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.
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:
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.
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:
