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prob_estimation.py
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prob_estimation.py
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# -*- coding: utf-8 -*-
""" Test run with Stommel model. """
import numpy as np
import dapper.mods.Stommel as stommel
import matplotlib.pyplot as plt
import os
from dapper.mods.Stommel.ref_forcing import exp_ref_forcing
from dapper.mods.Stommel.ref_forcing_da import exp_ref_forcing_da
from dapper.mods.Stommel.clima_forcing import exp_clima_forcing
from dapper.mods.Stommel.clima_forcing_da import exp_clima_forcing_da
def sample_stat(samples):
mu = np.mean(samples)
std = np.std(samples)
N = len(samples)
#r = np.array([t.ppf(.025,N), t.ppf(.975,N)]) * (std / np.sqrt(N))
r=np.quantile(samples,[.025,.975])
r=np.abs(r-mu)
return mu, std, r
def prob_figure():
plt.close('all')
fig = plt.figure(figsize=(8,4))
ax = fig.subplots(1,1)
return fig, [ax]
def plot_prob(ax, pos, probs):
ax[0].plot(np.ones_like(probs) * pos, probs, 'bo', alpha=.5)
mu, std, r = sample_stat(probs)
ax[0].errorbar(np.array([pos]),np.array([mu]),color='k',
marker='o',yerr=np.reshape(r,(2,-1)))
ax[0].set_ylabel('Probability SA [%]')
for ax1 in ax:
ax1.grid()
ax1.set_xlim(0,5)
ax1.set_ylim(0,100)
ax1.xaxis.set_ticks(np.array([1,2,3,4]))
ax1.xaxis.set_ticklabels(['Ref','Ref DA','Climate','Climate DA'])
def error(x, E):
return x - np.mean(E, axis=0)
def rmse(errors):
return np.sqrt(np.mean(errors**2))
def bootstrap(func, data, N, confidence=.9):
r = []
for _ in range(N):
data1 = np.random.choice(data, size=len(data))
r.append(func(data1))
f0 = func(data)
q = (1.-confidence) * np.array([.5, -.5]) + np.array([0., 1.])
return (f0, (np.abs(np.quantile(r,q[0])-f0),
np.abs(np.quantile(r,q[1])-f0)))
def error_figure():
plt.close('all')
fig = plt.figure(figsize=(11,6))
ax = fig.subplots(2,3)
fig.subplots_adjust(left=.1,right=.98,wspace=.3)
for ax1 in np.reshape(ax,(-1)):
ax1.grid()
return fig, ax
def plot_error(ax, errors):
draws = []
ax = np.reshape(ax,(-1))
for key in errors:
errors1 = np.array(errors[key])
temp = errors1[:,:,1]-errors1[:,:,0]
salt = errors1[:,:,3]-errors1[:,:,2]
x=np.arange(0,np.size(temp,1))
ax[0].plot(x, np.sqrt(np.mean(temp**2,axis=0)), label=key)
draw, = ax[1].plot(x, np.sqrt(np.mean(salt**2,axis=0)), label=key)
draws.append(draw)
for n,ax1 in enumerate(ax[3:]):
ax1.plot(x, np.sqrt(np.mean(errors1[:,:,n+4]**2,axis=0)))
ax[0].set_ylabel('RMSE temp diff. [C]')
ax[1].set_ylabel('RMSE salt diff. [ppt]')
ax[3].set_ylabel('RMSE temp_diff [mms-1]')
ax[4].set_ylabel('RMSE salt_diff [mms-1]')
ax[5].set_ylabel('RMSE gamma [ms-1]')
for ax1 in ax:
ax1.set_xlabel('Time [year]')
ax[1].legend(handles=draws, loc='upper left', framealpha=1.)
return draws
def plot_perror(ax, errors):
ax.set_ylabel('RMSE probability')
ax.set_ylim(0,1)
for key in errors:
x=np.arange(0, np.size(errors[key],1))
vals = np.mean(np.abs(np.array(errors[key])), axis=0)
ax.plot(x, vals, label=key)
def plot_spreads(ax, spreads):
draws = []
ax = np.reshape(ax,(-1))
for key in errors:
spread1 = np.array(spreads[key])
x=np.arange(0,np.size(spread1,1))
ax[0].plot(x, np.sqrt(np.mean(spread1[:,:,0]+spread1[:,:,1],axis=0)),
label=key)
draw, = ax[1].plot(x, np.sqrt(np.mean(spread1[:,:,3]+spread1[:,:,2],axis=0)),
label=key)
draws.append(draw)
for n,ax1 in enumerate(ax[3:]):
ax1.plot(x, np.sqrt(np.mean(spread1[:,:,n+4],axis=0)))
ax[0].set_ylabel('Spread temp diff. [C]')
ax[1].set_ylabel('Spread salt diff. [ppt]')
ax[3].set_ylabel('Spread temp_diff [mms-1]')
ax[4].set_ylabel('Spread salt_diff [mms-1]')
ax[5].set_ylabel('Spread gamma [ms-1]')
for ax1 in ax:
ax1.set_xlabel('Time [year]')
ax[1].legend(handles=draws, loc='upper left', framealpha=1.)
