Analyzing urban water supply through an acceptability-index-based interval approach

Incorporation of uncertainties within an urban water supply management system has been a challenging topic for many years. In this study, an acceptability-index-based two-step interval programming (AITIP) model was developed for supporting urban water supply analysis under uncertainty. AITIP improved upon the traditional two-step interval programming (TIP) through incorporating the acceptability level of constraints violation into the optimization framework. A four-layer urban water supply system, including water sources, treatment facilities, reservoirs, and consuming zones, was used to demonstrate the applicability of proposed method. The results indicated that an AITIP model was valuable to help understand the effects of uncertainties related to cost, constraints and decision maker’s judgment in the water supply network, and capable of assisting urban water managers gain an in-depth insight into the tradeoffs between system cost and constraints-violation risk. Compared with TIP, the solutions from AITIP were of lower degree of uncertainty, making it more reliable to identify effective water supply patterns by adjusting decision variable values within their solution intervals. The study is useful in helping urban water managers to identify cost-effective management schemes in light of uncertainties in hydrology, environment, and decisions. The proposed optimization approach is expected to be applicable for a wide variety of water resources management problems.     

Predicting salt intrusion into freshwater aquifers resulting from CO2 injection – A study on the influence of conservative assumptions

Brine migration and saltwater intrusion into freshwater aquifers are among the hazards which may result from injecting CO₂ into deep saline formations. Comprehensive risk assessment should include estimates of the salinization of freshwater aquifers, preferably based on numerical simulation results. A crucial task is to choose an appropriate conceptual model and relevant scenarios. Overly conservative assumptions may lead to estimation of unacceptably high risks, and thus prevent the implementation of a CO₂ storage project unnecessarily. On the other hand, risk assessment should not lead to an underestimation of hazards. This study compares two conceptual model approaches for the numerical simulation of brine-migration scenarios through a vertical fault and salt intrusion into a fresh water aquifer. The first approach calculates salt discharge into freshwater using an immiscible two-phase model with constant salinity in the brine phase. The second approach takes compositional effects into account and considers salinity as a variable parameter in the water phase. A spatial model coupling is introduced to adapt the increased model complexity to the required complexity of the physics. The immiscible two-phase model is applied in the CO₂ storage reservoir and spatially coupled to a single-phase (water) two-component (water, salt) model, where salt mass fraction is a variable. A Dirichlet–Neumann technique is used for the coupling conditions at the interface of the two models. The results show that the predicted salt discharges can vary by orders of magnitude depending on the choice of the model. The implications of the results for risk assessment are discussed.     

A precipiton‐based approach to model hydro‐sedimentary hazards induced by large sediment supplies in alluvial fans

Mountain ranges are frequently subjected to mass wasting events triggered by storms or earthquakes and supply large volumes of sediment into river networks. Besides altering river dynamics, large sediment deliveries to alluvial fans are known to cause hydro‐sedimentary hazards such as flooding and river avulsion. Here we explore how the sediment supply history affects hydro‐sedimentary river and fan hazards, and how well can it be predicted given the uncertainties on boundary conditions. We use the 2D morphodynamic model Eros with a new 2D hydrodynamic model driven by a sequence of flood, a sediment entrainment/transport/deposition model and a bank erosion law. We first evaluate the model against a natural case: the 1999 Mount Adams rock avalanche and subsequent avulsion on the Poerua river fan (West Coast, New Zealand). By adjusting for the unknown sediment supply history, Eros predicts the evolution of the alluvial riverbed during the first post‐landslide stages within 30 cm. The model is subsequently used to infer how the sediment supply volume and rate control the fan aggradation patterns and associated hazards. Our results show that the total injected volume controls the overall levels of aggradation, but supply rates have a major control on the location of preferential deposition, avulsion and increased flooding risk. Fan re‐incision following exhaustion of the landslide‐derived sediment supply leads to sediment transfer and deposition downstream and poses similar, but delayed, hydro‐sedimentary hazards. Our results demonstrate that 2D morphodynamics models are able to capture the full range of hazards occurring in alluvial fans including river avulsion aggradation and floods. However, only ensemble simulations accounting for uncertainties in boundary conditions (e.g., discharge history, initial topography, grain size) as well as model realization (e.g., non‐linearities in hydro‐sedimentary processes) can be used to produce probabilistic hazards maps relevant for decision making. Copyright © 2017 John Wiley & Sons, Ltd.     

