Embedding and response matrix techniques for maximizing steady-state ground-water extraction: computational comparison

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Journal of Ground Water





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Both response matrix and embedding techniques are used to compute optimal sustained‐yield ground‐water extraction strategies for confined aquifers. Historically, the response matrix method has been considered the most practical, because of numerical instability reported to occur when using the embedding approach for large aquifer systems. More recent studies have proven the embedding approach to be stable for large‐scale regional planning. Also, there is increasing emphasis on using microcomputers for ground‐water studies. Thus, it is appropriate to compare response matrix and embedding approaches to steady‐state problems in terms of computational efficiency and memory requirements.

For the hypothetical study area, a steady‐state embedding model requires less processing time than a comparable response matrix model. In addition, the embedding model sometimes requires less memory than a response matrix model. Required computer memory is frequently a function of the number of nonzero values in constraint equations. For embedding models, the number of nonzeroes is fixed for a particular study area. For response matrix models, the number of nonzeroes can increase dramatically in proportion to the number of pumping cells and cells at which heads must be constrained. For the sample system, if more than 25 percent of the cells can pump, the response matrix approach requires more memory than does the embedding approach. Before selecting an optimization model for a particular study, one should, as illustrated, evaluate potential memory requirements of both embedding and response matrix approaches. If there is a high percentage of pumping cells, or if many heads must be constrained or computed within the optimization model, the embedding approach seems preferable.

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