An inexact fuzzy-random-chance-constrained air quality management model

An inexact fuzzy-random-chance-constrained programming model (IFRCCMM) was developed for supporting regional air quality management under uncertainty. IFRCCMM was formulated through integrating interval linear programming within fuzzy-random-chance-constrained programming framework. It could deal with parameter uncertainties expressed as not only fuzzy random variables but also discrete intervals. Based on the stochastic and fuzzy chance-constrained programming algorithms, IFRCCMM was solved when constraints was satisfied under different satisfaction and violation levels of constraints, leading to interval solutions with different risk and cost implications. The proposed model was applied to a regional air quality management problem for demonstration. The obtained results indicated that the proposed model could effectively reflect uncertain components within air quality management system through employing multiple uncertainty-characterization techniques (in random, fuzzy and interval forms), and help decision makers analyze trade-offs between system economy and reliability. In fact, many types of solutions (i.e. conservative solutions with lower risks and optimistic solutions with higher risks) provided by IFRCCMM were suitable for local decision makers to make more applicable decision schemes according to their understanding and preference about the risk and economy. In addition, the modeling philosophy is general and applicable to many other environmental problems that may be complicated with multiple forms of uncertainties.     

Risk aversion based interval stochastic programming approach for agricultural water management under uncertainty

In this study, a risk aversion based interval stochastic programming (RAIS) method is proposed through integrating interval multistage stochastic programming and conditional value at risk (CVaR) measure for tackling uncertainties expressed as probability distributions and intervals within a multistage context. The RAIS method can reflect dynamic features of the system conditions through transactions at discrete points in time over the planning horizon. Using the CVaR measure, RAIS can effectively reflect system risk resulted from random parameters. When random events are occurred, the adjustable alternatives can be achieved by setting desired targets according to the CVaR, which could make the revised decisions to minimize the economic penalties. Then, the RAIS method is applied to planning agricultural water management in the Zhangweinan River Basin that is plagued by drought due to serious water scarcity. A set of decision alternatives with different combinations of risk levels employed to the objective function and constraints are generated for planning water resources allocation. The results can not only help decision makers examine potential interactions between risks under uncertainty, but also help generate desired policies for agricultural water management with a maximized payoff and a minimized loss.     

A theory of efficiency of storage-treatment systems

A simple expression is presented on the capability of storage-treatment systems to reduce non-point pollutant runoff load to natural waters. Their efficiency depends on the capacities of the facilities and probabilistic properties of runoff, such as interval, duration, volume, and concentration of runoff events. Assuming the compound Poisson process for runoff time series, the exact expressions of the ratio of treated load in terms of storage and treatment capacities are theoretically derived on the neighbourhoods of all boundaries of the domain on which the problem is defined. Then, an approximate expression over the whole domain is presented, of which the value and the first-order derivative coincide with those of the exact derived expressions near the boundaries. Accuracy is checked by Monte Carlo simulations.     

Water quality management in a wetland system using an inexact left-hand-side chance-constrained fuzzy multi-objective approach

Water quality management is a significant item in the sustainable development of wetland system, since the environmental influences from the economic development are becoming more and more obvious. In this study, an inexact left-hand-side chance-constrained fuzzy multi-objective programming (ILCFMOP) approach was proposed and applied to water quality management in a wetland system to analyze the tradeoffs among multiple objectives of total net benefit, water quality, water resource utilization and water treatment cost. The ILCFMOP integrates interval programming, left-hand-side chance-constrained programming, and fuzzy multi-objective programming within an optimization framework. It can both handle multiple objectives and quantify multiple uncertainties, including fuzziness (aspiration level of objectives), randomness (pollutant release limitation), and interval parameters (e.g. water resources, and wastewater treatment costs). A representative water pollution control case study in a wetland system is employed for demonstration. The optimal schemes were analyzed under scenarios at different probabilities (p _i , denotes the admissible probability of violating the constraint i). The optimal solutions indicated that, most of the objectives would decrease with increasing probability levels from scenarios 1 to 3, since a higher constraint satisfaction probability would lead to stricter decision scopes. This study is the first application of the ILCFMOP model to water quality management in a wetland system, which indicates that it is applicable to other environmental problems under uncertainties.     

