gradient_richardson_number

metpy.calc.gradient_richardson_number(height, potential_temperature, u, v, vertical_dim=0)

Calculate the gradient (or flux) Richardson number.

\[Ri = (g/\theta) * \frac{\left(\partial \theta/\partial z\)} {[\left(\partial u / \partial z\right)^2 + \left(\partial v / \partial z\right)^2}\]

See [Holton2004] pg. 121-122. As noted by [Holton2004], flux Richardson number values below 0.25 indicate turbulence.

Parameters

• height (pint.Quantity) – Atmospheric height

• potential_temperature (pint.Quantity) – Atmospheric potential temperature

• u (pint.Quantity) – X component of the wind

• v (pint.Quantity) – y component of the wind

• vertical_dim (int, optional) – The axis corresponding to vertical, defaults to 0. Automatically determined from xarray DataArray arguments.

Returns

pint.Quantity – Gradient Richardson number

friction_velocity tke