# create vertical grid:
z = np.asarray(np.linspace(-4000, 0, 80))
# create initial guess for buoyancy profile in the Atl
def b_Atl(z):
return bs * np.exp(z / 300.) + z / z[0] * bbot
#def b_Atl(z): return 0.3*bs+z/z[0]*(bbot-0.3*bs)
def b_Pac(z):
return bs * np.exp(z / 300.) + z / z[0] * bbot
# create N.A. overturning model instance
AMOC = Psi_Thermwind(z=z, b1=b_Atl, b2=0.01 * b_Atl(z))
# and solve for initial overturning streamfunction:
AMOC.solve()
# map North Atlantic overturning to isopycnal space:
[Psi_iso_Atl, Psi_iso_N] = AMOC.Psibz()
# create interbasin zonal overturning model instance
ZOC = Psi_Thermwind(z=z, b1=b_Atl, b2=b_Pac, f=1e-4)
# and solve for initial overturning streamfunction:
ZOC.solve()
# map inter-basin overturning to isopycnal space:
[Psi_zonal_Atl, Psi_zonal_Pac] = ZOC.Psibz()
# create S.O. overturning model instance for Atlantic sector
SO_Atl = Psi_SO(z=z, y=y, b=b_Atl(z), bs=bs_SO, tau=tau, L=Latl, KGM=K)
SO_Atl.solve()
# number of vertical buoyancy levels for isopycnal computations
nb = 500
# Set initial conditions
if pickup is not None:
b_basin = 1.0 * pickup['arr_0']
b_north = 1.0 * pickup['arr_1']
bs_SO = 1.0 * pickup['arr_2']
else:
b_basin = bs * np.exp(z / 400.) - 0.0001 * z / z[0]
b_north = bs_north - 0.0001*(z / z[0])**2.
bs_SO = bs_SO_eq.copy(); bs_SO[:6]= -0.0001
# create N.A. overturning model instance
AMOC = Psi_Thermwind(z=z, b1=b_basin, b2=b_north, f=1.2e-4)
# and solve for initial overturning streamfunction:
AMOC.solve()
# create S.O. overturning model instance
PsiSO = Psi_SO(
z=z, y=y, b=b_basin, bs=bs_SO, tau=tau, f=1.2e-4, L=L, KGM=kapGM
)
# and solve for initial overturning streamfunction:
PsiSO.solve()
# notice that the next few lines need to come after Psi_SO is computed
# in case the latter is fixed to the pickup conditions
bs_SO[-1] = bs
# make sure buoyancy at northern end of channel (serves as BC for diffusion) equals surface b in basin
# create vertical grid:
z = np.asarray(np.linspace(-4000, 0, 80))
# Initial conditions for buoyancy profile in the basin
def b_basin(z):
return bs * np.exp(z / 300.)
def b_north(z):
return bs_north * np.exp(z / 300.)
# create N.A. overturning model instance
AMOC = Psi_Thermwind(z=z, b1=b_basin, b2=b_north, f=1e-4)
# and solve for initial overturning streamfunction:
AMOC.solve()
# evaluate overturning in isopycnal space:
[Psi_iso_b, Psi_iso_n] = AMOC.Psibz()
# create S.O. overturning model instance
SO = Psi_SO(z=z,
y=y,
b=b_basin(z),
bs=bs_SO,
tau=tau,
f=1e-4,
L=5e6,
KGM=1000.,
c=0.1,
Diag=np.load('diags.npz')
# Notice that some of these variables may need to be adjusted to match the
# simulations to be plotted:
L=2e7
l=2e6;
nb=500
b_basin=1.0*Diag['arr_2'][:,-1];
b_north=1.0*Diag['arr_3'][:,-1];
bs_SO=1.0*Diag['arr_4'][:,-1];
z=1.0*Diag['arr_5'];
y=1.0*Diag['arr_7'];
tau=1.0*Diag['arr_9'];
kapGM=1.0*Diag['arr_10'];
AMOC = Psi_Thermwind(z=z,b1=b_basin,b2=b_north,f=1.2e-4)
AMOC.solve()
PsiSO=Psi_SO(z=z,y=y,b=b_basin,bs=bs_SO,tau=tau,f=1.2e-4,L=L,KGM=kapGM)
PsiSO.solve()
blevs=np.arange(-0.01,0.03,0.001)
plevs=np.arange(-28.,28.,2.0)
bs=1.*bs_SO;bn=1.*b_basin;
if bs[0]>bs[1]:
# due to the way the time-stepping works bs[0] can be infinitesimally larger
# than bs[0] here, which messe up interpolation
bs[0]=bs[1]
if bs[0]<bn[0]:
# Notice that bn[0] can at most be infinitesimally larger than bs[0]
# create grid:
z = np.asarray(np.linspace(-4000, 0, 80))
# Initial conditions for buoyancy profile in the basin:
def b_basin(z):
return bs * np.exp(z / 300.)
def b_north(z):
return 1e-3 * bs * np.exp(z / 300.)
