.. py:function:: 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.
:param t: temperature (K)
:type t: :class:`Fieldset` or ndarray
:param p: pressure (Pa)
:type p: :class:`Fieldset` or ndarray
:param layer: enable layer mode
:type layer: bool
:rtype: same type as ``t`` or None
The result is the static stability in :math:`m^{2} s^{-2} Pa^{-2}` units. On error None is returned. The following rules are applied when ``t`` is a :class:`Fieldset`:
* if ``t`` is a pressure level :class:`Fieldset` no ``p`` is needed
* for other level types ``p`` must be a :class:`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]_ :
.. math::
\sigma = - \frac{R_{d} T}{p} \frac{\partial log \Theta}{\partial p}
where
* :math:`R_{d}`` is the specific gas constant for dry air (287.058 J/(kg K)).
* :math:`\theta` is the potential temperature (K)
The ``layer`` argument specifies how the computations are carried out:
* when ``layer`` is False (this is the default) :math:`\sigma` is computed by using :func:`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:
.. math::
\sigma = - \frac{R_{d} \overline{T}}{\overline{p}} \frac{\Delta log\theta}{\Delta p}
where :math:`\overline{T}` and :math:`\overline{p}` are the mean layer values.
Please note that for the computations the formulas above are rewritten into the following equivalent forms:
.. math::
\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}
with :math:`\kappa = R_{d}/c_{pd}`.
.. note::
See also :func:`q_vector`.
.. mv-minigallery:: static_stability