Inexact stochastic dynamic programming method and application to water resources management in Shandong China under uncertainty

In this study, an interval parameter multistage joint-probability programming (IMJP) approach has been developed to deal with water resources allocation under uncertainty. The IMJP can be used not only to deal with uncertainties in terms of joint-probability and intervals, but also to examine the risk of violating joint probabilistic constraints in the context of multistage. The proposed model can handle the economic expenditure caused by regional water shortage and flood control. The model can also reflect the related dynamic changes in the multi-stage cases and the system safety under uncertainty. The developed method is applied to a case study of water resources allocation in Shandong, China, under multistage, multi-reservoir and multi-industry. The violating reservoir constraints are addressed in terms of joint-probability. Different risk levels of constraint lead to different planning. The obtained results can help water resources managers to identify desired system designs under various economic, environment and system reliability scenarios.     

Mapping of regional potential groundwater springs using Logistic Regression statistical method

Increasing demand for fresh water extraction in the semi-arid regions necessitates the exploration of groundwater spring potential areas notwithstanding the importance of both conservation and management aspects for planning development. Potential map of groundwater springs reduces the costs of horizontal well drilling that provides useful tool for engineers to locate probable region for groundwater existence. The objective of this study is to establish a model of the potential map of groundwater spring occurrences. A statistical and probabilistic Logistic Regression (LR) model was developed in association with the specified spring location and effective occurrence factors. The most statistically significant effective factors on spring occurrences were selected to zone groundwater spring potential areas. The proposed model was evaluated statistically. Results showed a satisfactory prediction for the proposed model. The outcome of this study facilitates the low-cost utilization of groundwater resources when policy makers need strategic development planning.     

Planning water resources management systems using a fuzzy-boundary interval-stochastic programming method

In this study, a fuzzy-boundary interval-stochastic programming (FBISP) method is developed for planning water resources management systems under uncertainty. The developed FBISP method can deal with uncertainties expressed as probability distributions and fuzzy-boundary intervals. With the aid of an interactive algorithm woven with a vertex analysis, solutions for FBISP model under associated α-cut levels can be generated by solving a set of deterministic submodels. The related probability and possibility information can also be reflected in the solutions for the objective function value and decision variables. The developed FBISP is also applied to water resources management and planning within a multi-reservoir system. Various policy scenarios that are associated with different levels of economic consequences when the pre-regulated water-allocation targets are violated are analyzed. The results obtained are useful for generating a range of decision alternatives under various system conditions, and thus helping decision makers to identify desired water resources management policies under uncertainty.     

Probabilistic evaluation of flood hazard in urban areas using Monte Carlo simulation

The goal of the presented research was the derivation of flood hazard maps, using Monte Carlo simulation of flood propagation at an urban site in the UK, specifically an urban area of the city of Glasgow. A hydrodynamic model describing the propagation of flood waves, based on the De Saint Venant equations in two‐dimensional form capable of accounting for the topographic complexity of the area (preferential outflow paths, buildings, manholes, etc.) and for the characteristics of prevailing imperviousness typical of the urban areas, has been used to derive the hydrodynamic characteristics of flood events (i.e. water depths and flow velocities). The knowledge of the water depth distribution and of the current velocities derived from the propagation model along with the knowledge of the topographic characteristics of the urban area from digital map data allowed for the production of hazard maps based on properly defined hazard indexes. These indexes are evaluated in a probabilistic framework to overcome the classical problem of single deterministic prediction of flood extent for the design event and to introduce the concept of the likelihood of flooding at a given point as the sum of data uncertainty, model structural error and parameterization uncertainty. Copyright © 2011 John Wiley & Sons, Ltd.     

Managing water resources system in a mixed inexact environment using superiority and inferiority measures

A superiority–inferiority-based fuzzy-stochastic integer programming (SI-FSIP) method is developed for water resources management under uncertainty. In the SI-FSIP method, techniques of fuzzy mathematical programming with the superiority and inferiority measures and joint chance-constrained programming are integrated into an inexact mixed integer linear programming framework. The SI-FSIP improves upon conventional inexact fuzzy programming by directly reflecting the relationships among fuzzy coefficients in both the objective function and constraints with a high computational efficiency, and by comprehensively examining the risk of violating joint probabilistic constraints. The developed method is applied to a case study of water resources planning and flood control within a multi-stream and multi-reservoir context, where several studied cases (including policy scenarios) associated with different joint and individual probabilities are investigated. Reasonable solutions including binary and continuous decision variables are generated for identifying optimal strategies for water allocation, flood diversion and capacity expansion; the tradeoffs between total benefit and system-disruption risk are also analyzed. As the first attempt for planning such a water-resources system through the SI-FSIP method, it has potential to be applied to many other environmental management problems.     

