l e - ioccg
TRANSCRIPT
EdLw
)0,(
)0,()(
d
wrs
E
LR
Remote-sensing reflectance (sr-1):
The ultimate objective of RS:Retrieval useful/important environmental information
How?
algorithm!
inputs outputs
algorithm
(Lw or Rrs)
(IOPs or [Chl] etc)
Empirical(explicit or implicit)
Semi-analytical(algebraic， LUT, optimization)
Bio-optical models： Yes
Bio-optical models： No need
Bottom Up Strategy (BUS)
Top Down Strategy (TDS)
(O’Reilly et al 1998)
Chl centered band-ratio algorithms
Chl based on band difference
)443()670(
443670
443555)443()555( rsrsrsrs RRRRCI
166.19149.0 sr0005.0;10 CIChl CI
(Hu et al 2012)
(Hu et al 2012)
(Lee et al 1998)
Empirical:
EdLw
)0,(
)0,()(
d
wrs
E
LR
Remote-sensing reflectance (sr-1):
Physics-based algorithms (mechanistic)
How is Rrs related to water’s optical (biogeochemical) properties?
Physics-based algorithms (mechanistic)How is Rrs related to water’s optical (biogeochemical) properties?
Radiative Transfer Equation (no inelastic scattering):
dLLcld
Ld),'()'()(
)(
dLzLczd
zLdu
u ),'()'(),(),(
)',,0(
'')'sin()',(),'(
)()',()',()(
)',()',(
2/
0
2
0
SodfLL
Sdrs
E
ddL
bfkc
Dr
4
1 )()(
)(),'()',(i
i
b
birs
ba
bpwqr
Albert and Mobley (2003) :
)()(
)()',(
)()(
)()'()',(
b
bpp
b
bwwrs
ba
bg
ba
bgr
Lee et al (2004)
4
1 )()(
)(),'()',(
i
i
b
bbirs
ba
bgr
Park and Ruddick (2005)
4
1
4
1
))]([ln())]()[ln('()]',(ln[j
jiij
irs baPr
Van Der Woerd and Pasterkamp (2008)
Exact solution (no inelastic scattering):)0(
)',0()',(
d
urs
E
Lr
(Zaneveld 1995)
0794.0,0949.0
;)()(
)(),(
21
2
1
gg
ba
bgr
i
i
b
birs
Gordon et al (1988):
)()(
)()',,()',(
b
brs
ba
bChlgr
Morel et al (1993, 1996, 2002):
rs
rsrs
w
LErs
r
r
R
r
n
ttR
7.11
52.0
12
R
r
n
ttR rs
w
LErs
12
)0(
d
wrs
E
LR
)0()0()0( udEd EEtE
)0(2
u
w
Lw L
n
tL
Solve Rrs for IOPs or in-water constituents?
rrs Rrs ?
Two basic strategies:
1. Bottom-up strategy (BUS): Assume we know the spectral shapes of the optically
active components
2. Top-down strategy (TDS):Only need the spectral shape information when it is
necessary
))(),(()( brs baFR
))(),(),(),(),(()( bpbwdgphwrs bbaaaFR
))(),(),(),(),(()(
))(),(),(),(),(()(
))(),(),(),(),(()(
222222
111111
nbpnbwndgnphnwnrs
bpbwdgphwrs
bpbwdgphwrs
bbaaaFR
bbaaaFR
bbaaaFR
# of unknowns > # of equations!
Have to increase # of equations or decrease # of unknowns!
What are we facing in RS algorithms?
An ill formulated math problem!
1. Bottom-up strategy (BUS):
)()()( bpbwb bbb
a(λ) = aw(λ) + axi(λ) bb(λ) = bbw(λ) + bbxi(λ)
Build-up an Rrs spectrum block-by-block:
)()()()( dgphw aaaa
)()()()( 21 dgphw aMaMaa
)()()( 3 bpbwb bMbb
)()()()()( gdphw aaaaa
Bio-optical models (forward model)
)(1)()(
phB
phph ChlAa
Example of one parameter hyperspectral aph(λ) model:
Bricaud et al (1995):
Lee (1994); Lee et al (1998):
PPaph )ln()(a)(a)( 10
P = aph(440)
Modeling aph spectrum
Example of two-parameters model: (Ciotti et al 2002)
(Hoepffner and Sathyendranath, 1993)
Multiple-parameters model:
2D Graph 1
400 450 500 550 600 650 700
0.0
0.2
0.4
0.6
0.8
1.0 HOPE (0.1)
HOPE (3.0)
GSM
Wavelength [nm]
Examples of modeled spectra)(pha)
(ph
a
Absorption components: adg spectrum shapes
)440()( Sdg ea S: 0.01 – 0.02 nm-1
(Bricaud et al 1981)
440)(bpb
)()(
)()(
b
brs
ba
bGR
)()()()()(
)()()(
321
3
bpbwdgphw
bpbw
rsbMbaMaMa
bMbGR
M1-3 are wavelength independent variables!Then they could be derived by comparing the modeled Rrs spectrum with the measured Rrs spectrum.
The blue-green domain: e.g., Hoge and Lyon (1996), Carder et al (1999)The red-infrared domain: e.g., Binding et al (2012)The entire spectrum (spectral optimization): e.g., Bukata et al (1995), Lee et al (1994,1996,1999), Maritorena et al (2002), Boss and Roesler (2006), Brando et al (2012)，Werdell et al (2013)
Spectral ranges used for solutions (e.g. examples of BUS):
Look-Up-Tables (LUT): e.g., Carder et al (1991); Mobley et al (2005)
3-variable model to describe an Rrs spectrum(Sathyendranath et al 1989)
Matching between measured and modeled Rrs
2
1
2
1
2
2
1
22
1
)(
)()(~
)(
)()(~
rs
rsrs
rs
rsrs
R
R
RRn
R
RRrs
Quantitative measure of the closure (error function):
Spectral Optimization
0
0.001
0.002
0.003
0.004
0.005
0.006
400 450 500 550 600 650 700 750 800
Mod. Rrs Mea. Rrs
Wavelength [nm]
Rrs
[sr-1
]
Logic (assumption) behind SOA:A unique set of bio-optical properties for each Rrs spectrum.