# create overturning model instance
AMOC = Psi_Thermwind(z=z, b1=b_basin, b2=b_north)
# and solve for initial overturning streamfunction:
AMOC.solve()
# evaluate overturning in isopycnal space:
[Psi_iso_b, Psi_iso_n] = AMOC.Psibz()
# Create figure:
fig = plt.figure(figsize=(6, 10))
ax1 = fig.add_subplot(111)
ax2 = ax1.twiny()
plt.ylim((-4e3, 0))
ax1.set_xlim((-5, 20))
ax2.set_xlim((-0.01, 0.04))
ax1.set_xlabel('$\Psi$', fontsize=14)
ax2.set_xlabel('b', fontsize=14)
# buoyancy profile in the basin:
def b_basin(z):
return 0.03 * np.exp(z / 300.) - 0.0004
# We will here assume b_N=0 (the default)
z = np.asarray(np.linspace(-4000, 0, 100))
# the next line would turn b_basin from a function to an array,
# which is also a valid input to Model_PsiNA
#b_basin=b_basin(z)
# create column model instance:
m = Psi_Thermwind(z=z, b1=b_basin)
# solve the model:
m.solve()
# Plot results:
fig = plt.figure(figsize=(6, 10))
ax1 = fig.add_subplot(111)
ax2 = ax1.twiny()
ax2.plot(b_basin(m.z), m.z, color='b')
ax1.plot(m.Psi, m.z, color='r')
plt.ylim((-4e3, 0))
ax1.set_xlim((-5, 20))
ax2.set_xlim((-0.01, 0.04))
ax1.set_xlabel('$\Psi$', fontsize=14)
ax2.set_xlabel('b', fontsize=14)
plt.show()
# create grid
z = np.asarray(np.linspace(-3500, 0, 70))
# we could also use an irregular grid that's finer near the surface:
#z=np.asarray(np.linspace(-(3500.**(3./4.)), 0, 40))
#z[:-1]=-(-z[:-1])**(4./3.)
# create initial guess for buoyancy profile in the basin
def b_basin(z):
return bs * np.exp(z / 300.) + bbot
# create overturning model instance
AMOC = Psi_Thermwind(z=z, b1=b_basin)
# and solve for initial overturning streamfunction:
AMOC.solve()
# Create figure and plot initial conditions:
fig = plt.figure(figsize=(6, 10))
ax1 = fig.add_subplot(111)
ax2 = ax1.twiny()
ax1.plot(AMOC.Psi, AMOC.z)
#ax2.plot(m.b_N, m.z)
ax2.plot(b_basin(z), z)
plt.ylim((-4e3, 0))
ax1.set_xlim((-5, 20))
ax2.set_xlim((-0.01, 0.04))
ax1.set_xlabel('$\Psi$', fontsize=14)
ax2.set_xlabel('b', fontsize=14)
kappa_s = 3e-5
kappa_4k = 3e-4
kappa = lambda z: (kappa_back + kappa_s * np.exp(z / 100) + kappa_4k * np.exp(
-z / 1000 - 4))
# create grid
z = np.asarray(np.linspace(-3500, 0, 100))
# create initial guess for buoyancy profile in the basin
def b_basin(z):
return bs * np.exp(z / 300.) + bbot
# create overturning model instance
AMOC = Psi_Thermwind(z=z, b1=b_basin)
# and solve for initial overturning streamfunction:
AMOC.solve()
# Create figure and plot initial conditions:
fig = plt.figure(figsize=(6, 10))
ax1 = fig.add_subplot(111)
ax2 = ax1.twiny()
ax1.plot(AMOC.Psi, AMOC.z)
#ax2.plot(m.b_N, m.z)
ax2.plot(b_basin(z), z)
plt.ylim((-4e3, 0))
ax1.set_xlim((-5, 20))
ax2.set_xlim((-0.01, 0.04))
ax1.set_xlabel('$\Psi$', fontsize=14)
ax2.set_xlabel('b', fontsize=14)