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.     

河西重点监视区烈度预测的研究

在前人研究的基础上，建立了适合于重点监视区烈度预测的概率方法的数学模型，并对该模型中影响预测结果的因素进行了灵敏度分析。发现预测的不确定性主要来自烈度衰减规律。根据概率分析中对正态分布函数不确定性校正的原理，提出了适于重点监视区内烈度预测中不确定性的校正方法，并将该方法应用于河西重点监视区。在确定震级－频度关系的过程中，考虑了地震活动性周期及震级间隔两方面的因素，使得求出的震级－频度关系更为精确     

A scenario-based water conservation planning support system (SB-WCPSS)

In this study a water consumption model is built into a scenario-based planning support system (SB-WCPSS). The SB-WCPSS consists of four components—(1) a model input graphic user interface, (2) a community spatial database, (3) a set of drinking water consumption models, and (4) output display. The SB-WCPSS is implemented with a commercial planning support system software package—CommunityViz. The model is applied using data in Cincinnati, Ohio, USA to demonstrate the scenario development. In the application, water consumption consists of land use based indoor, turf, and pool water usages. Climate change is reflected in monthly temperature and precipitation. By specifying anticipated future land uses and associated water consumption rates, temperature, and precipitation, SB-WCPSS users can analyze and compare water consumptions under various scenarios, using maps, graphs, and tables. Parcel-based daily water consumptions were computed and summarized spatially by neighborhood, block group, or land use type. The results demonstrate that water conservation strategies, such as xeriscape, can reduce turf water usage. Indoor water consumption depends on the number of people who use water and how they use water. The study shows that the SB-WCPSS structure is sound and user friendly. Future improvement will be on enhancing various components, such as using parcel-based data and more robust water consumption models. The system may be used by water resource managers and decision makers to adapt water resources (e.g., watersheds and infrastructure) to climate change and demographic and economic development.     

Preliminary Study on Probabilistic Prediction of Seismic Hazard in a Period of 10 Years

Many uncertainty factors need be dealt with in the prediction of seismic hazard for a 10-year period.Restricted by these uncertainties,the result of prediction is also uncertain to a certain extent,so the probabilistic analysis method of seismic hazard should be adopted.In consideration of the inhomogeneity of the time,location,and magnitude of future earthquakes and the probabilistic combination of the background of long-term seismic hazard(geology,geophysical field,etc.)and the precursors of earthquake occurrence,a model of probabilistic prediction of seismic hazard in a period of 10 years s proposed.Considering the inhomogeneity of data and earthquake precursors for different regions in China,a simplified model is also proposed in order to satisfy the needs of different regions around the country.A trial in North China is used to discuss the application of the model.The method proposed in this paper can be used in the probabilistic prediction of seismic hazard in a period of 10 years.According to the     

十年尺度地震危险性概率预测方法的初步研究

在十年尺度（５—１０年）地震危险性预测中，需要处理众多的不确定因素。受这些不确定因素的约束，地震预测的结果必然带有相当的不确定性，因此应该用概率分析的方法进行预测。考虑地震发生的时间、空间和强度的非均匀性及相关特征和地震危险性长期背景（地质、地球物理场等因素）与地震发生前兆的概率结合，提出了十年尺度地震危险性预测的概率模型。考虑资料的不均匀性和适宜不同地区的地震前兆方法的差异，本文还提出了概率预测模型简化形式，以满足全国不同地区的需要。本文以华北北部地区为例讨论了该模型的实际应用。文中提出的方法可以用于全国十年尺度地震危险性的概率预测。根据本项研究提供的结果和计算程序，可以满足地震对策和地震损失估计对地震中长期概率预测的需要。     

ITOM: an interval-parameter two-stage optimization model for stochastic planning of water resources systems

Planning of water resources systems is often associated with many uncertain parameters and their interrelationships are complicated. Stochastic planning of water resources systems is vital under changing climate and increasing water scarcity. This study proposes an interval-parameter two-stage optimization model (ITOM) for water resources planning in an agricultural system under uncertainty. Compared with other optimization techniques, the proposed modeling approach offers two advantages: first, it provides a linkage to pre-defined water policies, and; second, it reflects uncertainties expressed as probability distributions and discrete intervals. The ITOM is applied to a case study of irrigation planning. Reasonable solutions are obtained, and a variety of decision alternatives are generated under different combinations of water shortages. It provides desired water-allocation patterns with respect to maximum system benefits and highest feasibility. Moreover, the modeling results indicate that an optimistic water policy corresponding to higher agricultural income may be subject to a higher risk of system-failure penalties; while, a too conservative policy may lead to wastage of irrigation supplies.     