Resources and environmental systems management under synchronic interval uncertainties

Resources and environmental systems management (RESM) is challenged by the synchronic effects of interval uncertainties in the related practices. The synchronic interval uncertainties are misrepresented as random variables, fuzzy sets, or interval numbers in conventional RESM programming techniques including stochastic programming. This may lead to ineffectiveness of resources allocation, high costs of recourse measures, increased risks of unreasonable decisions, and decreased optimality of system profits. To fill the gap of few corresponding studies, a synchronic interval linear programming (SILP) method is proposed in this study. The proposition of interval sets and interval functions and coupling them with linear programming models lead to development of an SILP model for RESM. This enables incorporation of interval uncertainties in resource constraints and synchronic interval uncertainties in the programming objective into the optimization process. An analysis of the distribution-independent geometric properties of the feasible regions of SILP models results in proposition of constraint violation likelihoods. The tradeoff between system optimality and constraint violation is analyzed. The overall optimality of SILP systems under synchronic intervalness is quantified through proposition of integrally optimal solutions. Integration of these efforts leads to a violation-constrained interval integral method for optimization of RESM systems under synchronic interval uncertainties. Comparisons with selected existing methods reveal the effectiveness of SILP at eliminating negativity of synchronic intervalness, enabling risk management of and achieving overall optimality of RESM systems, and enhancing the reliability of optimization techniques for RESM problems. The exploited framework for analyzing synchronic interval uncertainties in RESM systems is helpful for addressing synchronisms of other uncertainties such as randomness or fuzziness and avoiding the resultant decision mistakes and disasters due to neglecting them.     

Characterization of the seismogenic process in the Aleutian island arc: I. Source relations of the large earthquakes of 1957, 1986, and 1996 in the Andreanof Islands

An interpretation of the type, size, and interrelations of sources is proposed for the three large Aleutian earthquakes of March 9, 1957, May 7, 1986, and June 10, 1996, which occurred in structures of the Andreanof Islands. According to our interpretation, the earthquakes were caused by steep reverse faults confined to different structural units of the southern slope of the Andreanof Islands and oriented along the strike of these structures. An E-W reverse fault that generated the largest earthquake of 1957 is located within the Aleutian Terrace and genetically appears to be associated with the development of the submarine Hawley Ridge. The western and eastern boundaries of this source are structurally well expressed by the Adak Canyon in the west (～177°W) and an abrupt change in isobaths in the east (～173°W). The character of the boundaries is reflected in the focal mechanisms. The source of the earthquake of 1957 extends for about 300 km, which agrees well with modern estimates of its magnitude (M _w = 8.6). Because the earthquake of 1957 caused, due to its high strength, seismic activation of adjacent areas of the Aleutian island arc, its aftershock zone appreciably exceeded in size the earthquake source. Reverse faults that activated the seismic sources of the earthquakes of 1986 and 1996 were located within the southern slope of the Andreanof Islands, higher than the Aleutian Terrace, outside the seismic source of the 1957 earthquake. The boundaries of these sources are also well expressed in structures and focal mechanisms. According to our estimate, the length of the 1986 earthquake source does not exceed 130–140 km, which does not contradict its magnitude (M _w = 8). The length of the 1996 earthquake source is ～100 km, which also agrees with the magnitude of the earthquake (M _w = 7.8).     

An assembly model for simulation of large-scale ground water flow and transport

When managing large-scale ground water contamination problems, it is often necessary to model flow and transport using finely discretized domains--for instance (1) to simulate flow and transport near a contamination source area or in the area where a remediation technology is being implemented; (2) to account for small-scale heterogeneities; (3) to represent ground water-surface water interactions; or (4) some combination of these scenarios. A model with a large domain and fine-grid resolution will need extensive computing resources. In this work, a domain decomposition-based assembly model implemented in a parallel computing environment is developed, which will allow efficient simulation of large-scale ground water flow and transport problems using domain-wide grid refinement. The method employs common ground water flow (MODFLOW) and transport (RT3D) simulators, enabling the solution of almost all commonly encountered ground water flow and transport problems. The basic approach partitions a large model domain into any number of subdomains. Parallel processors are used to solve the model equations within each subdomain. Schwarz iteration is applied to match the flow solution at the subdomain boundaries. For the transport model, an extended numerical array is implemented to permit the exchange of dispersive and advective flux information across subdomain boundaries. The model is verified using a conventional single-domain model. Model simulations demonstrate that the proposed model operated in a parallel computing environment can result in considerable savings in computer run times (between 50% and 80%) compared with conventional modeling approaches and may be used to simulate grid discretizations that were formerly intractable.     

