WSP10809

• File Number: 8273.500
• Description: Colorado River Basin Salinity Control - Federal Agency Reports - EPA
• Basin: Colorado Mainstem
• Water Division: 5
• Date: 4/1/1978
• Title: Integrating Desalination and Agricultural Salinity Control Alternatives
• Water Supply Pro - Doc Type: Report/Study

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range of reductions in salinity, and second, it would delineate
how much of these costs are to be expended in each river sub-
system. In other words, the evaluation of the optimal strategy
at level 4 involves systematic comparisons of level 3 cost-
effectiveness functions and once the strategy had been deter-
mined, it also yields the optimal costs or expenditures in each
level 3 alternative (river subsystem). In a similar vein, the
level 2 costs and policies are determined from a knowledge of
the level 3 optimal as determined during the level 4 analysis,
and so on. Thus, the cost-effectiveness function for any
alternative .within a level is:

1. the result of optimization of respective cost-
effectiveness functions at a lower level and
therefore a minimum cost relationship at every
point; and
2. the sum of costs from optimal investments into each
alternative at a lower leveL The "policy space"
is therefore a delineation of lower level cost-
effectiveness function.

The preceding paragraphs noted the detailing of salinity
control strategy once the optimal is known. Determining the
basin optimal, on the other hand, begins at level 1. A com-
parison of level 1 cost-effectiveness functions describing
each alternative at that level produces the array of level 2
functions. Similar steps yield each succeeding level's
optimal program. Thus, the multilevel approach described herein
involves a vertical integration up through the levels to deter-
mine the optimal policy and a backwards trace to delineate its
components.

Mathematical Salinity Control Model

Consider a
basin such that
written:

single salinity control measure within a sub-
its cost-effectiveness characteristic can be

y! = f (x!)
~ ~

.. .. . . .. .. .. .. .. .. .. .. .. .. . . .. . .. .. .. .. .. . ... . .. .. .. .. .. . .. . .. .. .. .. .. .. .. .. (32)

in which,

y!
~
x!
~

= total cost attributable to the ith control measure
at the first level of optimization; and
= annual salt loading decrease associated with an
expenditure of yi dollars on the ith salinity control
measure.

Superscripts will refer to model level whereas subscripts will
designate alternatives. It is assumed that the relationship
between yl and xl can be determined and that the total potential
reduction in salt loading for the ith measure at level 1 is X!.
~

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