Optimizing water resource development to reduce land-surface subsidence

Abstract

An optimization model was developed to allocate surface and groundwater resources under various water management policies which might be implemented to control land-surface subsidence. This model allocated the water resources of a region so that the overall cost of water development and land-surface subsidence was minimized. To use this model, a hydrologic model was developed to predict the piezometric heads in sand and clay layers caused by groundwater pumpage. A compaction, or subsidence model, used the resulting piezcmetric heads from the hydrologic model to predict land-surface subsidence. A linear programming model was then developed to optimally allocate ground and surface water resources within a region so that the cost of water and land subsidence was minimized. Using data from the land-subsidence area at Houston, Texas, a conceptual two-dimensional, vertical geologic profile was developed to describe the aquifer-aquitard system in the Houston area. This conceptual geologic profile was composed of a constant head boundary at the top, three layers of clay, two layers of sand, three layers of clay, two layers of sand, and one no-flow layer at the bottom. Field values for hydraulic conductivity, specific storage coefficient, pumpage rate, and initial piezometric head were used in the hydrologic model. Successive applications of the hydrologic and compaction models were made over a 10 year period for varying groundwater withdrawal rates. This information was used to develop a series of subsidence-pumpage curves for each of 15 surface grid points. The optimization model was independent of the hydrologic and compaction models, and independent of the grid dimensions and shape. Because the resulting subsidence-pumpage curves were non-linear, separable programming was used to approximate the subsidence-pumpage curves as the sum of a set of linear functions. Thus, a linear programming formulation of the optimization problem could be used. Three basic water use policies were evaluated and compared...