# MOSES, Statistic Calculation of Double Peak Jonswap Spectrum(-e_period)

1. Overview

The purpose of this document is to show what gamma values for 2JONSWAP spectrum MOSES calculate and what is reported when multiple periods are defined with an option "-e_periods". Multiple sea-states with varying mean periods are stored in the database for later use in statistic calculation.  After generating hydrodynamic pressure data, RAOs of the vessel is computed. Motion statistics for several sea-states are calculated with "-e_period" option. Then, statistics are calculated again with the same environment, but it is done without "-e_period" option. Then the values resulting from both sets of commands are compared to show the final results.

2. Peakedness factor, ɣ

a. Gamma Calculation

For 2JONSWAP spectrum, users do not need to input the peakedness factor since it is automatically calculated by MOSES based on DNV guidelines, which is shown in Table 2.1

Table 2.1: Peakedness Factor Calculation(click the image)

Table 2.2 below shows that the environment to be used and its resulting gamma values according to Table 2.1. These values are considered in the relevant computation.

Table 2.2: Sea-states and its Peakedness Factor(Click the image)

b. MOSES Output

- Pages 4 - 8 of MOSES output file, shows calculations without "e_period" option. All the gamma values MOSES reports are the exactly the same as shown in Table 2.2

- Pages 1 - 3 of MOSES output file, shows calculations with "e_period" option. Statistic values are reported in one page, because there are multiple periods, only the gamma value for the last period is reported in the "star" box. Furthermore, the reported wave height and mean period are the one specified in "e_period" option and "&env" command

c. Comparison

The results from both sets of commands show exactly the same statistic results.

3. Conclusion

Although there is only one gamma value reported, this does not mean single-peakedness factor is applied to every different period specified in "e_period" option. In other words, according to Table 2.1, MOSES computes all the peakedness factor for every single period specified in "e_period" option then applies these values to statistic calculation.