# Time Parameters
t0 = dt.datetime(2016, 5, 30, 0)
t1 = dt.datetime(2016, 6, 30, 0)
#t1 = t0 + dt.timedelta(hours=23.99)
# EDI Data
edi_data = edi.load_data('mms1',
'srvy',
optdesc='efield',
start_date=t0,
end_date=t1)
edi_data = edi_data.rename({'Epoch': 'time'})
# FGM Data
fgm_data = fgm.load_data('mms1', 'fgm', 'srvy', 'l2', t0, t1)
# MEC Data
sdc = api.MrMMS_SDC_API(sc,
'edp',
'fast',
level,
optdesc='dce',
start_date=t0,
end_date=t1)
r_gse_vname = '_'.join((sc, 'mec', 'r', 'gse'))
r_lbl_vname = '_'.join((sc, 'mec', 'r', 'gse', 'label'))
v_gse_vname = '_'.join((sc, 'mec', 'v', 'gse'))
v_lbl_vname = '_'.join((sc, 'mec', 'v', 'gse', 'label'))
def kinetic_entropy(sc, mode, start_date, end_date):
# Read the data
b = fgm.load_data(sc, mode, start_date, end_date)
dis_moms = fpi.load_moms(sc, mode, 'i', start_date, end_date)
des_moms = fpi.load_moms(sc, mode, 'e', start_date, end_date)
dis_dist = fpi.load_dist(sc, mode, 'i', start_date, end_date)
des_dist = fpi.load_dist(sc, mode, 'e', start_date, end_date)
# Philosopy
# - For the Maxwellian distributions, use the FPI moments data
# whenever possible
# - For the integrated moments, do not mix them with FPI moments
# Equivalent Maxwellian distribution
dis_max_dist = fpi.maxwellian_distribution(dis_dist,
N=dis_moms['density'],
bulkv=dis_moms['velocity'],
T=dis_moms['t'])
des_max_dist = fpi.maxwellian_distribution(des_dist,
N=des_moms['density'],
bulkv=des_moms['velocity'],
T=des_moms['t'])
# Spacecraft potential correction
edp_mode = mode if mode == 'brst' else 'fast'
scpot = edp.load_scpot(sc, edp_mode, start_date, end_date)
scpot_dis = scpot.interp_like(dis_moms, method='nearest')
scpot_des = scpot.interp_like(des_moms, method='nearest')
# Maxwellian entropy density
# - Calculated from FPI moments to stick with philosophy
# si_dist = fpi.entropy(dis_dist, scpot=scpot_dis)
# se_dist = fpi.entropy(des_dist, scpot=scpot_des)
si_max = fpi.maxwellian_entropy(dis_moms['density'], dis_moms['p'])
se_max = fpi.maxwellian_entropy(des_moms['density'], des_moms['p'])
# Velocity space entropy density
siv_dist = fpi.vspace_entropy(dis_dist,
# N=dis_moms['density'],
# s=si_dist,
scpot=scpot_dis)
sev_dist = fpi.vspace_entropy(des_dist,
# N=des_moms['density'],
# s=se_dist,
scpot=scpot_des)
siv_max = fpi.vspace_entropy(dis_max_dist,
N=dis_moms['density'],
s=si_max,
scpot=scpot_dis)
sev_max = fpi.vspace_entropy(des_max_dist,
N=des_moms['density'],
s=se_max,
scpot=scpot_des)
# M-bar
miv_bar = np.abs(siv_max - siv_dist) / siv_max
mev_bar = np.abs(sev_max - sev_dist) / sev_max
# Anisotropy
Ai = dis_moms['temppara'] / dis_moms['tempperp'] - 1
Ae = des_moms['temppara'] / des_moms['tempperp'] - 1
nrows = 8
ncols = 1
figsize = (5.5, 7.0)
fig, axes = plt.subplots(nrows=nrows, ncols=ncols,
figsize=figsize, squeeze=False)
# B
ax = axes[0,0]
ax = util.plot([b['B'][:,3], b['B'][:,0], b['B'][:,1], b['B'][:,2]],
ax=ax, labels=['|B|', 'Bx', 'By', 'Bz'],
xaxis='off', ylabel='B\n(nT)'
)
# N
ax = axes[1,0]
ax = util.plot([dis_moms['density'], des_moms['density']],
ax=ax, labels=['Ni', 'Ne'],
xaxis='off', ylabel='N\n($cm^{-3}$)'
)
# Velocity space ion entropy density
ax = axes[2,0]
ax = util.plot([siv_max, siv_dist],
ax=ax, labels=['$s_{i,V,max}$', '$s_{i,V}$'],
