def Trans_single(k, K, u_10, fetch, azimuth, divergence):
nk = k.shape[0]
c_beta = 0.04 # wind wave growth parameter
k_hat = wn_dless_single(k, u_10)
K_hat = K * fv(u_10)**2 / const.g
wind_exponent = wind_exp(k)
mk = wn_exp(k.reshape(nk, 1), u_10, fetch, azimuth)
c_tau = wind_exponent / (2 * c_beta) # constant
# transfer function
T = c_tau * k_hat**(-3 / 2) * mk * fv(u_10) * divergence / (
const.g * (1 + 1j * c_tau * k_hat**(-2) * K_hat))
return T
def GoM_Trans(k, K, u_10, fetch, azimuth, div):
nk = k.shape[2]
c_beta = 0.04 # wind wave growth parameter
k_hat = wn_dless(k, u_10)
K_hat = K * fv(u_10) ** 2 / const.g
wind_exponent = np.zeros([div.shape[0], div.shape[1], nk])
mk = np.zeros([div.shape[0], div.shape[1], nk])
for ii in np.arange(k.shape[0]):
for jj in np.arange(k.shape[1]):
wind_exponent[ii ,jj, :] = wind_exp(k[ii, jj, :])
mk[ii, jj, :] = wn_exp(k[ii, jj, :].reshape(nk, 1), u_10[ii, jj], fetch, azimuth)[:, 0]
c_tau = wind_exponent / (2 * c_beta) # constant
# transfer function
T = c_tau * k_hat ** (-3 / 2) * mk * fv(u_10)[:, :, None] * div[:, :, None] / (const.g*(
1 + 1j * c_tau * k_hat ** (-2) * K_hat[:, :, None]))
return T
def Trans(k, K, u_10, fetch, azimuth, tsc):
nk = k.shape[2]
c_beta = 0.04 # wind wave growth parameter
k_hat = wn_dless(k, u_10)
K_hat = K * fv(u_10)**2 / const.g
wind_exponent = np.zeros([tsc.shape[0], tsc.shape[1], nk])
mk = np.zeros([tsc.shape[0], tsc.shape[1], nk])
for ii in np.arange(k.shape[0]):
for jj in np.arange(k.shape[1]):
wind_exponent[ii, jj, :] = wind_exp(k[ii, jj, :])
mk[ii, jj, :] = wn_exp(k[ii, jj, :].reshape(nk, 1), u_10[ii, jj],
fetch, azimuth)[:, 0]
c_tau = wind_exponent / (2 * c_beta) # constant
# divergence of the sea surface current
divergence = np.gradient(tsc[:, :, 0], 1e3, axis=1) + np.gradient(
tsc[:, :, 1], 1e3, axis=0)
# transfer function
T = c_tau * k_hat**(
-3 / 2) * mk * fv(u_10)[:, :, None] * divergence[:, :, None] / (
const.g * (1 + 1j * c_tau * k_hat**(-2) * K_hat[:, :, None]))
return T
def WB_emp(K, kr, u_10, tsc):
# empirical wave breaking contrasts from Eq.17 in [Kudryavtsev, 2012]
cq = 470
U = fv(u_10)
kb = kr / 10
omegab = np.sqrt(const.g * kb + const.gamma * kb**3 / const.rho_water)
divergence = np.gradient(tsc[:, :, 0], 1e3, axis=1) + np.gradient(
tsc[:, :, 1], 1e3, axis=0)
wb_c = -cq * np.log(U * kb / np.sqrt(
const.g * K)) * const.g * divergence / (U**2 * kb * omegab)
return wb_c
def divergence(sst, lat, lon, wind_speed, K, phi, phi_w, s):
"""
:param sst: sea surface temperature
:param wind_speed:
:param K: wave number vector
:param phi: the direction of wave number vector
:param phi_w: the direction of wind velocity vector
:param s: sign of Coriolis parameter
:return:
"""
# interpolate data
sst = set_nan(sst)
sst = nearest_nan(sst, lat, lon)
sst = mean_zeros(sst)
## compute the divergence
T = np.fft.fft2(sst) # sst in fourier space
V = np.sqrt(const.rho_air/const.rho_water)*fv(wind_speed) # friction velocity in the water
diver = 1j * const.alpha * const.g * V * (s * np.sin(phi_w - phi) + 1j * const.yita ** (3 / 4) * const.nb ** 0.5 * V * K / abs(const.f)) * K ** 2 * T / (const.yita ** 0.25 * const.nb ** 0.5 * const.f ** 2)
# apply fan filter for divergence to show the structures
a = np.array(range(0, int(sst.shape[1] / 2)))
b = np.array(range(-int(sst.shape[1] / 2), 0))
n = np.append(a, b)
a = np.array(range(0, int(sst.shape[0] / 2)))
b = np.array(range(-int(sst.shape[0] / 2), 0))
m = np.append(a, b)
mf = np.sinc(m / 500)
mf[abs(m) > 500] = 0
nf = np.sinc(n / 500)
nf[abs(n) > 500] = 0
fan = mf.reshape(mf.shape[0], 1) * nf
diver = fan * diver
D = np.fft.ifft2(diver)
return D
def wn_dless_single(k, u_10):
# dimensionless wave number of wind waves
return k * fv(u_10)**2 / const.g
def wn_dless(k, u_10):
# dimensionless wave number of wind waves
return k * fv(u_10)[:, :, None]**2 / const.g
def MSS_em(K, u_10, tsc):
# Empirical mss from Eq.17 in [Kudryavtsev, 2012]
divergence = np.gradient(tsc[:, :, 0], 1e3, axis=1) + np.gradient(tsc[:, :, 1], 1e3, axis=0)
cs = 180
U = fv(u_10)
return -cs * divergence / (U * np.sqrt(const.ky * K))
def GoM_MSS_em(K, u_10, div):
# Empirical mss from Eq.17 in [Kudryavtsev, 2012]
cs = 180
U = fv(u_10)
return -cs * div / (U * np.sqrt(const.ky * K))
