2.3.
Constraints
49
The head Zi jt can be related to the storage in the reservoir by means of
empirical data for each reservoir, such as shown in Fig. 2.3. The figure
represents a least-squares fit of typical empirical data.
Z ijt
= 9.5367£ w - 15.180£* 7i + 1.1311£* y< - 0.0297885^,·*
On the other hand, if the reservoir is a constant-head reservoir, the energy
output is then directly proportional to the reservoir outflow. Maass. [1962]
indicated that the operating costs of power plants are essentially proportional to the size of the plant except at very low power capacities. We will
assume that the sizes of the power plants are given; hence they will not
be variables.
2.3.4. Recreation
Demands
and Related
Constraints
Some of the major benefits to be derived from the expansion of a water
resources system are the primary and secondary benefits to be derived from
recreation. Therefore, it appears important that models developed for the
analysis of such systems contain factors that represent the demand for
and supplies of recreation in a river basin. Recreational benefits can be
related to five factors: (1) the accessibility of recreational resources to the
public, (2) the relative attractiveness of the resources, (3) the competing
opportunities available, (4) the capacity of the facilities and resources to
accommodate the public, and (5) the willingness of the public to incur
expenses to enjoy the use of the recreational resources, if they exist. How
to measure these quantities and introduce them into a model of a river
basin is not entirely resolved, as one might expect. Some inroads are being
made [Ditton, 1969], but it is safe to say that we do not have enough current knowledge to quantify the recreation factors to the extent desired.
Therefore, we will assume that the following constraints are appropriate in
placing limits on water storage for recreation in reservoirs, but we will not
introduce terms into the objective function representing recreation benefits. However, if recreation benefits must be included in the objective function, one might take data for attendance versus reservoir capacity [U.S.
Corps of Engineers, 1962], fit it by regression
no. attendees = 3.65 - OMSj
+ 0.012S,
2
surface acre
evaluate each visitor day, say $1.00/day, and, using the relation between
surface acreage and storage such as Fig. 2.4 plus estimated attendance,
estimate the recreation benefits per month (or year).
Constraints
49
The head Zi jt can be related to the storage in the reservoir by means of
empirical data for each reservoir, such as shown in Fig. 2.3. The figure
represents a least-squares fit of typical empirical data.
Z ijt
= 9.5367£ w - 15.180£* 7i + 1.1311£* y< - 0.0297885^,·*
On the other hand, if the reservoir is a constant-head reservoir, the energy
output is then directly proportional to the reservoir outflow. Maass. [1962]
indicated that the operating costs of power plants are essentially proportional to the size of the plant except at very low power capacities. We will
assume that the sizes of the power plants are given; hence they will not
be variables.
2.3.4. Recreation
Demands
and Related
Constraints
Some of the major benefits to be derived from the expansion of a water
resources system are the primary and secondary benefits to be derived from
recreation. Therefore, it appears important that models developed for the
analysis of such systems contain factors that represent the demand for
and supplies of recreation in a river basin. Recreational benefits can be
related to five factors: (1) the accessibility of recreational resources to the
public, (2) the relative attractiveness of the resources, (3) the competing
opportunities available, (4) the capacity of the facilities and resources to
accommodate the public, and (5) the willingness of the public to incur
expenses to enjoy the use of the recreational resources, if they exist. How
to measure these quantities and introduce them into a model of a river
basin is not entirely resolved, as one might expect. Some inroads are being
made [Ditton, 1969], but it is safe to say that we do not have enough current knowledge to quantify the recreation factors to the extent desired.
Therefore, we will assume that the following constraints are appropriate in
placing limits on water storage for recreation in reservoirs, but we will not
introduce terms into the objective function representing recreation benefits. However, if recreation benefits must be included in the objective function, one might take data for attendance versus reservoir capacity [U.S.
Corps of Engineers, 1962], fit it by regression
no. attendees = 3.65 - OMSj
+ 0.012S,
2
surface acre
evaluate each visitor day, say $1.00/day, and, using the relation between
surface acreage and storage such as Fig. 2.4 plus estimated attendance,
estimate the recreation benefits per month (or year).