xaxis='off', ylabel='$s_{V}$\n$J/K/m^{3}$ $ln()$'
)
# Velocity space electron entropy density
ax = axes[3,0]
ax = util.plot([sev_max, sev_dist],
ax=ax, labels=['$s_{e,V,max}$', '$s_{e,V}$'],
xaxis='off', ylabel='$s_{V}$'
)
# Velocity space M-bar
ax = axes[4,0]
ax = util.plot([miv_bar, mev_bar],
ax=ax, labels=['$\overline{M}_{i,V}$', '$\overline{M}_{e,V}$'],
xaxis='off', ylabel='$\overline{M}_{V}$'
)
# Ion temperature
ax = axes[5,0]
ax = util.plot([dis_moms['temppara'], dis_moms['tempperp'], dis_moms['t']],
ax=ax, labels=['$T_{\parallel}$', '$T_{\perp}$, $T$'],
xaxis='off', ylabel='$T_{i}$\n(eV)'
)
# Electron temperature
ax = axes[6,0]
ax = util.plot([des_moms['temppara'], des_moms['tempperp'], des_moms['t']],
ax=ax, labels=['$T_{\parallel}$', '$T_{\perp}$, $T$'],
xaxis='off', ylabel='$T_{e}$\n(eV)'
)
# Anisotropy
ax = axes[7,0]
ax = util.plot([Ai, Ae],
ax=ax, labels=['$A_{i}$', '$A_{e}$'],
ylabel='A'
)
fig.suptitle('Plasma Parameters for Kinetic and Boltzmann Entropy')
plt.subplots_adjust(left=0.2, right=0.85, top=0.95, hspace=0.4)
# plt.setp(axes, xlim=xlim)
return fig, axes
def vspace_entropy(sc, mode, start_date, end_date):
# Read the data
b = fgm.load_data(sc, mode, start_date, end_date)
dis_moms = fpi.load_moms(sc, mode, optdesc='dis-moms',
start_date=start_date, end_date=end_date)
des_moms = fpi.load_moms(sc, mode, optdesc='des-moms',
start_date=start_date, end_date=end_date)
dis_dist = fpi.load_dist(sc, mode, optdesc='dis-dist',
start_date=start_date, end_date=end_date)
des_dist = fpi.load_dist(sc, mode, optdesc='des-dist',
start_date=start_date, end_date=end_date)
# Precondition the distributions
dis_kwargs = fpi.precond_params(sc, mode, 'l2', 'dis-dist',
start_date, end_date,
time=dis_dist['time'])
des_kwargs = fpi.precond_params(sc, mode, 'l2', 'des-dist',
start_date, end_date,
time=des_dist['time'])
f_dis = fpi.precondition(dis_dist['dist'], **dis_kwargs)
f_des = fpi.precondition(des_dist['dist'], **des_kwargs)
# Calculate moments
# - Use calculated moments for the Maxwellian distribution
Ni = fpi.density(f_dis)
Vi = fpi.velocity(f_dis, N=Ni)
Ti = fpi.temperature(f_dis, N=Ni, V=Vi)
Pi = fpi.pressure(f_dis, N=Ni, T=Ti)
ti = ((Ti[:,0,0] + Ti[:,1,1] + Ti[:,2,2]) / 3.0).drop(['t_index_dim1', 't_index_dim2'])
pi = ((Pi[:,0,0] + Pi[:,1,1] + Pi[:,2,2]) / 3.0).drop(['t_index_dim1', 't_index_dim2'])
Ne = fpi.density(f_des)
Ve = fpi.velocity(f_des, N=Ne)
Te = fpi.temperature(f_des, N=Ne, V=Ve)
Pe = fpi.pressure(f_des, N=Ne, T=Te)
te = ((Te[:,0,0] + Te[:,1,1] + Te[:,2,2]) / 3.0).drop(['t_index_dim1', 't_index_dim2'])
pe = ((Pe[:,0,0] + Pe[:,1,1] + Pe[:,2,2]) / 3.0).drop(['t_index_dim1', 't_index_dim2'])
# Equivalent (preconditioned) Maxwellian distributions
# fi_max = fpi.maxwellian_distribution(f_dis, N=Ni, bulkv=Vi, T=ti)
# fe_max = fpi.maxwellian_distribution(f_des, N=Ne, bulkv=Ve, T=te)
fi_max = fpi.maxwellian_distribution(f_dis, N=Ni, bulkv=Vi, T=ti)
fe_max = fpi.maxwellian_distribution(f_des, N=Ne, bulkv=Ve, T=te)
# Analytically derived Maxwellian entropy density
# si_max = fpi.maxwellian_entropy(Ni, pi)
# se_max = fpi.maxwellian_entropy(Ne, pe)
si_max = fpi.entropy(fi_max)
se_max = fpi.entropy(fe_max)
# Velocity space entropy density
siv_dist = fpi.vspace_entropy(f_dis)
sev_dist = fpi.vspace_entropy(f_des)