return draws
def plot_pspread(ax, spreads):
ax.set_ylabel('Spread probability')
ax.set_ylim(0,1)
for key in errors:
x=np.arange(0, np.size(errors[key],1))
vals = np.sqrt(np.mean(np.array(spreads[key]), axis=0))
ax.plot(x, vals, label=key)
def plot_ensemble(filename, xx, yy, Efor):
plt.close('all')
fig=plt.figure(figsize=(8,4))
ax = fig.subplots(1,2)
drawings = []
for ax1 in ax:
ax1.grid()
ax1.set_xlabel('Time [year]')
ax1.set_xlim(0,200)
ax[0].set_ylabel("Temperature difference [C]")
ax[0].set_ylim(-4,18)
ax[1].set_ylabel("Salinity difference [ppt]")
ax[1].set_ylim(0,4)
t=np.arange(0,np.size(Efor,0))
for x in np.transpose(Efor, (1,0,2)):
drawing, = ax[0].plot(t, x[:,1]-x[:,0], 'k-', c='0.9', label='member')
ax[1].plot(t, x[:,3]-x[:,2], 'k-', c='0.9', label='member')
drawings.append(drawing)
drawing, = ax[0].plot(t, np.mean(Efor[:,:,1]-Efor[:,:,0],axis=1), 'g-', label='forecast')
ax[1].plot(t, np.mean(Efor[:,:,3]-Efor[:,:,2],axis=1), 'g-', label='forecast')
drawings.append(drawing)
drawing,=ax[0].plot(t, xx[:,1]-xx[:,0], 'k-', label='truth')
ax[1].plot(t, xx[:,3]-xx[:,2], 'k-', label='truth')
drawings.append(drawing)
if len(yy)>0:
t = np.arange(1,len(yy)+1)
yy = np.array(yy)
drawing,=ax[0].plot(t, yy[:,1]-yy[:,0], 'bo', label='obs', markersize=.8)
ax[1].plot(t, yy[:,3]-yy[:,2], 'bo', label='obs', markersize=.8)
drawings.append(drawing)
ax[0].legend(handles=drawings,loc='lower right')
fig.savefig(os.path.join(stommel.fig_dir,'ens',filename), format='png', dpi=300)
def confusion_matrix(matrix, xx, Efor):
xfor = np.mean(Efor[-1], axis=0)
states=stommel.array2states(np.array([xx[-1], xfor]))
if states[0].regime=='TH' and states[1].regime=='TH':
matrix[0,0] += 1
elif states[0].regime!='TH' and states[1].regime=='TH':
matrix[1,0] += 1
elif states[0].regime=='TH' and states[1].regime!='TH':
matrix[0,1] += 1
elif states[0].regime!='TH' and states[1].regime!='TH':
matrix[1,1] += 1
return matrix
def plot_confusion_matrix(matrix):
plt.close('all')
fig = plt.figure(figsize=(8,8))
ax = np.reshape(fig.subplots(2,2),(-1))
for ax1, key in zip(ax, matrix):
drawing=ax1.pcolor(matrix[key]/np.sum(matrix[key]), vmin=0, vmax=1)
ax1.set_ylabel('Truth')
ax1.set_xticks([.5,1.5])
ax1.xaxis.set_ticklabels(['TH','SA'])
ax1.set_xlabel('Forecast')
ax1.set_yticks([.5,1.5])
ax1.yaxis.set_ticklabels(['TH','SA'])
plt.colorbar(drawing,ax=ax1)
ax1.set_title(key)
return fig, ax
def plot_entropy(entropy):
plt.close('all')
fig = plt.figure(figsize=(6,4))
ax = fig.subplots(1,1)
ax.set_xlabel('Time [year]')
ax.set_ylabel('Cross entropy')
ax.grid()
ax.set_xlim(0,200)
for key in entropy:
x=np.arange(0, np.size(entropy[key],1))
ax.plot(x, np.mean(np.array(entropy[key]), axis=0), label=key)
ax.legend(framealpha=1.)
