Response Functions - How Can Response Functions be Used?
Response functions describe the response of specific river reaches to ground water pumping or recharge at specific locations for specific times.  In physical situations where response functions are applicable (see section on assumptions), response functions may have several uses.

One of the most basic uses of response functions may be to obtain and convey a better understanding of the way in which surface water systems interact with ground water systems.  Graphs showing how response (stream depletion) changes with time are one way of gaining an understanding of the attenuation of pumping effects on surface water resources.  Superimposing these graphs on a map provides additional information on how impacts change depending on the location of pumping (see figure right).  Contouring response ratios (response functions at a single point in time) for an entire aquifer can portray how different pumping locations impact a given river reach.  In the Snake River Plain aquifer, contours of steady state response functions (response after many years of continuous pumping) can provide guidance to water managers as to the degree that pumping in any area impacts different reaches of the Snake River:  Upper Snake reaches, Blackfoot to Neeley reach, Neeley to Minidoka reach, and Kimberly to King Hill reach.

In many states, ground water and surface water supplies are being conjunctively managed (see Water Rights and Conjunctive Management page).  This integrated management philosophy may result in ground water users being held partially responsible for surface water shortages.  If this is the case, then the quantities that individuals or groups of ground water users are accountable for must be determined.  This determination is an essential step in development of mitigation plans.  Mitigation in the form of managed recharge will be designed to offset injury resulting from pumping.  Just as pumping impacts may be readily determined from response functions, the counter-effect of recharge may be assessed.  Response functions may be incorporated into spreadsheet water accounting programs to determine debits, credits, and balances associated with ground water pumping and recharge.

In a simple analytical expression, or a table of numbers, response functions can describe the response of a surface water body to ground water pumping or recharge at a selected location. Subdividing an aquifer into a series of zones allows representation of cause and effect relationships by a simple series of independent equations or tables.  These simplified relationships can then be incorporated into regional surface water or multi-disciplinary models that represent the aquifer as one component of a larger system (see figure below).  This allows the inclusion of ground water systems into more holistic ecosystem models.

The additive nature of response functions also makes them applicable to optimization techniques.  Optimization methods may be used to identify schemes to accomplish goals such as minimizing pumping cost or drawdown at specific locations.  Development of response functions is a necessary part of optimization in ground water systems.

Information supplied by Idaho Water Resource Research Institute, University of Idaho December 1998
Authors: Dr. Gary Johnson, Donna Cosgrove, and Mark Lovell.
Graphics: Sherry Laney and Mark Lovell of Idaho Water Resources Research Institute.
All State of Idaho images and graphics created with GIS files obtained through Idaho Department of Water Resources Public Domain GIS unless otherwise noted.
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