inverting in-water reflectance eric rehm darling marine center, maine 30 july 2004
TRANSCRIPT
Inverting In-Water Radiance
Estimation of the absorption and backscattering coefficients from in-water radiometric measurements
Stramska, Stramski, Mitchell, Mobley
Limnol. Oceanogr. 45(3), 2000, 629-641
SSA and QSSA don’t work in the water SSA assumes single scattering near surface
QSSA assumes that “Use the forumlas from SSA but treat bf as no scattering at all.
Stramska, et al. Approach
Empirical Model for estimating KE, a, bb Requires Lu,(z,) Eu(z,), and Ed(z,)
Work focuses on blue (400-490nm) and green (500-560 nm)
Numerous Hydrolight simulations Runs with IOPs that covaried with [Chl] Runs with independent IOPS Raman scattering, no Chl fluorescence
Field Results from CalCOFI Cruises, 1998
Conceptual Background
Irradiance Reflectance R = Eu/Ed Just beneath water: R(z=0-) = f *bb/a
f 1/0 where 0=cos()
Also (Timofeeva 1979)
Radiance Reflectance RL=Lu/Ed
Just beneath the water RL(z=0-) =(f/Q)(bb/a), where Q=(Eu/Lu
)
f and Q covary f/Q less sensitive to angular distribution of light
1R
Conceptual Background Assume
R(z) =Eu/Ed bb(z)/a(z)
RL(z) =Lu/Ed bb(z)/a(z), not sensitive to directional structure of light field
RL/R can be used to estimate Many Hydrolight runs to build in-water empirical model
KE can be computed from Ed, Eu Gershuns Law a=KE* Again, many Hydrolight runs to build in-water
empirical model of bb(z) ~ a(z)*RL(z)
1
Algorithm I1. Profile Ed(z), Eu(z), Lu(z)2. Estimate KE(z)
1. KE(z) = –d ln(Ed(z) –Eu(z)]/dz
3. Derive (z)1. (Z) ~ RL(z) /R(z) = Lu(z)/Eu(z)
1. est(b)=0.1993+(-37.8266*RL(b).^2+2.3338*RL(b)+0.00056)./Rb;
2. est(g)=0.080558+(-28.88966*RL(g).^2+3.248438*RL(g)-0.001400)./Rg
4. Inversion 1: Apply Gershun’s Law
1. a(z)=KE(z)*(z)
5. Inversion 2:
bb ~ a(z)*RL(z)
bb,est(b)=11.3334*RL(b).*a(b)-0.0002;
bb,est(g)=10.8764*RL(g).*a(g)-0.0003;
Curt’s Method 2 from LI-COR Lab!
A lovely result of the Divergence Law for
Irradiance
Algorithm II Requires knowledge of attenuation coefficient c Regress simulated vs Lu/Eu for variety of
bb/b and 0 = b/c best=0.5*(b1+b2)
b1=c – aest (underestimate)
b2=bw + (bb,est-.5*bw)/0.01811 (overestimate)
Compute0 = best/c Retrieve based on bb/b:
2,est = mi(0)*(Lu/Eu) + bi (0)
As before Use 2,est to retrieve a Use RL and a to retrieve bb
Model Caveats
Assumes inelastic scattering and internal light sources negligible Expect errors in bb to increase with depth and
decreasing Chl. Limit model to top 15 m of water column
Blue (400-490 nm) & Green (500-560 nm) Used Petzold phase function for simulations
Acknowledge that further work was needed here
My Model #1
Hydrolight Case 1 Raman scattering only Chlorophyll profile with 20 mg/L max at 2 m Co-varying IOPs 30 degree sun, 5 m/s wind, bb/b=.01
10-1
100
101
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
Chl [mg m-3]
z [m
]
10-1
100
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
Chl [mg m-3]
z [m
]
3
4
5
1
2
Chlorphyll Profile #1
AOP/IOP Retrieval Results
0.6 0.65 0.7 0.75 0.8
0.6
0.65
0.7
0.75
0.8
est
0.1 0.2 0.3 0.4
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
a (m-1)
a est (
m-1
