elevation time series are discrete, real-valued sequences with equal time intervals of t = nAt with At the 

 data collection interval. The total length of a time series is given by T = NAt where A^ is the total number 

 of data points. The TSAF code consists of 11 processes that may or not be used during the data analysis 

 sequence. These processes are concerned with either time domain or frequency domain analyses and are 

 listed in Table Al. 



Table Al. Analysis Options 



Time Domain 



Frequency Domain 



Strip charts of raw data* 



Single channel frequency response* 



Zero up crossing* 



Frequency response between 2 



channels 



Zero downcrossing* 



Cross spectral density 





Crest height 



Goda reflection analysis* 





Trough height 







Coherence function 







Auto- and cross-correlation 







* Denotes those used in present study. 



4. The strip chart option simply plots the raw time series data for one or more of the available gages. 

 The time series plots are scaled to facilitate/enhance readability and presentability. An example of a strip 

 chart plot of a typical raw water elevation time record recorded during an irregular wave test is presented 

 at Figure Al. Examples of the output from the TSAF analysis program are presented at Figures A2-A4. 

 The tables in Appendix B are derived from such output. 



5. For the up and downcrossing analyses, the program calculates statistics of wave elevation, wave 

 height, and period for the datum selected. This datum is typically the mean, but can be externally 

 imposed. For the surface elevation, the mean, root mean square, standard deviation, minimum, and 

 maximum values are calculated. Wave heights and periods corresponding to the diff'erence between the 

 minimum and maximum values between consecutive up or downcrossings are calculated (Figure A2). 

 Averages of these values for each three-gage array are also computed (Figure A4). Also, the total number 

 of waves (zero up or downcrossings) and maximum wave height are provided. Wave heights for each gage 

 are saved for later plotting and use with other processes. If desired, cumulative probabilities and Wiebull 

 distributions can be fitted and plotted. 



6. Spectral densities are calculated for each of the individual gages after detrending and windowing the 

 time series (Figure A3). Detrending options include removing the mean or a linear or second-order trend. 

 Window options include 10- to 50-percent cosine bell or cubic polynomial. The data are Fourier 

 transformed, band averaged between lower and upper cutoff frequencies, and plotted. Measured spectral 

 estimates for each gage are then used in the calculation of frequency response estimates and reflection 



A2 



