E qT+ Z Q.- 2 Q-+ J: Q- 1=0 (4-60) 



t:=i'- t:=i'- w=i'' i = 1 '^ 

 ■It 



The Q. are obtained using equation (4-58) and the appropriate q^ and b^ . 

 The subscript i equals 1, 2, 3, or 4 and corresponds to the subscripts in 

 Table 4-15. 



c. Sediment Budget Boundaries . Boundaries for the sediment budget are 

 determined by the area under study, the time scale of interest, and study 

 purposes. In a given study area, adjacent sand budget compartments (control 

 volumes) may be needed, with shore-perpendicular boundaries at significant 

 changes in the littoral system. For example, compartment boundaries may be 

 needed at inlets between eroding and stable beach segments, and between stable 

 and accreting beach segments. Shore-parallel boundaries are needed on both 

 the seaward and landward sides of the control volumes; they may be established 

 wherever needed, but the seaward boundary is usually established at or beyond 

 the limit of active sediment movement, and the landward boundary beyond the 

 erosion limit anticipated for the life of the study. The bottom surface of a 

 control volume should pass below the sediment layer that is actively moving, 

 and the top boundary should include the highest surface elevation in the 

 control volume. Thus, the budget of a particular beach and nearshore zone 

 would have shore-parallel boundaries landward of the line of expected erosion 

 and at or beyond the seaward limit of significant transport. A budget for 

 barrier island sand dunes might have a boundary at the bay side of the island 

 and the landward edge of the backshore. 



A schematic sediment budget analysis is shown in Figure 4-43. This example 

 considers a shoreline segment along which the incident wave climate can trans- 

 port more material than is entering from updrift. Therefore, the longshore 

 transport in the segment is being fed by a continuously eroding sea cliff. 

 The cliff is composed of 50 percent sand and 50 percent clay. The clay frac- 

 tion is assumed to be lost offshore, while the sand fraction feeds into the 

 longshore transport. 



2. Sources of Littoral Materials . 



a. Rivers . It is estimated that rivers of the world bring about 14.2 

 cubic kilometers (3.4 cubic miles) or 14.2 billion cubic meters (18.5 billion 

 cubic yards) of sediment to the coast each year (volume of solids without 

 voids) (Stoddard, 1969; from Strakhov, 1967). Only a small percentage of this 

 sediment is in the sand size range that is common on beaches. The large 

 rivers which account for most of the volume of sediment carry relatively 

 little sand. For example, it is estimated (Scruton, 1960) that the sediment 

 load brought to the Gulf of Mexico each year by the Mississippi River consists 

 of 50 percent clay, 48 percent silt, and only 2 percent sand. Even lower 

 percentages of sand seem probable for other large river discharges (see Gibbs, 

 1967, p. 1218, for information on the Amazon River), but smaller rivers 

 flowing through sandy drainage areas may carry 50 percent or more of sand 

 (Chow, 1964, p. 17-20). In southern California, sand brought to the coast by 

 the floods of small rivers is a significant source of littoral material 

 (Handin, 1951; Norris, 1964). 



4-115 



