def main():
xg, zg = np.meshgrid(np.arange(-2000., 2000., 10),
np.arange(-3000., 0., 10.))
N = 2e-3
k = -2.*np.pi/2000.
m = -2.*np.pi/2000.
om = gw.omega(N, k, m)
U = 0.0 # -om/k
u_0 = 0.1
phase_0 = 0. # np.pi
# for phase_0 in np.linspace(0., 2*np.pi, 10):
#
# ug = u2D(xg, zg, 0., k, m, om, u_0, U, phase_0)
#
# plt.figure()
# plt.pcolormesh(xg, zg, ug, cmap=plt.get_cmap('bwr'))
# plt.colorbar()
# plt.title("{:1.2f} rad".format(phase_0))
for t in np.arange(0., 10000., 500.):
ug = u2D(xg, zg, t, k, m, om, u_0, U, phase_0)
plt.figure()
plt.pcolormesh(xg, zg, ug, cmap=plt.get_cmap('bwr'))
plt.colorbar()
plt.title("{:g} s".format(t))
def drdt(r, t, phi_0, k, l, m, N=2e-3, U=0.3, V=0., Wf=0.1, f=0., phase_0=0.):
x = r[0]
y = r[1]
z = r[2]
om = gw.omega(N, k, m, l, f)
dxdt = U + gw.u(x, y, z, t, phi_0, k, l, m, om, f=f, U=U, phase_0=phase_0)
dydt = V + gw.v(x, y, z, t, phi_0, k, l, m, om, f=f, U=U, phase_0=phase_0)
dzdt = Wf + gw.w(x, y, z, t, phi_0, k, l, m, om, N, U=U, phase_0=phase_0)
return np.array([dxdt, dydt, dzdt])
def b_model(params, data):
phi_0, X, Y, Z, phase_0 = params
time, x, y, z, U, V, N, f = data
k = 2*np.pi/X
l = 2*np.pi/Y
m = 2*np.pi/Z
om = gw.omega(N, k, m, l, f)
b = gw.b(x, y, z, time, phi_0, k, l, m, om, N, U=U, V=V, phase_0=phase_0)
return b
def p_model(params, data):
phi_0, X, Y, Z, phase_0 = params
t, x, y, z, U, V, N, f = data
k = 2*np.pi/X
l = 2*np.pi/Y
m = 2*np.pi/Z
om = gw.omega(N, k, m, l, f)
p = gw.phi(x, y, z, t, phi_0, k, l, m, om, U=U, V=V, phase_0=phase_0)
return p
def v_model(params, data):
phi_0, X, Y, Z, phase_0 = params
time, x, y, z, U, V, N, f, w_data, u_data, v_data, b_data = data
k = 2*np.pi/X
l = 2*np.pi/Y
m = 2*np.pi/Z
om = gw.omega(N, k, m, l, f)
v = gw.v(x, y, z, time, phi_0, k, l, m, om, f=f, U=U, V=V, phase_0=phase_0)
return v
def w_model(params, data):
X, Y, Z, phase_0 = params
time, dist, depth, U, V, W, B, N, f = data
k = 2*np.pi/X
l = 2*np.pi/Y
m = 2*np.pi/Z
om = gw.omega(N, k, m, l, f)
phi_0 = np.max(W)*(N**2 - f**2)*m/(om*(k**2 + l**2 + m**2))
w = gw.w(dist, 0., depth, time, phi_0, k, l, m, om, N, phase_0=phase_0)
return w - W
def full_model(params, data):
phi_0, X, Y, Z, phase_0 = params
time, x, y, z, U, V, N, f, w_data, u_data, v_data, b_data = data
k = 2*np.pi/X
l = 2*np.pi/Y
m = 2*np.pi/Z
om = gw.omega(N, k, m, l, f)
u = gw.u(x, y, z, time, phi_0, k, l, m, om, f=f, U=U, V=V, phase_0=phase_0)
v = gw.v(x, y, z, time, phi_0, k, l, m, om, f=f, U=U, V=V, phase_0=phase_0)
w = gw.w(x, y, z, time, phi_0, k, l, m, om, N, U=U, V=V, phase_0=phase_0)
b = gw.b(x, y, z, time, phi_0, k, l, m, om, N, U=U, V=V, phase_0=phase_0)
return np.hstack((w - w_data, u - u_data, v - v_data, b - b_data))
def w_model(params, pfl, zlim, deg):
phi_0, X, Z, phase_0 = params
zmin, zmax = zlim
nope = np.isnan(pfl.z) | (pfl.z < zmin) | (pfl.z > zmax)
t = 60*60*24*(pfl.UTC - np.nanmin(pfl.UTC))
x = 1000.*(pfl.dist_ctd - np.nanmin(pfl.dist_ctd))
k = 2*np.pi/X
l = 0.
