Wayne Woldt

Numerical solute transport simulation using fuzzy sets approach

Abstract This paper applies fuzzy sets and fuzzy arithmetic to incorporate imprecise information into transport modeling of nonreactive solute materials in groundwater flow. The method is applied to both one- and two-dimensional uniform flow fields. Emphasis is on the solution methods of the fuzzy numerical model of solute transport, which is a function of fuzzy variables. The solution techniques, including the vertex method and the fuzzy-numerical simulation method (i.e. the single-value simulation method), are discussed in detail. The solute concentration outputs from the fuzzy finite-difference numerical models based on these two solution methods are compared with those from the fuzzy analytical models. The vertex method can avoid the widening of the fuzzy function value set, in this case, the fuzzy solute concentration function. This widening is due to multi-occurrence of variables in the function expression when using conventional interval analysis. However, in fuzzy finite-difference numerical simulation of solute transport, the vertex method may still overestimate the uncertainty in the concentration outputs since all the fuzzy variables in the fuzzy numerical model are taken to be independent. The fuzzy-numerical simulation method can control the growth of the imprecision in the solute concentration calculations by taking into account the interaction (dependence) of concentration variables in both space and time dimensions in the fuzzy finite-difference model of solute transport. It has the advantage of allowing the use of imprecise data for modeling and also processing the fuzzy information using generated crisp values of fuzzy variables. The adoption of fuzzy sets allows common-sense knowledge to be represented in defining values through the use of a membership function. This enables the subjective information to be incorporated in system modeling in a formal algorithm.

Steady State Groundwater Flow Simulation With Imprecise Parameters

A methodology based on fuzzy set theory is developed to incorporate imprecise parameters into steady state groundwater flow models. In this case, fuzzy numbers are used to represent parameter imprecision. As such, they are also used as a measure for the uncertainty associated with the hydraulic heads due to the imprecision in the input parameters. The imprecise input parameters may come from indirect measurements, subjective interpretation, and expert judgment of available information. In the methodology, a finite difference method is combined with level set operations to formulate the fuzzy groundwater flow model. This fuzzy modeling technique can handle imprecise parameters in a direct way without generating a large number of realizations. Two numerical solution methods are used to solve the fuzzy groundwater flow model: the groundwater model operator method proposed in this methodology and the iterative algorithm based on conventional interval arithmetics. The iterative method is simple but may overestimate the uncertainty of hydraulic heads. The groundwater model operator method not only provides the hull of the solution set for the hydraulic heads but also considers the dependence of hydraulic head coefficients which are functions of imprecise parameters. Sensitivity analysis shows that the dependence of hydraulic head coefficients has a critical impact on the model results, and neglecting this dependence may result in significant overestimation of the uncertainty of hydraulic heads. A numerical model based on the methodology is tested by comparing it with the analytical solution for a homogeneous radial flow problem. It is also applied to a simplified two-dimensional heterogeneous flow case to demonstrate the methodology.

Fuzzy rule-based approach to describe solute transport in the unsaturated zone

Abstract A fuzzy rule-based model is developed for simulation of solute transport processes in the vadose zone. Underlying physical processes of solute transport described by appropriate differential equations are captured in fuzzy rules. These rules are derived from a training set obtained from different test runs of the SWMS_2D model which simulates water flow and solute transport in two-dimensional variably saturated media. Fuzzy rules operate between two adjacent cells at each time step. Solute concentration of the upper cell, and solute concentration difference between two adjacent cells are used as premises. For a given time step, the solute flux between the two cells is taken as the response, which is combined with the conservation of mass to update the new solute concentration for the new time step. The methodology is applied to solve the breakthrough curve of bromide movement in a soil column. It is also generalized to the same problem under different soil and boundary conditions. In both cases, the fuzzy solution appears to be similar to the measured bromide concentration as well as the SWMS_2D model results. The methodology provides a more efficient alternative to existing modeling methods.

Decision support system for water transfer evaluation

A decision support system (DSS) is developed to help decision makers analyze the economic, social, and ecological ramifications of water transfers. Such a DSS is needed because the U.S. is evolving from a development water economy to a more complex one that emphasizes conservation and reallocation (i.e., transfers). The DSS is composed of three main modules: (1) a conjunctive surface-ground water model, (2) the impact analysis segment which uses a geographical information system that integrates model output with information from the study area to estimate economic, social, and ecological impacts, and (3) a multicriteria decision making algorithm that ranks the transfer schemes based on trade-offs of indicators which are assembled into a hierarchical structure. A case study in which 10 different water transfer alternatives are examined is provided to demonstrate an application of the proposed DSS.

Evaluation of uncertainties in a three-dimensional groundwater contamination plume

Abstract Geostatistical simulation and groundwater modeling are combined to estimate the probability of exceeding a threshold contamination level an aquifer. The analysis is completed in three dimensions with two sources of uncertainty considered: initial plume characterization, and acquifer parameter estimation. Initial plume location and intensity are based on a limited number of borehole measurements. Conditional simulation is used to generate possible plume configurations which provide initial conditions for a groundwater model. Simultaneously, acquifer parameters are also simulated, and repeated running of the groundwater model provides a frequency distribution of contaminant level at a selected compliance surface and future time. The method has been tested at a low-level radioactive waste reprocessing facility. Numerical results show that the effect of uncertain initial plume characterization may have a larger impact on the modeling process than the effect of uncertain aquifer parameter. Both effects should be considered in order to evaluate the need for additional aquifer remediation efforts.

