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<br />INTRODUCfION
<br />
<br />To design an economic and efficient urban
<br />storm drainage system requires an accurate estimation
<br />of inflows at all drainage inlets. However, to accom-
<br />plish this objective, one must first know the manner
<br />in which storm rainfall occurs, Temporal and spatial
<br />variations in ralnfall intensity or depth within an
<br />urban drainage area are reflected in the varying inlet
<br />discharges which must be accommodated in all
<br />considerations of the sizing and economics of storm
<br />sewer design, Knowledge of the time and space
<br />distribution of ralnfall in heavy storms thus consti.
<br />tutes a basis for design of an urban storm drainage
<br />system.
<br />
<br />To develop a design hyetograph for an urban
<br />highway watershed is a formidable task. The elemen-
<br />tal urban highway watershed is a small drainage area
<br />of less than 0.1 square miles between two highway
<br />cross-sections which pass two adjacent highway drain-
<br />age inlets (spaced from 400 to 1,000 feet) within the
<br />right-of-way (varied from 200 to 400 feet), The
<br />drainage areas under consideration consist of paved
<br />roadway, paved shoulder, sideslope or back slope
<br />(paved or grassed), median, gutter (paved or grassed),
<br />side ditch, and natural drainage areas. All the urban
<br />interstate highway cross-sections are by and large
<br />standardized in the design. However, runoff from
<br />physiographically similar urban highway watersheds
<br />may differ due mainly to rainfall input. Therefore,
<br />the formulation of a desired design hyetograph for
<br />each of such elemental watersheds is essential to the
<br />accurate computation of runoff hydrographs at the
<br />drainage inlets and hence the successful design of a
<br />storm sewer system including all the inlets. In view of
<br />a great variety of rainfail records collected for many
<br />years at many weather stations over the country, to
<br />develop a single design hyetograph for all urban
<br />highway watersheds is impractical, if not impossible,
<br />No attempt will be made to develop such a unified
<br />design hyetograph except for some general guidelines
<br />and criteria set in the evaluation of storm parameters.
<br />
<br />Several methods have been developed to
<br />formulate the synthetic (design) storm pattern for
<br />runoff study, Most of the approaches can be grouped
<br />into four general types. Storm patterns formulated on
<br />the basis of the first approach are more or less
<br />arbitrary temporal distributions of intensity, assumed
<br />symmetrical in time or in some fashion that appears
<br />reasonable (e.g" Horner and Jens, 1942; Schiff, 1943;
<br />Ogrosky, 1964). In the second approach, storm
<br />
<br />pattems are derived from the rainfall intensity-dur-
<br />ation.frequency relationship to represent merely a
<br />series of average values from a variety of storms
<br />rather than a sequence of intensities in a particular
<br />burst of intense rainfall (e.g., Rousculp, 1927, 1940;
<br />Williams, 1943, 1950; U,S. Corps of Engineers, 1948;
<br />Kiefer and Chu, 1957; Bandyopadhyay, 1972; Preul
<br />and Papadakis, 1973). The third approach is the
<br />development of average storm patterns for complete
<br />storms, rather than intense bursts of individual
<br />rainfall, based on observed rain gage records (e.g.,
<br />Blumenstock, 1939; Leopold, 1944; U.S. Weather
<br />Bureau, 1947; Hershfield and Wilson, 1960; Bock,
<br />1960; Hershfield, 1962; Huff, 1967, 1970; Pilgrim
<br />and Cordery, 1975), A method combining the second
<br />and third approaches using the rainfall intensity-duro
<br />ation-frequency relationship has been developed by
<br />Miller and Frederick (1972) and Frederick et al,
<br />(1973) for long-duration storms, The fourth approach
<br />is the formulation of a stochastic model to generate a
<br />sequence of short. period rainfall (e,g., Raudkivi and
<br />Lawgun, 1970),
<br />
<br />If there is no reliable record of single bursts of
<br />intense rain for a particular region-usually the case
<br />for the design of urban highway drainage facilities, it
<br />appears that the second approach is the only way to
<br />formulate the temporal storm patterns without re-
<br />sorting to such intense rainfall records, yet gives a
<br />theoretically sound basis for the derivation of design
<br />temporal pattern. It is true that storm patterns
<br />derived from the second approach in no way repre-
<br />sent the characteristics of complete storms with long
<br />durations. It may be justified, however, for such a
<br />small drainage area as an urban highway watershed to
<br />have a design hyetograph which represents an intense
<br />burst of a short duration rather than a complete
<br />storm of a long duration. For lack of a better method
<br />presently available in the formulation of design
<br />hyetographs for such small watersheds, the second
<br />approach will be generalized by using a unified
<br />time.coordinate system to describe a temporal pat-
<br />tern before and after the peak of a storm.
<br />
<br />Following the extensive review of literature on
<br />the development of the rainfall intensity-dur-
<br />ation-frequency relationships and the subsequent
<br />development of design storm patterns based on such
<br />relationships, a method will be developed to formu-
<br />late the generalized design hyetograph equations
<br />using the unified time-coordinate system, An optimi-
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