Hydrological 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.

• Contaminant remediation in aquifers.{{Cite journal|last1=Ahlfeld|first1=David P.|last2=Mulvey|first2=John M.|last3=Pinder|first3=George F.|last4=Wood|first4=Eric F.|author-link4=Eric Franklin Wood|date=1988|title=Contaminated groundwater remediation design using simulation, optimization, and sensitivity theory: 1. Model development|journal=Water Resources Research|language=en|volume=24|issue=3|pages=431–441|doi=10.1029/WR024i003p00431|issn=1944-7973|bibcode=1988WRR....24..431A}} The decision problem is where to locate wells, and choose a pumping rate, to minimize the cost to prevent spread of a contaminant. The constraints are associated with the hydrogeological flows.

• Water allocation to improve wetlands. This optimization model recommends water allocation and invasive vegetation control to improve wetland habitat of priority bird species. These recommendations are subject to constraints like water availability, spatial connectivity, hydraulic infrastructure capacities, vegetation responses, and available financial resources.{{cite journal|doi=10.1002/2015WR018105 | volume=52 | issue=9 | title=Systems modeling to improve the hydro-ecological performance of diked wetlands | journal=Water Resources Research | pages=7070–7085 | last1 = Alminagorta | first1 = Omar| year=2016 | bibcode=2016WRR....52.7070A | s2cid=31097159 | url=https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=1018&context=water_pubs }}

• Maximizing well abstraction subject to environmental flow constraints.{{Cite journal|last1=Feyen|first1=Luc|last2=Gorelick|first2=Steven M.|date=2005|title=Framework to evaluate the worth of hydraulic conductivity data for optimal groundwater resources management in ecologically sensitive areas|journal=Water Resources Research|volume=41|issue=3|pages=03019|doi=10.1029/2003WR002901|bibcode=2005WRR....41.3019F|s2cid=108490062 }} The goal is to measure the effects of each user's water use on other users and on the environment, as accurately as possible, and then optimize over the available feasible solutions.

• Improving water quality. A simple optimization model identifies the cost-minimizing mix of best management practices to reduce the excess of nutrients in a watershed.{{Cite journal |doi = 10.1061/(ASCE)WR.1943-5452.0000224|title = Simple Optimization Method to Determine Best Management Practices to Reduce Phosphorus Loading in Echo Reservoir, Utah|journal = Journal of Water Resources Planning and Management|volume = 139|pages = 122–125|year = 2013|last1 = Alminagorta|first1 = Omar|last2 = Tesfatsion|first2 = Bereket|last3 = Rosenberg|first3 = David E.|last4 = Neilson|first4 = Bethany|url = https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=1773&context=cee_facpub}}

• Hydrological optimization is now being proposed for use with smart markets for water-related resources.{{Cite journal|last1=Santhosh|first1=Apoorva|last2=Farid|first2=Amro M.|last3=Youcef-Toumi|first3=Kamal|date=2014|title=Real-time economic dispatch for the supply side of the energy-water nexus|url=http://amfarid.scripts.mit.edu/resources/Journals/EWN-J10.pdf|journal=Applied Energy|volume=122|pages=42–52|doi=10.1016/j.apenergy.2014.01.062|bibcode=2014ApEn..122...42S|access-date=2019-08-09|archive-date=2020-09-25|archive-url=https://web.archive.org/web/20200925233116/http://amfarid.scripts.mit.edu/resources/Journals/EWN-J10.pdf|url-status=dead}}
• Pipe network optimization with genetic algorithms.{{Cite journal|last1=Dandy|first1=Graeme C.|last2=Simpson|first2=Angus R.|last3=Murphy|first3=Laurence J.|date=1996|title=An improved genetic algorithm for pipe network optimization|url=https://pdfs.semanticscholar.org/14f3/7a77cb58a1d29eb5de08faf64cc7f2c476b9.pdf|archive-url=https://web.archive.org/web/20190810054355/https://pdfs.semanticscholar.org/14f3/7a77cb58a1d29eb5de08faf64cc7f2c476b9.pdf|url-status=dead|archive-date=2019-08-10|journal=Water Resources Research|volume=32|issue=2|pages=449–458|doi=10.1029/95WR02917|hdl=2440/1073|bibcode=1996WRR....32..449D|s2cid=16097463 |hdl-access=free}}

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:

• Groundwater flow equation
• Primitive equations
• Saint-Venant equations

Other environmental processes to consider as inputs include:

• Evapotranspiration
• Geomorphology
• Sediment transport

• Drainage research
• Geographic information system
• Integrated water resources management
• Optimal control
• Pipe network analysis
• Water in California

• Boyd, Stephen P.; Vandenberghe, Lieven (2004). [https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf Convex Optimization] (PDF). Cambridge University Press. {{ISBN|978-0-521-83378-3}}.
• Loucks, Daniel P.; van Beek, Eelco (2017). [https://www.springer.com/gp/book/9783319442327 Water Resource Systems Planning and Management: An Introduction to Methods, Models, and Applications]. Springer. {{ISBN|9783319442327|}}.
• Nocedal, Jorge; Wright, Stephen (2006). [https://www.springer.com/gp/book/9780387303031 Numerical Optimization]. Springer Series in Operations Research and Financial Engineering, Springer. {{ISBN|9780387303031}}.
• Qin, Youwei; Kavetski, Dmitri; Kuczera, George (2018). [https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2017WR022489 "A Robust Gauss-Newton Algorithm for the Optimization of Hydrological Models: Benchmarking Against Industry-Standard Algorithms"]. Water Resources Research. 54 (11): 9637-9654.
• Tayfur, Gokmen (2017). [https://link.springer.com/article/10.1007/s11269-017-1694-6 "Modern Optimization Methods in Water Resources Planning, Engineering and Management"]. Water Resources Management. 31: 3205-3233.

• [https://ocw.mit.edu/courses/civil-and-environmental-engineering/1-731-water-resource-systems-fall-2006/index.htm Water Resource Systems] (MIT OpenCourseWare)
• [https://ocw.mit.edu/courses/civil-and-environmental-engineering/1-731-water-resource-systems-fall-2006/lecture-notes/ Lecture notes]

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Category:Hydraulics

Category:Hydraulic engineering

Category:Hydrology

Category:Mathematical optimization

Category:Optimal control

Category:Water resources management