Hydrological optimization

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Hydrological optimization applies mathematical optimization techniques (such as dynamic programming, linear programming, integer programming, or quadratic programming) to water-related problems. These problems may be for surface water, groundwater, or the combination. The work is interdisciplinary, and may be done by hydrologists, civil engineers, environmental engineers, and operations researchers.

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Simulation versus optimization

Groundwater and surface water flows can be studied with hydrologic simulation. A typical program used for this work is MODFLOW. However, simulation models cannot easily help make management decisions, as simulation is descriptive. Simulation shows what would happen given a certain set of conditions. Optimization, by contrast, finds the best solution for a set of conditions. Optimization models have three parts:

  1. An objective, such as "Minimize cost"
  2. Decision variables, which correspond to the options available to management
  3. Constraints, which describe the technical or physical requirements imposed on the options

To use hydrological optimization, a simulation is run to find constraint coefficients for the optimization. An engineer or manager can then add costs or benefits associated with a set of possible decisions, and solve the optimization model to find the best solution.

Examples of problems solved with hydrological optimization

PDE-constrained optimization

Partial differential equations (PDEs) are widely used to describe hydrological processes, suggesting that a high degree of accuracy in hydrological optimization should strive to incorporate PDE constraints into a given optimization. Common examples of PDEs used in hydrology include:

Other environmental processes to consider as inputs include:

See also

Related Research Articles

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<span class="mw-page-title-main">Mathematical optimization</span> Study of mathematical algorithms for optimization problems

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  5. Additional water pressurizing components such as pumping stations may need to be situated at the outlet of underground or aboveground reservoirs or cisterns.
  6. A pipe network for distribution of water to consumers and other usage points
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<span class="mw-page-title-main">Christine Shoemaker</span> American environmental engineer

Christine A. Shoemaker joined the Department of Industrial Systems Engineering & Management and the Department of Civil and Environmental Engineering as NUS Distinguished Professor on 31 August 2015. Prof Shoemaker obtained her Ph.D. in mathematics from the University of Southern California supervised by Richard Bellman in Dynamic Programming. Upon her graduation, she joined the School of Civil and Environmental Engineering and later the School of Operations Research and Information Engineering at Cornell University, Ithaca, NY, USA. She was promoted to full Professor in 1985. From 1985 to 1988, Professor Shoemaker was the Chair of the Department of Environmental Engineering at Cornell University. In 2002 Prof. Shoemaker was appointed the Joseph P. Ripley Professor of Engineering at Cornell University, USA. In 2015, Prof. Shoemaker became Distinguished Professor at National University of Singapore, in both Industrial Systems Engineering and Management Department and Civil and Environmental Engineering Department. While in Singapore she has worked with Singapore water agency to apply her global optimization algorithms to improve the selection of parameters for computationally expensive partial differential equation models for lake hydrodynamics and complex multi-species water quality elements. These results used her group's new parallel algorithms.

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Further reading