5.5. Stochastic
Analysis of a Water Resources
System
139
5.5. Stochastic Analysis of a Water Resources System
A major assumption made in the formulation of the mathematical model
of the water resources system discussed in Chapter 4 was that all the system inputs and parameters, such as the hydrological inputs, future demand
profiles, and reservoir costs, were deterministic. Although deterministic
analysis leads to useful results, most of the significant water resources
parameters are in truth stochastic in nature because of the uncertainty in
rainfall distributions, population growth, and future economic conditions.
A few brief remarks on some of the routes to stochastic water resources
planning are appropriate at this point insofar as they attempt to answer
the same questions that are posed in a sensitivity analysis.
If simulation is to be used in the planning for a water resources system,
three successively more comprehensive strategies can be employed with a
stochastic runoff, stream flow, demand, and so on: (1) simulation analyses
using only historical sequences of data, (2) simulation analyses using a
number of possible future sequences of data, and (3) simulation followed
by deterministic optimization followed by regression.
Method 1 presumes that the sequence of stream flows, runoff, water
demands, and so on that occurred in the past will occur in the future. It
leads to operational policies that are based on the assumption that the
worst that has occurred historically will occur once again. Method 1 was
employed long before the current digital computational capability existed,
and would be optimal only if the expectation of penalties for the worst
event greatly outweighed all other considerations. Method 1 subsumes the
use of "critical period hydrology'' a technique that has been greatly
favoured by Hall and co-workers (see Section 2.1).
Method 2, which can be characterized as ordinary simulation, was developed by members of the Harvard Water Program in the early 1960s.
Stream flow, runoff, and similar data are fitted by probability distributions
and functions of time and distance. Then these relationships together with
a random-number generator can be used to generate equally likely future
data sets. Operational decisions, target levels, and physical configuration
are set, and a simulation study is run for a number of possible future sequences. The main difficulty with method 2 is not so much that it does not
adequately represent reality but that the results generated may not be
conclusive. Four levels of simulation are present: hydrology, operational
policy, commitment level, and physical facilities. The decisions to be
reached regarding operational policy and physical facility configuration
and timing are highly dimensional. To adequately span the population of
Analysis of a Water Resources
System
139
5.5. Stochastic Analysis of a Water Resources System
A major assumption made in the formulation of the mathematical model
of the water resources system discussed in Chapter 4 was that all the system inputs and parameters, such as the hydrological inputs, future demand
profiles, and reservoir costs, were deterministic. Although deterministic
analysis leads to useful results, most of the significant water resources
parameters are in truth stochastic in nature because of the uncertainty in
rainfall distributions, population growth, and future economic conditions.
A few brief remarks on some of the routes to stochastic water resources
planning are appropriate at this point insofar as they attempt to answer
the same questions that are posed in a sensitivity analysis.
If simulation is to be used in the planning for a water resources system,
three successively more comprehensive strategies can be employed with a
stochastic runoff, stream flow, demand, and so on: (1) simulation analyses
using only historical sequences of data, (2) simulation analyses using a
number of possible future sequences of data, and (3) simulation followed
by deterministic optimization followed by regression.
Method 1 presumes that the sequence of stream flows, runoff, water
demands, and so on that occurred in the past will occur in the future. It
leads to operational policies that are based on the assumption that the
worst that has occurred historically will occur once again. Method 1 was
employed long before the current digital computational capability existed,
and would be optimal only if the expectation of penalties for the worst
event greatly outweighed all other considerations. Method 1 subsumes the
use of "critical period hydrology'' a technique that has been greatly
favoured by Hall and co-workers (see Section 2.1).
Method 2, which can be characterized as ordinary simulation, was developed by members of the Harvard Water Program in the early 1960s.
Stream flow, runoff, and similar data are fitted by probability distributions
and functions of time and distance. Then these relationships together with
a random-number generator can be used to generate equally likely future
data sets. Operational decisions, target levels, and physical configuration
are set, and a simulation study is run for a number of possible future sequences. The main difficulty with method 2 is not so much that it does not
adequately represent reality but that the results generated may not be
conclusive. Four levels of simulation are present: hydrology, operational
policy, commitment level, and physical facilities. The decisions to be
reached regarding operational policy and physical facility configuration
and timing are highly dimensional. To adequately span the population of