine to be between 45 and 77 sr and AOD at 532 nm during the dust events range between 0.84 to 0.494.

Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations

This thesis is concerned with uniformly convergent finite element methods for numerically solving singularly perturbed parabolic partial differential equations in one space variable. First, we use Petrov-Galerkin finite element methods to generate three schemes for such problems, each of these schemes uses exponentially fitted elements in space. Two of them are lumped and the other is non-lumped. On meshes which are either arbitrary or slightly restricted, we derive global energy norm and L2 norm error bounds, uniformly in the diffusion parameter. Under some reasonable global assumptions together with realistic local assumptions on the solution and its derivatives, we prove that these exponentially fitted schemes are locally uniformly convergent, with order one, in a discrete L∞norm both outside and inside the boundary layer. We next analyse a streamline diffusion scheme on a Shishkin mesh for a model singularly perturbed parabolic partial differential equation. The method with piecewise linear space-time elements is shown, under reasonable assumptions on the solution, to be convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 outside layers and almost order 3/4 inside the boundary layer. Numerical results for the above schemes are presented. Finally, we examine a cell vertex finite volume method which is applied to a model time-dependent convection-diffusion problem. Local errors away from all layers are obtained in the l2 seminorm by using techniques from finite element analysis.