Hydrological optimization applies
mathematical optimization techniques (such as
dynamic programming
Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. ...
,
linear programming,
integer programming
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective ...
, or
quadratic programming
Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constr ...
) to water-related problems. These problems may be for
surface water,
groundwater
Groundwater is the water present beneath Earth's surface in rock and soil pore spaces and in the fractures of rock formations. About 30 percent of all readily available freshwater in the world is groundwater. A unit of rock or an unconsolidated ...
, or the combination. The work is interdisciplinary, and may be done by
hydrologist
Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and environmental watershed sustainability. A practitioner of hydrology is calle ...
s,
civil engineers,
environmental engineer
Environmental engineering is a professional engineering discipline that encompasses broad scientific topics like chemistry, biology, ecology, geology, hydraulics, hydrology, microbiology, and mathematics to create solutions that will protect an ...
s, and
operations research
Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decis ...
ers.
Simulation versus optimization
Groundwater and surface water flows can be studied with hydrologic
simulation
A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the s ...
. A typical program used for this work is
MODFLOW
MODFLOW is the U.S. Geological Survey modular finite-difference flow model, which is a computer code that solves the groundwater flow equation. The program is used by hydrogeologists to simulate the flow of groundwater through aquifers. The so ...
. 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 markets 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 gene ...
.
PDE-constrained optimization
Partial differential equations
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function.
The function is often thought of as an "unknown" to be solved for, similarly to ...
(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 Used in hydrogeology, the groundwater flow equation is the mathematical relationship which is used to describe the flow of groundwater through an aquifer. The transient flow of groundwater is described by a form of the diffusion equation, similar ...
*
Primitive equations
The primitive equations are a set of nonlinear partial differential equations that are used to approximate global atmospheric flow and are used in most atmospheric models. They consist of three main sets of balance equations:
# A '' continuity e ...
*
Saint-Venant equations
Other environmental processes to consider as inputs include:
*
Evapotranspiration
Evapotranspiration (ET) is the combined processes by which water moves from the earth’s surface into the atmosphere. It covers both water evaporation (movement of water to the air directly from soil, canopies, and water bodies) and transpi ...
*
Geomorphology
*
Sediment transport
See also
*
Drainage research Drainage research is the study of agricultural drainage systems and their effects to arrive at optimal system design.
Aspects to be covered
Agricultural land drainage has agricultural, environmental, hydrological, engineering, economical, soc ...
*
Geographic information system
*
Integrated water resources management
Water resources are natural resources of water that are potentially useful for humans, for example as a source of drinking water supply or irrigation water. 97% of the water on the Earth is salt water and only three percent is fresh water; slightl ...
*
Optimal control
*
Pipe network analysis
*
Water in California
California's interconnected water system serves over 30 million people and irrigates over of farmland. As the world's largest, most productive, and potentially most controversial water system, it manages over of water per year.
Water and wate ...
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, anyw ...
)
*
Lecture notes
{{DEFAULTSORT:Hydrological Optimization
Hydraulics
Hydraulic engineering
Hydrology
Mathematical optimization
Optimal control
Water resources management