# The Maxwellian is already preconditioned
# - There are three options for calculating the v-space entropy of
# the Maxwellian distribution: using
# 1) FPI integrated moments,
# 2) Custom moments of the measured distribution
# 3) Custom moments of the equivalent Maxwellian distribution
# Because the Maxwellian is built with discrete v-space bins, its
# density, velocity, and temperature do not match that of the
# measured distribution on which it is based. If NiM is used, the
# M-bar term will be negative, which is unphysical, so here we use
# the density of the measured distribution and the entropy of the
# equivalent Maxwellian.
siv_max = fpi.vspace_entropy(fi_max, N=Ni, s=si_max)
sev_max = fpi.vspace_entropy(fe_max, N=Ne, s=se_max)
# M-bar
miv_bar = (siv_max - siv_dist) / siv_max
mev_bar = (sev_max - sev_dist) / sev_max
# Anisotropy
Ai = dis_moms['temppara'] / dis_moms['tempperp'] - 1
Ae = des_moms['temppara'] / des_moms['tempperp'] - 1
nrows = 8
ncols = 1
figsize = (5.5, 7.0)
fig, axes = plt.subplots(nrows=nrows, ncols=ncols,
figsize=figsize, squeeze=False)
# B
ax = axes[0,0]
ax = util.plot([b['B_GSE'][:,3], b['B_GSE'][:,0],
b['B_GSE'][:,1], b['B_GSE'][:,2]],
ax=ax, labels=['|B|', 'Bx', 'By', 'Bz'],
xaxis='off', ylabel='B\n(nT)'
)
# N
ax = axes[1,0]
ax = util.plot([dis_moms['density'], des_moms['density']],
ax=ax, labels=['Ni', 'Ne'],
xaxis='off', ylabel='N\n($cm^{-3}$)'
)
# Velocity space ion entropy density
ax = axes[2,0]
ax = util.plot([siv_max, siv_dist],
ax=ax, labels=['$s_{i,V,max}$', '$s_{i,V}$'],
xaxis='off', ylabel='$s_{V}$\n$J/K/m^{3}$'
)
# Velocity space electron entropy density
ax = axes[3,0]
ax = util.plot([sev_max, sev_dist],
ax=ax, labels=['$s_{e,V,max}$', '$s_{e,V}$'],
xaxis='off', ylabel='$s_{V}$'
)
# Velocity space M-bar
ax = axes[4,0]
ax = util.plot([miv_bar, mev_bar],
ax=ax, labels=['$\overline{M}_{i,V}$', '$\overline{M}_{e,V}$'],
xaxis='off', ylabel='$\overline{M}_{V}$'
)
# Ion temperature
ax = axes[5,0]
ax = util.plot([dis_moms['temppara'], dis_moms['tempperp'], dis_moms['t']],
ax=ax, labels=['$T_{\parallel}$', '$T_{\perp}$', 'T'],
xaxis='off', ylabel='$T_{i}$\n(eV)'
)
# Electron temperature
ax = axes[6,0]
ax = util.plot([des_moms['temppara'], des_moms['tempperp'], des_moms['t']],
ax=ax, labels=['$T_{\parallel}$', '$T_{\perp}$', 'T'],
xaxis='off', ylabel='$T_{e}$\n(eV)'
)
# Anisotropy
ax = axes[7,0]
ax = util.plot([Ai, Ae],
ax=ax, labels=['$A_{i}$', '$A_{e}$'],
ylabel='A'
)
fig.suptitle('Velocity Space Entropy')
plt.subplots_adjust(left=0.2, right=0.85, top=0.95, hspace=0.4)
return fig, axes
def kinetic_entropy(sc, mode, start_date, end_date, **kwargs):
# Read the data
b = fgm.load_data(sc, mode, start_date, end_date)
dis_moms = fpi.load_moms(sc, mode, 'i', start_date, end_date)
des_moms = fpi.load_moms(sc, mode, 'e', start_date, end_date)
dis_dist = fpi.load_dist(sc, mode, 'i', start_date, end_date)
des_dist = fpi.load_dist(sc, mode, 'e', start_date, end_date)
# Equivalent Maxwellian distribution
dis_max_dist = fpi.maxwellian_distribution(dis_dist,
N=dis_moms['density'],
bulkv=dis_moms['velocity'],
T=dis_moms['t'])
des_max_dist = fpi.maxwellian_distribution(des_dist,
N=des_moms['density'],
bulkv=des_moms['velocity'],
T=des_moms['t'])
# Entropy density
si_dist = fpi.entropy(dis_dist, **kwargs)
se_dist = fpi.entropy(des_dist, **kwargs)
# si_max = fpi.maxwellian_entropy(dis_moms['density'], dis_moms['p'])
# se_max = fpi.maxwellian_entropy(des_moms['density'], des_moms['p'])
si_max = fpi.entropy(dis_max_dist, **kwargs)
se_max = fpi.entropy(des_max_dist, **kwargs)
# Velcoity space entropy density
siv_dist = fpi.vspace_entropy(dis_dist,
N=dis_moms['density'],
s=si_dist,
**kwargs)
sev_dist = fpi.vspace_entropy(des_dist,
N=des_moms['density'],
s=se_dist,
**kwargs)
siv_max = fpi.vspace_entropy(des_max_dist,
N=dis_moms['density'],
s=si_max,
**kwargs)
sev_max = fpi.vspace_entropy(des_max_dist,
N=des_moms['density'],
s=se_max,
**kwargs)
# M-bar
mi_bar = np.abs(si_max - si_dist) / si_max
me_bar = np.abs(se_max - se_dist) / se_max
miv_bar = np.abs(siv_max - siv_dist) / siv_max