Algorithms using information in the red-infrared bands
)67(
)75(
xRrs
xRrsfChl
)70(
)75(
)67(
)75(
xRrs
xRrs
xRrs
xRrsfChl
(Gitelson et al 2007)
Two bands Three bands
)()(
)()(
)(
)(
)(
)(
111
212
2
1
2
1
redphredw
redphredw
redbp
redbp
redrs
redrs
aMa
aMa
b
b
R
R
Proper contrast of Rrs at λ1 and λ2 then leads to M1.
)()(
)()(
1
3
phw
bp
rsaMa
bMGR
)()()()()(
)()()(
321
3
bpbwdgphw
bpbw
rsbMbaMaMa
bMbGR
aph
2. Top-down strategy (TDS):
b
brs
ba
bGR
Remote sensing measures the total effect:
Water clarity (or turbidity) is also a measure of total effect.
Rrs bb&a ax
Clarity (Secchi depth, light depth, TSM/SPM, etc)
Examples of TDS:
Loisel & Stramski (2000), QAA (Lee et al, 2002); Smyth et al (2006); Doran et al (2007).
The Quasi-Analytical Algorithm (QAA)
(a,bb,etc) Rrs
Forward modeling:
QAA:
(a,bb) Rrs
b
brs
ba
bR
05.0
0
0bpbp )()( bb
rrs()
0 w 0 0( ) ( ) ( )a a a
)(),(),(F)( 0bw0020bp barb rs
)(),(),(F)( bwbp3 bbra rs
η
The data flow of QAA:
)443()443()443()443(
)443()443()411()411( w
dgphw
dgph
aaaa
aaaa
)443(
)411(
)443(
)411(
dg
dg
ph
ph
a
a
a
a
(Lee et al 2002)
wavelength (nm)
400 450 500 550 600 650
absorp
tion c
oeffic
ient (
m-1
)
0.0
0.1
0.2
0.3
0.4
pure water
[C] = 0.03
[C] = 1.0
[C] = 5.0
For a reference wavelength, λ0, variation of a(λ0) is limited.
λ0
λ0
Known a(λ0), enables calculation of bb(λ0) from Rrs(λ0); propagate bb(λ0) to
bb(λ), then enables calculation of a(λ) from Rrs(λ).
No need of spectral model of ax(λ) in this process!
Logic behind QAA (and its updated versions):
)667()490(
)667(5)(
)490()443(log
0 rs
rs
rsrs
rsrs
rr
rr
rr
2469.0366.1146.110)550()550( waa
aw(550) = 0.0565
Empirical!
When 550 nm as the reference wavelength (λ0)
a(555) (m-1
)
0.05 0.2 0.50.1
a(5
55
) (m
-1)
0.05
0.2
0.5
0.1
a(550) [m-1]
a(5
50
) [
m-1
]
rrs(λ) = Rrs(λ)/(0.52 + 1.7 Rrs(λ))
1
1
2
00
2
)(*4
)()(
)()(
g
rggg
ba
bu
rs
b
b
g0=0.089,g1=0.125
2
10
b
b
b
brs
ba
bg
ba
bgr
Rrs rrs {a&bb}
Invert Rrs:
)550()550(1
)550()550()550( bwbp b
u
aub
550)550()( bpbp bb
2469.0366.1146.110)550()550( waa
0 1 2 3 4 5
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
data
v4
v5
rrs(443)/rrs(550)
η
)55(
)443(9.0exp2.110.2
xr
r
rs
rs
Empirical:
)(
)())(1()(
u
bua b
)()()( bpbwb bbb
).440()440()440()440(
),440()440()410()410(
dgphw
dgphw
aaaa
aaaa
).440()440()440()440(
),410()410()410()410(
dgphw
dgphw
aaaa
aaaa
)()()()( dgphw aaaa
)440(
)410(
ph
ph
a
a
)440(
)410(
dg
dg
a
a
).440()440()440()440(
,)440()410()440()410(
)440(
dgwph
wwg
aaaa
aaaaa
).440()440()440()440(
),440()440()410()410(
dgphw
dgphw
aaaa
aaaa
0 2 4 6 8
0.005
0.010
0.015
0.020
0.025
0.030
data
v5
0 2 4 6 8
0.0
0.2
0.4
0.6
0.8
1.0
1.2
data
v5
rrs(443)/rrs(550)rrs(443)/rrs(550)
a ph(4
12
)/a p
h(4
43
)
S [
nm
-1]
)550(/)443(8.0
2.074.0
rsrs rr
)550(/)443(6.0
002.0015.0
,)411443(
rsrs
S
rrS
e
Empirical!
1 2( ) ( ) M ( ) ( )w ph dga a a M a
Ensemble solutions:
Wang et al. 2006; Zheng et al. 2015
(Zheng et al. 2015)
Key Points:
1. Various inversion algorithms for IOPs have been developed; but more/better ones are also expected.
2. BUS derives every component first, then (simultaneously) derives the total optical property.
Assume the spectral shapes of the optically active components are well characterized! BUS relies more on the accuracy of forward
bio-optical model
TDS relies more on the accuracy of Rrs measurement
3. TDS derives total first, then decompose to separate components.