m = 2*np.pi/Z
f = gsw.f(pfl.lat_start)
N = np.mean(np.sqrt(pfl.N2_ref[~nope]))
om = gw.omega(N, k, m, l, f)
w = gw.w(x, 0., pfl.z, t, phi_0, k, l, m, om, N, phase_0=phase_0)
return w[~nope] - pfl.Ww[~nope]
def u_model(params, pfl, zlim, deg):
phi_0, X, Z, phase_0 = params
zmin, zmax = zlim
nope = np.isnan(pfl.zef) | (pfl.zef < zmin) | (pfl.zef > zmax)
t = 60*60*24*(pfl.UTCef - np.nanmin(pfl.UTCef))
x = 1000.*(pfl.dist_ef - np.nanmin(pfl.dist_ef))
k = 2*np.pi/X
l = 0.
m = 2*np.pi/Z
f = gsw.f(pfl.lat_start)
N = np.mean(np.sqrt(pfl.N2_ref[~nope]))
om = gw.omega(N, k, m, l, f)
u = gw.u(x, 0., pfl.zef, t, phi_0, k, l, m, om, phase_0=phase_0)
return u[~nope] - utils.nan_detrend(pfl.zef[~nope], pfl.U[~nope], deg)
def model_basic(phi_0, X, Y, Z, phase_0=0., oparams=default_params):
Ufunc = oparams['Ufunc']
f = oparams['f']
N = oparams['N']
# Float change in buoyancy with velocity.
Wf_pvals = oparams['Wf_pvals']
# Wave parameters
k = 2 * np.pi / X
l = 2 * np.pi / Y
m = 2 * np.pi / Z
om = gw.omega(N, k, m, l, f)
args = (phi_0, Ufunc, Wf_pvals, k, l, m, om, N, f, phase_0)
# Integration parameters.
dt = oparams['dt']
t_0 = 0.
t_1 = oparams['t_1']
t = np.arange(t_0, t_1, dt)
# Initial conditions.
x_0 = oparams['x_0']
y_0 = oparams['y_0']
z_0 = oparams['z_0']
r_0 = np.array([x_0, y_0, z_0])
# This integrator calls FORTRAN odepack to solve the problem.
r = odeint(drdt, r_0, t, args)
uargs = (phi_0, Ufunc(r[:, 2]), k, l, m, om, N, f, phase_0)
u = gw.wave_vel(r, t, *uargs)
u[:, 0] += Ufunc(r[:, 2])
b = gw.buoy(r, t, *uargs)
return t, r, u, b
def model_basic(phi_0, X, Y, Z, phase_0=0., oparams=default_params):
Ufunc = oparams['Ufunc']
f = oparams['f']
N = oparams['N']
# Float change in buoyancy with velocity.
Wf_pvals = oparams['Wf_pvals']
# Wave parameters
k = 2*np.pi/X
l = 2*np.pi/Y
m = 2*np.pi/Z
om = gw.omega(N, k, m, l, f)
args = (phi_0, Ufunc, Wf_pvals, k, l, m, om, N, f, phase_0)
# Integration parameters.
dt = oparams['dt']
t_0 = 0.
t_1 = oparams['t_1']
t = np.arange(t_0, t_1, dt)
# Initial conditions.
x_0 = oparams['x_0']
y_0 = oparams['y_0']
z_0 = oparams['z_0']
r_0 = np.array([x_0, y_0, z_0])
# This integrator calls FORTRAN odepack to solve the problem.
r = odeint(drdt, r_0, t, args)
uargs = (phi_0, Ufunc(r[:, 2]), k, l, m, om, N, f, phase_0)
u = gw.wave_vel(r, t, *uargs)
u[:, 0] += Ufunc(r[:, 2])
b = gw.buoy(r, t, *uargs)
return t, r, u, b
# ax.yaxis.set_ticks_position('both')
# ax.yaxis.set_label_position('right')
colors = ['blue', 'green', 'grey']
N = 2.2e-3
f = gsw.f(-57.5)
for i, M in enumerate(Ms):
phi_0 = M.trace('phi_0')[:]
k = np.pi*2./M.trace('X')[:]
l = np.pi*2./M.trace('Y')[:]
m = np.pi*2./M.trace('Z')[:]
print("complete wavelength = {}".format(np.mean(np.pi*2/np.sqrt(k**2 + l**2 + m**2))))
om = gw.omega(N, k, m, l, f)
print("om/N = {}".format(np.mean(om/N)))
w_0 = gw.W_0(phi_0, m, om, N)
Edens = gw.Edens(w_0, k, m, l)
Efluxz = gw.Efluxz(w_0, k, m, N, l, f)
Mfluxz = gw.Mfluxz(phi_0, k, l, m, om, N)
colprops={'color': colors[i]}
data = [k, l, m]
axs[0].boxplot(data, boxprops=colprops,
whiskerprops=colprops, capprops=colprops,
medianprops=colprops, showfliers=False,
labels=['$k$', '$l$', '$m$'])
axs[1].boxplot(om/N, boxprops=colprops,
whiskerprops=colprops, capprops=colprops,
medianprops=colprops, showfliers=False,
def model_verbose(phi_0, X, Y, Z, phase_0=0., oparams=default_params):
"""Return loads and loads of info."""