Risk assessment of agricultural irrigation water under interval functions

In recent years, water shortages and unreliable water supplies have been considered as major barriers to agricultural irrigation water management in China, which are threatening human health, impairing prospects for agriculture and jeopardizing survival of ecosystems. Therefore, effective and efficient risk assessment of agricultural irrigation water management is desired. In this study, an inexact full-infinite two-stage stochastic programming (IFTSP) method is developed. It incorporates the concepts of interval-parameter programming and full-infinite programming within a two-stage stochastic programming framework. IFTSP can explicitly address uncertainties presented as crisp intervals, probability distributions and functional intervals. The developed model is then applied to Zhangweinan river basin for demonstrating its applicability. Results from the case study indicate that compromise solutions have been obtained. They provide the desired agricultural irrigation water-supply schemes, which are related to a variety of tradeoffs between conflicting economic benefits and associated penalties attributed to the violation of predefined policies. The solutions can be used for generating decision alternatives and thus help decision makers to identify desired agricultural irrigation targets with maximized system benefit and minimized system-failure risk. Decision makers can adjust the existing agricultural irrigation patterns, and coordinate the conflict interactions among economic benefit, system efficiency, and agricultural irrigation under uncertainty.     

Climate threats,water supply vulnerability and the risk of a water crisis in the Monterrey Metropolitan Area (Northeastern Mexico)

This paper evaluates the risk of a water crisis – a substantial, sudden reduction in water supply – in the Monterrey Metropolitan Area (MMA), posed by climate threats and the vulnerability of its water supply system. Our analysis of long-term precipitation, water supply and water availability data reveals that the MMA is highly vulnerable to recurring periods of exceptionally low precipitation and scarce surface water availability. We identify two episodes in the recent past (1998 and 2013) when the MMA water supply system almost collapsed as reservoirs neared depletion in the face of abnormally dry weather. Furthermore our climate projections point to warmer and drier future conditions for the region and consequently, heightened climate threats. We conclude that the risk of a water crisis in the MMA is substantial and probably will increase due to climate change. This establishes a clear and pressing need for a comprehensive package of adaptation measures to mitigate the consequences of a water crisis should one occur as well as to reduce the likelihood of such an event.     

Water resources management under uncertainty: factorial multi-stage stochastic program with chance constraints

Due to rapid growth of population and development of economy, water resources allocation problems have aroused wide concern. Therefore, optimization of water resources systems is complex and uncertain, which is a severe challenge faced by water managers. In this paper, a factorial multi-stage stochastic programming with chance constraints approach is developed to deal with the issues of water-resources allocation under uncertainty and risk as well as their interactions. It can deal with uncertainties described as both interval numbers and probability distributions, and can also support the risk assessment within a multistage context. The solutions associated with different risk levels of constraint violation can be obtained, which can help characterize the relationship between the economic objective and the system risk. The inherent interactions between factors at different levels and their effects on total net benefits can be revealed through the analysis of multi-parameter interactions.     

Probabilistic-fuzzy health risk modeling

Health risk analysis of multi-pathway exposure to contaminated water involves the use of mechanistic models that include many uncertain and highly variable parameters. Currently, the uncertainties in these models are treated using statistical approaches. However, not all uncertainties in data or model parameters are due to randomness. Other sources of imprecision that may lead to uncertainty include scarce or incomplete data, measurement error, data obtained from expert judgment, or subjective interpretation of available information. These kinds of uncertainties and also the non-random uncertainty cannot be treated solely by statistical methods. In this paper we propose the use of fuzzy set theory together with probability theory to incorporate uncertainties into the health risk analysis. We identify this approach as probabilistic-fuzzy risk assessment (PFRA). Based on the form of available information, fuzzy set theory, probability theory, or a combination of both can be used to incorporate parameter uncertainty and variability into mechanistic risk assessment models. In this study, tap water concentration is used as the source of contamination in the human exposure model. Ingestion, inhalation and dermal contact are considered as multiple exposure pathways. The tap water concentration of the contaminant and cancer potency factors for ingestion, inhalation and dermal contact are treated as fuzzy variables while the remaining model parameters are treated using probability density functions. Combined utilization of fuzzy and random variables produces membership functions of risk to individuals at different fractiles of risk as well as probability distributions of risk for various alpha-cut levels of the membership function. The proposed method provides a robust approach in evaluating human health risk to exposure when there is both uncertainty and variability in model parameters. PFRA allows utilization of certain types of information which have not been used directly in existing risk assessment methods.     