Development of probability distributions for urban hydrologic model parameters and a Monte Carlo analysis of model sensitivity

This paper proposes an approach to estimating the uncertainty related to EPA Storm Water Management Model model parameters, percentage routed (P_R) and saturated hydraulic conductivity (K_sat), which are used to calculate stormwater runoff volumes. The methodology proposed in this paper addresses uncertainty through the development of probability distributions for urban hydrologic parameters through extensive calibration to observed flow data in the Philadelphia collection system. The established probability distributions are then applied to the Philadelphia Southeast district model through a Monte Carlo approach to estimate the uncertainty in prediction of combined sewer overflow volumes as related to hydrologic model parameter estimation. Understanding urban hydrology is critical to defining urban water resource problems. A variety of land use types within Philadelphia coupled with a history of cut and fill have resulted in a patchwork of urban fill and native soils. The complexity of urban hydrology can make model parameter estimation and defining model uncertainty a difficult task. The development of probability distributions for hydrologic parameters applied through Monte Carlo simulations provided a significant improvement in estimating model uncertainty over traditional model sensitivity analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

The Effect of Groundwater Allocation on Economic Welfare Loss

Water scarcity has become a constraint for regional economic development in many cities and regions. Water rationing serves as one instrument to constrain water consumption to persuade users to save water and to moderate their consumption. When the supply of water is unable to satisfy demand, a loss of welfare for the water users will usually occur. This paper conducts an empirical case study on a Chicago suburban county, McHenry County, to evaluate effective water allocation strategies under possible water scarcity scenarios, by specifically taking into consideration of the economic welfare loss under water rationing. It points out the inefficiency of equal rationing and tests a more effective optimal rationing regime which could significantly lower the overall welfare loss for McHenry County. Instead of a conventional watershed‐based approach that would provide little advantage for an area that mostly relies on groundwater, this study adopts regional planning/political boundaries as its spatial analytical units. The outcomes suggest that municipality‐level water resources management models, powered under economic welfare objective functions, are both possible and practical. The planning strategy drawn under such optimization models suggests a variety of promising approaches to manage groundwater resources at county scales.     

Numerical modelling of stream–aquifer interaction: Quantifying the impact of transient streambed permeability and aquifer heterogeneity

Stream–aquifer interaction plays a vital role in the water cycle, and a proper study of this interaction is needed for understanding groundwater recharge, contaminants migration, and for managing surface water and groundwater resources. A model‐based investigation of a field experiment in a riparian zone of the Schwarzbach river, a tributary of the Rhine River in Germany, was conducted to understand stream–aquifer interaction under alternative gaining and losing streamflow conditions. An equivalent streambed permeability, estimated by inverting aquifer responses to flood waves, shows that streambed permeability increased during infiltration of stream water to aquifer and decreased during exfiltration. Aquifer permeability realizations generated by multiple‐point geostatistics exhibit a high degree of heterogeneity and anisotropy. A coupled surface water groundwater flow model was developed incorporating the time‐varying streambed permeability and heterogeneous aquifer permeability realizations. The model was able to reproduce varying pressure heads at two observation wells near the stream over a period of 55 days. A Monte Carlo analysis was also carried out to simulate groundwater flow, its age distribution, and the release of a hypothetical wastewater plume into the aquifer from the stream. Results of this uncertainty analysis suggest (a) stream–aquifer exchange flux during the infiltration periods was constrained by aquifer permeability; (b) during exfiltration, this flux was constrained by the reduced streambed permeability; (c) the effect of temporally variable streambed permeability and aquifer heterogeneity were found important to improve the accurate capture of the uncertainty; and (d) probabilistic infiltration paths in the aquifer reveal that such pathways and the associated prediction of the extent of the contaminant plume are highly dependent on aquifer heterogeneity.     

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.     

Probabilistic and ensemble simulation approaches for input uncertainty quantification of artificial neural network hydrological models

Artificial neural network (ANN) has been demonstrated to be a promising modelling tool for the improved prediction/forecasting of hydrological variables. However, the quantification of uncertainty in ANN is a major issue, as high uncertainty would hinder the reliable application of these models. While several sources have been ascribed, the quantification of input uncertainty in ANN has received little attention. The reason is that each measured input quantity is likely to vary uniquely, which prevents quantification of a reliable prediction uncertainty. In this paper, an optimization method, which integrates probabilistic and ensemble simulation approaches, is proposed for the quantification of input uncertainty of ANN models. The proposed approach is demonstrated through rainfall-runoff modelling for the Leaf River watershed, USA. The results suggest that ignoring explicit quantification of input uncertainty leads to under/over estimation of model prediction uncertainty. It also facilitates identification of appropriate model parameters for better characterizing the hydrological processes.     

