q_vector¶

metpy.calc.q_vector(u, v, temperature, pressure, dx, dy, static_stability=1)[source]¶

Calculate Q-vector at a given pressure level using the u, v winds and temperature.

\[\vec{Q} = (Q_1, Q_2) = - \frac{R}{\sigma p}\left( \frac{\partial \vec{v}_g}{\partial x} \cdot \nabla_p T, \frac{\partial \vec{v}_g}{\partial y} \cdot \nabla_p T \right)\]

This formula follows equation 5.7.55 from [Bluestein1992], and can be used with the the below form of the quasigeostrophic omega equation to assess vertical motion ([Bluestein1992] equation 5.7.54):

\[\left( \nabla_p^2 + \frac{f_0^2}{\sigma} \frac{\partial^2}{\partial p^2} \right) \omega = - 2 \nabla_p \cdot \vec{Q} - \frac{R}{\sigma p} \beta \frac{\partial T}{\partial x}.\]

Parameters

u ((M, N) ndarray) – x component of the wind (geostrophic in QG-theory)
v ((M, N) ndarray) – y component of the wind (geostrophic in QG-theory)
temperature ((M, N) ndarray) – Array of temperature at pressure level
pressure (pint.Quantity) – Pressure at level
dx (float or ndarray) – The grid spacing(s) in the x-direction. If an array, there should be one item less than the size of u along the applicable axis.
dy (float or ndarray) – The grid spacing(s) in the y-direction. If an array, there should be one item less than the size of u along the applicable axis.
static_stability (pint.Quantity, optional) – The static stability at the pressure level. Defaults to 1 if not given to calculate the Q-vector without factoring in static stability.

Returns

tuple of (M, N) ndarrays – The components of the Q-vector in the u- and v-directions respectively