No / Multiproxy palaeohydrological records from three raised bogs in Northern Ireland indicate that a major shift to wetter/cooler climatic conditions postdated the rapid decrease in solar activity at 2800 cal. BP by ~100 years. This event is bracketed by two wiggle-match radiocarbon-dated cryptotephra layers in each profile, enabling a high degree of chronological precision. These replicated data corroborate previous findings based on Irish peat humification profiles, and may indicate spatial complexity in the climatic response to solar activity between oceanic and continental areas.

Immersed boundary (IB) methods are attractive due to their ability to simulate flow over complex geometries on a simple Cartesian mesh. Unlike conformal grid formulation, the mesh does not need to conform to the shape and orientation of the boundary. This eliminates the need for complex mesh and/or re-meshing in simulations with moving/morphing boundaries, which can be cumbersome and computationally expensive. However, the imposition of boundary conditions in IB methods is not straightforward and numerous modifications and refinements have been proposed and a number of variants of this approach now exist. In a nutshell, IB methods in the literature often suffer from numerical oscillations, implementation complexity, time-step restriction, burred interface, and lack of generality. This limits their ability to mimic conformal grid results and enforce Neumann boundary conditions. In addition, there is no generic IB capable of solving flow with multiple potentials, closely/loosely packed structures as well as IBs of infinitesimal thickness. This dissertation describes a novel 2$ ^{\text{nd}} $ order direct forcing immersed boundary method designed for simulation of two- and three-dimensional incompressible flow problems with complex immersed boundaries. In this formulation, each cell cut by the IB is reshaped to conform to the shape of the IB. IBs are modeled as a series of 2D planes in 3D space that connect seamlessly at the edges of the cut cells, in a way that mimics conformal grid. IBs are represented in a continuous and consistent fashion from one cell to another, thus eliminating spatial pressure oscillations originating from inconsistent description of the IB as well as the traditional stair-step problem, leading to a more accurate resolution of the boundary layer. Boundary conditions are enforced at the exact location of the IB devoid of interpolation, which guarantees sound simulations even on grids with high aspect ratio, and enables simulations of flow packed with multiple IBs in close proximity. Boundary conditions for each phase across the IB are enforced independently, yielding a unique capability to solve flows with zero-thickness IBs. Simulations of a large number of 2D and 3D test cases confirm the prowess of the devised immersed boundary method in solving flows over multiple loosely/closely-packed IBs; stationary, moving and highly morphing IBs; as well as IBs with zero-thickness. Extension of the proposed scheme to solve flow with multiple potentials is demonstrated by simulating transfer and transport of a passive scalar from an array of side-by-side and tandem cylinders in cross-flow. Aquatic vegetation represented by a colony of circular cylinders with low to high solid fraction is simulated to showcase the prowess of the current numerical technique in solving flow with closely packed structures. Aquatic vegetation studies are extended to a colony of flat plates with different orientations to show the capability of the developed method in modeling zero-thickness structures.

I explore five topics in topology using set-theoretic techniques. The first of these is a generalization of 2-point sets called slice sets. I show that, for any small-in-cardinality subset A of the real line, there is a subset of the plane meeting every line in a topological copy of A. Under Martin's Axiom, I show how to improve this result to any totally disconnected A. Secondly, I show that it is consistent with and independent of ZFC to have a topologically rigid subset of the real line that is smaller than the continuum. Thirdly, I define and examine a new cardinal function related to cleavability. Fourthly, I explore the Toronto Problem and prove that any uncountable, Hausdorff, non-discrete Toronto space that is not regular falls into one of two strictly-defined classes. I also prove that for every infinite cardinality there are precisely 3 non-T1 Toronto spaces up to homeomorphism. Lastly, I examine a notion of dimension called the "neight", and prove several theorems that give a lower bound for this cardinal function.