if __name__=='__main__':
NG = 50 #number of instances
N = 50 #ensemble members per instant
prob_flip, errors, spread, cmatrix, perrors, pspread, pentropy={}, {}, {}, {}, {}, {}, {}
for key in ['ref','ref_da','clima','clima_da']:
prob_flip[key] = []
errors[key] = []
spread[key] = []
cmatrix[key] = np.zeros((2,2))
perrors[key] = []
pspread[key] = []
pentropy[key] = []
seed=1000
for ng in range(NG):
print('Running instant ', ng)
np.random.seed(seed)
xp, HMM, model = exp_ref_forcing(N, seed)
xx, yy = HMM.simulate()
Efor, Eana = xp.assimilate(HMM, xx, yy)
perrors['ref'].append(stommel.error_prob(xx, Efor))
pspread['ref'].append(stommel.spread_prob(Efor))
pentropy['ref'].append(stommel.cross_entropy(xx,Efor))
errors['ref'].append(np.mean(Efor,axis=1)-xx)
spread['ref'].append(np.var(Efor,axis=1,ddof=1))
cmatrix['ref']=confusion_matrix(cmatrix['ref'], xx, Efor)
plot_ensemble("ens_ref_{:02d}".format(ng), xx, yy, Efor)
np.random.seed(seed)
xp, HMM, model = exp_ref_forcing_da(N, seed)
xx, yy = HMM.simulate()
Efor, Eana = xp.assimilate(HMM, xx, yy)
perrors['ref_da'].append(stommel.error_prob(xx, Efor))
pspread['ref_da'].append(stommel.spread_prob(Efor))
pentropy['ref_da'].append(stommel.cross_entropy(xx,Efor))
errors['ref_da'].append(np.mean(Efor,axis=1)-xx)
spread['ref_da'].append(np.var(Efor,axis=1,ddof=1))
cmatrix['ref_da']=confusion_matrix(cmatrix['ref_da'], xx, Efor)
plot_ensemble("ens_ref_da_{:02d}".format(ng), xx, yy, Efor)
np.random.seed(seed)
xp, HMM, model = exp_clima_forcing_da(N, seed)
xx, yy = HMM.simulate()
Efor, Eana = xp.assimilate(HMM, xx, yy)
perrors['clima_da'].append(stommel.error_prob(xx, Efor))
pspread['clima_da'].append(stommel.spread_prob(Efor))
pentropy['clima_da'].append(stommel.cross_entropy(xx,Efor))
errors['clima_da'].append(np.mean(Efor,axis=1)-xx)
spread['clima_da'].append(np.var(Efor,axis=1,ddof=1))
cmatrix['clima_da']=confusion_matrix(cmatrix['clima_da'], xx, Efor)
plot_ensemble("ens_clima_da_{:02d}".format(ng), xx, yy, Efor)
np.random.seed(seed)
xp, HMM, model = exp_clima_forcing(N, seed)
xx, yy = HMM.simulate()
Efor, Eana = xp.assimilate(HMM, xx, yy)
perrors['clima'].append(stommel.error_prob(xx, Efor))
pspread['clima'].append(stommel.spread_prob(Efor))
pentropy['clima'].append(stommel.cross_entropy(xx,Efor))
errors['clima'].append(np.mean(Efor,axis=1)-xx)
spread['clima'].append(np.var(Efor,axis=1,ddof=1))
cmatrix['clima']=confusion_matrix(cmatrix['clima'], xx, Efor)
plot_ensemble("ens_clima_{:02d}".format(ng), xx, yy, Efor)
seed+=20
#fig,ax = prob_figure()
#for n, key in enumerate(prob_flip):
# plot_prob(ax, n+1, prob_flip[key])
#fig.savefig(os.path.join(stommel.fig_dir, 'probabilities.png'),
# format='png', dpi=500)
#Plot errors
fig, ax = error_figure()
plot_error(ax, errors)
plot_perror(ax[0,2], perrors)
#Save figure
fig.savefig(os.path.join(stommel.fig_dir, 'rmse_time.png'),
format='png', dpi=500)
#Plot spread
fig, ax = error_figure()
plot_spreads(ax, spread)
plot_pspread(ax[0,2], pspread)
#Save figure
fig.savefig(os.path.join(stommel.fig_dir, 'spread_time.png'),
format='png', dpi=500)
fig,ax = plot_confusion_matrix(cmatrix)
fig.savefig(os.path.join(stommel.fig_dir, 'confusion_matrix.png'),
format='png', dpi=500)
plot_entropy(pentropy)
plt.savefig(os.path.join(stommel.fig_dir, 'entropy.png'),
format='png', dpi=500)