Understanding spread data for directional wave spectrum

[jtgrasb]

I am working with the directional wave example to create a streamlined approach between MHKiT full directional waves and WEC-Sim's approach to creating and modeling the waves. I am also trying to stay consistent with the IEC standard:

In WEC-Sim, the spread is defined such that it sums to 1 across all directions. Thus, the energy is maintained between the omni-directional spectrum (indexed by each frequency) and the full directional spectrum (indexed by frequency and direction). In the directional wave example, the matrix defining the spread does not sum to 1 (instead it sums to 28.65 for each frequency). When defining the full directional wave spectrum, should the spread be scaled to 1? Or is there something I'm missing in how the spread and spectrum are defined by MHKiT?

[jtgrasb]

After reviewing further, my mistake is that the integral of the directional spread from -pi to pi should be equal to 1, not the sum. The MHKiT formulation satisfies this condition. I do think the units for the spread may be off though. In the example, the spread spectrum units are listed as 1/Hz/deg, but I believe they should be 1/Hz/rad.

[akeeste]

Thanks @jtgrasb apologies for not getting to this earlier. Was the units issue in the example just a matter of labeling or is there a factor incorrect? Also can you refer me to the where you see radians input?

Here I see degrees used for the spectral wave direction and the directional_waves.ipynb defines the directions using degrees

[jtgrasb]

The units issue is simply a matter of labeling of the dataarray and on the plot, not too important. I am referring to the directional wave spectrum ( $D(f,\theta)$ ), the units for which are not defined by NDBC as far as I can tell.

The key part of the directional wave spectrum is that the integral from -pi to pi radians is equal to 1, implying that it is in units of 1/Hz/rad. From the IEC standard (and consistent with the values from MHKiT:

[akeeste]

@jtgrasb Okay I see what you're saying now. I think the plots are consistent with the directions used to define the spreading function (degrees). Perhaps they shouldn't even denote degrees or radians.

I think this is ultimately coming down to angles being unitless. NDBC notes that that R1 and R2 in the spreading function equation are unitless, which should make the NDBC spreading function $D(f,\theta)$ unitless. Since angles are unitless, the integrals of D are both unitless too $\int_{-\pi [rad]}^{\pi [rad]} D(\theta)d\theta = \int_{-180 [deg]}^{180 [deg]} D(\theta)d\theta = 1 [-]$

[jmcvey3]

I'll jump in here.

@jtgrasb Yes, you are correct, the units are wrong in MHKiT, and they should be 1/Hz/rad. We never do np.rad2deg() on the final spreading function.

I'll also note the "spreading function" is not the same as the scalar value called wave spread. It is a normalized parameter that describes the directional distribution of wave energy around the unit circle. One must multiply it by the vertical energy spectrum to return the directional wave spectra.

Another note for MHKiT from the pdf you screen-captured: we should also subtract the final value from 270 degrees. Out of the box, directional spread is mathematically "radians counterclockwise to East". Subtracting the entire matrix from 270 will convert it to "radians clockwise from North", which is what people usually expect.