q_vector

metpy.calc.q_vector(u, v, temperature, pressure, dx=None, dy=None, static_stability=1, x_dim=- 1, y_dim=- 2)[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) xarray.DataArray or pint.Quantity) – x component of the wind (geostrophic in QG-theory)

  • v ((…, M, N) xarray.DataArray or pint.Quantity) – y component of the wind (geostrophic in QG-theory)

  • temperature ((…, M, N) xarray.DataArray or pint.Quantity) – Array of temperature at pressure level

  • pressure (pint.Quantity) – Pressure at level

  • dx (pint.Quantity, optional) – 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. Optional if xarray.DataArray with latitude/longitude coordinates used as input.

  • dy (pint.Quantity, optional) – 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. Optional if xarray.DataArray with latitude/longitude coordinates used as input.

  • 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.

  • x_dim (int, optional) – Axis number of x dimension. Defaults to -1 (implying […, Y, X] order). Automatically parsed from input if using xarray.DataArray.

  • y_dim (int, optional) – Axis number of y dimension. Defaults to -2 (implying […, Y, X] order). Automatically parsed from input if using xarray.DataArray.

Returns

tuple of (…, M, N) xarray.DataArray or pint.Quantity – The components of the Q-vector in the u- and v-directions respectively

Changed in version 1.0: Changed signature from (u, v, temperature, pressure, dx, dy, static_stability=1)

See also

static_stability

potential_vorticity_barotropic shearing_deformation