mev_bar = np.abs(sev_max - sev_dist) / sev_max
# Epsilon
ei = fpi.epsilon(dis_dist,
N=dis_moms['density'],
V=dis_moms['velocity'],
T=dis_moms['t'],
**kwargs)
ee = fpi.epsilon(des_dist,
N=des_moms['density'],
V=des_moms['velocity'],
T=des_moms['t'],
**kwargs)
# Setup the plot
nrows = 9
ncols = 1
figsize = (5.5, 7.0)
fig, axes = plt.subplots(nrows=nrows,
ncols=ncols,
figsize=figsize,
squeeze=False)
# B
ax = axes[0, 0]
ax = util.plot([b['B'][:, 3], b['B'][:, 0], b['B'][:, 1], b['B'][:, 2]],
ax=ax,
labels=['|B|', 'Bx', 'By', 'Bz'],
xaxis='off',
ylabel='B\n(nT)')
# Ion entropy density
ax = axes[1, 0]
ax = util.plot([si_max, si_dist],
ax=ax,
labels=['$s_{i,max}$', '$s_{i}$'],
xaxis='off',
ylabel='s\n$J/K/m^{3}$ $ln(s^{3}/m^{6})$')
# Electron entropy density
ax = axes[2, 0]
ax = util.plot([se_max, se_dist],
ax=ax,
labels=['$s_{e,max}$', '$s_{e}$'],
xaxis='off',
ylabel='s')
# Ion M-bar
ax = axes[3, 0]
ax = util.plot(mi_bar,
ax=ax,
legend=False,
xaxis='off',
ylabel='$\overline{M}_{i}$')
# Ion Epsilon
ax = ax.twinx()
ei.plot(ax=ax, color='g')
ax.set_ylabel('$\epsilon_{i}$\n$(s/m)^{3/2}$')
ax.yaxis.label.set_color('g')
ax.tick_params(axis='y', colors='g')
ax.set_xticklabels([])
# Electron M-bar
ax = axes[4, 0]
ax = util.plot(me_bar,
ax=ax,
legend=False,
xaxis='off',
ylabel='$\overline{M}_{e}$')
# Electron Epsilon
ax = ax.twinx()
ee.plot(ax=ax, color='r')
ax.set_ylabel('$\epsilon_{e}$\n$(s/m)^{3/2}$')
ax.yaxis.label.set_color('r')
ax.tick_params(axis='y', colors='r')
ax.set_xticklabels([])
# Velocity space ion entropy density
ax = axes[5, 0]
ax = util.plot([siv_max, siv_dist],
ax=ax,
labels=['$s_{i,V,max}$', '$s_{i,V}$'],
xaxis='off',
ylabel='$s_{V}$\n$J/K/m^{3}$ $ln()$')
# Velocity space electron entropy density
ax = axes[6, 0]
ax = util.plot([sev_max, sev_dist],
ax=ax,
labels=['$s_{e,V,max}$', '$s_{e,V}$'],
xaxis='off',
ylabel='$s_{V}$')
# Velocity space ion M-bar
ax = axes[7, 0]
ax = util.plot(miv_bar,
ax=ax,
legend=False,
xaxis='off',
ylabel='$\overline{M}_{i,V}$')
# Velocity space electron M-bar
ax = axes[8, 0]
ax = util.plot(mev_bar, ax=ax, legend=False, ylabel='$\overline{M}_{e,V}$')
fig.suptitle('Total and Velocity Space Entropy Density')
plt.subplots_adjust(left=0.2, right=0.85, top=0.95, hspace=0.4)
# plt.setp(axes, xlim=xlim)
return fig, axes
def kinetic_entropy(sc, mode, start_date, end_date, **kwargs):
# Read the data
b = fgm.load_data(sc=sc, mode=mode,
start_date=start_date, end_date=end_date)
dis_dist = fpi.load_dist(sc=sc, mode=mode, optdesc='dis-dist',
start_date=start_date, end_date=end_date)
des_dist = fpi.load_dist(sc=sc, mode=mode, optdesc='des-dist',
start_date=start_date, end_date=end_date)
# Precondition the distributions
dis_kwargs = fpi.precond_params(sc, mode, 'l2', 'dis-dist',
start_date, end_date,
time=dis_dist['time'])
des_kwargs = fpi.precond_params(sc, mode, 'l2', 'des-dist',
start_date, end_date,
time=des_dist['time'])
f_dis = fpi.precondition(dis_dist['dist'], **dis_kwargs)
f_des = fpi.precondition(des_dist['dist'], **des_kwargs)
# Calculate Moments
Ni = fpi.density(f_dis)
Vi = fpi.velocity(f_dis, N=Ni)
Ti = fpi.temperature(f_dis, N=Ni, V=Vi)
Pi = fpi.pressure(f_dis, N=Ni, T=Ti)
ti = ((Ti[:,0,0] + Ti[:,1,1] + Ti[:,2,2]) / 3.0).drop(['t_index_dim1', 't_index_dim2'])
pi = ((Pi[:,0,0] + Pi[:,1,1] + Pi[:,2,2]) / 3.0).drop(['t_index_dim1', 't_index_dim2'])
Ne = fpi.density(f_des)
Ve = fpi.velocity(f_des, N=Ne)
Te = fpi.temperature(f_des, N=Ne, V=Ve)
Pe = fpi.pressure(f_des, N=Ne, T=Te)
te = ((Te[:,0,0] + Te[:,1,1] + Te[:,2,2]) / 3.0).drop(['t_index_dim1', 't_index_dim2'])
pe = ((Pe[:,0,0] + Pe[:,1,1] + Pe[:,2,2]) / 3.0).drop(['t_index_dim1', 't_index_dim2'])
# Equivalent (preconditioned) Maxwellian distributions
fi_max = fpi.maxwellian_distribution(f_dis, N=Ni, bulkv=Vi, T=ti)
fe_max = fpi.maxwellian_distribution(f_des, N=Ne, bulkv=Ve, T=te)
# Entropy density
si_dist = fpi.entropy(f_dis)
se_dist = fpi.entropy(f_des)
si_max = fpi.entropy(fi_max)
se_max = fpi.entropy(fe_max)
# Velcoity space entropy density
siv_dist = fpi.vspace_entropy(f_dis, N=Ni, s=si_dist)
sev_dist = fpi.vspace_entropy(f_des, N=Ne, s=se_dist)