Persistent condensation trails are clouds, induced by the exhaust of an aircraft engine in a cold and ice-supersaturated environment. These artificial ice clouds can both cool and heat the atmosphere by scattering solar radiation and absorbing terrestrial radiation, respectively. The influence of condensation trails on the Earth-atmosphere energy balance and therewith the answer to the question of the dominating process had been mostly approximated on a global scale by treating the condensation trail as plane parallel layer with constant optical properties. Individual condensation trails and the influence of the solar angle had been analyzed, always using a course spatial grid and never under consideration of the aircraft performance, generating the condensation trail. For a trajectory optimization, highly precise results of the impact of condensation trails on the radiation budget and the influence of the aircraft performance on this impact is needed, so that future air traffic may consider the main factors of flight performance on the environmental impact of condensation trails. That’s why, a model is developed in this thesis to continuously estimate the scattering and absorption properties and their dependence on the aircraft performance. / Langlebige Kondensstreifen sind Eiswolken, welche durch Kondensation von Wasserdampf an Rußpartikeln in einer eisübersättigten Atmosphäre entstehen. Der Wasserdampf entstammt einerseits aus dem Triebwerkabgas und andererseits aus der Atmosphäre. Kondensstreifen können die Atmosphäre durch Rückstreuung solarer Strahlung kühlen und durch Rückstreuung und Absorption terrestrischer Strahlung erwärmen. Der Einfluss von Kondensstreifen auf den Wärmehaushalt der Atmosphäre und damit die Antwort auf die Frage nach dem dominierenden Effekt wurde bisher zumeist auf globaler Ebene ermittelt, wobei der Kondensstreifen als planparallele Schicht mit konstanten optischen Eigenschaften angenähert wurde. Individuelle Kondensstreifen und der Einfluss des Sonnenstandes wurden bisher nur mithilfe eines groben Rasters betrachtet und niemals unter Berücksichtigung der Flugleistung des Luftfahrzeuges, welches den Kondensstreifen generiert hat. Für eine Trajektorienoptimierung sind jedoch präzise Berechnungen des Strahlungseinflusses und eine gewissenhafte Berücksichtigung der Flugleistung notwendig. Nur so kann der zukünftige Luftverkehr die Haupteinflussfaktoren der Flugeigenschaften auf den Strahlungseinfluss der Kondensstreifen berücksichtigen. Aus diesem Grund wurde in dieser Arbeit ein Modell entwickelt, welches die Eigenschaften des Strahlungstransfers durch den Kondensstreifen kontinuierlich bestimmt und die aus der Flugleistung resultierenden Parameter berücksichtigt.

An investigation into the light scattering properties of Saharan dust grains is presented. An electrodynamic trap has been used to levitate single dust particles. By adjusting the trap parameters, partial randomisation of the particle orientation has been introduced. While levitated, the particles were illuminated by a laser, and a rotating half-wave retarder enabled selection of vertically or horizontally polarized incident light. A laser diffractometer and linear photodiode array have been used to measure intensity at scattering angles between 0.5° and 177°. Combining these measurements with Fraunhofer diffraction as calculated for a range of appropriately-sized apertures allows the calculation of the phase function and degree of linear polarization. The phase functions and degree of linear polarisation for four case study particles are presented - the phase functions are found to be featureless across most of the scattering region, with none of the halo features or rainbow peaks associated with regularly shaped particles such as hexagonal columns or spheres. Particle models comprised of large numbers of facets have been constructed to resemble the levitated particles. Utilizing Gaussian random sphere methods, increasing levels of roughness have been added to the surfaces of these models. A Geometric Optics model and a related model, Ray Tracing with Diffraction on Facets, have been modified to calculate scattering on these particle reconstructions. Scattering calculations were performed on each of these reconstructions using a range of refractive indices and two rotation regimes – one where the orientations of the reconstructed particle were limited to match those observed when the particle was levitated, and one where the orientation was not limited. Qualitative comparisons are performed on the phase functions and degree of linear polarization, where it is observed that the addition of roughness to the modelled spheroids causes the computed phase functions to increasingly resemble those from the levitated particles. Limiting the orientation of the particles does not affect the scattering noticeably. The addition of a very small absorption coefficient does not change the comparisons considerably. As the absorption coefficient is increased, however, the quality of the comparisons decreases rapidly in all cases but one. The phase functions are quantitatively compared using RMS errors, and further comparison is performed using the asymmetry parameter.

This thesis examines the method of forcing in set theory and focuses on aspects that are set aside in the usual presentations or applications of forcing. It is shown that forcing can be formalized in Peano arithmetic (PA) and that consis- tency results obtained by forcing are provable in PA. Two ways are presented of overcoming the assumption of the existence of a countable transitive model. The thesis also studies forcing as a method giving rise to interpretations between theories. A notion of bi-interpretability is defined and a method of forcing over a non-standard model of ZFC is developed in order to argue that ZFC and ZF are not bi-interpretable. 1

The Earth's climate system is driven by varying insolation from the Sun. The dominant variations in insolation are at 23 and 40 thousand year periods, yet for the past million years the Earth's climate has glacial cycles at approximately 100 kyr periodicity. These cycles are a coupled variation in temperature, ice volume, and atmospheric CO₂. Somehow the Earth system's collective response to 23 and 40 kyr insolation forcing produces 100 kyr glacial-interglacial cycles. Generally it has been assumed that the causative mechanisms are a combination of ice dynamics (high ice reflectivity controlling temperature) and ocean circulation (changing carbon partitioning between the deep ocean and the atmosphere, and heat transport to the poles). However, these proposed mechanisms have not yet resulted in a compelling theory for all three variations, particularly CO₂. This thesis explores the role of volcanic CO₂ emissions in glacial cycles. I calculate that glacial-driven sea level change alters the pressure on mid-ocean ridges (MORs), changing their CO₂ emissions by approximately 10%. This occurs because pressure affects the thermodynamics of melt generation. The delay between sea level change and the consequent change in MOR CO₂ emissions is several tens-of-thousands-of-years, conceptually consistent with a coupled non-linear oscillation that could disrupt glacial cycles from a 40 kyr mode to a multiple of that period. I develop an Earth system model to investigate this possibility, running for approximately one million years and explicitly calculating global temperatures, ice sheet configuration, and CO₂ concentration in the atmosphere. The model is driven by insolation, with all other components varying in response (and according to their own interactions). This model calculates that volcanism is capable of causing a transition to ̃100 kyr glacial cycles, however the required average volcanic CO₂ emissions are barely within the 95% confidence interval. Therefore it is possible for volcanic systems and glacial cycles to form a 100 kyr coupled oscillation.