Agricultural effluent control under uncertainty: An inexact double-sided fuzzy chance-constrained model

An inexact double-sided fuzzy chance-constrained programming (IDFCCP) method was developed in this study and applied to an agricultural effluent control management problem. IDFCCP was formulated through incorporating interval linear programming (ILP) into a double-sided fuzzy chance-constrained programming (DFCCP) framework, and could be used to deal with uncertainties expressed as not only possibility distributions associated with both left- and right-hand-side components of constraints but also discrete intervals in the objective function. The study results indicated that IDFCCP allowed violation of system constraints at specified confidence levels, where each confidence level consisted of two reliability scenarios. This could lead to model solutions with high system benefits under acceptable risk magnitudes. Furthermore, the introduction of ILP allowed uncertain information presented as discrete intervals to be communicated into the optimization process, such that a variety of decision alternatives can be generated by adjusting the decision-variable values within their intervals. The proposed model could help decision makers establish various production patterns with cost-effective water quality management schemes under complex uncertainties, and gain in-depth insights into the trade-offs between system economy and reliability.     

Comparison between two approaches to the implementation of the optimization method for reconstructing a nonlinear force-free field

A comparative testing of two methods for reconstructing a nonlinear force-free field in a bounded spatial domain has mainly been studied based on the optimization method, using (1) fixed boundary values and weighting function and (2) purposefully varied boundary values. The quantitative and qualitative characteristics, reflecting the degree of correspondence between the calculated and known model fields, are presented. It is indicated that the second approach to the implementation of the optimization method gives the best approximation to the required solution, corresponding to the finite solution in an unbounded domain, and the quality of this solution remains unchanged up to the reconstruction domain boundaries.     

Influence of advection on scales of ecological studies in a coastal equilibrium flow

Spatial patterns are generated as a result of the coupling between biogeochemical and physical processes and the ability to capture and reproduce patchiness is crucial for the better comprehension of an ecosystem and its response to external perturbations. A 1D reaction–diffusion–advection equation is used to investigate the formation of patterns and relevant time and spatial scales and thus define an approach for the determination of a critical domain size that allows differentiation of the role of local and internal cycling from advective fluxes across the open boundaries in a shallow coastal ecosystem. By using a 3D numerical model, in conjunction with an extensive field data set, it is shown that domain sizes must be larger than this critical value in order to capture the patterns generated within the system. For smaller domains, the evolution of the system is controlled by transport processes across the boundaries misleading the interpretation of the internal ecological dynamics. The study of the influence of boundary fluxes on ecological patchiness was motivated by the need to define the size of the domain necessary for the assessment of the impact of a sewage outflow on a coastal regime.     

Perfectly matched layer boundary conditions for the second-order acoustic wave equation solved by the rapid expansion method

We derive a governing second-order acoustic wave equation in the time domain with a perfectly matched layer absorbing boundary condition for general inhomogeneous media. Besides, a new scheme to solve the perfectly matched layer equation for absorbing reflections from the model boundaries based on the rapid expansion method is proposed. The suggested scheme can be easily applied to a wide class of wave equations and numerical methods for seismic modelling. The absorbing boundary condition method is formulated based on the split perfectly matched layer method and we employ the rapid expansion method to solve the derived new perfectly matched layer equation. The use of the rapid expansion method allows us to extrapolate wavefields with a time step larger than the ones commonly used by traditional finite-difference schemes in a stable way and free of dispersion noise. Furthermore, in order to demonstrate the efficiency and applicability of the proposed perfectly matched layer scheme, numerical modelling examples are also presented. The numerical results obtained with the put forward perfectly matched layer scheme are compared with results from traditional attenuation absorbing boundary conditions and enlarged models as well. The analysis of the numerical results indicates that the proposed perfectly matched layer scheme is significantly effective and more efficient in absorbing spurious reflections from the model boundaries.     