)
0.01 0.02 0.03 0.04 0.05
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
bb (m-1)
b b,es
t (m
-1)
Relative Error for RetrievalAOP/IOP Stramska Me Comments
(z) < 12% <22.3% Max errors in blue = 2X max in green
a(z) < 12 % < 25 % No dependence on l
Underestimates a by 25% in large Chl max. Otherwise noisy overestimate
bb(z) < 30% <28%
<169%
< 1 m, > 5.5 m
2-5m (Chl max)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-25
-20
-15
-10
-5
0
a (m-1)
dept
h (m
)
0 0.01 0.02 0.03 0.04 0.05 0.06-25
-20
-15
-10
-5
0
bb (m-1)
dept
h (m
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-25
-20
-15
-10
-5
0
KE (m-1)
dept
h (m
)400410
420
430440
450
460470
480
490500
510
520530
540
550560
– model
– estimate
0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9-25
-20
-15
-10
-5
0
dept
h (m
)
Relative Error Distribution
-25 -20 -15 -10 -5 0 5 10 15 20 250
1
2
3
4
5
6
7
8
9
10
a - Relative Error %
Fre
quen
cy
-25 -20 -15 -10 -5 0 5 10 150
2
4
6
8
10
12
14
= Relative Error %
Fre
quen
cy
400
450
500
550
600
0
5
10
15
20
25
-25
-20
-15
-10
-5
0
5
10
15
Depth (m)
Wavelength
Relative Error est
vs. Hydrolight
(%)
Error %
400
420
440
460
480
500
520
540
560
0
5
10
15
20
-20
-10
0
10
20
Depth (m)
Wavelength
Error Estimating a
Error %
400
450
500
550
0
5
10
15
20
-500
50100
150200
Depth (m)
Wavelength (nm)
Error Estimating bb
Relative Error %
My Model #2
Hydrolight Case 2 IOPs
AC-9 from 9 July 2004 Ocean Optics cruise Cruise 2, Profile 063, ~27 m bottom bb/b = 0.019 (bb from Wetlabs ECOVSF)
Raman scattering only Well mixed water, [Chl] ~3.5 ug/L 50% cloud cover
400 420 440 460 480 500 520 540 5600.05
0.1
0.15
0.2
0.25
0.3
wavelength (nm)
a,c
m-1
a, c: Cruise 2
AOP/IOP Retrieval Results
0.2 0.4 0.6 0.8 1 1.20.2
0.4
0.6
0.8
1
1.2
est
0.05 0.1 0.15 0.2 0.25 0.3
0.05
0.1
0.15
0.2
0.25
0.3
a (m-1)
a est (
m-1
)
0.01 0.02 0.03 0.04 0.05 0.06 0.07
0.01
0.02
0.03
0.04
0.05
0.06
0.07
bb (m-1)
b b,es
t (m
-1)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35-25
-20
-15
-10
-5
0
a (m-1)
dept
h (m
)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-25
-20
-15
-10
-5
0
bb (m-1)
dept
h (m
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4-25
-20
-15
-10
-5
0
dept
h (m
)
– model
– estimate
400
420
440
460
480
500
520
540
560
0
5
10
15
20
0.1
0.15
0.2
0.25
0.3
0.35
0.4
depth (m)
wavelength (nm)
m-1
KE - Cruise 2
400
450
500
550
0
5
10
15
20
0.20.4
0.60.8
11.2
1.4
depth (m)
wavelength (nm)
est
- Cruise 2
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07-25
-20
-15
-10
-5
0
RL (sr-1)
dept
h (m
)
400410
420
430440
450
460470
480
490500
510
520530
540
550560
0 0.05 0.1 0.15 0.2 0.25-25
-20
-15
-10
-5
0
R (sr-1)de
pth
(m)
400410
420
430
440450
460
470
480490
500
510520
530
540
550560
Conclusions
Stramska, et al. model is highly tuned to local waters CalCOFI Cruise Petzold Phase Function 15 m limitation is apparent
Requires 3 expensive sensors Absorption is most robust measurement retrieved by
this approach 3-D graphics are useful for visualization of multi-
spectral profile data and error analysis Lots of work to do to theoretical and practical to
advance IOP retrieval from in-water E and L.