uu = []; tt = []
vspec = np.zeros(ks.xspec.shape[1], np.float)
x = np.arange(N)
fig, ax = plt.subplots()
line, = ax.plot(x, ks.x.squeeze())
ax.set_xlim(0,N-1)
ax.set_ylim(-3,3)
#Init only required for blitting to give a clean slate.
def init():
global line
line.set_ydata(np.ma.array(x, mask=True))
return line,
# spinup
for n in range(nmin):
ks.advance()
def updatefig(n):
global tt,uu,vspec
ks.advance()
vspec += np.abs(ks.xspec.squeeze())**2
u = ks.x.squeeze()
line.set_ydata(u)
print(n,u.min(),u.max())
uu.append(u); tt.append(n*dt)
return line,
ani = animation.FuncAnimation(fig, updatefig, np.arange(1,nmax+1), init_func=init,
interval=25, blit=True, repeat=False)
plt.show()
dt = 0.5; npts = 128
diffusion_truth = 1.0
# for forecast model (same as above for perfect model expt)
# for simplicity, assume dt and npts stay the same.
#diffusion = 0.9
diffusion = diffusion_truth
rstruth = np.random.RandomState(42) # fixed seed for truth run
rsens = np.random.RandomState() # varying seed for ob noise and ensemble initial conditions
# model instance for truth (nature) run
model = KS(N=npts,dt=dt,diffusion=diffusion_truth,rs=rstruth)
# mode instance for forecast ensemble
ensemble = KS(N=npts,members=nens,dt=dt,diffusion=diffusion,rs=rsens)
for nt in range(ntstart): # spinup truth run
model.advance()
# sample obs from truth, compute climo stats for model.
xx = []; tt = []
for nt in range(ntimes):
model.advance()
xx.append(model.x[0]) # single member
tt.append(float(nt)*model.dt)
xtruth = np.array(xx,np.float)
timetruth = np.array(tt,np.float)
xtruth_mean = xtruth.mean()
xprime = xtruth - xtruth_mean
xvar = np.sum(xprime**2,axis=0)/(ntimes-1)
xtruth_stdev = np.sqrt(xvar.mean())
if verbose:
print 'climo for truth run:'
uu = []; tt = []
vspec = np.zeros(ks.xspec.shape[1], np.float)
x = np.arange(N)
fig, ax = plt.subplots()
line, = ax.plot(x, ks.x.squeeze())
ax.set_xlim(0,N-1)
ax.set_ylim(-3,3)
#Init only required for blitting to give a clean slate.
def init():
global line
line.set_ydata(np.ma.array(x, mask=True))
return line,
# spinup
for n in range(nmin):
ks.advance()
def updatefig(n):
global tt,uu,vspec
ks.advance()
vspec += np.abs(ks.xspec.squeeze())**2
u = ks.x.squeeze()
line.set_ydata(u)
print n,u.min(),u.max()
uu.append(u); tt.append(n*dt)
return line,
ani = animation.FuncAnimation(fig, updatefig, np.arange(1,nmax+1), init_func=init,
interval=25, blit=True, repeat=False)
plt.show()
from KS import KS, KSAssim
import numpy as np
"""
Author Benjamin Pachev <*****@*****.**> 2020
"""
def fourier_projector(spec, modes=21):
mod_spec = spec.copy()
mod_spec[:, modes:] = 0
return np.fft.irfft(mod_spec, axis=-1)
if __name__ == "__main__":
#See if the data assimilation works
true = KS()
assimilator = KSAssim(fourier_projector,
mu=1,
diffusion=3,
update_params=True)
max_n = 100
for n in range(max_n):
target = fourier_projector(true.xspec)
assimilator.set_target(target)
assimilator.advance()
true.advance()
print(assimilator.error(true))
diffusion_truth = 1.0
# for forecast model (same as above for perfect model expt)
# for simplicity, assume dt and npts stay the same.
#diffusion = 0.9
diffusion = diffusion_truth
rstruth = np.random.RandomState(42) # fixed seed for truth run
rsens = np.random.RandomState(
) # varying seed for ob noise and ensemble initial conditions
# model instance for truth (nature) run
model = KS(N=npts, dt=dt, diffusion=diffusion_truth, rs=rstruth)
# mode instance for forecast ensemble
ensemble = KS(N=npts, members=nens, dt=dt, diffusion=diffusion, rs=rsens)
for nt in range(ntstart): # spinup truth run
model.advance()
# sample obs from truth, compute climo stats for model.
xx = []
tt = []
for nt in range(ntimes):
model.advance()
xx.append(model.x[0]) # single member
tt.append(float(nt) * model.dt)
xtruth = np.array(xx, np.float)
timetruth = np.array(tt, np.float)
xtruth_mean = xtruth.mean()
xprime = xtruth - xtruth_mean
xvar = np.sum(xprime**2, axis=0) / (ntimes - 1)
xtruth_stdev = np.sqrt(xvar.mean())
if verbose:
