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Update dyn.py #13

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67 changes: 67 additions & 0 deletions OceanLab/dyn.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2,6 +2,73 @@
import numpy as np
import seawater as sw

# ===========================================================
# SURFACE AGEOSTROPHIC VELOCITY
# ===========================================================
def curvature(ssh_grad, dxt, dyt):
''' Curvature of the sea surface height contours
==============================================================================
INPUT:
SSH = sea surface height gradient [Y,X]
dxt = zonal distance between the grid cells in meter [Y,X]
dyt = meridional distance between the grid cells in meter [Y,X]

OUTPUT:
k = curvature of the flow
==============================================================================
'''

ssh_grad_y, ssh_grad_x = ssh_grad[0], ssh_grad[1]

# Terms in the norminator
nominator_1st = (np.gradient(ssh_grad_y/dyt)[0]/dyt)*(ssh_grad_x/dxt)**2
nominator_2nd = (np.gradient(ssh_grad_x/dxt)[1]/dxt)*(ssh_grad_y/dyt)**2
nominator_3rd = 2*(np.gradient(ssh_grad_y/dyt)[1]/dxt)*(ssh_grad_x/dxt)*(ssh_grad_y/dyt)

# Terms in the denominator
denominator_1st = (ssh_grad_x/dxt)**2
denominator_2nd = (ssh_grad_y/dyt)**2
denominator = pow(denominator_1st + denominator_2nd, 3/2)

k = (-1*nominator_1st - 1*nominator_2nd + 2*nominator_3rd)/denominator

return k

def ageostrophic_vel(LON, LAT, SSH):
''' Surface ageostrophic velocity from gradient wind balance through the
combination of the surface geostrophic velocity and curvature of the flow
==============================================================================
INPUT:
LON = longitudes [Y,X]
LAT = latitude [Y,X]
SSH = sea surface height in meter [Y,X]

OUTPUT:
u_ag_vel = zonal component of the surface ageostrophic velocity
v_ag_vel = meridional component of the surface ageostrophic velocity
==============================================================================
'''
g = 9.8
f = sw.f(LAT)
[trash,dlonx] = np.gradient(LON)
dx = dlonx*np.cos(LAT*np.pi/180)*111195.
[dlaty,trash] = np.gradient(LAT)
dy = dlaty*111195.
SSH_gradient = np.gradient(SSH)
k = curvature(SSH_gradient, dx, dy)

## Estimating the surface geostrophic velocity from SSH
u_geo_vel = (-g/f)*(SSH_gradient[0]/dy)
v_geo_vel = (g/f)*(SSH_gradient[1]/dx)
## Reconstructing the surface velocity from the combinantion of the geostrophic velocity and curvature of the flow
u_total = (2*u_geo_vel)/(1 + np.sqrt(1 + 4*k*np.sqrt(u_geo_vel**2 + v_geo_vel**2)/f))
v_total = (2*v_geo_vel)/(1 + np.sqrt(1 + 4*k*np.sqrt(u_geo_vel**2 + v_geo_vel**2)/f))
## Computing the surface ageostrophic velocity as the difference between the total and geostrophic fields
u_ag_vel = u_total - u_geo_vel
v_ag_vel = v_total - v_geo_vel

return u_ag_vel, v_ag_vel

# ===========================================================
# DYNAMICAL MODES AMPLITUDE
# ===========================================================
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