# The Maxwellian is already preconditioned
# - There are three options for calculating the v-space entropy of
# the Maxwellian distribution: using
# 1) FPI integrated moments,
# 2) Custom moments of the measured distribution
# 3) Custom moments of the equivalent Maxwellian distribution
# Because the Maxwellian is built with discrete v-space bins, its
# density, velocity, and temperature do not match that of the
# measured distribution on which it is based. If NiM is used, the
# M-bar term will be negative, which is unphysical, so here we use
# the density of the measured distribution and the entropy of the
# equivalent Maxwellian.
siv_max = fpi.vspace_entropy(fi_max, N=Ni, s=si_max)
sev_max = fpi.vspace_entropy(fe_max, N=Ne, s=se_max)
# M-bar
mi_bar = np.abs(si_max - si_dist) / si_max
me_bar = np.abs(se_max - se_dist) / se_max
miv_bar = np.abs(siv_max - siv_dist) / siv_max
mev_bar = np.abs(sev_max - sev_dist) / sev_max
# Epsilon
ei = fpi.epsilon(f_dis, N=Ni, V=Vi, T=ti)
ee = fpi.epsilon(f_des, N=Ne, V=Ve, T=te)
# Setup the plot
nrows = 9
ncols = 1
figsize = (5.5, 7.0)
fig, axes = plt.subplots(nrows=nrows, ncols=ncols,
figsize=figsize, squeeze=False)
# B
ax = axes[0,0]
ax = util.plot([b['B_GSE'][:,3], b['B_GSE'][:,0],
b['B_GSE'][:,1], b['B_GSE'][:,2]],
ax=ax, labels=['|B|', 'Bx', 'By', 'Bz'],
xaxis='off', ylabel='B\n(nT)'
)
# Ion entropy density
ax = axes[1,0]
ax = util.plot([si_max, si_dist],
ax=ax, labels=['$s_{i,max}$', '$s_{i}$'],
xaxis='off', ylabel='s\n$J/K/m^{3}$ $ln(s^{3}/m^{6})$'
)
# Electron entropy density
ax = axes[2,0]
ax = util.plot([se_max, se_dist],
ax=ax, labels=['$s_{e,max}$', '$s_{e}$'],
xaxis='off', ylabel='s'
)
# Ion M-bar
ax = axes[3,0]
ax = util.plot(mi_bar,
ax=ax, legend=False,
xaxis='off', ylabel='$\overline{M}_{i}$'
)
# Ion Epsilon
ax = ax.twinx()
ei.plot(ax=ax, color='g')
ax.set_ylabel('$\epsilon_{i}$\n$(s/m)^{3/2}$')
ax.yaxis.label.set_color('g')
ax.tick_params(axis='y', colors='g')
ax.set_xticklabels([])
ax.set_title('')
# Electron M-bar
ax = axes[4,0]
ax = util.plot(me_bar,
ax=ax, legend=False,
xaxis='off', ylabel='$\overline{M}_{e}$'
)
# Electron Epsilon
ax = ax.twinx()
ee.plot(ax=ax, color='r')
ax.set_ylabel('$\epsilon_{e}$\n$(s/m)^{3/2}$')
ax.yaxis.label.set_color('r')
ax.tick_params(axis='y', colors='r')
ax.set_xticklabels([])
ax.set_title('')
# Velocity space ion entropy density
ax = axes[5,0]
ax = util.plot([siv_max, siv_dist],
ax=ax, labels=['$s_{i,V,max}$', '$s_{i,V}$'],
xaxis='off', ylabel='$s_{V}$\n$J/K/m^{3}$ $ln()$'
)
# Velocity space electron entropy density
ax = axes[6,0]
ax = util.plot([sev_max, sev_dist],
ax=ax, labels=['$s_{e,V,max}$', '$s_{e,V}$'],
xaxis='off', ylabel='$s_{V}$'
)
# Velocity space ion M-bar
ax = axes[7,0]
ax = util.plot(miv_bar,
ax=ax, legend=False,
xaxis='off', ylabel='$\overline{M}_{i,V}$'
)
# Velocity space electron M-bar
ax = axes[8,0]
ax = util.plot(mev_bar,
ax=ax, legend=False,
ylabel='$\overline{M}_{e,V}$'
)
fig.suptitle('Total and Velocity Space Entropy Density')
plt.subplots_adjust(left=0.2, right=0.85, top=0.95, hspace=0.4)
# plt.setp(axes, xlim=xlim)
return fig, axes
def overview(sc, mode, start_date, end_date, **kwargs):
# Read the data
b = fgm.load_data(sc=sc, mode=mode,
start_date=start_date, end_date=end_date)
e = edp.load_data(sc=sc, mode=mode,
start_date=start_date, end_date=end_date)
dis_moms = fpi.load_moms(sc=sc, mode=mode, optdesc='dis-moms',
start_date=start_date, end_date=end_date)
des_moms = fpi.load_moms(sc=sc, mode=mode, optdesc='des-moms',
