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

Notes

If inputs have more than two dimensions, they are assumed to have either leading dimensions of (x, y) or trailing dimensions of (y, x), depending on the value of dim_order.