Partial reconstruction of the trajectories of a discretely observed branching diffusion with immigration and an application to inference

In this treatise we consider finite systems of branching particles where the particles move independently of each other according to d-dimensional diffusions. Particles are killed at a position dependent rate, leaving at their death position a random number of descendants according to a position dependent reproduction law. In addition particles immigrate at constant rate (one immigrant per immigration time). A process with above properties is called a branching diffusion withimmigration (BDI). In the first part we present the model in detail and discuss the properties of the BDI under our basic assumptions. In the second part we consider the problem of reconstruction of the trajectory of a BDI from discrete observations. We observe positions of the particles at discrete times; in particular we assume that we have no information about the pedigree of the particles. A natural question arises if we want to apply statistical procedures on the discrete observations: How can we find couples of particle positions which belong to the same particle? We give an easy to implement 'reconstruction scheme' which allows us to redraw or 'reconstruct' parts of the trajectory of the BDI with high accuracy. Moreover asymptotically the whole path can be reconstructed. Further we present simulations which show that our partial reconstruction rule is tractable in practice. In the third part we study how the partial reconstruction rule fits into statistical applications. As an extensive example we present a nonparametric estimator for the diffusion coefficient of a BDI where the particles move according to one-dimensional diffusions. This estimator is based on the Nadaraya-Watson estimator for the diffusion coefficient of one-dimensional diffusions and it uses the partial reconstruction rule developed in the second part above. We are able to prove a rate of convergence of this estimator and finally we present simulations which show that the estimator works well even if we leave our set of assumptions.

Using sulfur isotope fractionation to understand the atmospheric oxidation of SO 2

Sulfate aerosol plays an important but uncertain role in cloud formation and radiative forcing of the climate, and is also important for acid deposition and human health. The oxidation of SO2 to sulfate is a key reaction in determining the impact of sulfate in the environment through its effect on aerosol size distribution and composition. This thesis presents a laboratory investigation of sulfur isotope fractionation during SO2 oxidation by the most important gas-phase and heterogeneous pathways occurring in the atmosphere. The fractionation factors are then used to examine the role of sulfate formation in cloud processing of aerosol particles during the HCCT campaign in Thuringia, central Germany. The fractionation factor for the oxidation of SO2 by ·OH radicals was measured by reacting SO2 gas, with a known initial isotopic composition, with ·OH radicals generated from the photolysis of water at -25, 0, 19 and 40°C (Chapter 2). The product sulfate and the residual SO2 were collected as BaSO4 and the sulfur isotopic compositions measured with the Cameca NanoSIMS 50. The measured fractionation factor for 34S/32S during gas phase oxidation is αOH = (1.0089 ± 0.0007) − ((4 ± 5) × 10−5 )T (°C). Fractionation during oxidation by major aqueous pathways was measured by bubbling the SO2 gas through a solution of H2 O2

Sources and pathways of methane formed in oxidative environments

Methane is the most abundant reduced organic compound in the atmosphere. As the strongest known long-lived greenhouse gas after water vapour and carbon dioxide methane perturbs the radiation balance of Earth’s atmosphere. The abiotic formation of methane requires ultraviolet irradiation of organic matter or takes place in locations with high temperature and/or pressure, e.g. during biomass burning or serpentinisation of olivine, under hydrothermal conditions in the oceans deep or below tectonic plates. The biotic methane formation was traditionally thought to be formed only by methanogens under strictly anaerobic conditions, such as in wetland soils, rice paddies and agricultural waste. rnIn this dissertation several chemical pathways are described which lead to the formation of methane under aerobic and ambient conditions. Organic precursor compounds such as ascorbic acid and methionine were shown to release methane in a chemical system including ferrihydrite and hydrogen peroxide in aquatic solution. Moreover, it was shown by using stable carbon isotope labelling experiments that the thio-methyl group of methionine was the carbon precursor for the methane produced. Methionine, a compound that plays an important role in transmethylation processes in plants was also applied to living plants. Stable carbon isotope labelling experiments clearly verified that methionine acts as a precursor compound for the methane from plants. Further experiments in which the electron transport chain was inhibited suggest that the methane generation is located in the mitochondria of the plants. The abiotic formation of methane was shown for several soil samples. Important environmental parameter such as temperature, UV irradiation and moisture were identified to control methane formation. The organic content of the sample as well as water and hydrogen peroxide might also play a major role in the formation of methane from soils. Based on these results a novel scheme was developed that includes both biotic and chemical sources of methane in the pedosphere.rn