10-m wave gage using the SPM formula during the short-term experiments 

 when both measurements could be obtained. This would allow the SPM 

 formula to be calibrated with measured values. Then the calibrated formula 

 could be applied to the entire wave data set to obtain a refined estimate of the 

 annual longshore transport rate. 



The SPM (1984) lists several similar formulas to calculate P^,, the longshore 

 energy flux, depending upon the wave data available. To test these formulas, 

 the wave data were shoaled over the relatively simple nearshore topography off 

 the mouth of the Colorado River to the breaker pomt using Snell's Law and 

 linear shoaling (i.e., assuming that all the spectral energy occurs at the peak 

 frequency). New direction angles were calculated at 3-m intervals from the 

 wave gage to the breakpoint. In addition to the use of Equation 3 discussed 

 above, having bodi deepwater and breaker values for wave height, length, and 

 direction allowed computation of the longshore energy flux in four additional 

 ways corresponding to SPM (1984) Equations 4-40 (the most exact of the 

 various equations), 4-44, 4-46, and 4-47. These four equations are: 



SPM (4 -40) P^^ = -Bf H^"- C^, sin2a, (6) 

 16 



SPM{A-AA) P,^ = 0.0884 pg^'^///'^sin2a^ (7) 



5/>M(4-46) Pj^ =0.00996 p^^ri^o^sinaj costtp (8) 



H 

 SPM (4-47) P,^ = 1.572 pg — ^ sina^ (9) 



where the subscript means deep water and the subscript b means the breaker 

 line. Cgi, is the wave group speed at the breaker line, a function of the wave 

 period and water depth. Then values of Q were calculated using Equation 5a 

 or 5b. 



Then the OBS-derived transport rates were compared to the various wave 

 gage-derived transport rates using simple linear regression of the form: 



y^mx+b (10) 



where y is the OBS data set and x is the SPM data set. The slope of the 

 regression is m, and b is the offset. Correlation coefficients were also 

 calculated. These values could be used to produce a transport formula of the 

 form Q^ = m*Q„^ +b. The results are shown in Tables 13 and 14. 



Chapter 5 Prediction of Sediment Transport Rates 47 



