Finding the Kraus decomposition from a master equation and vice versa

For any master equation which is local in time, whether Markovian, non-Markovian, of Lindblad form or not, a general procedure is reviewed for constructing the corresponding linear map from the initial state to the state at time t, including its Kraus-type representations. Formally, this is equivalent to solving the master equation. For an N-dimensional Hilbert space it requires (i) solving a first order N^2 x N^2 matrix time evolution (to obtain the completely positive map), and (ii) diagonalising a related N^2 x N^2 matrix (to obtain a Kraus-type representation). Conversely, for a given time-dependent linear map, a necessary and sufficient condition is given for the existence of a corresponding master equation, where the (not necessarily unique) form of this equation is explicitly determined. It is shown that a `best possible' master equation may always be defined, for approximating the evolution in the case that no exact master equation exists. Examples involving qubits are given.Comment: 16 pages, no figures. Appeared in special issue for conference QEP-16, Manchester 4-7 Sep 200

Categorising virtual water transfers through China's electric power sector

Water consumption in thermoelectric and hydropower plants in China increased from 1.6 and 6.1 billion m3, respectively, to 3.8 and 14.6 billion m3 from 2002 to 2010. Using the concept of virtual water, we attribute to different electricity users the total water consumption by the electric power sector. From 2002 to 2010, virtual water embodied in the final consumption of electricity (hereinafter referred to as VWEF) increased from 1.90 to 7.35 billion m3, whilst virtual water in electricity used by industries (hereinafter referred to as VWEI) increased from 5.82 to 11.13 billion m3. The inter-provincial virtual water trades as a result of spatial mismatch of electricity production and consumption are quantified. Nearly half (47.5% in 2010) of the physical water inputs into the power sector were virtually transferred across provincial boundaries in the form of virtual water embodied in the electricity produced, mainly from provinces in northeast, central and south China to those in east and north China. Until 2030, VWEF and VWEI are likely to increase from 5.27 and 14.89 billion m3 to 7.19 and 20.33 billion m3, respectively. Climate change mitigation and water conservation measures in the power sector may help to relieve the regional pressures on water resources imposed by the power sector

Impacts of Droughts and Acidic Deposition on Long-Term Surface Water Dissolved Organic Carbon Concentrations in Upland Catchments in Wales

Concerns have been raised about rising trends in surface water dissolved organic carbon (DOC) concentrations in UK upland catchments over the past decades. Several mechanisms have been proposed to explain these trends, including changes in climate and declines in sulfate deposition across Europe. Drier summers and wetter winters are projected in the UK, and there is an increasing interest in whether the rising trends of DOC would be continued or stabilized. In this paper, the INCA (INtegrated CAtchment) water quality model was applied to the upland catchment of the River Severn at Plynlimon in Wales and used to simulate the effects of both climate and sulfate deposition on surface water DOC concentrations. We introduced new parameter sets of INCA to explain enzymatic latch effect in peatlands during droughts. The model was able to simulate recent past (1995-2013) rising trends in DOC in Plynlimon. Climatic projections were employed to estimate the future trends on DOC in the uplands and to consider potential impacts on catchment management. The model was run with climatic scenarios generated using the weather@home2 climate modeling platform and with sulfate deposition scenarios from the European Monitoring and Evaluation Programme (EMEP) for 1975-2100. The modeling results show that the rising DOC trends are likely to continue in the near future (2020-2049) and the level of DOC concentrations is projected to stabilize in the far future (2070-2099). However, in the far future, the seasonal patterns of DOC concentrations will change, with a post-drought DOC surge in autumn months

Assessment of risks to public water supply from low flows and harmful water quality in a changing climate

Water resources planning and management by water utilities have traditionally been based on consideration of water availability. However, the reliability of public water supplies can also be influenced by the quality of water bodies. In this study, we proposed a framework that integrates the analysis of risks of inadequate water quality and risks of insufficient water availability. We have developed a coupled modeling system that combines hydrological modeling of river water quantity and quality, rules for water withdrawals from rivers into storage reservoirs, and dynamical simulation of harmful algal blooms in storage reservoirs. We use this framework to assess the impact of climate change, demand growth, and land‐use change on the reliability of public water supplies. The proposed method is tested on the River Thames catchment in the south of England. The results show that alongside the well‐known risks of rising water demand in the south of England and uncertain impacts of climate change, diffuse pollution from agriculture and effluent from upstream waste water treatment works potentially represent a threat to the reliability of public water supplies in London. We quantify the steps that could be taken to ameliorate these threats, though even a vigorous pollution‐prevention strategy would not be sufficient to offset the projected effects of climate change on water quality and the reliability of public water supplies. The proposed method can help water utilities to recognize their system vulnerability and evaluate the potential solutions to achieve more reliable water supplies. supplie

Development and appraisal of long-term adaptation pathways for managing heat-risk in London

The risk of residential overheating and mortality is increasing due to the effects of global warming and the urban heat island effect and needs to be addressed through climate change adaptation. ‘Adaptation pathways’ have become widely recognised as an adaptation planning approach, but they have not been utilised for long-term planning for city-scale urban heat risk management. This paper applies adaptation pathway methodology to urban heat risk management. We use spatially coherent downscaled probabilistic climate change projections that account for changes in urban-land cover and the urban heat island to appraise adaptation pathways and inform long-term adaptation planning. We demonstrate that adaptation strategies focusing solely on urban greening or building level adaptation based on current best practice are unlikely to cope with the increasing levels of risk. Air-conditioning may play a growing role in managing heat-risk; however, increasing air-conditioning will exacerbate the urban heat island and further increase the risks of overheating

