How do we handle the terminator? One way is to use a model for airglow VER. Treating VER as known has two aspects:

How does this change the onion-peeling?
What location do we ascribe the resulting wind to?

For item 1:

Measurement model: $$ \underbrace{g_i}_{\textrm{measured interferogram}} = \sum_{j=1}^{N} ~~~\underbrace{a(\bar{r}_{ij})}_{\textrm{VER}}~~~~ \underbrace{f(\bar{r}_{ij})}_{\textrm{interferogram}} ~~~~~\underbrace{\Delta s_{ij}}_{\textrm{path length}}$$

Usually we assume:

VER is spherically symmetric: $ a(\bar{r}_{ij}) = a(r_{j}) $
winds and temps are spherically symmetric: $ f(\bar{r}_{ij}) = f(r_{j}) $

$$ g_i= \sum_{j=1}^{N} a(r_{j})f(r_{j}) \Delta s_{ij}$$

And we solve for $a(r_{j})f(r_{j})$ by creating path length matrix using $\Delta s_{ij}$

If airglow is known:

VER is not spherically symmetric: $ a(\bar{r}_{ij})$
winds and temps are spherically symmetric: $ f(\bar{r}_{ij}) = f(r_{j}) $

$$ g_i= \sum_{j=1}^{N} f(r_{j}) a(\bar{r}_{ij}) \Delta s_{ij}$$

Solve for $f(r_{j})$ by creating path length matrix using $a(\bar{r}_{ij}) \Delta s_{ij}$

Test using:

Spherically symmetric VER, winds, and temperatures
Treat airglow as known in the inversion

In [501]:

npzfile = load(truthfn)
truth_alts = npzfile['tang_alts']
truth_winds = npzfile['truth_winds']
truth_amps = npzfile['truth_amps']
npzfile.close()

plot(truth_winds, truth_alts, 'k-', label='Truth')


fn = L21_fn
npzfile = load(fn)
wind = npzfile['los_wind']
alt_of_wind = npzfile['alt_los_wind']
npzfile.close()

plot(wind_naive, alt_of_wind, 'b.-', markersize=3, label='Orig Recon.')
plot(wind, alt_of_wind, 'r.-', markersize=3, label='New Recon.')
ylabel('Altitude [km]')
xlabel('LoS Velocity [m/s]')
legend(loc='best',numpoints=1,prop={'size':6},fancybox=True)
tight_layout()

In [502]:

# Ignore satellite motion for now. (Include velocity in phase, though).
dt = datetime(2013,9,23,2,0,0) # UT
icon_alt = 550.
icon_lat = 20.5
icon_lon = 180. # daytime
icon_velocity = 0.0 # this will likely not be implemented
az = 90. # so that we're only measuring zonal wind
ze_top = 103
ze_bot = 109
ny = 50
nk = 101
#ny = 50
#nk = 501
impose_spherical_symmetry_winds = True
impose_spherical_symmetry_temps = True
impose_spherical_symmetry_ver = False


satlla = [icon_lat, icon_lon, icon_alt]
# Let's say that ICON is going purely east. This shouldn't matter, since velocity is zero.
icon_ecef_ram_vector = ICON.ven_to_ecef(satlla, [0, 1, 0])


# LOAD MIGHTI CONSTANTS/PARAMETERS
emission_color = 'red' # 'red' or 'green'
day = True

emissions =  MIGHTI.get_emission_constants()
true_params = MIGHTI.get_instrument_constants()

true_params['exptime'] =        60.   # sec
true_params['lam'] =            emissions[emission_color]['lam']
true_params['frq'] =            emissions[emission_color]['frq']
true_params['mass'] =           emissions[emission_color]['mass']
if day: # 10% reduction in aperture size during "day", and shorter exposure time
    true_params['aperture_area'] =  true_params['aperture_area'] * 0.1
    true_params['exptime'] =        30.


ray_length = 6000./nk
print '%.2f km steps' % ray_length

tanlla_top = ICON.tangent_point(satlla, az, ze_top)
tanlla_bot = ICON.tangent_point(satlla, az, ze_bot)

zevec = linspace(ze_bot, ze_top, ny)
mighti_ecef_vectors = zeros((ny,3))
alts_along_ray = zeros((nk,ny))
lats_along_ray = zeros((nk,ny))
lons_along_ray = zeros((nk,ny))
tang_alts      = zeros(ny)
tang_lats      = zeros(ny)
tang_lons      = zeros(ny)

for i in range(ny):
    ze = zevec[i]
    # Determine tangent point
    tang_pt = ICON.tangent_point(satlla, az, ze)
    tang_alts[i] = tang_pt[2]
    tang_lats[i] = tang_pt[0]
    tang_lons[i] = tang_pt[1]
    # Determine the ECEF look direction and record it
    mighti_ecef_vectors[i,:] = ICON.azze_to_ecef(satlla, az, ze)
    # Project the line of sight and record winds, temps, and amplitudes along the ray
    xyz_proj,lla_proj = ICON.project_line_of_sight(satlla, az, ze, \
                                                   step_size = ray_length, total_distance=ray_length*nk)
    alts_along_ray[:,i] = lla_proj[2,:]
    lats_along_ray[:,i] = lla_proj[0,:]
    lons_along_ray[:,i] = lla_proj[1,:]

print '%.1f - %.1f km' % (tang_alts[-1], tang_alts[0])

59.41 km steps
372.4 - 172.4 km

Test using:

Spherically symmetric winds and temps
Terminator-like VER distribution
Treat airglow as known in the inversion

In [506]:

i = 2
figure(figsize=(9,3))
subplot(1,3,1)
plot(winds_along_ray[:,i],'k')
ylabel('LoS wind [m/s]')
xlabel('Steps along ray')
subplot(1,3,2)
plot(temps_along_ray[:,i],'k')
ylabel('Temperature [K]')
xlabel('Steps along ray')
subplot(1,3,3)
plot(emission_along_ray_r[:,i],'k')
ylabel('VER [ph/cm^3/s]')
xlabel('Steps along ray')
tight_layout()

In [533]:

npzfile = load(truthfn)
truth_alts = npzfile['tang_alts']
truth_winds = npzfile['truth_winds']
truth_amps = npzfile['truth_amps']
npzfile.close()

plot(truth_winds, truth_alts, 'k-', label='Truth')


fn = L21_fn
npzfile = load(fn)
wind = npzfile['los_wind']
alt_of_wind = npzfile['alt_los_wind']
npzfile.close()

plot(wind_naive, alt_of_wind, 'b.-', markersize=3, label='Orig Recon.')
plot(wind, alt_of_wind, 'r.-', markersize=3, label='New Recon.')
ylabel('Altitude [km]')
xlabel('LoS Velocity [m/s]')
legend(loc='best',numpoints=1,prop={'size':6},fancybox=True)
tight_layout()

#xlim((-80,-65))

Major problems under certain conditions (not shown).

In [ ]:

Simulate L1 data product¶

Create functions that know about wind, temperature, and VER at every point¶

The following code has been more or less copied from MIGHTI_Convert_EnglandFile_to_UIUCL1.¶

Generate interferogram¶

Add Noise (skipped for now)¶

L1 processing¶

Obtain truth los winds and save to separate file¶

Run the files through the L1-L2.1 processing.¶

This is copied from the central source of this code: MIGHTI_UIUCL1_to_L21.ipynb¶

Modified inversion using known airglow¶

Test using non-spherically symmetric VER¶