The document discusses several key concepts in ocean color remote sensing: 1) It defines normalized water-leaving radiance and describes its importance for comparing field and satellite measurements. 2) It outlines the steps to calculate normalized water-leaving radiance from radiance and irradiance measurements in the field and from satellite sensors. 3) It explains how atmospheric corrections and other factors are used to transfer measurements between field and satellite contexts.

1. Alexandra Olivier, Biospherical Instruments, San Diego, CA
http://sos.noaa.gov/images/atmosphere/biosphere.png

2. Independent of ambient light
Depend on composition, morphology, and concentration of
particles
IOPs:
Beam Attenuation Coefficient (c)
c = a + b
Scattering Phase Function (β)
Absorption Coefficient (a)
depends on the material and also on the wavelength of light which is
being absorbed.
Volume Scattering Function (b)
Petzold’s measurements

3. Depend on medium & directional structure of ambient light
field
Show regular features & stability
Radiance/various irradiances are not AOPs
AOPs:
Various reflectances (𝐸 𝑢/𝐸 𝑑, 𝐿 𝑢/𝐿 𝑑, etc.)
Average cosines (µ)
Diffuse attenuation coefficients (i.e., 𝐾 𝑑, 𝐾𝐿𝑢...)
“K-Functions”-logarithmic derivatives
units: 1/m or “per meter”

4. • Determined by using above
or in water measurements
• Carries information about
the water column and bottom
conditions
• Usually measured, but can be
calculated taking atmospheric
corrections into considerationhttp://remotesensing.spiedigitallibrary.org/data/Journals/APPRES/926148/JARS_7_1_073558_f003.png

5. Process of removing contributions by surface glint and
atmospheric scattering from the measured total radiance to
get 𝐿 𝑤
NIR & SWIR bands are used for determination
𝐿 𝑤 = 0.54𝐿 𝑢(σ, λ) or 𝐿 𝑤(λ) =
1−𝜌
𝑛2 𝐿 𝑢 0−
, λ
𝐿 𝑤 = 𝐸 𝑑ℜ
𝑓
𝑄
𝑏 𝑏
𝑎
ℜ = [
1− 𝜌
1− 𝑟𝑅
1−𝜌
𝑛2 ]

6. Causes upwelling radiance values and remote sensing reflectance to
be too low
Affected by marine and atmospheric conditions; dependent on solar
zenith angle
Simulated responses with or without the presence of a shading
object are computed using the Monte Carlo Simulation
The magnitude of error depends on wavelength, sensor size, water
turbidity, and illumination conditions; greatest at small solar zenith
angles.

7. Shading error for 𝐿 𝑢 in general sky conditions
𝜀 =
𝜀 𝑠𝑢𝑛 λ +𝜀 𝑠𝑘𝑦(λ)
1+ℎ
ℎ =
𝜀 𝑠𝑘𝑦(λ)
𝜀 𝑠𝑢𝑛 λ
Shading error for 𝐸 𝑑 in general sky conditions:
𝜀 =
𝜀 𝑠𝑢𝑛+𝜀 𝑠𝑘𝑦 𝑓
1+𝑓
Fractional shading error (no atmospheric scattering):
𝜀 = 1 − 𝑒(−𝑘′ 𝑎𝑟) 𝑘′ =
𝑦
𝑡𝑎𝑛𝜃0
′

8. K = constant that depends on measurement type & illumination
conditions
𝐿 𝑢, E 𝑢 = corrected radiance, irradiance
𝐿 𝑢, 𝐸 𝑢 =measured radiance, irradiance
a = water beam absorption coefficient
r = radius of housing
𝜀 𝑠𝑢𝑛 = shading error for direct sunlight from appropriate sun angle
𝜀 𝑠𝑘𝑦 = shading error for indirect sunlight
𝑓 = increase with increased solar zenith angle and increased
chlorophyll concentration
𝜃′
= refracted solar zenith angle
𝑦 = empirical factor for which they give values determined by fitting
their model results (𝑦 ≈ 2)