Application of fuzzy set theory to industrial pollution prevention: production system modeling and life cycle assessment

Abstract This research describes a framework and case study application that merges fuzzy set methods, pollution prevention, and sustainable production concepts. There is a direct linkage between industrial pollution prevention, sustainability, and the solution of large-scale environmental problems. This linkage stems from the inherent desire for economic production, while at the same time protecting the environment from further degradation. The methodology combines systems analysis under imprecise conditions with a life cycle assessment method that is able to accept imprecise data. Analysis of systems under imprecise conditions is accomplished through analysis of process flow diagrams using fuzzy set techniques. Introduction of imprecision into life cycle assessment is accomplished by integration of fuzzy set approaches into a decision support system utilizing multiple criteria decision making. The framework is described and a case study application of an industrial parts cleaning system using an open top vapor degreaser is presented. Results of applying the method show that: (1) It is well suited for analysis of complex systems in which input data is sparse and expensive to collect. (2) The proposed framework includes a decision support system that is able to consider life cycle assessment concepts, and is able to reconcile differing opinions on available options for modification of production systems, thereby leading to more sustainable solutions.

Future Directions for Automated Weed Management in Precision Agriculture

In cropping systems, integrated weed management is based on diversification. Rather than relying solely on one or two herbicides, a multiplicity of weed control strategies is employed. Yet, integrated weed management as currently practiced is far from integrated; every weed is still managed the same regardless of location or season. The recent development of precision application technology is now allowing for smaller treatment units by making applications according to site-specific demands. The automated systems of the future will have sensor and computer technologies that first categorize each and every plant in the field as either weed or crop and then identify the species of weed. Following identification, multiple weed control tools located on a single platform are applied at micro-rates to individual plants based on their biology. For example, if the system identified a weed resistant to Roundup, it could be spritzed with a different herbicide or nipped with an onboard cutter or singed with a burst of flame. This system and others like it will be capable of targeting different weed-killing tools to specific weeds. This chapter will discuss the challenges and tools of the future.

SPATIAL PATTERNS ANALYSIS OF FIELD MEASURED SOIL NITRATE

The purpose of this study was to assess the spatial variability of residual soil nitrate, measured in three contiguous 16 ha fields. Available data for residual soil nitrate were examined using conventional statistics. Data tended to be skewed with the mean greater than the median. Geostatistical methods were used to characterize and model the spatial structure. Three dimensional spatial variability was examined using two semivariograms: horizontal-spatial and vertical. Two dimensional horizontal-spatial semivariograms were also computed for each 0.3m (lft) layer. Semivariogram analysis showed that there were similarities in the patterns of spatial variability for all fields. The results suggest that the spatial patterns in residual soil nitrate may be correlated with irrigation practices. Furthermore, a trend was found to be present along the vertical direction, which may be related to the time of sampling.

Waste Assessment of Agricultural Chemicals, Petroleum Products and Maintenance Residuals on Farmsteads

The purpose of this study was to evaluate waste management practices of purchasing, handling, storage, and disposal of agricultural chemicals, petroleum products, and maintenance residuals. One-hundred surveys were returned by agricultural producers from three Nebraska counties selected based on unique environmental and waste management issues. Twenty-four questions concerning agricultural chemicals and 16 questions directed to petroleum products and maintenance residuals are discussed. A follow-up interview with 45 respondents was conducted “on-site” to gain insight into their reported practices, perceptions, and actual practices. Most farmers (66%) tended to purchase pesticides in 3.8 to 10 L (1-2.5 gal) containers and most (79%) were willing to participate in a recycling program for pesticide containers. Most of the respondents burned soft/hard plastic and paper pesticide containers, or returned the metal containers to the supplier. Few farmers took pesticide containers to landfills, or buried or stored containers in their field. Most farmers (76%) applied left-over diluted chemical residues or rinsates evenly on the field just sprayed. Eighty-one percent of the farmers stored pesticides and 89% stored fertilizers at locations greater than 31 m (101 ft) from a water source. Only 9% of the respondents indicated they had containment barriers for stationary bulk pesticides, fertilizer storage tanks, or transportable nurse tanks. Seventy-nine percent of the respondents and 84% of the interviewed farmers did not record or monitor volumes of petroleum storage. Farmers tended to have trash dumps (62%) and junk piles (57%) on their farmsteads. Geographic location within the state and size of the farmstead had an effect on whether the farms had dumps. Most farmers (94%) felt they used appropriate recycling methods to deal with waste products. However, over half of the farmers were unaware of the location of the petroleum (oil) recycling station. Most farmers (94%) indicated they felt they purchased replacement items based on long life instead of lowest price.

Comparison of Two Transport Models for Predicting Nitrates in Percolating Water

The movement of nutrients and pesticides in soils is an important aspect of agriculture. Numerous models have been developed to predict the movement and transformations of such materials with varying degrees of complexity. The objective of this article is to present and compare the performance of a specialized unsaturated zone transport model (TDNIT) in simulating nitrogen transport dynamics in soils against a widely accepted model (EPIC) as well as documented field studies in the study area. The model TDNIT is evaluated in simulating nitrogen transport and transformation and attendant hydrologic processes in a 13-year continuous corn cultivation series. Water percolation from the root zone, plant transpiration, soil evaporation, plant nitrogen uptake, and crop yield from the two models compared favorably. The results of this study indicate that TDNIT performed well in predicting nitrate loadings below the root zone with TDNIT predicting a relatively reduced amount of total mineralization and denitrification. Even without calibration, TDNIT was found to be suitable for simulating nitrogen dynamics under the site conditions for which it was evaluated. The relative simplicity of TDNIT makes it a very suitable tool in simulating nitrogen transport through the unsaturated or vadose zones.