The myriad challenges of the Paris Agreement

The much awaited and intensely negotiated Paris Agreement was adopted on 12 December 2015 by the Parties to the United Nations Framework Convention on Climate Change. The agreement set out a more ambitious long-term temperature goal than many had anticipated, implying more stringent emissions reductions that have been under-explored by the research community. By its very nature a multidisciplinary challenge, filling the knowledge gap requires not only climate scientists, but the whole Earth system science community, as well as economists, engineers, lawyers, philosophers, politicians, emergency planners and others to step up. To kick start cross-disciplinary discussions, the University of Oxford's Environmental Change Institute focused its 25th anniversary conference upon meeting the challenges of the Paris Agreement for science and society. This theme issue consists of review papers, opinion pieces and original research from some of the presentations within that meeting, covering a wide range of issues underpinning the Paris Agreement

Have coastal embankments reduced flooding in Bangladesh?

From the 1960s, embankments have been constructed in south western coastal region of Bangladesh to provide protection against flooding, but the success of the polder programme is disputed. We present analysis of floods during the years 1988–2012, diagnosing whether the floods were attributable to monsoonal precipitation (pluvial flooding), high upstream river discharge into the tidal delta (fluvio-tidal flooding), or cyclone-induced storm surges. We find that pluvial flooding was the most frequent, but typically resulted in less flooded area (11.44% of the region on average)compared with the other forms of flooding. The greatest area of inundation (48% of total area)occurring in 2001 as a consequence of fluvio-tidal and surge flooding, whilst cyclone Sidr in 2007 flooded 35% of the area. We modelled these different forms of inundation to estimate what flooding might have been had the polders not been constructed. For the ‘no embankment’ counter-factual scenario, our model demonstrated that because of a combination of subsidence and inadequate drainage, construction of the polders has increased the pluvial flooded area by 6.5% on average (334 km2). However, during the 1998 fluvio-tidal flood, the embankments protected an estimated 54% of the area from flooding. During the cyclone Sidr storm surge event, embankment failure in several polders and pluvial inundation resulted in 35% area inundation, otherwise, the total inundation would have been 18% area. We conclude that whilst polders have provided protection against storm surges and fluvio-tidal events of moderate severity, they have exacerbated more frequent pluvial flooding and promoted potential flooding impacts during the most extreme storm surges

Tackling the Trickle: Ensuring Sustainable Water Management in the Arab Region

Abstract Water scarcity in the Arab region is intensifying due to population growth, economic development, and the impacts of climate change. It is manifested in groundwater depletion, freshwater ecosystem degradation, deteriorating water quality, low levels of water storage per capita, and added pressures on transboundary water resources. High‐income Arab countries have sought to circumvent the ever‐present challenges of water scarcity through agricultural imports (virtual water trade), desalination, and, increasingly, wastewater reuse. In this review article, we argue that the narrative of water scarcity and supply‐side technological fixes masks more systemic issues that threaten sustainable water management, including underperforming water utilities, protracted armed conflict and displacement, agricultural policies aimed at self‐sufficiency, evolving food consumption behaviors, the future of energy markets, and educational policy. Water management challenges, particularly on the demand side, and responses in the Arab region cannot be understood in isolation from these broader regional and international political and socioeconomic trends. Recognizing the complex and interdependent challenges of water management is the first step in reforming approaches and shifting to more sustainable development outcomes and stability in the Arab region and beyond

Strategic analysis of the drought resilience of water supply systems

Severe droughts can result in shortages of water supplies, with widespread social and economic consequences. Here we use a coupled simulation model to assess the reliability of public water supplies in England, in the context of changing scenarios of water demand, water regulation and climate change. The coupled simulation model combines climate simulations, a national-scale hydrological model and a national-scale water resource systems model to demonstrate how extreme meteorological droughts translate into hydrological droughts and water shortages for water users. We use this model to explore the effectiveness of strategic water resource options that are being planned in England to secure water supplies to most of England's population up to a drought return period of 1 in 500 years. We conclude that it is possible to achieve a 1-in-500-years standard in locations where strategic resource options are used, while also reducing water abstraction to restore the aquatic environment. However, the target will be easier to achieve if effective steps are also taken to reduce water demand. This article is part of the Royal Society Science+ meeting issue ‘Drought risk in the Anthropocene’

Multi-scale assessment of the economic impacts of flooding: evidence from firm to macro-level analysis in the Chinese manufacturing sector

We present an empirical study to systemically estimate flooding impacts, linking across scales from individual firms through to the macro levels in China. To this end, we combine a detailed firm-level econometric analysis of 399,356 firms with a macroeconomic input-output model to estimate flood impacts on China's manufacturing sector over the period 2003-2010. We find that large flooding events on average reduce firm outputs (measured by labor productivity) by about 28.3% per year. Using an input-output analysis, we estimate the potential macroeconomic impact to be a 12.3% annual loss in total output, which amounts to 15,416 RMB billion. Impacts can propagate from manufacturing firms, which are the focus of our empirical analysis, through to other economic sectors that may not actually be located in floodplains but can still be affected by economic disruptions. Lagged flood effects over the following two years are estimated to be a further 5.4% at the firm level and their associated potential effects are at a 2.3% loss in total output or 2,486 RMB billion at the macro-level. These results indicate that the scale of economic impacts from flooding is much larger than microanalyses of direct damage indicate, thus justifying greater action, at a policy level and by individual firms, to manage flood risk