9. Shading corrections should be routinely applied to upwelling
light measurements from in-water instruments
Corrected radiance:
𝐿 𝑢 =
𝐿 𝑢(0−−λ)
1−𝜀(λ)
Corrected irradiance:
𝐸 𝑢 =
𝐸 𝑢(0−−λ)
1−𝜀(λ)

10. Statistical simulation technique that provides approximate solution
to mathematically expressed problems
Method that utilizes the sequence of random numbers to perform
simulations
Does not give an exact answer, instead a statistical estimate with
error
Most common use is evaluation of integral and calculation of
mathematical constant variable
Essential feature is that the known probability of occurrence of each
separate event in sequence of events is used to establish probability
of occurrence of entire sequence

11. a reasonable approach to developing a Monte Carlo algorithm:
figure out how to numerically simulate a process as it occurs in
nature
then figure out how to simulate another, perhaps artificial, process
that will give the same answer as the "natural" process, but with
less computational time.
Process:
Consider how photons propagate through a medium
Using a ratio of scattering efficiency to total extinction efficiency
(“attenuance”) to determine the probability of photon survival in any
particular interaction:
1. Draw a random number, t, from a U[0.1] distribution. 2.
Compare t with ω0 .
• If ω0 < t, then the photon is scattered.
• If ω0 > t, then the photon is absorbed.

12. Use of optical measurements made from satellites or aircraft to
obtain information about the constituents of natural waters,
corresponding IOPs, or bottom depth and type
Two types:
Active: signal of known characteristics sent from sensor platform,
to the ocean & the return signal is detected after time of delay
Passive: observe light that’s naturally emitted or reflected by
water body
Ocean Color Remote Sensing:
The term “Ocean Color” is loosely used to mean radiometric data
at two or more visible wavelengths, from which useful
information about water bodies can be extracted

13. http://eijournal.sensorsandsystems.com/newsite/wp-content/uploads/2013/12/astrium_figure-11.jpg

14. Some of the current applications of ocean color data:
Mapping of chlorophyll concentrations
Measurement of IOPs
Determination of phytoplankton physiology, phenology, and
functional groups
Studies of ocean carbon fixation & cycling
Monitoring of ecosystem changes resulting from climate
change
Fisheries management
Monitoring of water quality for recreation
Detection of harmful algal blooms & pollution events

15. From Field:
[𝐿 𝑤] 𝑁 =
𝐿 𝑤 𝜆,𝜃,∅
𝐸 𝑑 0+,𝜆
𝐹0(λ) = 𝑅 𝑟𝑠(λ, 𝜃, ∅) 𝐹0(λ) µW𝑐𝑚−2
𝑛𝑚−1
𝑠𝑟−1
From Satellite:
[𝐿 𝑤] 𝑁 = 𝐹0ℜ(ϴ’)
f(ϴ0
)
𝑄(ϴ0,ϴ
′
,∆∅)
∙
𝑏 𝑏
𝑎
µW𝑐𝑚−2 𝑛𝑚−1 𝑠𝑟−1

16. From Field:
[𝐿 𝑤] 𝑁
𝑒𝑥
= [𝐿 𝑤
𝑖𝑛𝑤
] 𝑁 ∙
𝑓0
𝑄𝑛(0)
(
𝑓(ϴ0)
𝑄𝑛(ϴ0)
)−1
µW𝑐𝑚−2
𝑛𝑚−1
𝑠𝑟−1
From Satellite:
[𝐿 𝑤] 𝑁
𝑒𝑥
= 𝐹0ℜ0
𝑓0
𝑄0
∙
𝑏 𝑏
𝑎
µW𝑐𝑚−2 𝑛𝑚−1 𝑠𝑟−1
Transferring [𝐿 𝑤] 𝑁 to [𝐿 𝑤] 𝑁
𝑒𝑥
:
[𝐿 𝑤] 𝑁
𝑒𝑥
= [𝐿 𝑤] 𝑁
ℜ0
ℜ θ′
𝑓0
𝑄0
(
𝑓 𝜃0
𝑄(𝜃0,𝜃,∆∅)
)

