XI, has doutled, from 5>11?^ to 10.13^. Thus, these several variables may 

 enter the least-squares relations more effectively as logarithms or as 

 variables raised to some power. Of particluar interest is water density, 

 which in the linear sense is quite negligible (only 0.65^), but in the 

 quadratic has risen to nearly 12^. This is an illustration of one limita- 

 tion of a strictly linear analysis: some variables that have virtually no 

 linear effect may become quite strong in a model that explicity includes 

 non-linear effects. 



DEPOSITION AED EROSION ON THE LOWER FORESHORE 



Time Lag In Peak Interaction 



In a sequential multiregression analysis of the interaction of the 

 Mission Beach, California, foreshore slope to the four independent variables- 

 of wave height, wave period, angle of wave approach, and longshore- current 

 velocity, Krumbein (1961, p. k^) found that the maximum effect of these 

 combined independent variables occurred (in a least-squares sense at least) 

 sometime between 6 and 12 hours prior to the time of the measurement of 

 foreshore slope. In regard to wave period, the analysis indicated that 

 the greatest effect on foreshore slope was exerted some 30 hours prior to 

 the time of measurement of beach slope. Because of the laboratory and 

 field evidence for the delay in time in the peak interaction of certain 

 dependent variables like beach slope and the independent variables that 

 influence them significantly, the four interaction studies at Virginia 

 Beach that follow were investigated over five or six "lag periods." 



In the case of modification of the segment of the lower foreshore 

 that is covered and uncovered by the tide, it is necessary to standardize 

 the times of slope measurement so that the measurement times are repre- 

 sentative of similar dynamic conditions on the beach. Low-tide time is 

 a convenient reference time and was adopted here. Figure 2 shows the 

 scheme adopted at Virginia Beach for makiing foreshore measurements in 



June and July of 1963. The ticks marks designated P3_, P2, P3, 



Pllj^ represent the standard times during the 25-day period when the in- 

 dependent variables were measured or for which interpolated values were 



obtained. The tick marks designated B.^.} ^o} ^-3 ^oc represent the 



times of low tide when measurements of the altitudes of the lower fore- 

 shore stations were made. This measurement time (Rn) is seen (fig. 2) 

 to progress through the times of measixrement of the other variables. 

 Because each lag period is h hours in length, the measurements for all 

 of the independent variables for lag period 1 will have been made to 

 h hours prior to the foreshore- altitude measurements, for lag period 2 

 they will have been made U to 8 ho\irs prior, and so on. Because the 

 precise time of peak interaction between a dependent variable (j-f, K.^) 

 measured at low-tide time and one or more independent variables is un- 

 known, it is probably just as well that bias has not been introduced by 

 setting up lag times of fixed numbers of hours prior to measurement of 

 the dependent variable. 



30 



