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<br />9 <br /> <br />"..' <br />.-" <br /> <br />watersheds and measurements. Therefore, tho Law of Stir... Length '~at.. ' <br />lepgth of a Itreaa iDcreaees with f:.ncreal1ng ,)rd.r nuaber~- <br />to a direct eometrical sa uence I!.nd plots of data fall ~ <br />line Figure 4). <br /> <br /> <br />Law of Basin Areas. The Law of Basin Areas is of the same basic form <br />as the Laws of Stream Numbers and Stream Length. The area of a basin of a <br />particular stream order is defined as the total area of surface <br />contributing to all first order channels plul; all included interbasin <br />areas. In practice, basin areas are measured with a planimeter. Mean <br />areas of the basins of each order plotted against order, produce a <br />straight-line regression of positive exponential form. Therefore, the,Law <br />of Basin Areas states that the mean basin areas of succ:e8sive strelllll or'd'e'rs <br />tend to form a geometric serie. beginning wi,!:h the meall area of the first <br />order basin. and increasing according to a c~nstant are,a ratio. <br /> <br />Law of Stream Slopes. The relationship between channel slope and <br />stream order is based upon the observation that a typical profile of a <br />graded stream is upwardly concave and shows EI progressive flattenillg of <br />slope in the downstream direction. Channel .slope is thereby definl~d as the <br />ratio of verticle drop to horizontal distance measured from the upper end <br />to the lower end of a single stream segment ,of a given order, When the <br />slopes of all first order segments in a basil! are measured and avenged, a <br />mean slope value is obtained for that stream order. Sia1larly, <br />measurements are then made for successive orders. The mean slope c)f <br />channel for each stream order, plotted against order, produces a <br />straight-line regression of negative exponential form. Therefore, the ~ <br />of Stream Slopes has been formulated as follows: The mean slopes of stream <br />segments of successively higher orders in a given basin tend to fOI~ <br />inverse geometric series, decreasing according to a constant slope ratio. <br />Slope ratios must be less than 1.0 and values from 0.3 to 0.6 are typical. <br />Individual slope ratios may differ from order to order due to vari~Ltions in <br />the resistance of the geomorphology through 1.hich the stream flows. <br />Despite the high degree of variability withil2 large drainage basins: the Law <br />of Stre... Slopes appears to be generlilly val:ld. <br /> <br />Some workers argue that, although there are correlations betwe,en <br />stream order and some aerial and evetl relief (third dim,ension) geomorphic <br />characteristics (Strahler 1975, Morisawa 1968), stream -order is not, <br />universally lipplicable for comparing stream sizes, wate.rshed areas, or <br />watershed relief, much less tbe biotic charac:teristics ,of streams (Hughes <br />and Omernik 1981). This argUIllent is based uJlon the fact that 60 percent of <br />the nation's topographic watersheds lire categorized as humid with effluent <br />streams. Effluent streams are defined as those streams where groundwater <br /> <br />moves toward, and seep. into the stre8lll ehantLe!. It is difficult at best <br />to delineate topographic watersheds on the rE,maining 40 percent of the land <br />area of the conterminous United States (Hughes and Omernik 1981). Reasons <br />for this difficulty result from a nulllber of geomorphic or climatic <br />characteristics including: (1) areas with intermittent or interrupted <br />