Transcript Modelling Bottom Reflectance

Modelling Bottom Reflectance
Wendy Clavano & Bill Philpot
Goal: To develop an analytical model that portrays the reflectance
of an irregular bottom.
How much will bottom morphology alter the magnitude,
distribution and spectral quality of the light reflected from
the bottom?
Uses:
1. Estimate the importance of multiple reflections on
• BRDF
• spectral quality of the reflectance
2. Provide a check for Monte Carlo models
3. Framework for modeling reflectance from a textured
surface.
Image by Fred Voetsch, Death Valley, 042902
http://www.picturesof.net/cgi-bin/wallpaper_gallery.cgi
Modelling Bottom Reflectance
Goal: To develop an analytical model that portrays the reflectance
of an irregular bottom.
Assumptions:
a. The bottom is locally Lambertian.
b. Bottom morphology modeled using an infinitely repeating
sine wave. Roughness is adjusted by adjusting the
amplitude and length of the bottom sine wave.
c. The solar plane is the reference azimuth.
d. Shadowing and obscuration will be significant under some
conditions.
e. 2nd (and higher) order reflections will be significant under
some conditions.
f. Surface texture may be treated by adjusting the height and
length of the bottom waveform (modelled as a sine wave).
Modelling Bottom Reflectance
Modelling Bottom Reflectance
First Order Reflectance
Modelling Bottom Reflectance
First & Second Order
Far-Field Reflectance
Modelling Bottom Reflectance
Shadowing for 1st and 2nd Order Reflections
• Some parts of the
waveform are not directly
illuminated.
• Reflectance includes
contribution by interreflections.
Modelling Bottom Reflectance
Obscuration for 1st and 2nd Order Reflections
• Some parts of the wave,
although may be
illuminated, are hidden
from the detector’s view.
The effects of
illumination and
viewing angles are
not equivalent.
Results
a) In the absence of shadowing and obscuration, the
BRDF remains smooth and cosine-like (for a single
sine wave) .
b) Reflectance decreases with increasing roughness
c) Reduction in 1st order reflectance due to bottom
roughness is mitigated by 2nd order reflectance for a
realistic range of wave height/length ratios.
Next steps
a) Consider spectral characteristics in modelling water
attenuation and bottom reflectance.
b) Expand model structure to consider 3D sine waves
both in the near-field and in the far-field, for both
variable sun incidence angles and viewing angles.
c) Compare results against Monte Carlo model results.
Inverting Spectral Reflectance
Peggy Imboden & Bill Philpot
Goal: To develop analytical or
semi-analytical methods
for extracting information
about water properties
from hyperspectral data.
Assumptions:
a. Algorithm development will be most effective
if guided by a radiative transfer model.
b. Properly applied, spectral derivatives will be an
effective method for extracting information
from the spectral data.
Research Questions:
a. To what extent can spectral derivatives be
related to the water IOPs?
b. Can we extract more information about pigment
composition by considering the more subtle
spectral features?
c. Can phytoplankton taxa be characterized with
this approach?
Reflectance Approximation:
1st
dR
1

dλ (a + bb )2
Derivative:
bb
R f
a + bb
da 
 dbb
- bb
a

d

d



Approximations
1) Backscattering is relatively strong, spectral dependence of
scattering is very weak compared to that of absorption:
dbb
da
a
<<
b
If
b
dλ
dλ
and if bb << a then:
dR
 1 da 
 R 

d
 a d 
 The slope of the reflectance spectrum is dominated by
the absorption spectrum
Reflectance Approximation:
1st
dR
1

d (a + bb )2
Derivative:
bb
R
a + bb
da 
 dbb
- bb
a

d

d



Approximations
2) Backscattering is weak relative to absorption, spectral
dependence of scattering is relatively strong, such that:
dbb
if a
dλ
bb
da
dλ
and if bb << a then:
dR 1 dbb


d a d
bb
R
a + bb
Reflectance Approximation:
2nd
Derivative:
d2 R W
-2

3
dλ 2
 a + bb 
d  dR  d 
1





2
d

d

d

 d   a  bb 2
d2 R
da  
 dbb
a d  bb d  

2
2

da db b
1
 db b  
 da 
a
b
b
+
a
+



b
b


 
2
dλ
dλ
dλ
dλ
 

   a + b b 

 d 2 bb
d 2a 
a dλ 2 - b b dλ 2 


Approximation:
1) Assume that the spectral dependence of scattering is relatively weak:
if a
d 2 bb
d
2
bb
d 2a
d
2
 db 
and a  b 
 d 
2
 da 
bb  
 d 
2
2
d 2 R W -2  da db b
da
   -b b d a
 3 a
- bb    + 2
2
2
dλ
a  dλ dλ
 dλ   a dλ
2
and bb
a
or,
d 2 R W -b b d 2 a
with luck, dλ 2  a 2 dλ 2
Rrs 
bb
a + bb
Reflectance Approximation:
N
R
r X
n
n 0
n
bb
X
a + bb
Using only two non-zero terms,
the 1st Derivative becomes:

2bb
dR 
1
  r1 
r2 
dλ 
a  bb  (a + bb )2
da 
 dbb
a
b


b
d 
 d
Tasks:
a. Formulate basic model & derivatives.
(done)
b. Review data for phytoplankton species that are typical
for selected sites.
(ongoing)
c. Run Hydrolight / OOPS to model water-leaving radiance
for typical water optical components over expected
ranges.
(in process)
d. Sensitivity analysis.
e. Develop algorithms for analyzing spectral water-leaving
radiance.
Need:
- pigment composition (w/ relative concentrations) for
major phytoplankton taxa.