start_date=start_date, end_date=end_date)
nrows = 7
ncols = 1
figsize = (6.0, 7.0)
fig, axes = plt.subplots(nrows=nrows, ncols=ncols,
figsize=figsize, squeeze=False)
locator = mdates.AutoDateLocator()
formatter = mdates.ConciseDateFormatter(locator)
# B
ax = axes[0,0]
b['B_GSE'][:,3].plot(ax=ax, label='|B|')
b['B_GSE'][:,0].plot(ax=ax, label='Bx')
b['B_GSE'][:,1].plot(ax=ax, label='By')
b['B_GSE'][:,2].plot(ax=ax, label='Bz')
ax.set_xlabel('')
ax.set_xticklabels([])
ax.set_ylabel('B [nT]')
ax.set_title('')
# Create the legend outside the right-most axes
leg = ax.legend(bbox_to_anchor=(1.05, 1),
borderaxespad=0.0,
frameon=False,
handlelength=0,
handletextpad=0,
loc='upper left')
# Color the legend text the same color as the lines
for line, text in zip(ax.get_lines(), leg.get_texts()):
text.set_color(line.get_color())
# Ion energy spectrogram
nt = dis_moms['omnispectr'].shape[0]
nE = dis_moms['omnispectr'].shape[1]
x0 = mdates.date2num(dis_moms['time'])[:, np.newaxis].repeat(nE, axis=1)
x1 = dis_moms['energy']
y = np.where(dis_moms['omnispectr'] == 0, 1, dis_moms['omnispectr'])
y = np.log(y[0:-1,0:-1])
ax = axes[1,0]
im = ax.pcolorfast(x0, x1, y, cmap='nipy_spectral')
ax.images.append(im)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.set_xticklabels([])
ax.set_xlabel('')
ax.set_yscale('log')
ax.set_ylabel('E ion\n(eV)')
cbaxes = inset_axes(ax,
width='2%', height='100%', loc=4,
bbox_to_anchor=(0, 0, 1.05, 1),
bbox_transform=ax.transAxes,
borderpad=0)
cb = plt.colorbar(im, cax=cbaxes, orientation='vertical')
cb.set_label('$log_{10}$DEF\nkeV/($cm^{2}$ s sr keV)')
# Electron energy spectrogram
nt = des_moms['omnispectr'].shape[0]
nE = des_moms['omnispectr'].shape[1]
x0 = mdates.date2num(des_moms['time'])[:, np.newaxis].repeat(nE, axis=1)
x1 = des_moms['energy']
y = np.where(des_moms['omnispectr'] == 0, 1, des_moms['omnispectr'])
y = np.log(y[0:-1,0:-1])
ax = axes[2,0]
im = ax.pcolorfast(x0, x1, y, cmap='nipy_spectral')
ax.images.append(im)
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
ax.set_xticklabels([])
ax.set_xlabel('')
ax.set_yscale('log')
ax.set_ylabel('E e-\n(eV)')
cbaxes = inset_axes(ax,
width='2%', height='100%', loc=4,
bbox_to_anchor=(0, 0, 1.05, 1),
bbox_transform=ax.transAxes,
borderpad=0)
cb = plt.colorbar(im, cax=cbaxes, orientation='vertical')
cb.set_label('$log_{10}$DEF')
# N
ax = axes[3,0]
dis_moms['density'].plot(ax=ax, label='Ni')
des_moms['density'].plot(ax=ax, label='Ne')
ax.set_xlabel('')
ax.set_xticklabels([])
ax.set_ylabel('N\n($cm^{-3}$)')
ax.set_title('')
leg = ax.legend(bbox_to_anchor=(1.05, 1),
borderaxespad=0.0,
frameon=False,
handlelength=0,
handletextpad=0,
loc='upper left')
for line, text in zip(ax.get_lines(), leg.get_texts()):
text.set_color(line.get_color())
# Vi
ax = axes[4,0]
dis_moms['velocity'][:,0].plot(ax=ax, label='Vx')
dis_moms['velocity'][:,1].plot(ax=ax, label='Vy')
dis_moms['velocity'][:,2].plot(ax=ax, label='Vz')
ax.set_xlabel('')
ax.set_xticklabels([])
ax.set_ylabel('Vi\n(km/s)')
ax.set_title('')
leg = ax.legend(bbox_to_anchor=(1.05, 1),
borderaxespad=0.0,
frameon=False,
handlelength=0,
handletextpad=0,
loc='upper left')
for line, text in zip(ax.get_lines(), leg.get_texts()):
text.set_color(line.get_color())
# Ve
ax = axes[5,0]
des_moms['velocity'][:,0].plot(ax=ax, label='Vx')
des_moms['velocity'][:,1].plot(ax=ax, label='Vy')
des_moms['velocity'][:,2].plot(ax=ax, label='Vz')
ax.set_xlabel('')
ax.set_xticklabels([])
