static_stability

static_stability(t[, p, layer=False])

Computes the static stability used in the quasi-geostrophic (QG) theory. It is a measure of the stability of the atmosphere in hydrostatic equilibrium with respect to vertical displacements.

Parameters

  • t (Fieldset or ndarray) – temperature (K)

  • p (Fieldset or ndarray) – pressure (Pa)

  • layer (bool) – enable layer mode

Return type

same type as t or None

The result is the static stability in \(m^{2} s^{-2} Pa^{-2}\) units. On error None is returned. The following rules are applied when t is a Fieldset:

  • if t is a pressure level Fieldset no p is needed

  • for other level types p must be a Fieldset defining the pressure on the same levels as t.

The computation is based on the following formula defined in Chapter 2.2. of [Lackman2012] :

\[\sigma = - \frac{R_{d} T}{p} \frac{\partial log \Theta}{\partial p}\]

where

  • \(R_{d}\) is the specific gas constant for dry air (287.058 J/(kg K)).

  • \(\theta\) is the potential temperature (K)

The layer argument specifies how the computations are carried out:

  • when layer is False (this is the default) \(\sigma\) is computed by using pressure_derivative()

  • when layer is True t must contain exactly 2 levels defining the layer. The result will be a single level computed by the following formula:

\[\sigma = - \frac{R_{d} \overline{T}}{\overline{p}} \frac{\Delta log\theta}{\Delta p}\]

where \(\overline{T}\) and \(\overline{p}\) are the mean layer values.

Please note that for the computations the formulas above are rewritten into the following equivalent forms:

\[ \begin{align}\begin{aligned}\sigma = \frac{\kappa R_{d}}{p^{2}} T - \frac{R_{d}}{p} \frac{\partial T}{\partial p}\\\sigma = \frac{\kappa R_{d}}{\overline{p}^{2}} \overline{T} - \frac{R_{d}}{\overline{p}} \frac{\Delta T}{\Delta p}\end{aligned}\end{align} \]

with \(\kappa = R_{d}/c_{pd}\).

Note

See also q_vector().