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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
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<br />rapidly developing melropolilan area which includes <br />Salt Lake City and several suburban communities in <br />Salt Lake County, Utah. Because of rapid urban growth <br />and the consequent effects on runoff and potential <br />damage, flood control is of increasing concern 10 city <br />and county officials. <br /> <br />The Salt Lake Valley is in the Great Basin. It is <br />a nUn shaped valley bordered on the easl and wesl by <br />mountains and by lower spurs of these mountain <br />ranges to I.he soulh. The valley, which is about 15 <br />miles wide (east and west) and 25 miles long, is bi- <br />sected by Ihe Jordan River which flows northward <br />and discharges into Ihe Great Salt Lake. The average <br />elevation of the valley floor is approximalely 4,000 <br />feet above mean sea level. The valley is semiarid with <br />an annual average of 15 inches of rainfall. <br /> <br />The Wasatch Mountains, with peaks up to 11,000 <br />feet above sea level, rise abruptly on the east side of <br />the valley. Because of this sharp rise, much of the pre. <br />cipitalion is produced by the orographic lifting of air <br />masses moving In an easterly direction and falls in the <br />mountains. The Wasalch Mounlain Range Ihus pro- <br />vides a large portion of the waler supply for the valley <br />beiow. Several small streams run weslward from moun. <br />lain canyons inlo the valley and discharge Inlo the <br />Jordan River. <br /> <br />The site selected for this sludy is limiled to the <br />part of the eastern side of the valley shown In Figure <br />1.1. This specific area was chosen because of the his- <br />tory of flood conlrol proposals that would affect the <br />inhabitants. This area is bordered on the west by the <br />Jordan River, on the easl by the Wasatch Mountains, <br />on the north by the heavily urbanized Parley's Creek <br />drainage, and on the south by the less urbanized but <br />developing lillie Collonwood Creek watershed. Al- <br />together, the area contains about one-half of the east- <br />ern section of the Salt Lake Valley. <br /> <br />The population within the 1970 census tracts <br />of the study area, was 131,882. It is of varying den- <br />sity and growing rapidly. From the 1970 figure of <br />383,035 people, the population of Salt Lake Counly <br />is expected to grow 10 about 785,000 people by 1985. <br />The area's proximity to the cen tral business dislricl <br />of Salt Lake City and present rapid developmenl sug- <br />gest that a large partof lhis expected growth will oc- <br />cur In the sludy area as Indicated by Ihe masler plan <br />for the county (A Master Plan for Salt Lake County, <br />1965). The area has a long history of flooding (Corps <br />of Engineers, 1969A: 11-19), and continuing urban <br />development is Increasing the urgency of the flood <br />problem. Some of the presenl development is occur. <br />ing in the flood plains and moun lain canyons and <br />"new residential developments are rapidly expand' <br />ing. . ." (Corps of Engineers, 1969 A: 5). This urban <br />growth nol only allers run-off relationships by pro- <br /> <br />ducing higher peak flows, but also increases Ihe dam. <br />age potential from a flood. <br /> <br />The Process of Model Development <br /> <br />Computer Simulation Models <br /> <br />In a computer simulation model, one uses an <br />underslanding of the fundamenlal processes and the <br />coupling relationships among them to predict the con- <br />sequences of possible changes. For example, one <br />could predict changes which result from increasing <br />urbanization and the consequenl flood damage and <br />demand for flood control. Mathematical simulation <br />is achieved by using arithmetic relationships to repre- <br />sent Ihe various processes within the prototype sys- <br />lem and by linking these equations inlo a model that <br />represents the functioning of the system as a whole. <br />Thus, compuler simulation uses a model developed <br />to behave like a prolotype system 10 predicl probable <br />responses to situations for which protolype response <br />has not been recorded or responses one mighl expect <br />from the prololype to be altered. <br /> <br />Steps in Developing a Working Model <br /> <br />A computer model simplifies the real world in <br />representing it and thus becomes an abstraction from <br />reality. The degree of simplification is a function of <br />bolh modeling inlent and knowledge aboullhe real <br />world. Verbal information and conceptualization are <br />translated into mathematical form for use in a com. <br />puter (Forrester, 1961). Model development proceeds <br />from verbal symbols which result from theoretical and <br />empirical studies to the mathematical symbols which <br />compose the model. <br /> <br />The development of a working malhematical <br />model thus requires two major sleps. The firsl is the <br />creation of a conceptual model of the various elements <br />of the system and Ihe interrelalionships among them. <br />In practice, the hypotheses necessary for Ihe real world <br />for a parlicular study area are formulated from the <br />most pertinent and accurale dala available. As addi- <br />tional informalion is obtained, the conceptual model <br />is improved and revised to more closely approximale <br />reality. <br /> <br />The second step is the operationallzation of the <br />conceptual model inlo a working compuler. During <br />this slep, an allempt is made 10 express the various <br />processes and relationships identified or hypothesized <br />in Ihe conceptual model in mathematical form. This <br />step usually requires further simplification and thus <br />means thallhe resulting model is further removed <br />from reality. <br /> <br />The loss of information, first, between the real <br />world and the conceptual model and, second, between <br /> <br />3 <br />
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