Clarification on directional axis in 2D spectral output in spherical coordinates

[Yoshino-san]

Hello everyone!

I have a question regarding the definition of the directional axis in the two-dimensional spectral output.

As I understand, the spectrum is defined as a function of frequency and direction. In a planar coordinate system, the wave propagation direction and the directional axis in the output spectrum are naturally aligned. However, when working in spherical coordinates (e.g., for global simulations), I am not sure how the direction is defined.

Specifically, I would like to know whether the direction in the 2D spectra refers to:

1. The direction within the local tangent plane (i.e., locally Cartesian), or
2. The direction with respect to the global spherical coordinate system (i.e., relative to lat-lon grid or meridians).

Understanding this is crucial for interpreting the energy propagation across large domains and in verifying ray-tracing algorithms.

I have reviewed the user manual but could not find a clear description regarding this point. I would appreciate any clarification or guidance.

Thank you very much for your time and support!

Best regards,
Hiyori Yoshino
PhD student, University of Tokyo