Frontogenesis3D

class rojak.turbulence.diagnostic.Frontogenesis3D(u_wind, v_wind, potential_temperature, geopotential, divergence, vector_derivatives)

Three-dimensional frontogenesis CAT diagnostic

The 3D frontogenesis equation is defined in [Bluestein1993] (p. 253) as,

\[\mathbf{F} = \frac{D}{Dt} | \nabla \theta |\]

where \(\frac{D}{Dt}\) is the material derivative and \(\theta\) is the potential temperature.

This implementation is based on the ECMWF implementation in the IFS which ignores terms related to diabatic heating, negligible horizontal gradients of the vertical velocity and that \(\frac{ \partial w }{ \partial z } = - \delta\). It is defined in [Bechtold2021] as,

\begin{aligned} \mathbf{F} = - \frac{1}{|\nabla\theta|} &\left[\frac{ \partial \theta }{ \partial x } \left( \frac{ \partial u }{ \partial x } \frac{ \partial \theta }{ \partial x } + \frac{ \partial v }{ \partial x } \frac{ \partial \theta }{ \partial y } \right) \right. + \left. \frac{ \partial \theta }{ \partial y } \left( \frac{ \partial u }{ \partial y } \frac{ \partial \theta }{ \partial x } + \frac{ \partial v }{ \partial y } \frac{ \partial \theta }{ \partial y } \right) \right. \\ &+ \left. \frac{ \partial \theta }{ \partial z } \left( \frac{ \partial u }{ \partial z } \frac{ \partial \theta }{ \partial x } + \frac{ \partial v }{ \partial z } \frac{ \partial \theta }{ \partial y} - \delta \frac{ \partial \theta }{ \partial z }\right) \right] \end{aligned}

where \(\delta\) is the divergence, i.e. \(\delta = \frac{ \partial u }{ \partial x } + \frac{ \partial v }{ \partial y }\)

Parameters:

• u_wind (DataArray) – Zonal wind speeds in m/s

• v_wind (DataArray) – Meridional wind speeds in m/s

• geopotential (DataArray) – Geopotential in m^2/s

• divergence (DataArray) – Horizontal divergence of wind in m/s

• vector_derivatives (dict[VelocityDerivative, DataArray]) – Dictionary containing all 4 velocity derivatives

• potential_temperature (DataArray)

__init__(u_wind, v_wind, potential_temperature, geopotential, divergence, vector_derivatives)

Parameters:

• name – Name of the diagnostic

• u_wind (DataArray)

• v_wind (DataArray)

• potential_temperature (DataArray)

• geopotential (DataArray)

• divergence (DataArray)

• vector_derivatives (dict[VelocityDerivative, DataArray])

Return type:

None

Methods

__init__(u_wind, v_wind, ...)
to_zarr(output_base_dir, *[, file_name])	Export computed_value to a zarr store
x_component(dtheta_dx, dtheta_dy)	x-component of the (un-normalised) 3D frontogenesis vector, i.e. the 1st term in the &\left[... line.
y_component(dtheta_dx, dtheta_dy)	y-component of the (un-normalised) 3D frontogenesis vector, i.e. the 2nd term in the &\left[... line.
z_component(dtheta_dx, dtheta_dy, dtheta_dz)	z-component of the (un-normalised) 3D frontogenesis vector, i.e. the + \left[... line.

Attributes

computed_value	The diagnostic's computed value
name	Name of the diagnostic