Aerosols contribute the largest uncertainty to estimates of radiative forcing of the Earth’s atmosphere, which are thought to exert a net negative radiative forcing, offsetting a potentially significant but poorly constrained fraction of the positive radiative forcing associated with greenhouse gases. Aerosols perturb the Earth’s radiative balance directly by absorbing and scattering radiation and indirectly by acting as cloud condensation nuclei, altering cloud albedo and potentially cloud lifetime. One of the major factors governing the uncertainty in estimates of aerosol direct radiative forcing is the poorly constrained aerosol single scattering albedo, which is the ratio of the aerosol scattering to extinction. In this thesis, I describe a new instrument for the measurement of aerosol optical properties using photoacoustic and cavity ring-down spectroscopy. Characterisation is performed by assessing the instrument minimum sensitivity and accuracy as well as verifying the accuracy of its calibration procedure. The instrument and calibration accuracies are assessed by comparing modelled to measured optical properties of well-characterised laboratory-generated aerosol. I then examine biases in traditional, filter-based absorption measurements by comparing to photoacoustic spectrometer absorption measurements for a range of aerosol sources at multiple wavelengths. Filter-based measurements consistently overestimate absorption although the bias magnitude is strongly source-dependent. Biases are consistently lowest when an advanced correction scheme is applied, irrespective of wavelength or aerosol source. Lastly, I assess the sensitivity of the direct radiative effect of biomass burning aerosols to aerosol and cloud optical properties over the Southeast Atlantic Ocean using a combination of offline radiative transfer modelling, satellite observations and global climate model simulations. Although the direct radiative effect depends on aerosol and cloud optical properties in a non-linear way, it appears to be only weakly dependent on sub-grid variability.

The advective motion of seawater governs the transport of almost everything, animate or inanimate, present in the ocean and those lacking the ability to outswim the currents have to follow the flow. This makes modelling of advective ocean transports a powerful tool in various fields of science where a displacement of something over time is studied. The present thesis comprises four different applications of ocean-transport modelling, ranging from large-scale heat transports to the dispersion of juvenile marine organisms. The aim has been to adapt the method not only to the object of study, but also to the available model-data sets and in situ-observations. The first application in the thesis is a study of the oceanic heat transport. It illustrates the importance of wind forcing for not only the heat transport from the Indian to the Atlantic Ocean, but also for the net northward transport of heat in the Atlantic. In the next study focus is on the particle-transport differences between an open and a semi-enclosed coastal area on the Swedish coast of the Baltic Sea. The modelled patterns of sedimentation and residence times in the two basins are examined after particles having been released from a number of prescribed point sources. In the two final studies the transport-modelling framework is applied within a marine-ecology context and the transported entities are larvae of some Scandinavian sessile and sedentary species and non-commercial fishes (e.g. the bay barnacle, the blue mussel, the shore crab and the gobies). The effects of depth distribution of dispersing larvae on the efficiency of the Marine Protected Areas in the Baltic Sea are examined. Further, the diversity in dispersal and connectivity depending on vertical behaviour is modelled for regions with different tidal regimes in the North Sea, the Skagerrak and the Kattegat. The spatial scales dealt with in the studies varied from global to a highly resolved 182-metres grid. The model results, excepting those from the global study, are based on or compared with in situ-data. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Submitted. Paper 3: Submitted. 4: Manuscript.</p>

An investigation of the high spectral resolution signatures and radiative forcing of tropospheric aerosol in the thermal infrared was conducted. To do so and to support advanced modeling of optical properties, a high spectral resolution library of atmospheric aerosol optical constants was developed. This library includes new optical constants of sulfate-nitrate-ammonium aqueous solutions and the collection of a broad range of existing optical constants for aerosol components, particularly mineral optical constants. The mineral optical constants were used to model and study infrared dust optical signatures as a function of composition, size, shape and mixing state. In particular, spherical and non-spherical optical models of dust particles were examined and compared to high spectral resolution laboratory extinction measurements. Then the performance of some of the most common effective medium approximations for internal mixtures was examined by modeling the optical constants of the newly determined sulfate-nitrate-ammonium mixtures. The optical signature analysis was applied to airborne and satellite high spectral resolution thermal infrared radiance data impacted by Saharan dust events. A new technique to retrieve dust microphysical properties from the dust spectral signature was developed and compared to a standard technique. The microphysics retrieved from this new technique and from a standard technique were then used to investigate the effects of dust on radiative forcing and cooling rates in the thermal IR.