ax.set_ylabel('Ve\n(km/s)')
ax.set_title('')
leg = ax.legend(bbox_to_anchor=(1.05, 1),
borderaxespad=0.0,
frameon=False,
handlelength=0,
handletextpad=0,
loc='upper left')
for line, text in zip(ax.get_lines(), leg.get_texts()):
text.set_color(line.get_color())
# E
ax = axes[6,0]
e['E_GSE'][:,0].plot(ax=ax, label='Ex')
e['E_GSE'][:,1].plot(ax=ax, label='Ey')
e['E_GSE'][:,2].plot(ax=ax, label='Ez')
ax.set_xlabel('')
ax.set_xticklabels([])
ax.set_ylabel('E\n(mV/m)')
ax.set_title('')
ax.xaxis.set_major_locator(locator)
ax.xaxis.set_major_formatter(formatter)
for tick in ax.get_xticklabels():
tick.set_rotation(45)
leg = ax.legend(bbox_to_anchor=(1.05, 1),
borderaxespad=0.0,
frameon=False,
handlelength=0,
handletextpad=0,
loc='upper left')
for line, text in zip(ax.get_lines(), leg.get_texts()):
text.set_color(line.get_color())
fig.suptitle(sc.upper())
plt.subplots_adjust(left=0.2, right=0.8, top=0.95, hspace=0.2)
return fig, axes
def fsm_spectra(sc, start_date, end_date):
# FSM only has burst mode data
mode = 'brst'
# Load the data
fgm_data = fgm.load_data(sc=sc, mode=mode,
start_date=start_date, end_date=end_date)
scm_data = scm.load_data(sc=sc, mode=mode, level='l2',
start_date=start_date, end_date=end_date)
fsm_data = fsm.load_data(sc=sc, start_date=start_date, end_date=end_date)
# Determine sample rate
fs_fgm = (np.diff(fgm_data['time']).mean().astype(int) / 1e9)**(-1)
fs_scm = (np.diff(scm_data['time']).mean().astype(int) / 1e9)**(-1)
fs_fsm = (np.diff(fsm_data['time']).mean().astype(int) / 1e9)**(-1)
# Length of FFT -- aim for 10 second increments
duration = (end_date - start_date).total_seconds()
tperseg = 10.0
nseg = duration // tperseg
if nseg == 0:
nseg = 1
tperseg = duration
nperseg_fgm = tperseg * fs_fgm
nperseg_scm = tperseg * fs_scm
nperseg_fsm = tperseg * fs_fsm
# PWelch
f_fgm, pxx_fgm = welch(fgm_data['B_GSE'], axis=0,
fs=fs_fgm, window='hanning', nperseg=nperseg_fgm,
detrend='linear', return_onesided=True,
scaling='density')
f_scm, pxx_scm = welch(scm_data['B_GSE'], axis=0,
fs=fs_scm, window='hanning', nperseg=nperseg_scm,
detrend='linear', return_onesided=True,
scaling='density')
f_fsm, pxx_fsm = welch(fsm_data['B_GSE'], axis=0,
fs=fs_fsm, window='hanning', nperseg=nperseg_fsm,
detrend='linear', return_onesided=True,
scaling='density')
# Plot the data
fig, axes = plt.subplots(nrows=3, ncols=1, squeeze=False,
figsize=(8.5, 5))
# Bx PSD
ax = axes[0,0]
ax.plot(f_fsm, np.sqrt(pxx_fsm[:,0]), label='FSM')
ax.plot(f_scm, np.sqrt(pxx_scm[:,0]), label='SCM')
ax.plot(f_fgm, np.sqrt(pxx_fgm[:,0]), label='FGM')
ax.set_xscale('log')
ax.set_xlabel('f (Hz)')
ax.set_yscale('log')
ax.set_ylabel('Bx PSD\n(nT/$\sqrt{Hz}$)')
ax.legend()
# By PSD
ax = axes[1,0]
ax.plot(f_fsm, np.sqrt(pxx_fsm[:,1]), label='FSM')
ax.plot(f_scm, np.sqrt(pxx_scm[:,1]), label='SCM')
ax.plot(f_fgm, np.sqrt(pxx_fgm[:,1]), label='FGM')
ax.set_xscale('log')
ax.set_xlabel('f (Hz)')
ax.set_yscale('log')
ax.set_ylabel('By PSD\n(nT/$\sqrt{Hz}$)')
ax.legend()
# Bz PSD
ax = axes[2,0]
ax.plot(f_fsm, np.sqrt(pxx_fsm[:,2]), label='FSM')
ax.plot(f_scm, np.sqrt(pxx_scm[:,2]), label='SCM')
ax.plot(f_fgm, np.sqrt(pxx_fgm[:,2]), label='FGM')
ax.set_xscale('log')
ax.set_xlabel('f (Hz)')
ax.set_yscale('log')
ax.set_ylabel('Bz PSD\n(nT/$\sqrt{Hz}$)')
ax.legend()
# Timestamp
if start_date.date() == end_date.date():
tstamp = ' '.join((start_date.strftime('%Y-%m-%d'),
start_date.strftime('%H:%M:%S'), '-',
end_date.strftime('%H:%M:%S')))
else:
tstamp = ' '.join((start_date.strftime('%Y-%m-%d'),
