in which qs = bed-material discharge in tons per day per foot; q = water discharge in cubic feet per second per foot; Cm = measured concentration of suspended bed-material discharge in milligrams per liter; and 0.0027 is the conversion factor for the indicated units. Table 15-8 shows a factor to convert concentration in parts per million to milligrams per liter. Example 15-8: Given mean flow depth d = 10 ft, mean channel width b = 300 ft, mean velocity v = 3 fps, measured concentration of suspended bed material discharge Cm = 100 ppm, calculate the total bed material discharge by the Colby 1957 method. From Fig. 15-11 , the uncorrected unmeasured sediment discharge is qu' = 10 ton/ d/ ft. From Fig. 15-12, the relative concentration of suspended sands is Cr = 380 ppm. The availability ratio is 100/ 380 = 0.26. From Fig. 15-13, the correction factor is C = 0.6. Therefore, qu = 6 ton/d/ft. The water discharge per unit width is q = vd = 3 X 10 = 30 ft3/s/ft. From Eq. 15-23, the sediment discharge per unit width is qs = (0 .0027 X 100 X 30) + 6 = 14.1 ton/ d/ ft. Therefore, the bed-material discharge by the Colby 1957 method is Qs = qsb = 14.1 X 300 = 4230 ton/d. Colby's 1964 Method. In 1964, Colby published a method to calculate discharge of sands (i .e., bed-material discharge) in sand-bed streams and rivers. The development of the method was guided by the Einstein bed-load function and supported by large amounts of laboratory and field data. The method has been shown to provide a reasonably good prediction of sediment transport rates, particularly for sand-size particles. The following data are needed in an application of the Colby 1964 method: (1) mean flow depth d, (2) mean channel width b, (3) mean velocity v, (4) water temperature, (5) concentration of fine-material load (Le., wash load), and (6) median bedmaterial size. The procedure is as follows :

1. Use Fig. 15-14 to determine the uncorrected discharge of sands qu (in tons per day per foot of width) as a function of mean velocity, flow depth, and sediment size.

2. For water temperature of 60°F, negligible wash load concentration (less than 1000 ppm), and sediment size in the range 0.2 to 0.3 mm, no further calculations are required, and qu is the discharge of sands qs.

3. For conditions other than the preceding, use Fig. 15-15 to obtain the correction factor k1 as a function of flow depth and water temperature, k2 as a function of flow depth and concentration of fine-material load, and k3 as a function of median size of bed material.