17. Step 1- Water Leaving Radiance (if not measured):
𝐿 𝑤 = 𝐸 𝑑ℜ
𝑓
𝑄
𝑏 𝑏
𝑎
OR 𝐿 𝑤 = 𝐹𝐿 λ [𝑆𝑓𝑐 − 𝜌𝑆 𝑘𝑦] µW𝑐𝑚−2
𝑛𝑚−1
𝑠𝑟−1
Step 2- Normalized Water Leaving Radiance:
[𝐿 𝑤] 𝑁 =
𝐿 𝑤
𝐸 𝑑
𝐹0 = 𝑅 𝑟𝑠 𝐹0 µW𝑐𝑚−2
𝑛𝑚−1
𝑠𝑟−1
Step 3- Exact Normalized Water Leaving Radiance:
[𝐿 𝑤] 𝑁
𝑒𝑥
= [𝐿 𝑤
𝑖𝑛𝑤] 𝑁 ∙
𝑓0
𝑄𝑛(0)
(
𝑓(ϴ0)
𝑄𝑛(ϴ0)
)−1 µW𝑐𝑚−2
𝑛𝑚−1
𝑠𝑟−1

18. Step 1- Normalized Water Leaving Radiance:
[𝐿 𝑤] 𝑁 = 𝐹0ℜ(ϴ’)
f(ϴ0
)
𝑄(ϴ0,ϴ
′
,∆∅)
∙
𝑏 𝑏
𝑎
µW𝑐𝑚−2
𝑛𝑚−1
𝑠𝑟−1
Step 2- Exact Normalized Water Leaving Radiance:
[𝐿 𝑤] 𝑁
𝑒𝑥
= 𝐹0ℜ0
𝑓0
𝑄0
∙
𝑏 𝑏
𝑎
µW𝑐𝑚−2
𝑛𝑚−1
𝑠𝑟−1

19. 𝐹0 = extraterrestrial solar spectral irradiance at mean earth-sun distance (𝑑0)
𝐹0 = extraterrestrial solar flux at 𝑑0
𝑅 𝑟𝑠 =Remote-sensing reflectance
ℜ = reflection x refraction
𝑄 = ratio of the upwelling irradiance just beneath the ocean surface to the upwelling
radiance just beneath the ocean surface
𝑏 𝑏
𝑎
=backscatter to absorption ratio
𝑄𝑛 = for nadir viewing
𝐹𝐿 λ = instrument’s unknown radiance response calibration factor
𝑆𝑓𝑐 =shipboard radiometer measured radiance from the sea surface at Zenith
𝜌 = total skylight actually reflected from wave-roughened sea surface into direction divided
by sky radiance
𝑆 𝑘𝑦 =sky radiance measured with radiometer looking upward
𝑛2 =light incident upon medium of index
𝜌 = the air–water Fresnel reflection at the interface for the whole (Sun + Sky) downwelling
irradiance
𝑟 = the water–air Fresnel reflection for the whole diffuse upwelling irradiance

20. Radiance and irradiance are measured together because separately, they do not
make good candidates for AOPs.
Fail to meet the requirement of being stable enough to be a useful descriptor of
water
Exact normalized water leaving radiance is the only measurement that can be
successfully compared for validation
Ocean Color Remote Sensing:
reveals large and small scale structures that are very difficult to observe from the
surface.
Locates and enables monitoring of regions of high and low bio-activity
Food (phytoplankton associated with chlorophyll)
Climate (phytoplankton possible CO2 sink)
Reveals ocean current structure and behavior:
Seasonal influences
River and Estuary influences
Boundary currents

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