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<title>Hydrological optimization</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Hydrological optimization</span></span>

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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p><b>Hydrological optimization</b> applies <a href="Mathematical_optimization" title="Mathematical optimization">mathematical optimization</a> techniques (such as <a href="Dynamic_programming" title="Dynamic programming">dynamic programming</a>, <a href="Linear_programming" title="Linear programming">linear programming</a>, <a href="Integer_programming" title="Integer programming">integer programming</a>, or <a href="Quadratic_programming" title="Quadratic programming">quadratic programming</a>) to water-related problems. These problems may be for <a href="Surface_water" title="Surface water">surface water</a>, <a href="Groundwater" title="Groundwater">groundwater</a>, or the combination. The work is interdisciplinary, and may be done by <a href="Hydrologist" class="mw-redirect" title="Hydrologist">hydrologists</a>, <a href="Civil_engineer" title="Civil engineer">civil engineers</a>, <a href="Environmental_engineer" class="mw-redirect" title="Environmental engineer">environmental engineers</a>, and <a href="Operations_research" title="Operations research">operations researchers</a>.

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<div class="mw-heading mw-heading2"><h2 id="Simulation_versus_optimization">Simulation versus optimization</h2></div>

<p>Groundwater and surface water flows can be studied with hydrologic <a href="Simulation" title="Simulation">simulation</a>. A typical program used for this work is <a href="MODFLOW" title="MODFLOW">MODFLOW</a>. 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:

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<ol><li>An objective, such as "Minimize cost"</li>

<li>Decision variables, which correspond to the options available to management</li>

<li>Constraints, which describe the technical or physical requirements imposed on the options</li></ol>

<p>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.

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<div class="mw-heading mw-heading2"><h2 id="Examples_of_problems_solved_with_hydrological_optimization">Examples of problems solved with hydrological optimization</h2></div>

<ul><li>Contaminant remediation in aquifers.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> 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.</li></ul>

<ul><li>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.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li></ul>

<ul><li>Maximizing well abstraction subject to environmental flow constraints.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> 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.</li></ul>

<ul><li>Improving water quality. A simple optimization model identifies the cost-minimizing mix of <a href="Best_management_practice_for_water_pollution" title="Best management practice for water pollution">best management practices</a> to reduce the excess of nutrients in a watershed.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li></ul>

<ul><li>Hydrological optimization is now being proposed for use with <a href="Smart_market" title="Smart market">smart markets</a> for water-related resources.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li>

<li>Pipe network optimization with <a href="Genetic_algorithm" title="Genetic algorithm">genetic algorithms</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li></ul>

<div class="mw-heading mw-heading2"><h2 id="PDE-constrained_optimization">PDE-constrained optimization</h2></div>

<p><a href="Partial_differential_equation" title="Partial differential equation">Partial differential equations</a> (PDEs) are widely used to describe hydrological processes, suggesting that a high degree of accuracy in hydrological optimization should strive to incorporate <a href="PDE-constrained_optimization" title="PDE-constrained optimization">PDE constraints into a given optimization</a>. Common examples of PDEs used in hydrology include:

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<ul><li><a href="Groundwater_flow_equation" title="Groundwater flow equation">Groundwater flow equation</a></li>

<li><a href="Primitive_equations" title="Primitive equations">Primitive equations</a></li>

<li><a href="Shallow_water_equations#One-dimensional_Saint-Venant_equations" title="Shallow water equations">Saint-Venant equations</a></li></ul>

<p>Other environmental processes to consider as inputs include:

</p>

<ul><li><a href="Evapotranspiration" title="Evapotranspiration">Evapotranspiration</a></li>

<li><a href="Geomorphology" title="Geomorphology">Geomorphology</a></li>

<li><a href="Sediment_transport" title="Sediment transport">Sediment transport</a></li></ul>

<ul><li><a href="Drainage_research" title="Drainage research">Drainage research</a></li>

<li><a href="Geographic_information_system" title="Geographic information system">Geographic information system</a></li>

<li><a href="Integrated_water_resources_management" class="mw-redirect" title="Integrated water resources management">Integrated water resources management</a></li>

<li><a href="Optimal_control" title="Optimal control">Optimal control</a></li>

<li><a href="Pipe_network_analysis" title="Pipe network analysis">Pipe network analysis</a></li>