A multistage simulation-based optimization model for water resources management in Tarim River Basin, China

In this study, a multistage simulation-based optimization model is developed for supporting water resources management under uncertainty. The system couples a lumped rainfall-runoff model with an inexact multistage stochastic program, where its random parameter is provided by the statistical analysis of simulation outcomes. Moreover, penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. The developed model can also reflect dynamic features of the system conditions through transactions at discrete points in time over a multistage context. The developed model is applied to a real case of planning water resources management in Tarim River Basin, which is one of the most serious water-shortage regions of China. A variety of policies associated with different water-allocation targets are analyzed. The results are helpful for decision makers identifying optimal water-allocation plans for mitigating the conflict among ecological protection, economic development, and regional sustainability.     

SWAT model application and prediction uncertainty analysis in the Lake Tana Basin,Ethiopia

Lake Tana Basin is of significant importance to Ethiopia concerning water resources aspects and the ecological balance of the area. Many years of mismanagement, wetland losses due to urban encroachment and population growth, and droughts are causing its rapid deterioration. The main objective of this study was to assess the performance and applicability of the soil water assessment tool (SWAT) model for prediction of streamflow in the Lake Tana Basin, so that the influence of topography, land use, soil and climatic condition on the hydrology of Lake Tana Basin can be well examined. The physically based SWAT model was calibrated and validated for four tributaries of Lake Tana. Sequential uncertainty fitting (SUFI‐2), parameter solution (ParaSol) and generalized likelihood uncertainty estimation (GLUE) calibration and uncertainty analysis methods were compared and used for the set‐up of the SWAT model. The model evaluation statistics for streamflows prediction shows that there is a good agreement between the measured and simulated flows that was verified by coefficients of determination and Nash Sutcliffe efficiency greater than 0·5. The hydrological water balance analysis of the basin indicated that baseflow is an important component of the total discharge within the study area that contributes more than the surface runoff. More than 60% of losses in the watershed are through evapotranspiration. Copyright © 2009 John Wiley & Sons, Ltd.     

Anticipating the effects of groundwater withdrawal on seawater intrusion and soil settlement in urban coastal areas

Intensive pumping in urban coastal areas is a common threat to water resource quality due to seawater intrusion. In those areas where subsurface water resources are not usually used for human consumption or irrigation, intensive pumping is associated with other activities like the lowering of the water table necessary to support underground structures and building foundations. This activity also increases the likelihood of soil settlement that affects building stability and the corrosion of concrete structures due to groundwater salinity. Under these circumstances, the awareness of a certain municipality (Calonge, NE Spain) of the potential effects of groundwater withdrawal upon foundations has led to an integrated approach to anticipate seawater intrusion related to urban development. Geological mapping and correlation of borehole logs, electrical resistivity tomography, and hydrochemical data provide comprehensive knowledge of the geology and hydrogeology of the area and act as screening tools necessary to discern the influence of hydrological processes in coastal areas. Developing Strack's analytical solution, new comprehensive, dimensionless expressions are herein derived to determine the critical pumping rate necessary to prevent seawater intrusion, as well as to reproduce the evolution of the wedge toe and the water table stagnation point under different withdrawal rates. Furthermore, the Dupuit–Forchheimer well discharge formula allows the estimation of the effects of the water table lowering due to such critical pumping in the surrounding building foundations. Field data from the Calonge coastal plain illustrate this approach and provide assessment criteria for future urban development and planning. Copyright © 2012 John Wiley & Sons, Ltd.     

Hydrological uncertainty processor based on a copula function

Quantifying the uncertainty in hydrological forecasting is valuable for water resources management and decision-making processes. The hydrological uncertainty processor (HUP) can quantify hydrological uncertainty and produce probabilistic forecasts under the hypothesis that there is no input uncertainty. This study proposes a HUP based on a copula function, in which the prior density and likelihood function are explicitly expressed, and the posterior density and distribution obtained using Monte Carlo sampling. The copula-based HUP was applied to the Three Gorges Reservoir, and compared with the meta-Gaussian HUP. The Nash-Sutcliffe efficiency and relative error were used as evaluation criteria for deterministic forecasts, while predictive QQ plot, reliability, resolution and continuous rank probability score (CRPS) were used for probabilistic forecasts. The results show that the proposed copula-based HUP is comparable to the meta-Gaussian HUP in terms of the posterior median forecasts, and that its probabilistic forecasts have slightly higher reliability and lower resolution compared to the meta-Gaussian HUP. Based on the CRPS, both HUPs were found superior to deterministic forecasts, highlighting the effectiveness of probabilistic forecasts, with the copula-based HUP marginally better than the meta-Gaussian HUP.