Correction of the influence of the atmosphere using
forward and inverse neural networks
Roland Doerffer
Retired from
Helmholtz Zentrum Geesthacht
Institute of Coastal Research
roland.doerffer@hzg.de
Space Shuttle 335 km
20060720 , NASA
Atmospheric correction using models
The NN associates
a large number of
independent
components (IOPs)
with the dependent
reflectances
Top of Atmosphere
(TOA) reflection
Atmosphere: molecule &
aerosol scattering, gas abs.:
Pathradiance,transmittance
Air/sea interface,
refractive index: Rfresnel
Water reflection Rw
Optical properties:
a(),b (),Fl.,
Water constituents
Phytoplankton, SPM etc
Bottom reflection
Forward
model
inverse
model
Replace a complex radiative transfer model by
a neural network, which is trained with
simulations using the RTF
Type of Neural networks
Angular dependent
reflectances
Angular dependent
Reflectances + aux
angles,T, S,
out
in
Forward
NN
Inverse
NN
In
out
Independent:
IOPs, angles,
T, S,
Independent:
IOPs
Very flexible, can be adapted
To bands, conditions
But: slow, more noise, ambiguities
During run
Further NNs:
autoNN,
errorNN,
Normalisation NN
Combination of
Inverse and forward
NN
Fixed to bands, conditions,
Harder to train, incl.
ambiguities
But: very fast, less noise
Inverse Modellierung using NN in Optimization Procedures
Start by
Inverse NN
ReflexionSpektra
Satellite
Start values
Modell
Parameters
IOP / Konz
Radiative transfer
Model or
Forward NN
Change
Parameters
ReflexionSpektra
simulated
Do spectra
agree ?
Determine
Search direction
Downhill in cost function
yes
Parameters
are the
IOPs / Konz.
no
Test = ∑(Rsim(i) – Rsat(i))2
Also measure of quality !
Training of a neural network for atmospheric correction
Atmosphere-optical model
1
Bio-optical model
7
NNforward water
(based on Hydrolight simulations)
RLw
9
12
Transmittance
L_up
5
MC code
2
RLpath_noglint
RLpath_glint
Ed_boa
Tau_aerosole
RLpath
Ed_boa
Tau_aerosole
4
6
Optional
Polarisation
correction
8
Selection
Max sunglint
Max tau_aerosol
Min. Rlw(560)
Etc.
10
RLtosa
RLpath
Ed_boa
RLw
Tau_aerosole
11
Training &
Test data set
13
Aerosol Optical Properties used for NN Training data set
Angström Coefficient
RTF models used for
simulation of training
data sets:
• Monte Carlo photon tracing
• 6Sv
• Aeronet based model by
R. Santer
• Water: Hydrolight C. Mobley
Aerosol Optical Thickness (AOT) at 550 nm
Turbid water reflectances
Amazone 20050803
Rio de la Plata 20080613
Rw pin1, 2 compute from RLtosa
Rw computed from RLpath
0.2
0.2
0.15
Rw pin1
Rw pin2
0.1
Rw
Rw
0.15
0.05
Rw_p1
Rw_p2
Rw_p3
0.1
0.05
0
300
400
500
600
700
800
0
300
900
400
600
700
800
900
wavelength [nm]
wavelength [nm]
Amazone: Rw 0.18 at 681nm
Plata: Rw 0.17 at 681nm
Yangtse 20050809
Barent Sea, Cocco, 20040801
Rw computed from RL_toa
Rw computed from Ltoa
0.25
0.14
Rw P1
Rw P2
Rw P3
Rw P4
Rw P5
0.15
0.1
Rwp1
Rwp2
Rwp3
Rwp4
Rwp5
Rwp6
Rwp7
Rwp8
0.12
0.1
0.08
Rw
0.2
Rw
500
0.06
0.04
0.05
0.02
0
300
400
500
600
700
800
900
wavelength [nm]
Yangtse: Rw 0.2 at 681nm
0
-0.02300
400
500
600
700
800
wavelength [nm]
Cocco: Rw 0.12 at 560 nm
900
Simulations with Hydrolight
•
•
•
Hydrolight 5.1 for computation of bi-directional water leaving radiance
reflectance spectra (RLw)
Extension of Hydrolight with the pure water model of this project
– Temperature
– Salinity
– Refractive index
– Uncertainties
bio-optical model:
– 5 optical components
• Absorption coefficients of pigment, detritus, yellow substance
• Scattering coefficients of particles and white particles
Inverse NN for atmospheric correction – CC version
Input (18)
Output (43)
RLtosa
12 bands
sun zenith
view x
View y
View z
Neural Network
