Direct measurement of stream or spring depletion by pumping is possible in relatively few cases. Measurement of depletion resulting from pumping of a specific well is possible only when the well is relatively close to the stream or spring and well pumping is a significant proportion of the stream or spring flow. It is also sometimes difficult to isolate the effects of a single well from other influences that may be causing changes in discharge. When it is possible to measure the relationships between pumping and stream or spring discharge, the proportion of depletion can be determined from measurements of stream or spring flow and well discharge. The depletion changes with time, so observations are required at different times. The response function can be represented by the proportion of well pumping appearing as depletion of the stream or spring. The response function will be valid within some limits of pumping rate, stream flow, and aquifer water level. These limits are site-specific and related to the assumptions identified in the section "Assumptions Supporting Response Functions".
Analytical methods have been developed and used to estimate the effects of ground water pumping on stream depletion. Methods such as those of Jenkins (1968) and Glover (1968) are burdened with intensive assumptions such as straight and fully penetrating streams, fully penetrating wells, and homogeneous and infinite aquifers. These methods, however, can be employed to develop response functions when data are inadequate to use more sophisticated techniques. In these cases, response functions involve little more than plugging the site-specific data into explicit equations.
Response functions can be developed from numerical models in situations where more data are available and numerical models have been developed. Some model codes generate response functions directly, in other situations it may be necessary to run multiple simulations, each simulating response to ground water pumping at a specific location (model grid with well). MODFLOW is the most widely used code for ground water modeling. It is accepted as the industry standard for numerical modeling of ground water systems. A detailed description of the use of MODFLOW for developing response functions can be found in the technical article Use of MODFLOW for Development of Response Functions. Simulated changes, when divided by the magnitude of the pumping rate, yield response functions. The simulations must be based on linear equations. This means that changes in aquifer thickness from pumping must be small relative to total thickness, and head-dependent boundary conditions must be linear functions of aquifer head. This is perhaps the most restrictive condition relative to the use of response functions. If springs dry up, streams transition between hydraulically connected and perched, or other non-linear conditions develop, and if these features significantly affect the operation of the system, then response functions should not be used. Their use should be limited to the range of conditions where these sort of changes do not significantly impact the system. This topic is also addressed in the section "Assumptions Supporting Response Functions".
Regardless of the technique used to develop the response functions, it must be recognized that the response functions are only as good as our conceptual understanding of the system and the data used in the development of the models!
Response functions describe the changes in the system (ground water levels or stream and spring discharge) resulting from ground water pumping or recharge at a specified site for a specified time duration. The response functions become useful tools because of the ability to the add effects of multiple pumping or recharge events. The events may be occurring at the same location sequentially, at multiple locations simultaneously, or both. This makes it most effective to generate response functions for the shortest duration of pumping that is of interest. The response to longer periods of pumping can then be developed by adding the effects from one pumping period to that of a second period immediately following the first. These sorts of operations are ideally suited to spreadsheets and data bases.