t, r, u, b = model_basic(phi_0, X, Y, Z, phase_0, oparams)
Ufunc = oparams['Ufunc']
f = oparams['f']
N = oparams['N']
# Float change in buoyancy with velocity.
Wf_pvals = oparams['Wf_pvals']
# Wave parameters
w_0 = oparams['w_0']
k = 2 * np.pi / X
l = 2 * np.pi / Y
m = 2 * np.pi / Z
om = gw.omega(N, k, m, l, f)
u_0 = gw.U_0(phi_0, k, l, om, f)
v_0 = gw.V_0(phi_0, k, l, om, f)
w_0 = gw.W_0(phi_0, m, om, N)
b_0 = gw.B_0(phi_0, m, om, N)
if oparams['print']:
print("N = {:1.2E} rad s-1.\n"
"om = {:1.2E} rad s-1.\n"
"u_0 = {:1.2E} m s-1.\n"
"v_0 = {:1.2E} m s-1.\n"
"w_0 = {:1.2E} m s-1.\n"
"phi_0 = {:1.2E} m2 s-2.\n"
"b_0 = {:1.2E} m s-2.\n"
"X = {:1.0f} m.\n"
"k = {:1.2E} rad m-1.\n"
"Y = {:1.0f} m.\n"
"l = {:1.2E} rad m-1.\n"
"Z = {:1.0f} m.\n"
"m = {:1.2E} rad m-1.\n"
"".format(N, om, u_0, v_0, w_0, phi_0, b_0, X, k, Y, l, Z, m))
output = utils.Bunch(Ufunc=Ufunc,
U=Ufunc(r[:, 2]),
f=f,
N=N,
Wf_pvals=Wf_pvals,
w_0=w_0,
k=k,
l=l,
m=m,
om=om,
phi_0=phi_0,
u_0=u_0,
v_0=v_0,
b_0=b_0,
t=t,
z_0=oparams['z_0'],
r=r,
u=u,
b=b,
oparams=oparams)
return output
p = -z.copy() ppos = 10. * np.ones_like(z) #ppos[ppos.size/2:] = 50. # Wave params X = -2000. Y = -2000. Z = -2000. N = 2e-3 phi_0 = 0.03 k = np.pi * 2. / X l = np.pi * 2. / Y m = np.pi * 2. / Z om = gw.omega(N, k, m, l) wave = (k, l, m, om, phi_0, N) w_0 = 0. z_0 = z[0] X_0 = np.array([z_0, w_0]) t_max = 5000. dt = 1. t = np.arange(0., t_max + dt, dt) M = 27.179 p_0 = 2000. k_0 = 16. V_0 = 0.0262
def model_verbose(phi_0, X, Y, Z, phase_0=0., oparams=default_params):
"""Return loads and loads of info."""
t, r, u, b = model_basic(phi_0, X, Y, Z, phase_0, oparams)
Ufunc = oparams['Ufunc']
f = oparams['f']
N = oparams['N']
# Float change in buoyancy with velocity.
Wf_pvals = oparams['Wf_pvals']
# Wave parameters
w_0 = oparams['w_0']
k = 2*np.pi/X
l = 2*np.pi/Y
m = 2*np.pi/Z
om = gw.omega(N, k, m, l, f)
u_0 = gw.U_0(phi_0, k, l, om, f)
v_0 = gw.V_0(phi_0, k, l, om, f)
w_0 = gw.W_0(phi_0, m, om, N)
b_0 = gw.B_0(phi_0, m, om, N)
if oparams['print']:
print("N = {:1.2E} rad s-1.\n"
"om = {:1.2E} rad s-1.\n"
"u_0 = {:1.2E} m s-1.\n"
"v_0 = {:1.2E} m s-1.\n"
"w_0 = {:1.2E} m s-1.\n"
"phi_0 = {:1.2E} m2 s-2.\n"
"b_0 = {:1.2E} m s-2.\n"
"X = {:1.0f} m.\n"
"k = {:1.2E} rad m-1.\n"
"Y = {:1.0f} m.\n"
"l = {:1.2E} rad m-1.\n"
"Z = {:1.0f} m.\n"
"m = {:1.2E} rad m-1.\n"
"".format(N, om, u_0, v_0, w_0, phi_0, b_0, X, k, Y, l, Z, m))
output = utils.Bunch(Ufunc=Ufunc,
U=Ufunc(r[:, 2]),
f=f,
N=N,
Wf_pvals=Wf_pvals,
w_0=w_0,
k=k,
l=l,
m=m,
om=om,
phi_0=phi_0,
u_0=u_0,
v_0=v_0,
b_0=b_0,
t=t,
z_0=oparams['z_0'],
r=r,
u=u,
b=b,
oparams=oparams)
return output
