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:r" ,'i,,' . ',.:: . '.<:;:! "P' , ! ~me relatively longer and narrower, .' nollletry characterizes the relationship be- een variables, but it does not offer an : explanation. , " ';.,'Ibe allometric, relationship between two ~;;nablesJPigpt be interpreted as represent- ing a dynamic 'equilibrium between two forces or processes, In the case of islands and bars in a stream channel, friction and turbulence combine to produce the ob- served form, which tends to minimize both processes, resulting in a minimum !oss of energy. Friction would be minimized if is- lands and bars were circular, so that the contact between sand and water would be minimal for a given surface area (or mass). Such islands are rare, however, because they create high turbulence. On the other hand, forms with minimum turbulence would be infinitely long and narrow, but such forms do not exist because they maximize friction, Existing forms adjust to achieve an equilibrium between the proces- sesof friction and turbulence to minimize the total energy loss, and in preserving these rela- tionshipsthe forms change alIometricaIly. Actual measurements can be accommo- dated by the model representing allometric TAMARISK IN TIlE COLORADO PLATEAU REGION change by using the measurements as input into a least-squares solution of the linear form of equation: log W = log a + (b) logL. Measurements for Land W were made from aerial photographs, maps, and field surveys to analyze dimensions for 143 is- lands and bars that are assumed to be in a variety of stages of development. Field measurements that duplicated photo meas- urements showed that photo measurement error was 5% or less. Solutions for equation 3 provided power functions for data from barren islands and bars plus four types of vegetated features: islands, bars in straight channel sections, point bars, and corner bars. Although dif- ferentiation between point bars and corner bars was somewhat arbitrary, corner bars seem to be readily identified by the radical difference in curvature between their inner and outer margins (see Fig. 11 for exam- ples). By connecting the end points of each bar with the midpoint of its outer margin, an angle is formed. A similar angle formed by the inner margin can be used for com- parative purposes. Corner bars were iden- 1499 (3) tified as those bars where the angle formed by the outer margin was at least 30" less than the inner-margin angle. The results in Table 4 and Figure 12 show that the power-fun(.tion model and allometric interpretation apply to all the vegetated features, However, the relation- ships are imperfect, because, as noted by Leopold and others (1964), few geomor- phic models can account for the complexity of environmental effects. The b values show that island widths change more rapidly than bars, because islands have two sides for accretion whereas bars have only one side exposed to the channel. DISCUSSION AND CONCLUSIONS Sediment samples from 10 cm (25 in.) below the surfaces of the annual bench, the tamarisk-stabilized surface, and the upper terrace show that materials do not differ from materials in the present river bottom. TABLE 4. SOLUTIONS FOR POWER FUNCTION MODEL FOR ISLAND AND BAR DIMENSIONS Regression analysis Feature n a b r Islands 26 0,58 0.84 0,83 Bars, straight 33 2,21 0.56 .0,64 reaches Point bars 8' 2,29 0.52 0.99 Corner bars 27 9,03 0.48 0.70 Barren bars 33 9.47 0.42 0.55 , Regression calculated for maximum width only as a limiting function; 16 additional features with less than maximum widths apparently are still building, and show substantial statistical scatter. igure 10. Bowknot Bend, miles 62.0 to 71.0, Green River, , Tamarisk-covered features appear as dark areas next to am. North is toward top of photo, which covers 5.1 km (3.2 mil oss. \f,t. i I , j ~ l..U