pydda.cost_functions.calculate_vertical_vorticity_gradient#

pydda.cost_functions.calculate_vertical_vorticity_gradient(u, v, w, dx, dy, dz, Ut, Vt, coeff=1e-05, upper_bc=1, upper_bc_mask=None)[source]#

Calculates the gradient of the cost function due to deviance from vertical vorticity equation. This is done by taking the functional derivative of the vertical vorticity cost function. :Parameters: * u (3D array) – Float array with u component of wind field

  • v (3D array) – Float array with v component of wind field

  • w (3D array) – Float array with w component of wind field

  • dx (float array) – Spacing in x grid

  • dy (float array) – Spacing in y grid

  • dz (float array) – Spacing in z grid

  • Ut (float) – U component of storm motion

  • Vt (float) – V component of storm motion

  • coeff (float) – Weighting coefficient

  • upper_bc (int) – Upper boundary (impermeability) condition. 0 disables it, 1 enforces w = 0 at the top of the domain, and 2 enforces w = 0 above the echo top as given by upper_bc_mask. The legacy booleans True and False are equivalent to 1 and 0.

  • upper_bc_mask (3D bool array or None) – The grid points at which w is held fixed when upper_bc is 2, as returned by pydda.cost_functions.calculate_echo_top_mask().

Returns:

Jv (1D float array) – Value of the gradient of the vertical vorticity cost function.

References

Potvin, C.K., A. Shapiro, and M. Xue, 2012: Impact of a Vertical Vorticity Constraint in Variational Dual-Doppler Wind Analysis: Tests with Real and Simulated Supercell Data. J. Atmos. Oceanic Technol., 29, 32–49, https://doi.org/10.1175/JTECH-D-11-00019.1 Shapiro, A., C.K. Potvin, and J. Gao, 2009: Use of a Vertical Vorticity Equation in Variational Dual-Doppler Wind Analysis. J. Atmos. Oceanic Technol., 26, 2089–2106, https://doi.org/10.1175/2009JTECHA1256.1