Ergodicity for SDEs and approximations: Locally Lipschitz vector fields and degenerate noise

The ergodic properties of SDEs, and various time discretizations for SDEs, are studied. The ergodicity of SDEs is established by using techniques from the theory of Markov chains on general state spaces, such as that expounded by Meyn-Tweedie. Application of these Markov chain results leads to straightforward proofs of geometric ergodicity for a variety of SDEs, including problems with degenerate noise and for problems with locally Lipschitz vector fields. Applications where this theory can be usefully applied include damped-driven Hamiltonian problems (the Langevin equation), the Lorenz equation with degenerate noise and gradient systems. The same Markov chain theory is then used to study time-discrete approximations of these SDEs. The two primary ingredients for ergodicity are a minorization condition and a Lyapunov condition. It is shown that the minorization condition is robust under approximation. For globally Lipschitz vector fields this is also true of the Lyapunov condition. However in the locally Lipschitz case the Lyapunov condition fails for explicit methods such as Euler-Maruyama; for pathwise approximations it is, in general, only inherited by specially constructed implicit discretizations. Examples of such discretization based on backward Euler methods are given, and approximation of the Langevin equation studied in some detail

Pesticides and metabolites in groundwater: examples from two major UK aquifers

Reducing the impact of anthropogenic pollution on groundwater bodies and ameliorating any deterioration of water quality is central to key legislative drivers such as the EU Water Framework Directive and the proposed daughter Directive relating to the protection of groundwater. Pesticide pollution has a direct impact on groundwater quality and an indirect impact on the associated aquatic ecosystems supported by groundwater. There is currently no legislative requirement to monitor pesticide metabolite concentrations in groundwater. Pesticide and metabolite results from two nationally important aquifers are presented, the Trassic Sandstone and the Chalk of Southern England. Aerobic microbial degradation of diuron in the soil can lead to the formation of three compounds; dichlorophenylmethyl urea (DCPMU), dichlorophenyl urea (DCPU) and dichloroanaline (DCA).Median diuron concentrations were significantly higher than each of the metabolites with outliers exceeding the PVC on at least one occasion. At nine sites in Kent, Southern England, (60%) metabolites were more prevalent than diuron. Both aquifers are an important source of water, locally supplying up to 80% of public drinking water. The sandstone site has a predominantly arable landuse with a potential diffuse source of pesticides although soakaways are possible point sources.The chalk site has a mixture of arable and industrial/urban landuse. A significant source has been from excessive applications of diuron (“over-spray”) on a number of public amenities. Data from both aquifers show that pesticide concentrations have a high degree of temporal variability. Elevated pesticide concentrations are associated with recharge events in both aquifer systems regardless of pesticide source terms. Pesticides from amenity use and diffuse agricultural sources both pose a threat to groundwater quality. Pesticide metabolites are present in significant concentrations in groundwaters. Systematic, long-term monitoring (5-10 years) is required to understand trends in groundwater quality

Macronutrient status of UK groundwater: nitrogen, phosphorus and organic carbon

Groundwater is a large, slowly changing pool of the macronutrients nitrogen (N), phosphorus (P) and dissolved organic carbon (DOC), with impacts on receptors, surface waters, dependent wetlands and coastal marine ecosystems. Sources of N to groundwater include fertilisers, animal wastes and septic effluents. N species are well-quantified in groundwater and NO3-N has a wide range of median values (0-12 mg/L). The highest concentrations are in the Chalk of East Anglia and Humberside and the Permo-Triassic Sandstone (PTS) of Staffordshire. The highest concentrations of NH4-N are found in confined aquifers. N concentrations have increased with time peaking during the 1980s. Changes in practice have led to the reduction observed in rapidly-responding aquifers. For the Chalk, where the unsaturated zone is thick, improvements may not be seen for decades. P is less well-characterised in UK groundwater reflecting the lack of historical interest in groundwater P, although it can be significant in some aquifer matrices. Groundwater P concentrations are elevated in sandstone formations compared to other lithology and highest in the PTS of the Midlands and northern England (median values >50 µg/L). Overall half of the aquifers studied in the UK have median TDP >50 g/L, with values of up to 100 µg/L under some urban areas, such as Manchester and Liverpool as well as the Lee Valley. P concentrations in arable areas are variable (20-100 µg/L), whereas under semi-natural conditions they are lower (20-50 µg/L). There is little information on P trends in groundwater. Most DOC is derived from soils, playing an important part in redox processes. The aquifer matrix can contain high OC and contribute significantly to groundwater DOC. Median values range between 0.4 and 9 mg/L, but rarely exceed 5 mg/L, except in the Chalk of Yorkshire and Humberside and PTS of Liverpool which have long legacies of anthropogenic pollution

Temporal variability of micro-organic contaminants in lowland chalk catchments: new insights into contaminant sources and hydrological processes

This paper explores the temporal variation of a broad suite of micro organic (MO) compounds within hydrologically linked compartments of a lowland Chalk catchment, the most important drinking water aquifer in the UK. It presents an assessment of results from relatively high frequency monitoring at a well-characterised site, including the type and concentrations of compounds detected and how they change under different hydrological conditions including exceptionally high groundwater levels and river flow conditions during 2014 and subsequent recovery. This study shows for the first time that within the Chalk groundwater there can be a greater diversity of the MOs compared to surface waters. Within the Chalk 26 different compounds were detected over the duration of the study compared to 17 in the surface water. Plasticisers (0.06–39 μg/L) were found to dominate in the Chalk groundwater on 5 visits (38.4%) accounting for 14.5% of detections but contributing highest concentrations whilst other compounds dominated in the surface water. Trichloroethene and atrazine were among the most frequently detected compounds. The limit for the total pesticide concentration detected did not exceed EU/UK prescribed concentration values for drinking water. Emerging organic compounds such as caffeine, which currently do not have water quality limits, were also detected. The low numbers of compounds found within the hyporheic zone highlight the role of this transient interface in the attenuation and breakdown of the MOs, and provision of an important ecosystem service

