Units for Output Variables of QG Simulation

[jejjohnson]

What are the final units for the saved tensor with the u, v, PV and stream function?

The tensor is stored as steps, Nx, Ny but I can’t figure out what the final units should be from the given parameters. Are they in seconds, km? And any idea for how to calculate them from the given parameters?

[hrkz]

Well, in main.py units are first non-dimensionalized (L 32 - 34) in order to be integrated. At the end of the simulation, all the variables are then unitless.

If you want to use the same dimensionalization, you can use t_unit() and l_unit() to transform them back to something relevant. For velocities in m/s, I believe that taking u * l_unit() / t_unit() should do the job.

[jejjohnson]

Makes sense.

btw: Are there any units for q (PV) and p (stream function)? (I don't know if this is a stupid question or not...)

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Below is some demo code for how one would do the conversion. Could you check if I'm correct?

Time Domain (steps): We want it in seconds.

time_unit: float = 1.2e6 # time domain conversion
dt: float = 480. / time_unit # time step
steps: np.ndarray = ...  # unit-less
steps *= time_unit       # unit-less -> seconds
time = steps * dt

Spatial Domain (Nx,Ny): we want it in meters.

space_unit: float = 504e4 / math.pi  # spatial domain conversion
Nx: np.ndarray = ...                 # unit-less
Ny: np.ndarray = ...                 # unit-less
Nx *= space_unit                     # meters
Ny *= space_unit                     # meters

U,V (u,v): we want it in meters per second.

time_unit: float = 1.2e6                # time domain conversion
space_unit: float = 504e4 / math.pi     # spatial domain conversion
vel_unit: float = space_unit / time_unit # velocity unit
u: np.ndarray = ...                     # unit-less
v: np.ndarray = ...                     # unit-less
u *= vel_unit                           # meters/second
v *= vel_unit                           # meters/second

[hrkz]

For vorticity q, the unit is often taken to be radians/s (its a rotating rate), which comes directly by taking the curl of the velocity, i.e. units are (m/m)/s. For streamfunction p, since you have grad(p) = (u, v) with velocities in m/s and dx, dy in m, unit of p should be m^2/s, but I did not find anything on the internet confirming that...

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Looks fine to me. Be careful, if you want the total temporal window of integration, it should be steps * dt. Also for velocities, vel_unit is space_unit / time_unit.

[jejjohnson]

Code Example: Awesome! Thanks so much!

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Units: So to confirm, are the output variables, q and p, variables are dimensionless as well? And so I would need to do the appropriate unit conversions based on your comments?

[hrkz]

Exactly, q and p are dimensionless and require unit conversions as well!