# Environmental Quality and Residuals Management: Report of a Research Program on Economic, Technological, and Institutional Aspects

By Allen V. Kneese; Blair T. Bower | Go to book overview

One major problem with a large nonlinear programming problem of the type discussed here is that it may frequently be nonconvex. If this is so, then the procedure for solving it may fail to find the optimum optimorum and instead come to a halt at a lesser peak in the objective function.

Appendix 5-B Natural Systems Models

In both the text and appendix 5-A, we have referred to models of natural environmental systems and the central role they play in analysis for REQM. In this appendix we present a brief discussion of the various types of such models and the procedures by which they are incorporated in the larger model discussed in appendix 5-A.

Natural systems models--air and water dispersion, sediment and nutrient runoff from land, chemical reaction, and biological systems--may be used to describe the impact on the environment of energy and material residuals discharged from the production and consumption activities included in a regional REQM model. Generally, natural systems models are used to specify steady state ambient concentrations of residuals and population sizes of species, at various points in space throughout the region of interest, given a set of values for such environmental variables as stream flow and velocity, groundwater flow and aquifer characteristics, slope and soil erodability, wind speed and direction, atmospheric stability, and atmospheric mixing depth.

Some environmental models are easier to deal with than others within a mathematical optimization framework. In general, this depends on the mathematical structure of the model. In terms of the complexity involved, it is useful to distinguish among four broad categories of models: (1) linear, explicit functions; (2) linear, implicit functions; (3) nonlinear, explicit functions; and (4) nonlinear, implicit functions.

Two natural systems submodels were actually used in conjunction with the regional REQM model discussed in appendix 5-A. The first, a linear atmospheric dispersion model, was used to predict ambient concentration levels of sulfur dioxide and suspended particulates throughout the region. The second, a nonlinear aquatic ecosystem model, was used to predict

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AUTHORS' NOTE: This appendix is based on material prepared by Walter O. Spofford, Jr., and Robert A. Kelly.

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