Estimating the leakage contribution of phosphate dosed drinking water to environmental phosphorus pollution at the national‐scale

Understanding sources of phosphorus (P) to the environment is critical for the management of freshwater and marine ecosystems. Phosphate is added at water treatment works for a variety of reasons: to reduce pipe corrosion, to lower dissolved lead and copper concentrations at customer’s taps and to reduce the formation of iron and manganese precipitates which can lead to deterioration in the aesthetic quality of water. However, the spatial distribution of leakage into the environment of phosphate added to mains water for plumbosolvency control has not been quantified to date. Using water company leakage rates, leak susceptibility and road network mapping, we quantify the total flux of P from leaking water mains in England and Wales at a 1 km grid scale. This is validated against reported leaks for the UKs largest water utility. For 2014, we estimate the total flux of P from leaking mains to the environment to be c. 1.2 kt P/yr. Spatially, P flux is concentrated in urban areas where pipe density is highest, with major cities acting as a significant source of P (e.g. London into the Thames, with potentially 30% of total flux). The model suggests the majority (69%) of the P flux is likely to be to surface water. This is due to leakage susceptibility being a function of soil corrosivity and shrink‐swell behaviour which are both controlled by presence of low‐permeability clays. The location of major cities such as London close to the coast results in a potentially significant flux of P from mains leakage to estuarine environments. The contribution of leakage of phosphate dosed mains water should be considered in future source apportionment and ecosystem management. The methodology presented is generic and can be applied in other countries where phosphate dosing is undertaken or used prior to dosing during investment planning

Phosphate dosing of mains water : novel approaches to water loss reduction through leakage detection and policy [abstract]

Detection and t racing of leakage in the environment are essential component s of water loss reduction strategies. Industry standard techniques for tracing leaks include analysis of chlorine and trihalomethane concentrations, but levels of these determinands can fall belo w detection limits due to their volatile nature 1 . Consequently additional tools to trace leakage in the environment are a useful step to move towards minimum losses

Persistent and emerging micro-organic contaminants in Chalk groundwater of England and France

The Chalk aquifer of Northern Europe is an internationally important source of drinking water and sustains baseflow for surface water ecosystems. The areal distribution of microorganic (MO) contaminants, particularly non-regulated emerging MOs, in this aquifer is poorly understood. This study presents results from a reconnaissance survey of MOs in Chalk groundwater, including pharmaceuticals, personal care products and pesticides and their transformation products, conducted across the major Chalk aquifers of England and France. Data from a total of 345 sites collected during 2011 were included in this study to provide a representative baseline assessment of MO occurrence in groundwater. A suite of 42 MOs were analysed for at each site including industrial compounds (n = 16), pesticides (n = 14) and pharmaceuticals, personal care and lifestyle products (n = 12). Occurrence data is evaluated in relation to land use, aquifer exposure, well depth and depth to groundwater to provide an understanding of vulnerable groundwater settings

Thinking about growth : a cognitive mapping approach to understanding small business development

School of Managemen

Urban groundwater quality in sub-Saharan Africa: current status and implications for water security and public health

Groundwater resources are important sources of drinking water in Africa, and they are hugely important in sustaining urban livelihoods and supporting a diverse range of commercial and agricultural activities. Groundwater has an important role in improving health in sub-Saharan Africa (SSA). An estimated 250 million people (40% of the total) live in urban centres across SSA. SSA has experienced a rapid expansion in urban populations since the 1950s, with increased population densities as well as expanding geographical coverage. Estimates suggest that the urban population in SSA will double between 2000 and 2030. The quality status of shallow urban groundwater resources is often very poor due to inadequate waste management and source protection, and poses a significant health risk to users, while deeper borehole sources often provide an important source of good quality drinking water. Given the growth in future demand from this finite resource, as well as potential changes in future climate in this region, a detailed understanding of both water quantity and quality is required to use this resource sustainably. This paper provides a comprehensive assessment of the water quality status, both microbial and chemical, of urban groundwater in SSA across a range of hydrogeological terrains and different groundwater point types. Lower storage basement terrains, which underlie a significant proportion of urban centres in SSA, are particularly vulnerable to contamination. The relationship between mean nitrate concentration and intrinsic aquifer pollution risk is assessed for urban centres across SSA. Current knowledge gaps are identified and future research needs highlighted

Exploring consumer brand name equity: Gaining insight through the investigation of response to name change

Purpose: Academic literature generally regards the brand name element as central to consumer brand equity. Unfortunately scant research has been carried out to justify such a position for established products and services. The purpose of this study is to address this research gap. Design/methodology/approach: A series of 25 semi-structured qualitative interviews was carried out with consumers, exploring functions performed by brand name for established products and services. In order to isolate the brand name element this focused on global marketing induced brand name changes. Findings: Many of the corporate-led functions performed by brand name within the literature received validation. This suggests that a concept of consumer brand name equity for established products and services can be justified. The study also indicated that a material proportion of the equity from a brand name was determined by the consumer. It revealed that many consumers had created their own associations for the brand name, positive and negative, independent of and different from those driven by the corporation. Originality/value: It provides needed empirical support for the concept of consumer brand name equity for established products and services. It also suggests that this may be usefully considered as a co-creation between corporation and consumer. © Emerald Group Publishing Limited