Applications of MCMC methods on function spaces

In the course of this thesis, several different applications of data assimilation will be looked at. In each case, a rigorous mathematical framework will be constructed, in a Bayesian context, to enable the use of various types of data to infer on various infinite dimensional parameters of the system that has been observed. After careful consideration of the forward problem, well-defined posterior distributions on function space are constructed. Using MCMC methods which are defined on these function spaces themselves, we can construct Markov chains whose invariant measures are the posterior of interest. From this point, we can implement these methods on a computer, having finally discretised the problem. The philosophy that we adhere to throughout, is the idea that numerical methods formulated on function space are robust under discretisation, and do not suffer from the curse of dimensionality typically suffered by sampling methods formulated after disretisation. The first few chapters (after the introductory chapter) will focus on various aspects of data assimilation of observations of Stokes ow dynamics. Chapter 2 will focus on Eulerian data where direct observations of the velocity of the fluid at various points in time and space will be made. Chapter 3 will concentrate on data assimilation of indirect observations of the field, in the form of the positions of passive tracers in the flow. In these two chapters we will assume that the forcing of the system is known and that we are merely trying to recover the initial condition of the flow field. In chapter 4 we will consider both Eulerian and Lagrangian data assimilation, with the added complexity of trying to use the data to not only infer on the initial condition but also on the space-time dependant forcing of the system. In chapter 5 we will try to show how these smoothing methods could be adapted into a filtering algorithm, and a simple example will be presented. In the final chapter, 6, this Bayesian framework on function space will be applied to a shape matching problem with applications in the biomedical sciences.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research Council (EPSRC)GBUnited Kingdo

Eleven years monitoring of Lesina lagoon (South Italy) using a biotic index (Λ)

1 - The scope of our work was to assess the ecological status of Lesina lagoon on the South Adriatic coast of Italy according to the biological priorities expressed by the directives of the government, priorities which can be summed up in the key words of bionomics, biomass and biodiversity. 2 - Our method was based on the characteristics of the sessile benthic macrofauna considered to be indicative of environmental status. We developed a biotic index (Λ) that grades from 1 to 10 the rising quality of the environment. The data required for applying the index, i.e. spatial distribution (Zonation), biomass (g ww/m2) and number of species of the benthic macrofauna, were obtained from samples of sediment taken at systematically distributed stations over the entire surface of the lagoon. Samples were taken in spring and again in autumn. 3 - Our first assessment in Jan. 1993 gave 8.48, a high value. No samples were taken in 1994 but quality probably remained high because in Nov. 1995 the index gave 7.86. In 1996 quality must have begun to decline because although we took no sample in that year, in May 1997 the index was 6.14, which is very low for spring, when quality is normally high. The situation did not improve until August 1998 when the index rose to 7.59. From then on till our last assessment in Oct. 2003 the environmental quality of Lesina was at a stable high, the index registering values above 7.00 with a peak of 8.15 in Aug. 1999. 4 - The index values that we registered closely coincided with the opinion on the state of the environment given by experienced fishermen whose livelihood depends on the quality of the lagoon

Population structure and spatial distribution of Loripes lacteus (Linnaeus, 1758) in Varano lagoon, SE Italy

In Varano lagoon (Puglia, Italy) the bivalve Loripes lacteus (Linnaeus, 1758) constitutes the most abundant species among the organisms of the benthic macrofauna. This work presents the results of five years (from 2001 at 2006) of observations on the abundance, size/age population structure and spatial distribution of this species within the basin (6500 ha). L. lacteus is one of the most common and frequent bivalve species in Mediterranean lagoons. It typically occurs in reduced sediments where it is able to live at low oxygen concentration due to a particular respiratory pigment haemoglobin. Lucinid bivalves house symbiotic, sulphur-oxydizing chemoautotrophic bacterias in their gills, which contribute substantially to their nutrition. 2 - The design was to perform two sampling campaignes on yearly basis during the intermediate seasons (Spring and Autumn), when possible. Each sampling was realized collecting 53 sampling units taken from 53 stations distributed regularly over the lagoon surface. Each sampling unit consisted in all the individuals contained in a solid 15 x 15 x 20 cm of sediment and held on 1 mm mesh. 3 - Growth patterns were determined with the Bhattacharya method which uses modal progression analysis from size frequency distribution. 4 - The results showed a spatial distribution of L. lacteus which occurred in patches and changed among samples. The population analysis showed two modal classes for each sampling time. 5 - L. lacteus is an \u201cr\u201d strategy species with small size, brief life cycle, with great capacity of recovery after environmental crises

Environmental heterogeneity patterns and assessment of trophic levels in two Mediterranean lagoons: Orbetello and Varano, Italy

The management of coastal lagoons is of particular interest due to their high economical importance. In spite of their great productivity, coastal lagoons are often impacted by human pressure which produces water eutrophication. The aim of this paper is to assess the trophic state of the two Mediterranean lagoons taking into account chemical-physical parameters, nutrient concentrations and biological parameters. Two Italian lagoons, Orbetello and Varano (respectively located in Tyrrhenian and Adriatic coast, Italy) were studied between May 2003 and April 2005. Both these systems receive treated urban outflows, agricultural effluents and rivers freshwater inputs. Field collected data showed that studied lagoons were characterized by different human and natural pressures. Orbetello showed the highest water eutrophication, highlighted by the trophic index values, while Varano showed lower eutrophication levels except for the summertime. The values of physical, chemical and biological parameters measured in Orbetello and Varano lagoons indicate that a wide spatial and seasonal gradient of the water characteristics was established during the study period, but in particular in winter. This gradient, typical of estuarine systems, was essentially due to the mixing of freshwater, seawater and anthropogenic inputs. Orbetello lagoon seemed much more affected by the urban impact and the fish-farming activities than Varano lagoon, but the latter showed a greater agriculture activities impact as showed by the remote sensing images. © 2008 Elsevier B.V. All rights reserved