58
2. Formulating
the
Problem
Table 2.2
List of Variables in the Mathematical Model
Variable
Description
Equation in which
it appears
Independent variables
ha
Qimt
Dependent variables
Designated whether return is available
Amount of imported water
Quantity of water flow
(2.1)
(2.7), (2.13), (2.14)
(2.7), (2.10),
(2.13), (2.16)
Designates whether water is imported
(2.13)
λ*
Designates whether capital must be
(2.1), (2.2)-(2.6)
provided
Diit
Water supplied for irrigation
(2.7), (2.12), (2.13)
Em
Evaporation losses from reservoir
(2.13)
F w
Amount of water supplied for industrial
(2.11), (2.13)
and municipal use
Sijt
Storage volume of water
(2.7)-(2.10),
(2.13), (2.15),
(2.17)
Xijt
Revenue from reservoir
(2.1), (2.7)
Geological Survey has collected all the available flow data, prior to 1951,
and published it in the form of compilation reports (e.g., U.S. Geological
Survey [1957]). For years subsequent to 1951, the collected flow data is
obtainable from the USGS annual Water Supply Papers for the same
basins (e.g., U.S. Geological Survey [1961]).
In Latin America the available hydrological data are limited. A study of
the relevant literature on countries as disparate as Colombia and Chile
[Bulkley et al. } 1965; Wallace, 1966; Posada et al, 1966; McLaughlin,
1967; King, 1967] reveals that the length of rainfall and streamflow records
in major river basins can vary from 5 to 50 years.
In the model, streamflows from a typical historical hydrological record
(Uijt)
can be used as inputs to constraint (2.13) as illustrated in Fig. 2.6.
2.5.2. The Budgetary
Constraint
The budgetary constraint is of the form suggested by Marglin [1962]
for participation by a national government in water resources projects.