A general Bayesian framework for calibrating and evaluating stochastic models of annual multi-site hydrological data

Multi-site simulation of hydrological data are required for drought risk assessment of large multi-reservoir water supply systems. In this paper, a general Bayesian framework is presented for the calibration and evaluation of multi-site hydrological data at annual timescales. Models included within this framework are the hidden Markov model (HMM) and the widely used lag-1 autoregressive (AR(1)) model. These models are extended by the inclusion of a Box–Cox transformation and a spatial correlation function in a multi-site setting. Parameter uncertainty is evaluated using Markov chain Monte Carlo techniques. Models are evaluated by their ability to reproduce a range of important extreme statistics and compared using Bayesian model selection techniques which evaluate model probabilities. The case study, using multi-site annual rainfall data situated within catchments which contribute to Sydney’s main water supply, provided the following results: Firstly, in terms of model probabilities and diagnostics, the inclusion of the Box–Cox transformation was preferred. Secondly the AR(1) and HMM performed similarly, while some other proposed AR(1)/HMM models with regionally pooled parameters had greater posterior probability than these two models. The practical significance of parameter and model uncertainty was illustrated using a case study involving drought security analysis for urban water supply. It was shown that ignoring parameter uncertainty resulted in a significant overestimate of reservoir yield and an underestimation of system vulnerability to severe drought.     

Hydrological modelling for assessing spatio-temporal groundwater recharge variations in the water-stressed Amathole Water Supply System,Eastern Cape,South Africa

To increase the resilience of regional water supply systems in South Africa in the face of anticipated climatic changes and a constant increase in water demand, water supply sources require diversification. Many water-stressed metropolitan regions in South Africa depend largely on surface water to cover their water demand. While climatic and river discharge data is widely available in these regions, information on groundwater resources – which could support supply source diversification – is scarce. Groundwater recharge is a key parameter that is used to estimate groundwater amounts that can be sustainably exploited at a sub-watershed level. Therefore, the objective of this study was to develop a reliable hydrological modelling routine that enables the assessment of regional spatio-temporal variations of groundwater recharge to discern the most promising areas for groundwater development. Accordingly, we present a semi-distributed hydrological modelling approach that incorporates water balance routines coupled with baseflow modelling techniques to yield spatio-temporal variations of groundwater recharge on a regional level. The approach is demonstrated for the actively managed catchment areas of the Amathole Water Supply System situated in a semi-arid part of the Eastern Cape of South Africa. In the investigated study area, annual groundwater recharge exhibits a high spatio-temporal heterogeneity and is estimated to vary between ~0.5% and 8% of annual rainfall. Despite some uncertainties induced by limited data availability, calibration and validation of the model were found to be satisfactory and yielded model results similar to (point) data of annual groundwater recharge reported in earlier studies. Our approach is therefore found to derive crucial information for efficiently targeting more detailed groundwater exploration studies and could work as a blueprint for orientating groundwater potential exploration in similar environments.     

Risk management of BTEX contamination in ground water--an integrated fuzzy approach

An integrated fuzzy simulation-assessment method (FSAM) was developed for assessing environmental risks from petroleum hydrocarbon contamination in ground water. In the FSAM, techniques of fuzzy simulation and fuzzy risk assessment were coupled into a general framework to reflect a variety of system uncertainties. A petroleum-contaminated site located in western Canada was selected as a study case for demonstrating applicability of the proposed method. The risk assessment results demonstrated that system uncertainties would significantly impact expressions of risk-level outputs. A relatively deterministic expression of the risks would have clearer representations of the study problem but may miss valuable uncertain information; conversely, an assessment under vaguer system conditions would help reveal potential consequences of adverse effects but would suffer from a higher degree of fuzziness in presenting the modeling outputs. Based on the risk assessment results, a decision analysis procedure was used to calculate a general risk index (GRI) to help identify proper responsive actions. The proposed method was useful for evaluating risks within a system containing multiple factors with complicated uncertainties and interactions and providing support for identifying proper site management strategies.     

Development of an inexact two-stage stochastic model with downside risk control for water quality management and decision analysis under uncertainty

Water quality management along rivers involves making water-allocation plans, establishing water quality goals, and controlling pollutant discharges, which is complicated itself but further challenged by existence of uncertainties. In this study, an inexact two-stage stochastic downside risk-aversion programming (ITSDP) model is developed for supporting regional water resources allocation and water quality management problems under uncertainties. The ITSDP method is a hybrid of interval-parameter programming, two-stage stochastic programming, and downside risk measure to tackle uncertainties described in terms of interval values and probability distributions. A water quality simulation model was provided for reflecting the relationship between the water resources allocation, wastewater discharge, and environmental responses. The proposed approach was applied to a hypothetical case for a shared stream water quality management with one municipal, three industrial and two agricultural sectors. A number of scenarios corresponding to different river inflows and risk levels were examined. The results demonstrated that the model could effectively communicate the interval-format and random uncertainties, and risk-aversion into optimization process, and generate a trade-off between the system economy and stability. They could be helpful for seeking cost-effective management strategies under uncertainties, and gaining an in-depth insight into the water quality management system characteristics, and make cost-effective decisions.     