start_date.strftime('%H:%M:%S'), '-',
end_date.strftime('%Y-%m-%d'),
end_date.strftime('%H:%M:%S')))
fig.suptitle('FGM, SCM, & FSM Spectra Comparison\n{0}'
.format(tstamp))
plt.subplots_adjust(left=0.12, right=0.95, top=0.9, bottom=0.12,
hspace=0.2, wspace=0.4)
return fig, axes
from pymms.data import fgm, anc
from matplotlib import pyplot as plt
# Use the Torbert Science (2018) data interval to test
sc = 'mms1'
t0 = dt.datetime(2017, 7, 11, 22, 33, 30)
t1 = dt.datetime(2017, 7, 11, 22, 34, 30)
# Load the data
# - Expand the time interval for DSS so the sun pulses encompass the data
# - FGM L2Pre has BCS and DBCS data
dss_data = load_sunpulse(sc=sc,
start_date=t0 - dt.timedelta(seconds=40),
end_date=t1 + dt.timedelta(seconds=40))
fgm_data = fgm.load_data(sc=sc, instr='dfg', mode='srvy', level='l2pre',
start_date=t0, end_date=t1,
coords=('bcs', 'dmpa'), team_site=True)
# Get the major principal axis vector
anc_data = anc.load_ancillary(sc, 'defatt', t0, t1)
# Rotate to MPA
mpa = anc_data.attrs['MPA']
z_bcs2smpa = mpa / np.linalg.norm(np.array(mpa))
y_bcs2smpa = np.cross(z_bcs2smpa, np.array([1, 0, 0]))
x_bcs2smpa = np.cross(y_bcs2smpa, z_bcs2smpa)
bcs2smpa = xr.DataArray(np.stack([x_bcs2smpa, y_bcs2smpa, z_bcs2smpa],
axis=1),
dims=['bcs', 'smpa'],
coords={'bcs': ['x', 'y', 'z'],
'smpa': ['x', 'y', 'z']})
def fsm_timeseries(sc, start_date, end_date):
# FSM only has burst mode data
mode = 'brst'
# Load the data
fgm_data = fgm.load_data(sc=sc, mode=mode,
start_date=start_date, end_date=end_date)
scm_data = scm.load_data(sc=sc, mode=mode,
start_date=start_date, end_date=end_date)
fsm_data = fsm.load_data(sc=sc, start_date=start_date, end_date=end_date)
# High-pass filter FSM data at 1 Hz to compare with SCM
f_Nyquist = 0.5 / (np.diff(fsm_data['time']).mean().astype(int) / 1e9)
order = 3 # filter order
fc = 1.0 # 1 Hz cut-off frequency
fc_norm = fc / f_Nyquist
b, a = butter(order, fc_norm, btype='high', analog=False)
fsm_data['dB_GSE'] = xr.DataArray(filtfilt(b, a, fsm_data['B_GSE'], axis=0),
dims=['time', 'b_index'])
# Plot the data
fig, axes = plt.subplots(nrows=4, ncols=2, squeeze=False,
figsize=(8.5, 6))
# Bx
ax = axes[0,0]
ax = util.plot([fgm_data['B_GSE'].loc[:,'x'],
fsm_data['B_GSE'].loc[:,'x']],
ax=ax, labels=['FGM', 'FSM'],
xaxis='off', ylabel='Bx\n(nT)'
)
# By
ax = axes[1,0]
ax = util.plot([fgm_data['B_GSE'].loc[:,'z'],
fsm_data['B_GSE'].loc[:,'z']],
ax=ax, labels=['FGM', 'FSM'],
xaxis='off', ylabel='By\n(nT)'
)
# Bz
ax = axes[2,0]
ax = util.plot([fgm_data['B_GSE'].loc[:,'z'],
fsm_data['B_GSE'].loc[:,'z']],
ax=ax, labels=['FGM', 'FSM'],
xaxis='off', ylabel='Bz\n(nT)'
)
# |B|
ax = axes[3,0]
ax = util.plot([fgm_data['B_GSE'].loc[:,'t'],
fsm_data['|B|']],
ax=ax, labels=['FGM', 'FSM'],
ylabel='|B|\n(nT)'
)
# dBx
ax = axes[0,1]
ax = util.plot([scm_data['B_GSE'].loc[:,'x'],
fsm_data['dB_GSE'].loc[:,'x']],
ax=ax, labels=['SCM', 'FSM'],
xaxis='off', ylabel='$\delta$Bx\n(nT)'
)
# dBy
ax = axes[1,1]
ax = util.plot([scm_data['B_GSE'].loc[:,'y'],
fsm_data['dB_GSE'].loc[:,'y']],
ax=ax, labels=['SCM', 'FSM'],
xaxis='off', ylabel='$\delta$By\n(nT)'
)
# dBz
ax = axes[2,1]
ax = util.plot([scm_data['B_GSE'].loc[:,'z'],
fsm_data['dB_GSE'].loc[:,'z']],
ax=ax, labels=['SCM', 'FSM'],
ylabel='$\delta$Bz\n(nT)'
)
fig.suptitle('FGM, SCM, & FSM Timeseries Comparison')
plt.subplots_adjust(left=0.1, right=0.90, top=0.95, bottom=0.12,
hspace=0.2, wspace=0.4)
# |dB|
ax = axes[3,1]
ax.axis('off')
return fig, axes
