Time Lag in Predictor-Predictand Relationships 



As is amply demonstrated in the main part of this report, there is 

 a time lag in the peak interaction of the most-important combination of 

 independent variables, as they influence the dependent variables. The 

 program used for the screening procedure is written to print out all of 

 the simple correlation coefficients between predictors and predictands. 

 This permits an informative analysis of the time variance of specific 

 predictors selected by the screening procedure. Figure Al is a graphical 

 presentation of one 5uch analysis, in which the simple correlation co- 

 efficient, r, for the first four predictors selected in run 5 (table Al) 

 is plotted versus time. 



DISCUSSION 



It is apparent that a great amount of useful information may be 

 derived from diagrams such as that of figure Al . The high positive 

 correlation of wind, velocity offshore during the second lag period (4-8 

 hours prior to measurement of the predictand) indicates the lag in this 

 factor's influence on beach erosion. The alternating negative and positive 

 correlations of mean longshore-current velocity wj-th beach erosion are to 

 a certain degree a mirror image of the curve for Uq£, which would be ex- 

 pected if one considers that onshore winds create waves that produce strong 

 longshore currents. The relatively constant value of the negative correla- 

 tion between slope of the lower foreshore and beach erosion suggests that 

 the slope itself, although having a real influence on beach erosion (table 

 Al , run 5), does not need to vary significantly for erosion to take place. 

 The correlation between the angle of wave approach is seen to be highest 

 in the immediate past and it does not show the clear lag tendency that is 

 shown by Uof. As the data matrix from Virginia Beach is enhanced, a repeat 

 of the present screening procedure will permit the plotting of more meaning- 

 ful diagrams such as that of figure Al . 



Turning to the predictor equations once again, it would be well to 

 remind the reader that these are best tested, by their application to a set 

 of independent data. This will be done in the near future when additional 

 data become available. It is also noted that the number of cases available 

 for the screening procedure (table Al , "N=..") needs considerable augmenta- 

 tion. ^ 



A comparison between the best four-variable equations selected by the 

 two multiregression computer programs is presented in table A2. In the case 

 given for V as the predictand, both programs happened to select the same 

 combination of Xs and, because Xs from just one lag period were involved, 

 the "%-SS-reduction" values were also identical. The results for Sg are 

 not quite the same. Although both computer programs selected the same kinds 

 of Xs for the best 4-variable predictor equations, the total variance reduc- 

 tion ("7o-SS-reduction") is slightly greater for the four predictors selected 



A-4 



