Variational Integrators for Almost-Integrable Systems

We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These integrators exploit that epsilon << 1 to increase their accuracy by constructing discrete Lagrangians based on the assumption that the integrator trajectory is close to that of the integrable system. Several of the integrators we present are equivalent to well-known symplectic integrators for the equivalent perturbed Hamiltonian systems, but their construction and error analysis is significantly simpler in the variational framework. One novel method we present, involving a weighted time-averaging of the perturbing terms, removes all errors from the integration at O(epsilon). This last method is implicit, and involves evaluating a potentially expensive time-integral, but for some systems and some error tolerances it can significantly outperform traditional simulation methods.Comment: 14 pages, 4 figures. Version 2: added informative example; as accepted by Celestial Mechanics and Dynamical Astronom

Natural Resources Wales's monitoring networks for groundwater level and quality: the story so far

Natural Resources Wales, which was formed in April 2013, has taken over the functions of the Countryside Council for Wales, Environment Agency Wales and Forestry Commission Wales, as well as some functions of Welsh Government. Its purpose is to ensure that the natural resources of Wales are sustainably maintained, enhanced and used, now and in the future. This includes ensuring that the quality of groundwater, surface water and coastal waters continues to improve. In Wales, groundwater only contributes around 3% of the total public water supply (Environment Agency, 2008a). However, it is still an important resource in rural areas where records held by local authorities identify at least 21,000 private water supplies, typically comprising shallow wells, boreholes and spring sources. Groundwater also provides baseflow to rivers and groundwater dependent wetlands. Therefore it is important that sufficient data is available to understand, manage, protect, forecast and report on the quality and availability of groundwater

Characterisation of seasonal temperature variation in a shallow, urban aquifer: implications for the sustainable development of ground source heating systems

Groundwater thermally enhanced by the Urban Heat Island effect can be utilised by ground source heating systems (GSHSs). However, the near subsurface is subject to seasonal temperature variation reflected in shallow groundwater that can differ by several degrees throughout the year. To sustainably manage the near surface thermal resource an understanding of factors which control variation in groundwater temperature and how these are transmitted through the aquifer is needed. We show that even in relatively small urban areas (Cardiff, U.K., situated on a shallow gravel aquifer) the Zone of Seasonal Fluctuation (ZSF) can vary in depth by 8m. GSHSs are more efficient if they are sited below the ZSF, where temperatures are more stable. In Spring 2014, 48 groundwater monitoring boreholes were profiled at a 1m resolution to measure groundwater temperature across Cardiff. These were reprofiled that Autumn and compared to the Spring temperatures, defining the ZSF. The average depth to the base of the ZSF was 9.5mbgl but ranged from 7.1-15.5mbgl. The amplitude of the differences between Spring and Autumn temperatures also varied. To better understand the high spatial variability 60 boreholes were instrumented with in situ temperature loggers, recording at half-hourly intervals. The first year’s data revealed the amplitudes of temperature variation within boreholes with loggers at similar depths were not always consistent. It was also noted that lag times between air temperature and groundwater temperature were not uniform across the sites. The data also showed that where gravels occurred at shallower depths the ZSF tended to be shallower and lag times shorter. The wide spatial variability of the ZSF may be partially explained by differing landuse. Those boreholes in open, grassed areas showed a deeper ZSF than those in built-up areas but built-up areas generally showed the greatest variation between Spring and Autumn temperature profiles, suggesting heat loss from buildings and underground infrastructure plays a part. Natural and anthropogenic factors affecting spatial and temporal groundwater temperatures, either separately or in combination, that have been considered in this study include landuse, depth, lithology/lithostratigraphy, material properties, hydrogeological setting, thermal conductivity, buried infrastructure, land surface temperature, weather effects and solar radiation. This study shows that urban groundwater temperatures can vary greatly across a small area, which has implications for the successful development, and long-term performance of open- and closed-loop GSHSs, and the environmental regulation of these systems. Key to the effective wide-scale use of GSHSs is an understanding of the hydrogeological setting, chiefly how heat is transferred across the aquifer. This study attempts to provide insight into an array of factors which determine heat transfer in the ZSF