A magnetic polarity time scale for the Early Cretaceous and Late Jurassic

The ages of polarity chrons in previous M-sequence magnetic polarity time scales were interpolated using basal sediment ages in suitably drilled DSDP holes. This method is subject to several sources of error, including often large paleontological age ranges. Magnetostratigraphic results have now tied the Early Cretaceous and Late Jurassic paleontological stage boundaries to the M-sequence of magnetic polarity. The numeric ages of most of these boundaries are inadequately known and some have been determined largely by intuition. An examination of relevant data suggests that 114 Ma, 136 Ma and 146 Ma are optimum estimates for the ages of the Aptian/Barremian, Cretaceous/Jurassic and Kimmeridgian/Oxfordian stage boundaries, respectively. Each of these boundaries has a good correlation to the M-sequence of magnetic reversals. The magnetostratigraphic tie-level ages are linearly related to the spreading distance and have been used to calculate a new magnetic polarity time scale for the Early Cretaceous and Late Jurassic. All stage boundaries in this time interval were correlated by magnetic stratigraphy to the proposed new time scale which was then used to estimate their numeric ages. These are, with the approximate relative errors of placement within the M-sequence:The absolute errors of these interpolated stage boundary ages depend on the accuracy of the tie-level ages.     

A new technique for the calculation of aeration development zones and nonaerated zones in turbulent flows on the spillway faces of dams and in prismatic flumes and its field verification

A new technique for calculating turbulent aerated and nonaerated flows on spillway faces of dams and in prismatic flumes is developed and validated against field data. The technique is based on original relationships and hypotheses proposed by the author and allowing one to identify the position in a watercourse of the section where aeration appears and the section of its stabilization and to calculate, within these boundaries, the distribution of the mean velocity of liquid phase, averaged aeration factors, and the aeration depths corresponding to the conventional upper boundary of flow section with the local value of the aeration factor a _loc = 0.99.     

Bayesian uncertainty quantification for flows in heterogeneous porous media using reversible jump Markov chain Monte Carlo methods

In this paper, we study the uncertainty quantification in inverse problems for flows in heterogeneous porous media. Reversible jump Markov chain Monte Carlo algorithms (MCMC) are used for hierarchical modeling of channelized permeability fields. Within each channel, the permeability is assumed to have a log-normal distribution. Uncertainty quantification in history matching is carried out hierarchically by constructing geologic facies boundaries as well as permeability fields within each facies using dynamic data such as production data. The search with Metropolis–Hastings algorithm results in very low acceptance rate, and consequently, the computations are CPU demanding. To speed-up the computations, we use a two-stage MCMC that utilizes upscaled models to screen the proposals. In our numerical results, we assume that the channels intersect the wells and the intersection locations are known. Our results show that the proposed algorithms are capable of capturing the channel boundaries and describe the permeability variations within the channels using dynamic production history at the wells.     

Effect of class-interval size on entropy

The value of Shannon entropy for a given set of data depends on the class interval chosen to compute the relative frequency of each class. For three data sets, expressed in dimensional as well as nondimensional form, the entropy value was computed for different class-interval sizes. Entropy was found to decrease with increasing class interval as well as with increasing sampling interval. It is suggested that these intervals should be selected with care.     

Condensed hyperelements method of non-vertical consistent boundaries for wave propagation analysis in irregular media

The study of wave propagation in finite/infinite media has many applications in geotechnical and structural earthquake engineering and has been a focus of research for the past few decades. This paper presents an analysis of 2D anti- plane problems （Love waves） and 2D in-plane problems （Rayleigh waves） in the frequency domain in media consisting of a near-field irregular and a far-field regular part. The near field part may contain structures and its boundaries with the far-field can be of any shape. In this study, the irregular boundaries of the near-field are treated as consistent boundaries, extending the concept of Lysmer＇s vertical consistent boundaries. The presented technique is called the Condensed Hyperelements Method （CHM）. In this method, the irregular boundary is limited to a vertical boundary at each end that is a consistent boundary at the far-field side. Between the two ends, the medium is discretized with hyperelements. Using static condensation, the stiffness matrix of the far-field is derived for the nodes on the irregular boundary. Examples of the application of the CHM illustrate its excellent accuracy and efficiency.     

