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<br />equations, and the seven-parameter alternate equations.
<br />A description of some of the models and variables that
<br />were partially successful, and even unsuccessful, is
<br />included to document the analytical efforts more fully.
<br />These models included the ratio method, the difference
<br />method, the log-Pearson Type III parameter method
<br />(method of moments). and a method described by Har-
<br />ley (1978).
<br />The suitability and accuracy of each method were
<br />assessed for the purpose of recommending a practical
<br />and accurate method. Suitability was evaluated on the
<br />basis of the relative ease of application and the logic of
<br />independent variables. Accuracy was judged primarily
<br />on the basis of computed standard error of estimates.
<br />Bias, linearity, and sensitivity were tested in various
<br />ways, as described in subsequent paragraphs.
<br />
<br />Selection of Data
<br />
<br />Previous parts of this report described the data
<br />base compiled for this study, which comprises 269 urban
<br />sites. For purposes of analysis, sites were selected from
<br />the data base according to certain assumptions and the
<br />availability of specific variables. When a variable selected
<br />for a specific analysis was unavailable for a site, that site
<br />was omitted from the analysis. No attempts were made
<br />to estimate missing variables. Because of missing data,
<br />fewer than 269 sites were used for most analyses.
<br />It was assumed that measures, or indexes, of tem-
<br />porary in-channel storage, or temporary detention stor-
<br />age, could not easily be quantified for inclusion in a
<br />statistical model of the type planned for this study. Stor-
<br />age of this type will be referred to in this report as deten-
<br />tion storage, and is defined as that occurring in planned
<br />or unplanned detention areas, intentionally behind such
<br />structures as detention dams and unintentionally behind
<br />highway or railroad embankments. The peak outflow
<br />rate from these detention areas is usually less than the
<br />peak inflow rate because of the effects of storage. The
<br />distinction between detention storage and other storage,
<br />ST, in the basin is that ST is storage in the permanent
<br />lakes, reservoirs, swamps, and wetlands depicted on
<br />topographic maps.
<br />Even though detention storage could not be easily
<br />quantified, sites were identified where such storage was
<br />believed or known to occur, and where this storage sig-
<br />nificantly reduced all or some peak discharges. A signif-
<br />icant reduction was assumed to be about 15 percent or
<br />more. Subjective determinations were made by examin-
<br />ing available high-water profile data, maps, bridge and
<br />highway plans, and surveys, and by making field inspec-
<br />tions. Of the 269 sites, 204 sites were identified as not
<br />having significant detention storage, 55 as having deten-
<br />tion storage. and the remaining 10 as unknown. All
<br />analyses were based on sites without detention storage
<br />
<br />10 flood Characteristics of Urban Watersheds
<br />
<br />to provide estimating procedures that would yield results
<br />unaffected by detention storage. More discussion regard-
<br />ing detention storage is given in a subsequent section of
<br />the report.
<br />
<br />Seven-Parameter Estimating Equations
<br />
<br />Peak discharges for the 2-, 5-, 10-, 25-, 50-, 100-,
<br />and SOD-year urban floods were related to seven indepen-
<br />dent variables by linear multiple-regression techniques.
<br />The significant variables account for the effect of basin
<br />size, A; channel slope, SL; basin rainfall, RI2; basin
<br />storage, ST; manmade changes to the drainage system,
<br />BDF; and impervious surfaces, IA. Regional runoff
<br />variations are accounted for in the equations through
<br />the use of the equivalent rural peak discharge, RQ. A
<br />detailed description of these variables is given in the
<br />Glossary and Data Base sections of this report. The
<br />equations, which follow, can be used to estimate the
<br />magnitude of urban peak discharges at ungaged sites
<br />within the accuracy and limitations discussed in subse-
<br />quent parts of this report.
<br />
<br />VQ2 = 2.35A.~ISVI?(RI2 + 3)~''''(ST + st 65(1) - DDFt "IA'URQ2,47 (3)
<br />
<br />
<br />UQ5 = 2. 70A'''SV''(RI2 + 3),.86(ST + sr.59(13 - BDF)- J'IA-"RQS'" (4)
<br />
<br />
<br />UQlO = 2.99A"SL.1'(R12 + )),.U(ST + Sr,no) - BDFY-"1A""RQIO". (5)
<br />
<br />UQ2S =2.78A'''SL"'"(R12 +3)' I'CST +8r.'5(13 - BDFf.l'1A'O'RQ2:5'iO (6)
<br />
<br />
<br />UQSO=2.67A.1"SL.1"(RI2 + 3)' '4(ST +8f.lJ(13 - BDFy-nIA,DliRQSO'U (7)
<br />
<br />
<br />UQlOO=2.S0A-'''SV'5(RI2+ 3)1.'~ST+ 8r"~13 - BDF)-.18IA-06RQHJO'.' (8)
<br />
<br />
<br />UQSOO= 2.27A-J"SL-16(RI2 +3)'.""(ST + Sr.'''(13....: BDFr."lA,(IIRQSOO u (9)
<br />
<br />The accuracy of the above equations can be ex-
<br />pressed by two standard statistical measures, the coeffi-
<br />cient of detennination, R', and the standard error of
<br />regression. The coefficient of determination, R', indicates
<br />the proportion of the total variation of the dependent
<br />variable that is explained by the independent variables.
<br />For instance, an R' of 0.93 would indicate that 93 percent
<br />of the variation is accounted for by the independent
<br />variables. The standard error of regression is, by defini-
<br />tion, one standard deviation on each side of the regres-
<br />sion equation and contains about two-thirds of the data
<br />within this range. Conversely, about one-third of the
<br />data will fall outside of the standard error of regression.
<br />For example, a standard error of regression of 0.1630
<br />log units would indicate that about two-thirds of the
<br />dependent variables used for a given regression analysis
<br />were within 0.1630 log units of the regression estimate.
<br />Converted to a percentage, this would indicate that
<br />about two-thirds of the dependent variables are within
<br />45 percent and - 31 percent, or an average of :!: 38 per-
<br />cent, of the regression estimate. The following table
<br />
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