Our objective is to monitor the changes in a proportion with correlated binary observations. All of the published work on this subject used the first-order Markov chain model for the data. Increasing the order of dependence above one by extending a standard Markov chain model entails an exponential increase of both the number of parameters and the dimension of the transition probability matrix. In this dissertation, we develop a particular Markov chain structure, the Multilevel Model (MLM), to model the correlation between binary data. The basic idea is to assign a lower probability to observing a 1 when all previous correlated observations are 0's, and a higher probability to observing a 1 as the last observed 1 gets closer to the current observation. We refer to each of the distinct situations of observing a 1 as a "level". For a given order of dependence, , at most different values of conditional probabilities of observing a 1 can be assigned. So the number of levels is always less than or equal to . Compared to a direct extension of the first-order Markov model to higher orders, our model is considerably parsimonious. The number of parameters for the MLM is only one plus the number of levels, and the transition probability matrix is . We construct a CUSUM control chart for monitoring a proportion with correlated binary observations. First, we use the probability structure of a first-order Markov chain to derive a log-likelihood ratio based CUSUM control statistic. Then, we model this CUSUM statistic itself as a Markov chain, which in turn allows for designing a control chart with specified statistical properties: the Markov Binary CUSUM (MBCUSUM) chart. We generalize the MBCUSUM to account for any order of dependence between binary observations through implying MLM to the data and to our CUSUM control statistic. We verify that the MBCUSUM has a better performance than a curtailed Shewhart chart. Also, we show that except for extremely large changes in the proportion (of interest) the MBCUSUM control chart detects the changes faster than the Bernoulli CUSUM control chart, which is designed for independent observations. / Ph. D.

The European Water Framework Directive 2000 established a new emphasis for the management of freshwaters by setting ecologically-based water quality targets that are to be achieved through holistic, catchment-scale, ecosystem management. However, significant knowledge gaps exist in the understanding of the cumulative effectiveness of multiple mitigation measures on a number of pollutants at a catchment scale. This research contributes to improved understanding of the effectiveness of an ecosystem management approach to deliver catchment-scale water quality improvements on the National Trust Holnicote Estate on Exmoor, UK. This research is part of a larger multi-objective project funded by the UK Department for Environment, Food and Rural Affairs (Defra), to demonstrate the benefits of land use interventions for the management of flood risk. This thesis evaluates the effects of upland ditch blocking on physico-chemical and biological parameters of water quality in an upland Horner Water catchment one year after habitat restoration, and establishes a solid baseline for the monitoring of the effects of current and future land management changes in a lowland, intensively managed, agricultural Aller catchment. The spatial variability of soil physical and chemical properties (bulk density, total carbon (TN), nitrogen (TN), C:N ratio, δ15N, total phosphorus (TP), inorganic phosphorus (IP), organic phosphorus (OP)) and water quality determinands (suspended sediment (SS), dissolved organic carbon (DOC), total particulate carbon (TPC), total oxidised nitrogen (TON) and dissolved reactive phosphorus (DRP)) in the two study catchments with contrasting land use has been characterised and linked to the prevailing land use. Agricultural land use resulted in extensive homogenisation of soil properties. The spatial dependence of all soil properties, except for bulk density and δ15N, was stronger in the agricultural than the semi-natural catchment (nugget:sill ratio 0.10-0.42 in the Aller and 0.15-0.94 in Horner Water), while bulk density, TP, inorganic phosphorus (IP), organic phosphorus (OP), C:N ratio, δ15N and carbon storage showed a longer range of spatial auto-correlation in the agricultural catchment (2,807-3,191 m in the Aller and 545-2,599 m Horner Water). The central tendency (mean, median) of all soil properties, except for IP and δ15N, also differed significantly between the two catchments (P < 0.01). The observed extensive alteration of soil physical and chemical properties in the agricultural catchment is likely to have long-term implications for the restoration of ecosystem functioning and water quality management. The intensive land use seems to have resulted in an altered ‘catchment metabolism’, manifested in a proportionally greater total fluvial carbon (dissolved and particulate) export from the agricultural than the semi-natural catchment. The agricultural catchment supported significantly higher DOC concentrations (P < 0.05) and the quality of DOC differed markedly between the two study catchments. The prevalence of more humic, higher molecular weight compounds in the agricultural catchment and simpler, lower molecular weight compounds in the semi-natural catchment, indicated enhanced microbial turnover of fluvial DOC in the agricultural catchment as well as additional allochtonous terrestrial sources. During an eight month period for which a comparable continuous turbidity record was available, the estimated SS yields from the agricultural catchment (25.5-116.2 t km2) were higher than from the semi-natural catchment (21.7-57.8 t km2). Further, the agricultural catchment exported proportionally more TPC (0.51-2.59 kg mm-1) than the semi-natural catchment (0.36-0.97 kg mm-1) and a similar amount of DOC (0.26-0.52 kg mm-1 in the Aller and 0.24-0.32 kg mm-1 in Horner Water), when normalised by catchment area and total discharge, despite the lower total soil carbon pool, thus indicating an enhanced fluvial loss of sediment and carbon from the intensively managed catchment. Whilst detection of catchment-scale effects of mitigation measures typically requires high resolution, resource-intensive, long term data sets, this research has found that simple approaches can be effective in bridging the gap between fine scale ecosystem functioning and catchment-scale processes. Here, the new macro-invertebrate index PSI (Proportion of Sediment-sensitive Invertebrates) has been shown to be more closely related to a physical measure of sedimentation (% fine bed sediment cover) (P = 0.002) than existing non-pressure specific macro-invertebrate metrics such as the Lotic Index for Flow Evaluation (LIFE) and % Ephemeroptera, Plecoptera & Trichoptera abundance (% EPT) (P = 0.014). Further testing of PSI along a pronounced environmental gradient is recommended as PSI and % fine bed sediment cover have the potential to become a sensitive tool for the setting and monitoring of twin sedimentation targets. Upland ditch management has not had any discernible effect on water quality in the semi-natural upland catchment one year after restoration, which may be due to the short-term post-restoration monitoring period but may also reflect benign effects of large-scale earth moving works on this high quality environment. The conceptual understanding of catchment processes developed in this thesis suggests that cumulatively, the recently completed mitigation works in the lowland agricultural catchment will likely result in reduced sediment and nutrient input into the aquatic environment. However, further research is needed to build on this detailed baseline characterisation and inform the understanding of the effectiveness of combined mitigation measures to reduce the flux of multiple contaminants at the catchment scale.