4. The discharge of sands is given by the following formula: qs = [ 1 + (k1k1 - 1) k1] qu(15-24) in which qs discharge of sands in tons per day per foot.
Example 15-9. Given mean flow depth d = 1 ft, mean channel width b = 30 ft, mean velocity v = 2 fps, water temperature 50°F, wash-load concentration Cw = 10,000 ppm, and median bedmaterial size d50 = 0.1 mm. Calculate the discharge of sands by the Colby 1964 method. From Fig. 15-14, qu = 9.3 ton/ d/ ft. From Fig. 15-15, k1 = 1.15, k2 = 1.20, k3 = 0.6. From Eq. 15-24, qs = [1 + (1.15 X 1.20 - 1) X 0.6] X 9.3 = 11.4 ton/d/ft. Therefore, the discharge of sands is Qs = 11.4 X 30 = 342 ton/ d. Other Methods for the Calculation of Sediment Discharge Many other methods have been proposed for the calculation of sediment discharge. Notable among them are the methods of Ackers and White , Engelund and Hansen , Toffaleti [39}, and Yang [46}. The various procedures vary in complexity and range of applicability. For details on these and other sediment transport formulas, see [2, 4, 25, 38}. Sediment Rating Curves A useful curve in sediment analysis is the sediment rating curve, defined as the relationship between water discharge and sediment discharge at a given gaging site. For a given water discharge, the sediment rating curve allows the estimation of sediment discharge, assuming steady equilibrium flow conditions. The sediment rating curve is an xy plot showing water discharge in the abscissas and sediment discharge in the ordinates. This plot is obtained either by the simultaneous measurement of water and sediment discharge or, alternatively, by the use of sediment transport formulas. For low-water discharges, the sediment rating curve usually plots as a straight line on logarithmic paper, showing an increase of sediment concentration with water discharge. However, for high water discharges, the sediment rating curve has a tendency to curve slightly downward, approaching a line of equal sediment concentration (i.e., a line having a 45° slope in the xy plane) . Like the single-valued stage-discharge rating, the single-valued sediment rating curve is strictly valid only for steady equilibrium flow conditions. For strongly unsteady flows, the existence of loops in both water and sediment rating curves has been demonstrated . These loops are complex in nature and are likely to vary from flood to flood. In practice, loops in water and sediment rating are commonly disregarded. Sediment Routing The calculation of sediment yield is lumped, i.e., it does not provide a measure of the spatial or temporal variability of sediment production within the catchment. Sediment transport formulas are invariably based on the assumption of steady equilibrium flow. Sediment routing, on the other hand, refers to the distributed and unsteady calculation of sediment production, transport and deposition in catchments, streams, rivers, reservoirs, and estuaries. Of necessity. sediment routing involves a large number of calculations and thereforeis ideally suited for use with a computer. Sediment routing should be used-in addition to sediment yield and sediment transport evaluations-in cases where the description of spatial and temporal variations of sediment production, transport, and deposition is warranted. Sediment routing methods are particularly useful in the detailed analysis of sediment transport and deposition in rivers and reservoirs. For example, the computer model HEC-6, "Scour and Deposition in Rivers and Reservoirs," is a sediment routing model developed by the U. S. Army Corps of Engineers . Several other sediment routing models have been developed in the last two decades; see, for instance,  and . 15_4 SEDIMENT DEPOSITION IN RESERVOIRS The concepts of sediment yield and sediment transport are essential to the study of sediment deposition in reservoirs. Sediment is first produced at upland and channel sources and then transported downstream by the action of flowing water. If the flowing water is temporarily detained, as in the case of an instream reservoir, its ability to continue to entrain sediment is substantially impaired, and deposition takes place. Sediment deposition occurs in the vicinity of reservoirs. typically as shown in Fig. 15-16 . First, deposition of the coarser-size fractions takes place near the entrance to the reservoir. As water continues to flow into the reservoir and over the dam, the delta continues to grow in the direction of the dam until it eventually fills the entire reservoir volume. The process is quite slow but relentless. Typically, reservoirs may take 50 to 100 y to fill. and in some instances, up to 500 y or more. The rate of sediment deposition in reservoirs is a matter of considerable economic and practical interest. Since reservoirs are key features of hydroelectric and water-resource development projects, the question of the design life of a reservoir is appropriate, given that most reservoirs will eventually fill with sediment. In an extreme example, the filling can occur in a single storm event, as in the case of a small sediment-retention basin located in a semiarid or arid region. On the other hand, the reservoir can take hundreds of years to fill , as in the case of a large reservoir located in a predominantly humid or subhumid environment. Reservoir Trap Efficiency The difference between incoming and outgoing sediment is the sediment deposited in the reservoir. The incoming sediment can be quantified by the sediment yield, i.e. , the total sediment load entering the reservoir. The outgoing sediment can be quantified by the trap efficiency. Trap efficiency refers to the ability of the reservoir to entrap sediment being transported by the flowing water. It is defined as the ratio of trapped sediment to incoming sediment, in percentage, and is a function of (1) the ratio of reservoir volume to mean annual runoff volume and (2) the sediment characteristics. The following procedure is used to determine trap efficiency :

1. Determine the reservoir capacity C in cubic hectometers or acre-feet.

2. Determine the mean annual (runoff volume) inflow I to the reservoir, in cubic hectometers or acre-feet.

3. Use Fig. 15-17 to determine the percentage trap efficiency as a function of the ratio C / I for any of three sediment characteristics. Estimate the texture of the incoming sediment by a study of sediment sources and/ or sediment transport by size fractions. The upper curve of Fig. 15-17 is applicable to coarse sands or flocculated sediments; the middle curve, to sediments consisting of a wide range of particle sizes; and the lower curve, to fine silts and clays.