18->25x30x40->43
temperature
Tau_aerosol 412, 550, 778, 865
Sun_glint ratio
a_tot, b_tot
MERIS band 1-10, 12,13
Ed_surface
Path radiance reflectance
RLw
salinity
RLw(,) =Lw (,) /Ed
For each water type
Atmospheric Correction using NN
1
L1 Ltoa
solar flux
2 date corrected
5
sun zeni, sun azi,
3 view zeni, view azi
4
press, altitude, wind
ozone, H2O, NO2
compute RLtosa
7
RL_tosa, angles, T, S
Temperature, Salinity
6
8
test range,
autoNN
aerosolNN
10
RLwlNN
12
out of range flag
14
out of scope
9 index, flag
_aerosol
11 angstrom
RLw, RLpath
13
Scheme for forwardNN based procedure
MERIS
RLtoa
RLtosa‘
RLath,
trans
Select
Bands
Variables
parameters
constraints
forNNatmo
3 par
forNNwater
n_lam
n_var (5)
Start values
Compare
RLtosa
RLtosa‘
Optim,
procedure
aaNN
OOS
Compute
RLtosa
Results:
RLw
IOPs
uncertainty
Test and validation
Test of NN 17x27x17
560 nm
Training with 5% random noise on rlw
Test of water algorithm forward NN
Relationship between the
measured and derived total
absorption coefficient a_total
at 443 nm using the neural
network algorithm. Red is the
1 by 1 line, blue the
regression. n=498 points
Test scene MERIS MER_RR__1PNPDK20080507
Separation atmosphere / water using inverse NN
MERIS band 5, 560 nm
Reflectance Spectra R_toa, R_path, Rw
Transect Test using forward NN
Forward NN
Inverse NN
Separation test: RLw vs RLpath
MERIS scene of
Hawaii 20040406
TOA radiance
reflectance band
13 with transect
Top of atmosphere, path
radiance and water
leaving radiance
reflectance along transect
of Hawaii scene
Band 5 560 nm
Rlw *10
Comparison as scatter plot
Comparison MOBY data with ACG processor
1
1
0
0
-1
-1
-2
-2
rhown_meris
Rw
Comparison MOBY data with ACG processor
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
-5
-4
-3
-2
-1
0
1
-5
-4
-3
rhow_moby
-2
-1
rhown_moby
Neural network AGC /C2R
Standard AC MERIS
MOBY 73 no glint cases, log10 scale
0
1
Comparison as scatter plot
Comparison MOBY data with ACG processor
1
1
0
0
-1
-1
-2
-2
Rw
Rw
Comparison MOBY data with ACG processor
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
-5
-4
-3
-2
-1
0
rhow_moby
Neural network AGC /C2R
73 no glint cases
1
-5
-4
-3
-2
-1
0
rhow_moby
Neural network AGC /C2R
85 high glint cases
1
Identify spectra, which are out of scope of the training set
Detection of out of scope conditions
•
2 Procedures have been developed
– Combination of an inverse and forward Neural Network
– Use of an autoassociative Neural Network
•
•
•
Both produce a reflection spectrum, which is compared with the input
spectrum
Deviation between input and output spectrum can be computed as a chi2
A threshold can be used to trigger an out of scope warning flag
• Combination
of inverse
and forward NN
R Input
• Auto-associative
NN
R Input
Inverse
NN
IOPs
Forward
R output
NN
autoassociative
NN
R output
Detection of out of scope conditions (MERIS processor)
Top of atmosphere
radiance spectra
at normal and
critical locations
Detection of out of scope conditions (MERIS processor)
Exeptional bloom,
Indicated by high Chi_square value
Chi_square is computed by
comparing
The input reflectance spectrum
with the output of the forward
NN
Detection of out of scope conditions using an aaNN
•
•
•
Important to detect toa radiance specta which are not in the simulated
training data set
These are out of scope of the atmospheric correction algorithm
Autoassociative neural network with a bottle neck layer
Functions also
as nonlinear PCA
i.e. bottle neck number of
neurons
Provide estimate of
Independent components
Bottleneck
Input
Hidden 1
layer
Hidden 3
output
layer
For the GAC training data
Set of ~ 1Mio. Cases
Bottleneck minimum was 4-5