Total consumption controlled water allocation management for multiple sources and users with inexact fuzzy chance-constrained programming: a case study of Tianjin,China

Environmental and ecological issues caused by water resources crisis have brought enormous challenges to the sustainable development of water-deficient area. Water resources allocation management balancing the relationship between the social-economic development and the ecological environment has become a hot topic in recent years. In this paper, an inexact fuzzy chance-constrained programming (IFCCP) approach is proposed for regional water resource allocation optimization with the aim of promoting the harmonious development of the social economic and the ecological environment, improving water utilization efficiency, and realizing water resources consumption control under uncertainties. The method is incorporated with interval parameter programming, fuzzy programming, and chance-constrained programming, for handling system uncertainties and balancing the optimal objectives with the risk of violating system constraints. Under this framework, an IFCCP model for water resources allocation management was successfully formulated and applied to a typical water-deficit area, Tianjin, China, for obtaining a better water resources plan among multiple users under resources and environmental limitation. Different total water consumption control policies are designed for assessing regional water allocation schemes. The results indicated that the gap of supply and demand will only be solved by foreign water, the transferred water from Luan River and Changjiang River would still be the main supplier in planning horizon. Moreover, the strict total water consumption control policy would guarantee the water requirement of ecological environment, lead to changes in the structure of water supply, actively guide on water conservation, and promote the large-scale utilization of desalted water and recycle water.     

Hydraulic modeling of flood pulses in the Middle Bussento Karst System (MBSKS), UNESCO Cilento Global Geopark,southern Italy

Karst systems provide water for domestic and industrial uses and for generating hydropower, but they can also create fluvial hazards, such as upstream back‐flooding and downstream karst flash‐flood events. However, these hazards are difficult to foresee due to the complex recharge‐discharge processes as well as the lack of information on the inside of the system, which has often not been completely surveyed by speleologists or explored by boreholes. To overcome these difficulties, hydro‐chemical data from the monitoring system in the Middle Bussento Karst System (MBSKS), one of the first Experimental Karst Systems in southern Italy, were recorded and previously discussed. Based on shared background in flood karst hydraulic modeling, this paper describes the conceptual premises and rationale of a general‐purpose hydraulic model that is suitable both for the MBSKS and for other Mediterranean, multi‐recharge, mature, conduit‐dominated karst systems. To test the reliability of the model, simulations of time–space behavior and response are performed using natural and artificial flood pulses “as tracers”, considering a “pulse” as a significant variation in water quantity and/or quality. The results of the model explain the interactions between allogenic, autogenic, and anthropogenic recharges from differentiated sources and phreatic conduit systems. These results also clarify the overall response of karst springs at typical time scales of flood pulses. Table acronym name     

An analysis of past and present megadrought impacts on a modern water resource system

Extended drought is a concern for water resource sustainability in the Colorado River Basin of the western USA. Recent instrumental data are a limited rendering of drought risk, while paleoclimate data provide evidence of megadrought that could reoccur; but their impact analyses have not been reported to date. A 645-year tree-ring reconstruction of central Arizona, USA, streamflows reveals several threatening periods including a severe 16th-century multi-decade event. This study translated that record to net basin water supply with comparison to instrumental records to drive an operations model of a key resource system serving metropolitan Phoenix, Arizona. Cumulative system impacts and demand sensitivities find no system depletion to inoperable conditions for any drought of the past several centuries. The megadrought presently afflicting the region has become more severe than any in the paleoclimate record and should be considered the new drought of record for adaptation planning.     

An inexact inventory-theory-based chance-constrained programming model for solid waste management

In this study, an inexact inventory-theory-based chance-constrained programming (IICP) model is proposed for planning waste management systems. The IICP model is derived through introducing inventory theory model into a general inexact chance-constrained programming framework. It can not only tackle uncertainties presented as both probability distributions and discrete intervals, but also reflect the influence of inventory problem in decision-making problems. The developed method is applied to a case study of long-term municipal solid waste (MSW) management planning. Solutions of total waste allocation, waste allocation batch and waste transferring period associated different risk levels of constraint violation are obtained. The results can be used to identify inventory-based MSW management planning with minimum system cost under various constraint-violation risks. Compared with the ICP model, the developed IICP model can more actually reflect the complexity of MSW management systems and provide more useful information for decision makers.     

