FLOOD09697

• County: Statewide
• Community: Nationwide
• Basin: Statewide
• Title: Mathematical Modeling of a Sociological and Hydrologic Decision System
• Date: 6/1/1978
• Prepared By: Institute for Social Science Research on Natural Resources, Utah State Univ.
• Floodplain - Doc Type: Educational/Technical/Reference Information

through time or during the process of project deter-
mination. It is true, however, that in order to predict
the results at the end of the evaluation process, some
way of predicting values al that point must be used;
this is ideally done by Ihe use of dynamic equalions
for Ihe variables2 or by the assumption Ihat the values
of relevant variables will remain the same or change
in a predetermined way.3

The blocks on the right of Figure 5.1 identify
specific equations which are used in the model. These
equations are developed later in this chapler. As in-
dicated by the equalion numbers within Ihe blocks,
the same equation may be used in two steps in some
inslances (see blocks 4 and 6 and 7 and 8). This means
lhat values for an agency in one of these steps were
also used later. In the evenl that a social occurrence
(such as Ihe ecology movemenl) alters basic public
values, Ihe equations would need 10 be recalibrated.
Allwo points in the flow chart (blocks 5 and 12) the
user of Ihe model must provide values for the para-
melers Ip depicllocal conditions.

The decision agency decides that a plan is need-
ed and asks the planning agency for a plan or for al-
lemate plans.4 Plans are then formulated by the plan-
ning agency and a decision made as to whether it is
feasible. If so, Ihe planning agency would forward it
on to the decision agency.

Equation I (5.4) and Equation 11 (5.6) and IF
statement A (5.7) are the only mathematical formu-
las used in Ihe model that are nol applications of the
basic conceptual equation of the decision process of
a group regarding a flood control proposal.

Detailed Development of the
Mathematical Model

Concepts in Formulalions of the
Mathematical Model

The mathemalical model of Ihe institutional
response to flood problems was formulated in terms

2A basic need expressed in Chapter VIII is to develop
equations for the perceived characteristics of proposals.

3 An analysis of the measured variables may indicate
which variables would have to change in value in order to
alter the results of a decision process or if change is even possi.
ble.

4Almost any plan could be submitted by the planning
agency for evaluation in the model. The computer program
could be modified so that the highest positively rated plan
would be submitted Illst. If this plan were rejected subse-
quently, the second highest rated plan could be submitted,
and so on. Also, the system could be established so that plans
are submitted in order of priority so long as a constraint is
not exceeded. An example would be a financial limitation,
in which case alternate plans would be submitted so long as
the total costs does not exceed a specified amount.

of representing Ihe interaction of four principal types
of components. They are:
I. Social characlerislics of the general public
and other populations (including organized
interesl groups) in the area concerned.
2. Agency characleristics of both aclion and
planning agencies.5
3. Physical characteristics of the proposed flood
conlrol melhods.
4. Hydrologic system characteristics.

The first two sels of characteristics are essentially
social, and Ihe second two are essentially physical. In.
leractions within and between subsets need to be de-
fmed and represenled in order 10 model the sociologic
response to hydrologic problems.

A linear form of relationships within the model
is generally easier to work with, therefore, it is desir-
able to use a linear model. However, appropriate
limits of applicability need to be set (Narayana et aI.,
1970).

Equations representing a subsystem can be cali-
braled using measurements of the perlinent variables.
Five major variables selected from previous tests to
be significant in the initial selection of a proposed pro-
ject plan are:
I. Flood control abiiity.
2. Cost per capita.
3. Oul.door aeslhelics provided or destroyed.
4. Recreation provided or deslroyed.
5. Ecological impact (disturbance or improve-
menl of natural conditions).

Values for these five variables are used by the com-
puter model to determine the acceptability of a possi-
ble plan. The variables in the equations (i.e., the sets
of characteristics) need to be operalionally deflned
for alternative flood conlrol proposals to be compared
on the same basis. A melhod was developed for assign-
ing numerical values to the perceived significant char~
acteristics of flood control proposals and of pertinenl
social groups to form scales thai may be treated as
interval or ratio data, a necessary level of measure-
ment for modeling purposes.6

As consistent measures are established, they can
be used in regression analysis to predict effects from
causes. Coefficients for the equations can be deter-

SThe planning and action agencies may be the same.
The categories of characteristics for the various types of agen-
cies involved will be largely the same, but appropriate values
of these characteristics need to be determined.
60rdinal data with a reasonably large number of res-
ponse categories over the range of the variable may be treated
as interval data with approximately correct results (Labovitz,
1970, Baker et al., 1971).

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