Distributions Systems II

Berry, J.W., Fleisher, L., Hart, W.E., Phillips, C.A., Watson, JP (2005) “Sensor Placement in Municipal Water Networks” J. Water Res. Plan. Mang. 131(3): pp 237- 243

In this paper Berry et al. expand on principles established in Lee and Deininger by applying integer programming to the problem of detecting contamination within a water distribution system. Although regulations requiring the monitoring of water quality within a distribution system have been around since the enactment of the Clean Water Act the events of September 11th brought the need for more rigorous monitoring of water distribution systems to the forefront.

In contrast to the previously reviewed work by Lee and Deininger, Berry et al were interested in detecting and minimizing the impacts of intentional contamination of a water supply. As such they were required to take into account the usage and population density at each demand node as a function of time. To further complicate the optimization the site where the contaminant was introduced to the water supply was allowed to vary between optimizations based on time of day and location. By using synthetic probability distributions Berry et al. were able to develop a compromise optimization that was designed to minimize the impacts of an intentional contamination.

Berry et al. followed a design process similar to the methods used by Lee and Deininger by employing increasingly complex hypothetical models before using a real world system. One key difference between the two papers is the location of the sensors within the system. While Lee and Deininger placed their sensors are distribution nodes Berry et al. placed the sensors in the pipes between the nodes. Although this might seem like a small difference it allows for contamination to be detected en route from one node to another and in theory would allow for a response to begin before the contaminant reached the next node. By assigning a weight to each node based on population density and use Berry et al. were able to create an optimized solution that placed sensors in areas where contamination would cause highest potential impacts.

Distribution Systems I

Lee, B.H., Deininger, RA. (1992) “Optimal Location of Monitoring Station In Water Distribution System” J. Env. Eng. 118(1): pp 4 -16

In this paper Lee and Deininger explore the application of integer programming to optimize monitoring stations in simulated and real world water distribution systems. Under the requirements of the Clean Water Act water distribution systems are required to monitor the quality of water within the distribution system to ensure adequate quality. Although the law specifies the standards for drinking water distribution there are no explicit regulations regarding how to establish a compliant network for monitoring water quality within the system. To begin filling this gap Lee and Deininger apply linear programming to two hypothetical distribution systems as a proof of concept experiment before applying the process to two real world distribution networks.

Lee and Deininger began with a simple case using a hypothetical distribution network composed of seven interconnected nodes with known demands at each node. The nodes were linked by eight pipes with known flows between each node. The integer program was based on two assumptions:

1) the quality of water at any given node is representative of the quality at each upstream node and,

2) the quality varies as a function of the flow through each path leading to the node.

Using these two assumptions as the basis for determining the “coverage” at any node allowed Lee and Deininger to design a knowledge matrix the related the degree of network coverage provided by each node. The knowledge matrix was then used in the integer program to determine the optimal location of monitoring stations for network. They then expanded the process from the simple test network and applied it to the distribution network for Flint. Michigan. In doing so they were able to increase the coverage of the distribution network from its current value of ~18% to 54% without increasing the number of monitoring stations. Lee and Deininger followed this step by applying the same process to a hypothetical and real world distribution network that included daily shifts in the demands and flow patterns.

Overall this paper establishes the utility of integer programming for optimizing the location of monitoring stations within water distribution systems. By evolving the process from a simple proof of concept to a simple real world system and then on to more complex hypothetical and real world systems Lee and Deininger demonstrated the robust nature of their process. Unfortunately they neglected to include measures such as water use (domestic v. industrial) and population density associated with each node and instead based their model solely on flow and demand measurements. Including usage and population density would most likely have resulted in a different allocation of the monitoring stations.

"Freedom is the recognition of necessity"

Garrett Hardin, "The Tragedy of the Commons," Science, 162(1968):1243-1248



In "The tragedy of the Commons" Hardin explores the inherent weaknesses of the socio-economic view (Post Adam Smith) when applied to areas of common property. Hardin argues against Smith's position that the decisions of individuals tend to be the best decision for society as a whole since each individual agent will act an a manner that increases their own benefits. Hardin argues that while Smith's "invisible hand" might have been true at some point in history it fails to hold up in modern times in the face of increased population density. Hardin's point that the increase in population density combined with "short sighted" individual optimizations leads to the inevitable degradation of common property is supported by the evolution of environmental legislation in this and other countries. As the population has increased in this country laws that progressively replace the common property nature of natural resources with more rigidly defined property rights have become prevalent at both state and federal levels. The impacts of these varying laws can be seen in the development on prior appropriation and riparian rights in water, evolving standards governing air quality and hazardous waste disposal.

Hardin's position about the self-selecting nature of conscience and the pathogenic effects of conscience deserve their own examinations and hopefully I'll get back to those points later in the week. Ultimately Hardin follows the demise of the concept of "the commons" as it is progressively legislated out of existence. Each new piece of legislation is born out of a new realization that "the situation has changed" and often the driver of that change has been the incessant growth in population. And although each new law has further infringed upon the rights of it citizens the uproar caused by the infringement tends to be short lived and is followed by general acceptance. This lead Hardin back to a quote from Hegel, which I shameless used, "Freedom is the recognition of necessity".

Groundwater Remediation

Atwood, D., Gorelick, S. (1985) "Hydraulic Gradient Control for Groundwater Contaminant Removal" J. Hydrology 76:85-106

In this paper Atwood and Gorelick explore the applications of linear programming and dispersion modeling to the remediation of a contaminated aquifer. The study focused on a contaminated aquifer under the Rocky Mountain Arsenal in Colorado. The work was divided into two sections to simplify the modeling and to avoid non-linearities within the system. The first section of the work modeled the behavior of a contaminant plume under the influence of a neutral groundwater gradient and a single centrally located remedial pump. Once the optimal site for the remedial pump was identified the change in the plumes geometry over time was simulated using dispersion modeling and groundwater flow equations. The second portion of the work focused on how to use the existing well fields to create a neutral hydraulic gradient around the contaminant plume and effectively hold it in place around the remedial pump. By using linear programming the authors found the optimal combination of pumping and recharge patterns to stabilize and contain the contaminant plume. This modeling required extensive knowledge of the existing hydraulic gradients, transmissivity and saturated depth of the aquifer. The authors used two different approaches in their optimization models. The first divided the mediation project into two management periods and used the knowledge of the contaminant plume geometry in each period to optimize the pumping and recharge operations of each period based on the plumes geometry. The second approach used no advanced knowledge of the plume's expected behavior and optimized based the plume's position in each time point. In both cases the systems were optimized to minimize the amount of pumping or recharge needed to stabilize the plume.
Interestingly, in both cases the overall pumping/recharge was similar although the two methods recommended different patterns of pumping and recharge stabilize the plume. The authors point out that the results of each method would have to be evaluated in an economic context to determine which was ultimately optimal (taking into account the costs of recharge water and the pumping expenses). This reinforces the point made by Liebman that in complex systems the optimization models can serve as decision making tools but not as the final word in decision making process.