Mapping shallow urban groundwater temperatures, a case study from Cardiff, UK

Low-enthalpy ground source heating systems can help to reduce our dependence on fossil fuels, in turn reducing greenhouse gas emissions and increasing energy security. To de-risk and support the sustainable development, regulation and management of ground source heating systems in urban areas, detailed baseline mapping of groundwater temperatures is required. Groundwater temperatures were measured in 168 monitoring boreholes primarily within a Quaternary sand and gravel aquifer in the city of Cardiff, UK. The data have been used to create the first city-wide map of shallow groundwater temperatures in the UK. This map can be used both to support development of ground source heating and to act as a detailed baseline from which to measure change. Shallow groundwater temperatures under the city were found to be 2°C warmer than the UK average groundwater temperature and this additional heat is attributed to the urban heat island. The zone of seasonal fluctuation varies from 7.1 and 15.5 m below ground level (mbgl) within the shallow Quaternary aquifer, averaging 9.5 mbgl. Deeper groundwater temperature profiles incorporating both the Quaternary and bedrock aquifers suggest that a ‘zone of anthropogenic influence’ exists down to about 70 mbgl. Around a third of the UK's greenhouse gas emissions are produced by space heating, and the UK Government recognizes the need to change the way heat is produced and consumed so as to reduce the impacts of climate change and improve energy security (DECC 2013). In response to this driver the UK Government has established targets in the legally binding Climate Change Act 2008 to reduce greenhouse gas emissions by 80% from the 1990 baseline by 2050. In Wales the Well-being of Future Generations (Wales) Act 2015 requires public bodies to take action to undertake sustainable development to drive social, economic and environmental benefits, both now and into the future. Low-enthalpy ground source heating systems, when deployed in a sustainable manner, can provide a low-cost, low-carbon and secure form of heating (e.g. Allen et al. 2003). Ground source heat pumps can broadly be classified as either ‘open-loop’ or ‘closed-loop’ systems. Open-loop systems require the abstraction of groundwater, which is passed through a heat exchanger before being returned to the aquifer. Open-loop systems can have a higher coefficient of performance (COP) and require fewer boreholes where shallow groundwater is available. Open-loop systems may not be suitable if water cannot be successfully recharged to the same aquifer and there are also requirements for abstraction licences and discharge permits or exemptions. The closed-loop system uses a sealed pipe that can be either laid flat or installed vertically into a borehole. These systems often require a greater number of boreholes, increasing cost; however, in the UK they do not require licensing and this can reduce costs. Sustainable development of ground source heat pump (GSHP) systems for both heating and cooling requires characterization of baseline groundwater temperatures. Knowledge of baseline conditions is important to support the design and regulation of GSHP. Baseline temperature data are required to assess the potential impacts of multiple ground source heating and cooling systems so as to avoid interactions between neighbouring systems (Fry 2009; Headon et al. 2009). It is anticipated that if negative interactions between ground source heating and cooling systems continue, some aquifers, mainly in densely populated cities, will need to be managed in terms of heat as well as groundwater resources (Banks et al. 2009). Regulators need legal, policy and scientific tools to support risk-based management of the subsurface, and one such tool is baseline temperature data and mapping of groundwater heat resources. The shallow gravel aquifer in Cardiff is a favourable geological setting in which to develop open-loop ground source heating systems. To support the sustainable development of this technology we have produced the first city-wide baseline map of groundwater temperatures and better defined the depth of the zone of seasonal fluctuation. The data and supporting map outputs will provide an independent source of information for system designers and installers, housing developers, space planners and regulators that is intended to help inform planning decisions and optimize design of GSHP schemes. Additionally, we describe observed seasonal groundwater temperature variation and define the base of the ‘zone of seasonal fluctuation’, which will allow developers to locate abstraction boreholes at depths unaffected by seasonal temperature changes. An initial estimate of available thermal energy that could be transferred from existing dewatering abstractions is made as an illustration of the city-wide potential

Shallow groundwater temperatures and the urban heat island effect: the first U.K. city-wide geothermal map to support development of ground source heating systems strategy

U.K. Government aims to reduce greenhouse gas emissions by 80% by 2050 (Climate Change Act, 2008). Ground source heating systems could contribute to the U.K.’s energy future but uptake has been slow due to a lack of case studies. The aim of this work was to produce the 1st U.K. city-wide heat map to support the development of ground source heating. We also sought to describe groundwater temperature variation with lithology & estimate the available thermal energy beneath the city

Surface-wave imaging of the weakly-extended Malawi Rift from ambient-noise and teleseismic Rayleigh waves from onshore and lake-bottom seismometers

Located at the southernmost sector of the Western Branch of the East African Rift System, the Malawi Rift exemplifies an active, magma-poor, weakly extended continental rift. To investigate the controls on rifting, we image crustal and uppermost mantle structure beneath the region using ambient-noise and teleseismic Rayleigh-wave phase velocities between 9 and 100 s period. Our study includes six lake-bottom seismometers located in Lake Malawi (Nyasa), the first time seismometers have been deployed in any of the African rift lakes. Noise-levels in the lake are lower than that of shallow oceanic environments and allow successful application of compliance corrections and instrument orientation determination. Resulting phase-velocity maps reveal slow velocities primarily confined to Lake Malawi at short periods (T 25 s) a prominent low-velocity anomaly exists beneath the Rungwe Volcanic Province at the northern terminus of the rift basin. Estimates of phase-velocity sensitivity indicates these low velocities occur within the lithospheric mantle and potentially uppermost asthenosphere, suggesting that mantle processes may control the association of volcanic centers and the localization of magmatism. Beneath the main portion of the Malawi Rift, a modest reduction in velocity is also observed at periods sensitive to the crust and upper mantle, but these velocities are much higher than those observed beneath Rungwe

GW190814: gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object

We report the observation of a compact binary coalescence involving a 22.2–24.3 Me black hole and a compact object with a mass of 2.50–2.67 Me (all measurements quoted at the 90% credible level). The gravitational-wave signal, GW190814, was observed during LIGO’s and Virgo’s third observing run on 2019 August 14 at 21:10:39 UTC and has a signal-to-noise ratio of 25 in the three-detector network. The source was localized to 18.5 deg2 at a distance of - + 241 45 41 Mpc; no electromagnetic counterpart has been confirmed to date. The source has the most unequal mass ratio yet measured with gravitational waves, - + 0.112 0.009 0.008, and its secondary component is either the lightest black hole or the heaviest neutron star ever discovered in a double compact-object system. The dimensionless spin of the primary black hole is tightly constrained to �0.07. Tests of general relativity reveal no measurable deviations from the theory, and its prediction of higher-multipole emission is confirmed at high confidence. We estimate a merger rate density of 1–23 Gpc−3 yr−1 for the new class of binary coalescence sources that GW190814 represents. Astrophysical models predict that binaries with mass ratios similar to this event can form through several channels, but are unlikely to have formed in globular clusters. However, the combination of mass ratio, component masses, and the inferred merger rate for this event challenges all current models of the formation and mass distribution of compact-object binaries