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# [python #BLO-430107]: Bulk Richardson number calculation - gradients?

• Subject: [python #BLO-430107]: Bulk Richardson number calculation - gradients?
• Date: Mon, 23 Mar 2020 19:06:16 -0600

```Greetings!

Apologies on the delayed response. I'm not sure if this will still be helpful,
but I can think of two ways.

The first, given that you already have an equation in terms of deltaU, deltaV,
deltaZ, deltaTheta would be to calculate those delta terms using a simple
forward difference. You can get this using `np.diff`:

delta_u = np.diff(uz)
delta_v = np.diff(vz)
delta_z = np.diff(z)
delta_theta = np.diff(vpt)

The other way would be to use metpy's `first_derivative` function (which uses
an O(N^2) accurate approximation, correct on variable spacing). Note: the first
derivative calculation is calculating e.g. Uprime = deltaU / deltaZ, so we
would need to reformulate the equation for Bulk Richardson number to:

Rb =  (g/tpt) * Thetaprime / (Uprime**2 + Vprime**2)

Then calculate the derivatives

import metpy.calc as mpcalc

theta_prime = mpcalc.first_derivative(vpt, x=z)
u_prime = mpcalc.first_derivative(uz, x=z)
v_prime = mpcalc.first_derivative(vz, x=z)

Hope this helps,

Ryan

> Hi,
> I am trying to calculate the bulk Richardson number for a given vertical
> profile. I have all of the necessary variables (pressure, temperature,
> mixing ratio), but am unsure as to how to calculate the gradients in an
> efficient way.
> I have experimented with your gradient function but cannot get the correct
> output.
>
> [image: image.png]
>
> http://glossary.ametsoc.org/wiki/Bulk_richardson_number
>
> Any advice you could provide would be much appreciated!

Ticket Details
===================
Ticket ID: BLO-430107
Department: Support Python
Priority: Low
Status: Closed
===================
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```