Detection of out of scope conditions aaNN:
example for L1 (TOA) data
High
SPM
Sun
glint
Transect
Detection of out of scope conditions aaNN: example
AutoNN test 12x5x12 Yellow Sea transect, MERIS band 7, 664.3 nm
1.40
1.35
1.30
AutoNN test 12x5x12 Yellow Sea transect, MERIS band 7, 664.3 nm
1.25
rel. deviation
1.20
rltoa
rltoa_aNN
0.06
ratio
0.07
difference
1.15
1.10
1.05
0.05
1.00
0.95
0.90
0.85
120
0.03
121
122
123
124
125
126
127
128
129
longitude
0.02
AutoNN test Yellow Sea transect 12x5x12, MERIS band 7, 664.3 nm
0.01
18
16
0.00
14
-0.01
120
121
122
123
124
125
126
127
longitude
significant deviation in area with
high SPM concentrations, but not in
sun glint area
128
129
Histogram of deviations
shows 2 maxima,
around 1 in sun glint
0.9 in high SPM area,
which out of scope
12
rel. frequency
RLtoa
0.04
10
8
6
4
2
0
0.85
0.90 0.95
1.00
1.05 1.10
1.15 1.20
1.25
rel. radiance reflectance ratio to true
1.30 1.35
1.40
TOSA, Path, Water Reflectance 708 nm
Inverse NN
Sun Glint correction
Sun glint problem: Hawai 20030705
Cross section Hawai scene
radiance_9 [mW/(m^2*sr*nm)]
200
180
160
140
120
radiance_9 [mW/(m^2*sr*nm)]
100
80
60
40
20
-160
-158
-156
-154
-152
longitude (deg)
-150
-148
0
-146
No glint and high glint TOA reflectance spectra
M ERIS spectra for no sun glint with RL_toa band 865 < 0.004
M ERIS spectra for sun glint with RL_toa band 865 > 0.06
0.08
0.085
0.07
0.080
0.06
0.075
RL_toa [sr-1]
0.05
0.04
0.070
0.03
0.065
0.02
0.060
0.01
0.00
400
450
500
550
600
650
700
wavelength [nm ]
750
800
850
900
0.055
400
450
500
550
600
650
700
wavelength [nm ]
750
800
850
900
Simulated Rayleigh path radiance reflectance and sun glint radiance reflectance
0.04
nadir view
0.035
sun zenith 20 deg
wind 3 m/s
Radiance refelctance [sr-1]
0.03
Rayleigh path radiance
0.025
0.02
sun glint
0.015
0.01
0.005
0
400
450
500
550
600
650
700
wavelength [nm]
750
800
850
900
Specular refleced radiance differences, ratio rel. to Lw
T5/S35
T25/S0
MERIS full resolution: Baltic and North Sea, 20080606
Stockhom
Sun glint
Oslo
Baltic Sea
North Sea
Sun glint
Copenhagen
Spatial resolution: 300 m
Hamburg
Swath: 1200 km, 4800 pixel
Water leaving radiance reflectance
Path radiance reflectance incl. Sun glint band 5 (560 nm)
Water leaving radiance reflectance band 5 (560 nm)
MERIS FR, Area of Gotland, TOA RLw RGB
Stockholm
Estonia
sunglint
Lettland
Ca. 100 km
Gotland
Baltic Sea
Water leaving radiance reflectance RGB
Gotland
Ca. 100 km
MERIS 20070505: TOA reflectances RGB
New York
reflectance RLpath MERIS
band 5 (560 nm)
reflectance RLw MERIS band 5
(560 nm)
Chlorophyll
MERIS FR USA East Coast 12.6.2008, Signal depth z90
Philadelphia
Chesapeake Bay
Washington
North Atlantic
Overview
•
•
•
•
•
•
•
Artificial neural networks (NN) can be used for atmospheric correction in
different ways
– As a forward model to determine the path radiance and transmittance
as a function of aerosol optical properties, wind (sun glint), angles
– As an inverse model, which determines water reflectances,
transmittances, path radiance from TOSA reflectance spectra
NN AC is based on association between water reflectance and top of
atmosphere reflectance
No negative reflectances
The relationship between TOSA reflectance, path radiance, transmittance
and the independent parameters (pressure, aerosols, wind/waves) must be
described with a radiative transfer model
NNs are then trained by a large number of simulated cases (> 1 Mio) by
minimizing the difference between the output of the NN and
For turbid coastal waters reflectance must include reflectance by water
For coastal waters include all bands for atmospheric corrections, no
extrapolation