An application of the adjoint technique to locating wastewater discharges into a surface water system

Water resource quantity and quality issues are often the most crucial factors to consider when governments plan for medium and long term economic development. Frequently, planners designate specific regions for various types and levels of development according to each region’s intrinsic attributes and relationship to those infrastructure systems required for development. The planning process is inherently difficult since the impact of development on water quality, and hence on the intended use of each area, is not known a priori. As a result, planning for development tends to follow a prescriptive rather than a proactive pattern. Inverse models for surface water quality in the context of planning appear to be advantageous since, for a given development strategy, the water quality standards needed to support and maintain a proposed development plan can be determined in advance. An explicit adjoint model for uniform flows is proposed in this paper that can be easily applied to 1 - or 2-dimensional surface water systems to identify feasible regions for siting waste water discharges while maintaining desired water quality standards at specified target regions.