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=True)[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

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