Optimization in Integrated Water Resources Management

Introduction
Optimization is a very large topic, even within the confines of water resources planning and management. For today, I would like to focus on a single application, which I found while reading the Journal of the American Water Resources Association (JAWRA). I highly recommend JAWRA as a great source on all things water resources and for updates on the latest issues. In the February 2011 issue (yes, I'm a little behind on my reading), there is an article called "Optimal Pollution Trading without Pollution Reductions: A Note". I would like to take the time to write up a review of this article.

Pollutant Trading Application

Pollutant trading is in it's infancy - the experimental stages. Current challenges include high transaction costs, difficulties in transferring liabilities, and pollution allowances in existing programs. This article describes how two different types of polluters (farm and factory) can collaborate in order to reduce the impact on receiving waters. While the factory discharges pollutants at a constant rate, irrespective of its surroundings, a farm might discharge in spikes depending on the occurrence of storm events. Optimization was used to minimize the environmental damage to the receiving water body. Factors considered in the optimization include uncertainty in runoff pollutants and enforcement costs.

Traditionally with pollutant trading, the thing being traded is a reduction in pollutant concentration. A reduction in pollutant load at point A is traded for an equal increase in pollutant load at point B on the receiving water body. In the case of this example, temporary retention of pollutants is instead being traded.



References:
Garcia, Jorge H., Heberling, Matthew T., Thurston, Hale W. "Optimal Pollution Trading without Pollution Reductions: A Note". JAWRA 2011, Vol. 47, No. 1, pg 52.

Modular Systems Modeling

It is necessary to study not only parts and processes in isolation, but also to solve the decisive problems found in the organization and order unifying them, resulting from dynamic interaction of parts, and making the behavior of parts different when studied in isolation or within the whole.

Systems
Modular systems modeling is an approach to modeling that can be very useful for applications in integrated water resources management because of its inherent structure and organization. Every system is designed to achieve some objective. A system is made up of a network of interrelated components, which may consist of data, data processors, reporting elements, and subsystems.

The term "Systems Modeling" was introduced in the early 1960's and became famous shortly after the birth of FORTRAN. Since that time, it grew steadily in popularity until finally plateauing in the year 2000. The term "Systems Approach" peaked in 1975 and has since been on a steady decline. The grandfather of the Systems approach is known by some to be Alfred James Lotka from his work entitled, "Elements of Physical Biology" (1925). We are indebted to him for the formulation of the basic concepts of the Systems approach to studying the behavior of interconnected pieces to understand the greater whole. It makes sense that the advent of the computer gave us the power to begin using the Systems approach on problems of increasing complexity.

A closed system is a system that works independently of its environment and an open system is influenced by its environment and also interacts with subsystems outside of it.

Systems often have the ability to self-regulate or self-adjust. They can adjust behavior based on influences from outside such as changes in input data. This is often accomplished through feedback logic in the model.

Systems are classified into two different categories.

• Deterministic Systems
• Probabilistic Systems

Deterministic systems respond to inputs supplied to them and they react in a way that is predictable. This does not mean these systems are necessarily simple but rather that respond to instructions given.

Probabilistic systems have varying degrees of outcomes. It is very difficult to predict what the outcome of a probabilistic system will be. Outcomes from these types of systems is characterized in terms of chance rather than a given, predicted value.

Feedback
Feedback plays an important role in systems modeling because it can be found naturally in most real-world systems we are trying to represent. Below is a depiction of a typical feedback scheme.

A common example found in IWRM is in the water conservation model, where new policies stimulate the population to conserve water use and therefore cause the revenue stream generated by the metered water customers to drop. This response causes a feedback stimulus to the water provider to increase water usage rates, thereby changing the stimulus on the population.

Representing the System Using a Schematic

Schematic representations of the system are very useful in depicting the elements of a system and their influences. The image below is a screen capture of a computer model representing a water supply system located in Southern Utah. This is a schematic representation of the real system.

The blue lines in this figure represent the flow of water, red lines represent influences on operations, and the gray lines represent monitoring. This schematic happens to represent a dynamic system model that is changing through time. Because it is dynamic, it must include self-regulating and self-adjusting logic in order to behave with a purpose. This is done with feedback loops (red lines) and monitoring logic (gray lines).

Systems Modeling for IWRM
While the systems modeling approach has been very useful for many different applications, it is even more so for Integrated Water Resources Management. It is important that the system to be modeled is understood, including the influences between components of the system. A schematic representation of the system should be laid out prior to constructing a computer model. All major interactions and feedback loops should also be mapped out in the schematic and a formulation for dealing with these sketched out. Doing this before beginning the modeling work will save time in the long run.

I hope this information was helpful. Please comment if you think so.

References:

• Awad, Elias M. "Systems Analysis and Design". 1979, Florida International University.
• Lillywhite, Jason "Performance of Water Supply Operations Measured by Reliability and Marginal Cost". 2008, University of Utah.
• GoldSim Technology Group, LLC. GoldSim Dynamic Simulation Software. 2011.
• Bertalanffy, Ludwig von. "General System Theory, Foundations, Development, Applications". 1968.
• Google Ngram Viewer for words "Systems Approach" and "Systems Modeling". 2011.