Evaluating sources of uncertainty in Australian runoff projections

Generating estimates of the future impacts of climate change on human and natural systems is confounded by cascading uncertainties which propagate through the impact assessment. Here, a simple stochastic rainfall–runoff model representing 238 river basins on the Australian continent was used to assess the sensitivity of the risk of runoff changes to various sources of uncertainty. Uncertainties included global mean temperature change, greenhouse gas stabilisation targets, catchment sensitivities to climatic change, and the seasonality of runoff, rainfall, and evaporation. Model simulations provided estimates of the first-order risk of climate change to Australian catchments, with several regions having high likelihoods of experiencing significant reductions in future runoff. Climate uncertainty (at global and regional scales) was identified as the dominant driving force in hydrological risk assessments. Uncertainties in catchment sensitivities to climatic changes also influenced risk, provided they were sufficiently large, whereas structural assumptions of the model were generally negligible. Collectively, these results indicate that rigorous assessment of climate risk to water resources over relatively long time-scales is largely a function of adequately exploring the uncertainty space of future climate changes.     

Probabilistic permanent fault displacement hazard via Monte Carlo simulation and its consideration for the probabilistic risk assessment of buried continuous steel pipelines

Permanent fault displacements (PFDs) because of fault ruptures emerging at the surface are critical for seismic design and risk assessment of continuous pipelines. They impose significant compressive and tensile strains to the pipe cross‐section at pipe‐fault crossings. The complexity of fault rupture, inaccurate mapping of fault location and uncertainties in fault‐pipe crossing geometries require probabilistic approaches for assessing the PFD hazard and mitigating pipeline failure risk against PFD. However, the probabilistic approaches are currently waived in seismic design of pipelines. Bearing on these facts, this paper first assesses the probabilistic PFD hazard by using Monte Carlo‐based stochastic simulations whose theory and implementation are given in detail. The computed hazard is then used in the probabilistic risk assessment approach to calculate the failure probability of continuous pipelines under different PFD levels as well as pipe cross‐section properties. Our probabilistic pipeline risk computations consider uncertainties arising from complex fault rupture and geomorphology that result in inaccurate mapping of fault location and fault‐pipe crossings. The results presented in this paper suggest the re‐evaluation of design provisions in current pipeline design guidelines to reduce the seismic risk of these geographically distributed structural systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Risk analysis for water resources management under dual uncertainties through factorial analysis and fuzzy random value-at-risk

Water resources systems are associated with a variety of complexities and uncertainties due to socio-economic and hydro-environmental impacts. Such complexities and uncertainties lead to challenges in evaluating the water resources management alternatives and the associated risks. In this study, the factorial analysis and fuzzy random value-at-risk are incorporated into a two-stage stochastic programming framework, leading to a factorial-based two-stage programming with fuzzy random value-at-risk (FTSPF). The proposed FTSPF approach aims to reveal the impacts of uncertainty parameters on water resources management strategies and the corresponding risks. In detail, fuzzy random value-at-risk is to reflect the potential risk about financial cost under dual uncertainties, while a multi-level factorial design approach is used to reveal the interaction between feasibility degrees and risk levels, as well as the relationships (including curvilinear relationship) between these factors and the responses. The application of water resources system planning makes it possible to balance the satisfaction of system benefit, the risk levels of penalty and the feasibility degrees of constraints. The results indicate that decision makers would pay more attention to the tradeoffs between the system benefit and feasibility degree, and the water allocation for agricultural section contributes most to control the financial loss of water. Moreover, FTSPF can generate a higher system benefit and more alternatives under various risk levels. Therefore, FTSPF could provide more useful information for enabling water managers to identify desired policies with maximized system benefit under different system-feasibility degrees and risk levels.     

Model uncertainty analysis by variance decomposition

Errors and uncertainties in hydrological, hydraulic and environmental models are often substantial. In good modelling practice, they are quantified in order to supply decision-makers with important additional information on model limitations and sources of uncertainty. Several uncertainty analysis methods exist, often with various underlying assumptions. One of these methods is based on variance decomposition. The method allows splitting the variance of the total error in the model results (as estimated after comparing model results with observations) in its major contributing uncertainty sources. This paper discusses an advanced version of that method where error distributions for rainfall, other inputs and parameters are propagated in the model and the “rest” uncertainties considered as model structural errors for different parts of the model. By expert knowledge, the iid assumption that is often made in model error analysis is addressed upfront. The method also addresses the problems of heteroscedasticity and serial dependence of the errors involved. The method has been applied by the author to modelling applications of sewer water quantity and quality, river water quality and river flooding.