<li><a href="Water_in_California" title="Water in California">Water in California</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFAhlfeldMulveyPinderWood1988" class="citation journal cs1">Ahlfeld, David P.; Mulvey, John M.; Pinder, George F.; <a href="Eric_Franklin_Wood" title="Eric Franklin Wood">Wood, Eric F.</a> (1988). "Contaminated groundwater remediation design using simulation, optimization, and sensitivity theory: 1. Model development". <i>Water Resources Research</i>. <b>24</b> (3): <span class="nowrap">431–</span>441. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1988WRR....24..431A">1988WRR....24..431A</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1029%2FWR024i003p00431">10.1029/WR024i003p00431</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1944-7973">1944-7973</a>.</cite></span>

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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFAlminagorta2016" class="citation journal cs1">Alminagorta, Omar (2016). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=1018&context=water_pubs">"Systems modeling to improve the hydro-ecological performance of diked wetlands"</a></span>. <i>Water Resources Research</i>. <b>52</b> (9): <span class="nowrap">7070–</span>7085. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2016WRR....52.7070A">2016WRR....52.7070A</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F2015WR018105">10.1002/2015WR018105</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:31097159">31097159</a>.</cite></span>

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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFFeyenGorelick2005" class="citation journal cs1">Feyen, Luc; Gorelick, Steven M. (2005). "Framework to evaluate the worth of hydraulic conductivity data for optimal groundwater resources management in ecologically sensitive areas". <i>Water Resources Research</i>. <b>41</b> (3): 03019. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005WRR....41.3019F">2005WRR....41.3019F</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1029%2F2003WR002901">10.1029/2003WR002901</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:108490062">108490062</a>.</cite></span>

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<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFAlminagortaTesfatsionRosenbergNeilson2013" class="citation journal cs1">Alminagorta, Omar; Tesfatsion, Bereket; Rosenberg, David E.; Neilson, Bethany (2013). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=1773&context=cee_facpub">"Simple Optimization Method to Determine Best Management Practices to Reduce Phosphorus Loading in Echo Reservoir, Utah"</a></span>. <i>Journal of Water Resources Planning and Management</i>. <b>139</b>: <span class="nowrap">122–</span>125. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1061%2F%28ASCE%29WR.1943-5452.0000224">10.1061/(ASCE)WR.1943-5452.0000224</a>.</cite></span>

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<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite id="CITEREFSanthoshFaridYoucef-Toumi2014" class="citation journal cs1">Santhosh, Apoorva; Farid, Amro M.; Youcef-Toumi, Kamal (2014). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200925233116/http://amfarid.scripts.mit.edu/resources/Journals/EWN-J10.pdf">"Real-time economic dispatch for the supply side of the energy-water nexus"</a> <span class="cs1-format">(PDF)</span>. <i>Applied Energy</i>. <b>122</b>: <span class="nowrap">42–</span>52. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014ApEn..122...42S">2014ApEn..122...42S</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.apenergy.2014.01.062">10.1016/j.apenergy.2014.01.062</a>. Archived from <a rel="nofollow" class="external text" href="http://amfarid.scripts.mit.edu/resources/Journals/EWN-J10.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2020-09-25<span class="reference-accessdate">. Retrieved <span class="nowrap">2019-08-09</span></span>.</cite></span>

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<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFDandySimpsonMurphy1996" class="citation journal cs1">Dandy, Graeme C.; Simpson, Angus R.; Murphy, Laurence J. (1996). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190810054355/https://pdfs.semanticscholar.org/14f3/7a77cb58a1d29eb5de08faf64cc7f2c476b9.pdf">"An improved genetic algorithm for pipe network optimization"</a> <span class="cs1-format">(PDF)</span>. <i>Water Resources Research</i>. <b>32</b> (2): <span class="nowrap">449–</span>458. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1996WRR....32..449D">1996WRR....32..449D</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1029%2F95WR02917">10.1029/95WR02917</a>. <a href="Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/2440%2F1073">2440/1073</a></span>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:16097463">16097463</a>. Archived from <a rel="nofollow" class="external text" href="https://pdfs.semanticscholar.org/14f3/7a77cb58a1d29eb5de08faf64cc7f2c476b9.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2019-08-10.</cite></span>

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<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><a href="Stephen_P._Boyd" title="Stephen P. Boyd">Boyd, Stephen P.</a>; Vandenberghe, Lieven (2004). <i><a rel="nofollow" class="external text" href="https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf">Convex Optimization</a></i> (PDF). Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-83378-3</bdi>.</li>

<li>Loucks, Daniel P.; van Beek, Eelco (2017)<i>. <a rel="nofollow" class="external text" href="https://www.springer.com/gp/book/9783319442327">Water Resource Systems Planning and Management: An Introduction to Methods, Models, and Applications</a></i>. Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9783319442327</bdi>.</li>

