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Update computation of vertical velocity and its uncertainty #63

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@bpoujol bpoujol commented Mar 28, 2023

Dear Geet,
Here is a new version of the file "regr_fn.py" that has the following changes :

  • Vertical velocity omega is computed as the integral of divergence with respect to pressure $\omega = \int D \mathrm{d}p$ . For that I needed to compute the pressure gradient $\mathrm{d}p$ and to extrapolate it close to the surface where the three first values are usually missing
  • Vertical velocity $w$ is then computed from $\omega$ as $w = -\omega/(\rho g)$
  • The standard error on $\omega$ is computed as $\sigma_\omega = \left( \int \sigma_D \mathrm{d}p \right) / \sqrt{N_{indep}}$ where $N_{indep}$ is the approximate number of independent divergent measurements between the surface and $z$. It is determined as $N = z/L$, with $L$ the vertical correlation length scale of divergence measurements. I have set $L$ to 500m for the moment in the code, based on a computation of this value in the dataset, but it is possible to change it.
  • Then the standard error on $w$ is deduced from the one on $\omega$.
  • The uncertainty on $\omega$ is stored in a new variable so that it can be easily used. It's not really necessary since error on w is already stored, but I thought it could be convenient (this required changes of "dicts.py" that I have put in another pull request)

I hope that I am clear, and that I did things correctly (I am really unfamiliar to GitHub and open source)
I tested the code, it runs well on my machine and give results that correspond well to what I had calculated on my side.

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