Evaluation of the four potential Cretaceous-Paleogene (K-Pg) boundaries in the Nanxiong Basin based on evidences from volcanic activity and paleoclimatic evolution

Determining the location of the Cretaceous-Paleogene(K-Pg) boundary in terrestrial strata is highly significant for studying the evolution of terrestrial ecosystems at the end of the Cretaceous(especially the extinction of non-avian dinosaurs). At present, research on terrestrial K-Pg boundaries worldwide is concentrated in the middle and high latitudes, such as North America and Northeast China. Although many studies have also been carried out in the Nanxiong Basin, located at low latitudes(which has become the standard for dividing and comparing the continental K-Pg stratigraphy in China), many researchers have proposed four possible boundaries from different perspectives. Therefore, the exact location remains to be determined. In this study, the total mercury(Hg) content, environmental magnetism, geochemistry, and other parameters for the samples collected near the four boundaries were determined and compared with existing records. Results indicated that: 1) The total Hg content significantly increased in the upper part of the Zhenshui Formation and Pingling part of the Shanghu Formation with sharp fluctuations. As per latest dating results of Deccan Traps, the significantly high Hg value was attributed to the Deccan Traps eruption. Boundary 1 was located in the middle of the Hg anomaly interval, which was consistent with the relationship between the global K-Pg boundary and time of volcanic eruption. 2) The reconstructed paleoclimate evolution curve revealed that the red sediments in the basin recorded the late Maastrichtian warming event(66.2 Ma). Regarding the relationship between the four boundaries and this warming event, only boundary 1 was found to be closest to the real K-Pg boundary of the Nanxiong Basin.     

ISMISIP: an inexact stochastic mixed integer linear semi-infinite programming approach for solid waste management and planning under uncertainty

An inexact stochastic mixed integer linear semi-infinite programming (ISMISIP) model is developed for municipal solid waste (MSW) management under uncertainty. By incorporating stochastic programming (SP), integer programming and interval semi-infinite programming (ISIP) within a general waste management problem, the model can simultaneously handle programming problems with coefficients expressed as probability distribution functions, intervals and functional intervals. Compared with those inexact programming models without introducing functional interval coefficients, the ISMISIP model has the following advantages that: (1) since parameters are represented as functional intervals, the parameter’s dynamic feature (i.e., the constraint should be satisfied under all possible levels within its range) can be reflected, and (2) it is applicable to practical problems as the solution method does not generate more complicated intermediate models (He and Huang, Technical Report, 2004; He et al. J Air Waste Manage Assoc, 2007). Moreover, the ISMISIP model is proposed upon the previous inexact mixed integer linear semi-infinite programming (IMISIP) model by assuming capacities of the landfill, WTE and composting facilities to be stochastic. Thus it has the improved capabilities in (1) identifying schemes regarding to the waste allocation and facility expansions with a minimized system cost and (2) addressing tradeoffs among environmental, economic and system reliability level.     

Inexact quadratic joint-probabilistic programming for water quality management under uncertainty in the Xiangxi River, China

An inexact quadratic joint-probabilistic programming model for water quality management (IQJWQ) is developed and applied to supporting multiple-point-source waste reduction in the Xiangxi River, China. The IQJWQ is a hybrid of interval quadratic programming, joint probabilistic programming and multi-segment water quality simulation. It has advantages in reflecting uncertainties expressed as joint probabilities of system risk, probability distributions of water quality standards, interval parameters and nonlinearities in the objective function. An interactive and derivative algorithm is employed for solving the IQJWQ model. The results indicate that the Pingyikou chemical plant and Liucaopo chemical plant contribute more to pollution of the main stream in the Xiangxi River, which should be the prior plants to reduce the wastewater discharge and enhance the wastewater treatment efficiencies. Meanwhile, the environmental agencies should choose the joint probability carefully to balance the tradeoff between production development and pollution control. Compared with the conventional chance-constrained programming method, the IQJWQ exhibits an increased robustness in handling the overall system risk in the optimization process. Although this study is the first application of the IQJWQ to water quality management, the proposed methods in the IQJWQ can also be applicable to many other environmental management problems under uncertainty.     

Contourlet based seismic reflection data non-local noise suppression

In this paper, we propose a non-local, transform domain noise suppression framework to improve the quality of seismic reflection data. The original non-local means (NLM) algorithm measures similarities in the data domain and we generalize it in the nonsubsampled contourlet transform (NSCT) domain. NSCT gives a multiscale, multiresolution and anisotropy representation of the noisy input. The redundancy information in NSCT subbands can be utilized to enhance the structures in the original seismic data. Like the wavelet transform, NSCT coefficients in each subband follow the generalized Gaussian distribution and the parameters can be estimated using appropriate techniques. These parameters are used to construct our proposed NSCT domain filtering algorithm. Applications for synthetic and real seismic data of the proposed algorithm demonstrate its effectiveness on seismic data random noise suppression.