<li><a href="Jorge_Nocedal" title="Jorge Nocedal">Nocedal, Jorge</a>; Wright, Stephen (2006)<i>. <a rel="nofollow" class="external text" href="https://www.springer.com/gp/book/9780387303031">Numerical Optimization</a></i>. Springer Series in Operations Research and Financial Engineering, Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780387303031</bdi>.</li>

<li>Qin, Youwei; Kavetski, Dmitri; Kuczera, George (2018). <a rel="nofollow" class="external text" href="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"</a>. <i>Water Resources Research</i>. <b>54</b> (11): 9637-9654.</li>

<li>Tayfur, Gokmen (2017). <a rel="nofollow" class="external text" href="https://link.springer.com/article/10.1007/s11269-017-1694-6">"Modern Optimization Methods in Water Resources Planning, Engineering and Management"</a>. <i>Water Resources Management</i>. <b>31</b>: 3205-3233.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://ocw.mit.edu/courses/civil-and-environmental-engineering/1-731-water-resource-systems-fall-2006/index.htm">Water Resource Systems</a> (<a href="MIT_OpenCourseWare" title="MIT OpenCourseWare">MIT OpenCourseWare</a>)

<ul><li><a rel="nofollow" class="external text" href="https://ocw.mit.edu/courses/civil-and-environmental-engineering/1-731-water-resource-systems-fall-2006/lecture-notes/">Lecture notes</a></li></ul></li></ul>

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</style><div id="Hydraulics57" style="font-size:114%;margin:0 4em"><a href="Hydraulics" title="Hydraulics">Hydraulics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Hydraulics" title="Hydraulics">Hydraulics</a></li>

<li><a href="Hydraulic_fluid" title="Hydraulic fluid">Hydraulic fluid</a></li>

<li><a href="Fluid_power" title="Fluid power">Fluid power</a></li>

<li><a href="Hydraulic_engineering" title="Hydraulic engineering">Hydraulic engineering</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modeling</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bernoulli's_principle" title="Bernoulli's principle">Bernoulli's principle</a></li>

<li><a href="Darcy%E2%80%93Weisbach_equation" title="Darcy–Weisbach equation">Darcy–Weisbach equation</a></li>

<li><a href="Groundwater_flow_equation" title="Groundwater flow equation">Groundwater flow equation</a></li>

<li><a href="Hazen%E2%80%93Williams_equation" title="Hazen–Williams equation">Hazen–Williams equation</a></li>

<li><a href="Open-channel_flow" title="Open-channel flow">Open-channel flow</a> (<a href="Manning_formula" title="Manning formula">Manning formula</a>)</li>

<li><a href="Pipe_network_analysis" title="Pipe network analysis">Pipe network analysis</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Technologies</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Hydraulic_machinery" title="Hydraulic machinery">Machinery</a></li>

<li><a href="Hydraulic_accumulator" title="Hydraulic accumulator">Accumulator</a></li>

<li><a href="Hydraulic_brake" title="Hydraulic brake">Brake</a></li>

<li><a href="Hydraulic_circuit" class="mw-redirect" title="Hydraulic circuit">Circuit</a></li>

<li><a href="Hydraulic_cylinder" title="Hydraulic cylinder">Cylinder</a></li>

<li><a href="Hydraulic_drive_system" class="mw-redirect" title="Hydraulic drive system">Drive system</a></li>

<li><a href="Hydraulic_manifold" title="Hydraulic manifold">Manifold</a></li>

<li><a href="Hydraulic_motor" title="Hydraulic motor">Motor</a></li>

<li><a href="Hydraulic_power_network" title="Hydraulic power network">Power network</a></li>

<li><a href="Hydraulic_press" title="Hydraulic press">Press</a></li>

<li><a href="Hydraulic_rescue_tools" class="mw-redirect" title="Hydraulic rescue tools">Rescue tools</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Public networks</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Liverpool_Hydraulic_Power_Company" title="Liverpool Hydraulic Power Company">Liverpool</a></li>

<li><a href="London_Hydraulic_Power_Company" title="London Hydraulic Power Company">London</a></li>

<li><a href="Manchester_Hydraulic_Power" title="Manchester Hydraulic Power">Manchester</a></li></ul>

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This article is issued from <a class="external text" title="Last edited on 2025-05-26" href="https://en.wikipedia.org/wiki/?title=Hydrological_optimization&oldid=1292388999">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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