(d) confusion arising from a typographic evvov -In one of the 

 equations defining profile retreat (Bruun, 1962); and 



(e) the perplexity caused by a discontinuity in the profile at 

 the closure depth which appeared in the original and all subsequent 

 diagramatic sketches illustrating the concept. 



The first three difficulties (a, b, and c) warrant serious consideration 

 before applying equation (1); items (d) and (e), although perhaps confusing, 

 should in no way discourage or limit use of equation (1). The following 

 paragraphs address each of these difficulties in reverse order. 



a. Discontinuity in the Profile (Item e) . Previous diagrams illustrate 

 the adjustment of a profile to higher water levels by literally disconnecting 

 the responding part of the bottom from the static region offshore. The appar- 

 ent profile discontinuity, at the juncture between the static and responding 

 regions, has some didactic value in diagrams to the extent it emphasizes the 

 congruency between initial and final profile shapes in the active region. 

 Unfortunately, it also creates the impression that the model is inadequate for 

 explaining the transition between the active and static parts of the profile. 

 The discontinuity is not, however, an inherent part of the concept but rather 

 an artifice of the diagrams. Rigidly translating a profile upward and shore- 

 ward does not necessarily lead to a discontinuity nor even a change in slope 

 as is demonstrated later in this report. 



b. Error in an Equation (Item d) . Bruun's equation (la) (Bruun, 1962, p. 

 124) is dimensionally incorrect as published. This error may have discouraged 

 some readers from giving Bruun's concept their full consideration. The prob- 

 lem equation is, however, unnecessary to the development of this concept 

 (correctly expressed in eq. lb of Bruun, 1962). The validity of the Bruun 

 concept and of equation (1) in the present report is demonstrated geometri- 

 cally in Figure 13. 



Figure 13(a) depicts a nearshore profile in quasi-equilibrium with wave 

 and wave-related forces. Note the closure depth below which the bottom 

 presumably does not adjust to surface wave and current conditions. To esti- 

 mate the ultimate shore retreat, the adjustment of the active profile is then 

 depicted as two rigid profile translations. 



The first translation moves the active profile (i.e., the profile between 

 the closure depth and the point of highest wave attack) up an amount, z, and 

 reestablishes the equilibrium depths below the elevated water surface (Fig. 

 13, b). This step requires a volume of sediment proportional to the product 

 of X (the width of the active zone) times z (change in water level); the 

 volume is made available by the second translation which is recession of the 

 profile (Fig. 13, c). Figure 13(c) shows that x units of recession provide a 

 volume of sediment proportional to the product of x times Z (the vertical 

 extent of the active profile from the critical depth up to the average eleva- 

 tion .of the highest erosion on the backshore). Equating the volumes produced 

 and required per unit length of shoreline by these two translations (eq. 2) 

 produces equation (1). 



27 



