Hydrological optimization
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Hydrological optimization applies
mathematical optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfiel ...
techniques (such as dynamic programming,
linear programming Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear function#As a polynomia ...
, integer programming, or quadratic programming) to water-related problems. These problems may be for
surface water Surface water is water located on top of land, forming terrestrial (surrounding by land on all sides) waterbodies, and may also be referred to as ''blue water'', opposed to the seawater and waterbodies like the ocean. The vast majority of surfac ...
,
groundwater Groundwater is the water present beneath Earth's surface in rock and Pore space in soil, soil pore spaces and in the fractures of stratum, rock formations. About 30 percent of all readily available fresh water in the world is groundwater. A unit ...
, or the combination. The work is interdisciplinary, and may be done by hydrologists,
civil engineer A civil engineer is a person who practices civil engineering – the application of planning, designing, constructing, maintaining, and operating infrastructure while protecting the public and environmental health, as well as improving existing i ...
s, environmental engineers, and
operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and ...
ers.


Simulation versus optimization

Groundwater and surface water flows can be studied with hydrologic
simulation A simulation is an imitative representation of a process or system that could exist in the real world. In this broad sense, simulation can often be used interchangeably with model. Sometimes a clear distinction between the two terms is made, in ...
. 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: # An objective, such as "Minimize cost" # Decision variables, which correspond to the options available to management # 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

* Contaminant remediation in aquifers. 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. * Maximizing well abstraction subject to environmental flow constraints. 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. * Hydrological optimization is now being proposed for use with
smart market A smart market is a periodic auction which is cleared by the operations research technique of mathematical optimization, such as linear programming. The smart market is operated by a market manager. Trades are not bilateral, between pairs of people, ...
s for water-related resources. *Pipe network optimization with
genetic algorithms In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to g ...
.


PDE-constrained optimization

Partial differential equations In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how ...
(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 The primitive equations are a set of nonlinear partial differential equations that are used to approximate global atmosphere, atmospheric flow and are used in most Global climate model, atmospheric models. They consist of three main sets of balance ...
* Saint-Venant equations Other environmental processes to consider as inputs include: *
Evapotranspiration Evapotranspiration (ET) refers to the combined processes which move water from the Earth's surface (open water and ice surfaces, bare soil and vegetation) into the Atmosphere of Earth, atmosphere. It covers both water evaporation (movement of w ...
*
Geomorphology Geomorphology () is the scientific study of the origin and evolution of topographic and bathymetric features generated by physical, chemical or biological processes operating at or near Earth's surface. Geomorphologists seek to understand wh ...
*
Sediment transport Sediment transport is the movement of solid particles (sediment), typically due to a combination of gravity acting on the sediment, and the movement of the fluid in which the sediment is entrained. Sediment transport occurs in natural systems wh ...


See also

* Drainage research *
Geographic information system A geographic information system (GIS) consists of integrated computer hardware and Geographic information system software, software that store, manage, Spatial analysis, analyze, edit, output, and Cartographic design, visualize Geographic data ...
* Integrated water resources management *
Optimal control Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations ...
* Pipe network analysis * Water in California


References


Further reading

* Boyd, Stephen P.; Vandenberghe, Lieven (2004).
Convex Optimization
' (PDF). Cambridge University Press. . *Loucks, Daniel P.; van Beek, Eelco (2017)''
Water Resource Systems Planning and Management: An Introduction to Methods, Models, and Applications
'. Springer. . * Nocedal, Jorge; Wright, Stephen (2006)''
Numerical Optimization
'. Springer Series in Operations Research and Financial Engineering, Springer. . *Qin, Youwei; Kavetski, Dmitri; Kuczera, George (2018)
"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)
"Modern Optimization Methods in Water Resources Planning, Engineering and Management"
''Water Resources Management''. 31: 3205-3233.


External links



(
MIT OpenCourseWare MIT OpenCourseWare (MIT OCW) is an initiative of the Massachusetts Institute of Technology (MIT) to publish all of the educational materials from its undergraduate- and graduate-level courses online, freely and openly available to anyone, anywh ...
) *
Lecture notes
{{DEFAULTSORT:Hydrological Optimization Hydraulics Hydraulic engineering Hydrology Mathematical optimization Optimal control Water resources management