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<br />Why Regression Equations are not Appropriate for Box Elder Creek <br /> <br />OENIo.O"'HYO.OCC <br /> <br />2 <br /> <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br /> <br />1. Regression equations are not applicable to tlte long, narrolV shape oj the Bar Elder Creek <br />watershed. <br /> <br />The Box Elder Creek watershed has an unusual shape. Figure 1-1, reproduced from the <br />Outfall Systems Planning Study, shows how long and narrow th,? watershed is. Most <br />watersheds are more "pear" shaped, with smaller length to widb ratios. <br /> <br />The hydrologic effect of Box Elder Creek's long, narrow shape is significant. Tributary <br />hydrographs entering the rnainstem channel do not tend to overlap and add together to the <br />same degree as they would in a watershed with a smaller length to width ratio. <br /> <br />Because the data on which the regression equations were derived came from watersheds <br />with smaller length to width ratios that Box Elder Creek, they will tend to overestimate <br />peak discharges when applied to the narrow Box Elder Creek wz.tershed. Tne <br />overestimation is less pronounced on Coyote Run because Coyole Run has a smaller length <br />to width ratio than Box Elder Creek. <br /> <br />The UDFCD study was not the only study concluding that regional regression equations do <br />not apply to the long, narrow shape of the Box Elder Creek wate.rshed. The 1'S Army Corps <br />of Engineers (COE) undertook a detailed hydrologic analysis of Box Elder Creek upstream <br />of Bootleg Reservoir. Their report, entitled the Section 22 Study, was submitted to the <br />Colorado Water Conservation Board (CWCB) on April 26, 1989. The COE report noted the <br />unusual shape of the Box Elder watershed and documented that a detailed rainfall-runoff <br />model (SWM101) was used to predict flood discharges so that the shape of the watershed <br />would be appropriately represented. <br /> <br />Figure 2 shows a comparison of estimated discharge profiles from the COE study and the <br />UDFCD study. In both cases, the discharge profiles are flat; in 0 :her words, discharges <br />reach a maximum and remain fairly constant over the length of Box Elder Creek, even <br />though watershed area keeps increasing in a downstream direct.on. This is because of the <br />long, narrow watershed shape. <br /> <br />The COE analysis included comparisons to discharges derived from a regional regression <br />equation (TM-1) and found that the equation yielded a peak discharge four times greater <br />than the model. The report stated "To use a regional analysis on. a basin that has vastly <br />different hydrologic characteristics, such as the unusual shape fZector of Box Elder Creek <br />Basin, may not be applicable, at least not without somehow adjusting the values to account <br />for inconsistencies in homogeneity." <br /> <br />2. USGS Water Supply Paper 1680 does not rq;resent best troailable ~'ydrologtJ far Bar Elder Creek. <br /> <br />The effective FIRtv! was based on USGS Water Supply Paper 1680. This simpliHed <br />approach, published in 1968, provides flood estimates for a huge watershed area consisting <br />of the ~lissouri River Basin upstream of Sioux Qty, Iowa. The approach, in Region 10 <br />(where Box Elder Creek is located) was based on discharge records from 6 to 22 years (from <br />1940 to 1962) for five gages on Cherry, Kiowa, and Bijou Creeks. None of these watersheds <br />are as long and narrow as the Box Elder Creek watershed. Predicted discharges are shown <br />to increase proportionally as watershed area increases, a relatiorship that holds true for <br />