FLOOD09697 - Laserfiche WebLink

Home Browse Search

CHAPTER V MATHEMATICAL MODEL OF THE SOCIAL SYSTEM Introduction of the Basic Elements of the Model Purpose and Approach The major objective of this study is to trans- lale the system in the conceptual modei shown in Figure 4.1 into a mathematical model for a compuler. The equations reflect the fundamental processes and complex interactions involved in the real world sys. tem. The chapter describes the process and derives a general form of the equations which may be applic- able to any area. This general equation is shown as Ihe summarization of the chapter. Succeeding chap- ters present Ihe actual compuler model, and Table 6.1 shows the equations as calibrated for the Sail Lake County sludy area. The model is based on using a multiple step re- gression technique to derive a general equation winch represents a decision process in regard to a proposal by any group, whether the group be an agency or Ihe public. Any group may be included in the model by calibrating Ihe equation for that group.! Thus the model may be enlarged to as complex a system as that ilIustraled in Figure 4.1 once appropriate data are collected on the additional groups. The model is viewed as an experimental attempt to mathemalically model a human behavior system and thus to provide a useful simulation tool for pian- ning based upon realistic behavioral data. The model includes complex muiti-relaled variables and provides trade off conditions with respect to Ihem. Although problems remain, Ihe system worked rather well in simulating behavior. It is expected Ihat further test- ing and application would improve it for more general use and similar equations could be adapted to many planning uses. lOther equations may also have to be adjusted because influences of the additional groups within the system would then be explicitly included. Flow Chart of Ihe Mathematical Model As il1uslrated in Figure 1.2, the working model is considerably more simplified than either Ihe real world or the conceplual model. Inevitably, informa- tion is lost as the mathematical flow model in Figure 5.1 is developed from Ihe conceptual model in Figure 4.1. Each line in Figure 5.1 shows a relationship which may occur in the decision process. The equations for each step are indicated on Ihe right side colullUl and are derived in this chapter. They are summarized in Table 6.1 for the model calibrated for Salt Lake County. From Equation III onward, Ihe "yes" and "no 11 labels indicate rejection or approval at that point of a particular flood control proposal by the related agency or group. As can be seen from the conceptual model, after an initial decision an agency may receive new information, reevaluate the situation, and change its mind. The model assumes that a time sequence occurs between each step. In the real world, this time lag is undefined and can vary from overlapping to long inler- vening periods depending on which steps are involved, the urgency of the situation, or other reasons. Evalua- tion and communication between an implementing agency and decision agency, for instance, may be rapid for a proposal, but the public input may take some time. The time involved is not explicitly ex- pressed in Ihe equations because of lack of detailed longitudinal data. The process is dynamic but data were collected at one time only under the assumption that Ihe situation had assumed an equilibrium. The resulting static model is comparatively easy to under- stand and appears to be adequate provided Ihat care is used in interpretation. Equations in the model could be applied at ear- lier slages in Ihe process and could give different re- results because the various values of the dependent variables may vary through time. The basic assump- tion for the validity of the equations is that the rela- lionships belween the factors contained in the equa- tions and the dependent variables is consistent and not Ihal the values of these variables do nol change 57