DN to Reflectance
HONDA Kiyoshi
Contents
Definition of NDVI
| Radiance
| Reflectance
| How to Calculate Radiance from DN
| Irradiance
|
1
Definition of NDVI
NDVI =
ρ NIR − ρVR
ρ NIR + ρVR
ρ NIR : Reflectance at Near Infrared
ρVR : Reflectance at Visible Red
Reflectance
|
|
Ratio of Radiant Energy Reflected to Incident Energy
Radiant Energy = Integral of vertical components of
Radiance Measured ( by satellite to be scaled back
from DN )
ρλ =
πLλ
Gλ
=
πLλ
µ s E sλ
ρ λ : Spectral Reflectance
Lλ : Spectral Radiance of the Surface W / m 2 ⋅ sr ⋅ µm
E
πL
θ
G : Spectral Irradiance W / m 2 ⋅ µm
Esλ : Spectral Solar Irradiance W / m 2 ⋅ µm
µ s = cos(θ s ),θ s : Solar zenith angle
2
DN ?
DN ( Digital Number ) you can see in
the RS image files is not Reflectance.
| So you have to derive Reflectance from
the DN
| Then what is DN ?
|
DN is a scaled Radiance
|
DN is scaled from Radiance measured
by sensors
http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter6/chapter6.html
3
Radiance
|
Energy in unit time, unit
solid angle, unit wavelenth
Z
unit : J / s ⋅ m 2 ⋅ sr ⋅ µ m = W / m 2 ⋅ sr ⋅ µ m
Energyreceived
Lλ =
dtdAdωdλ
dλ
dω
dA
http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter6/chapter6.html
QCALMAX
DN to Radiance (Lλ)
Lλ = gain × DN + offset
or
Lλ =
LMAX λ − LMIN λ
(QCAL − QCALMIN ) + LMIN λ
QCALMAX − QCALMIN
QCALMIN
LMAX λ − LMIN λ
QCALMAX − QCALMIN
LMAX λ − LMIN λ
offset = −
+ LMIN λ
QCALMAX − QCALMIN
DN = QCAL, offset = bias
gain =
|
Have to find out LMAX,
LMIN, QCALMAX,
QCALMIN
4
LMIN, LMAX of LANDSAT7
|
LMIN, LMAX List
LMAX
LMIN
http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11/chapter11.html
LANDSAT 7 Gain Setting for January
http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter6/htmls/january_gains.html
5
How to Find the Constants for
Scaling factor of Radiance
|
Metadata file .met
z
|
Sample ftp://cgceopush3.geo.msu.edu/push3_2/137/043/p137r43_7x000228/p137r043_7x20000228.met
Identify Hi-Gain or Low Gain
z
EROS Data Center Gateway
• http://edcimswww.cr.usgs.gov/pub/imswelcome/
|
Obtain Hi-Gain and Low-Gain parameters
z
USGS LANDSAT Page
• http://landsat7.usgs.gov/technical_details/calibration_files/
Header file/record
| Data Handling Manuals
|
z
Processed in Japan, China, Thailand ….
How to obtain TOA Irradiance
|
Spectral Exo-atmospheric Irradiance
ρλ =
πLλ
E sλ =
Gλ
=
πLλ
µ s E sλ
ESUN λ
2
ds
Esλ : Exo - atmospheric Solar Spectral Irradiance W / m 2 ⋅ µm
ESUN λ : Average Exo - atmospheric Solor Spectral Irradiance W / m 2 ⋅ µm
d s : Earth - Sun distance in astronomical units
µ s = cos(θ s ),θ s : Solar zenith angle
http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11/chapter11.html
6
Average Solar Spectral Irradiance ESUNλ
|
ρλ =
Average Solor Spectral
Exo-atmospheric
Irradiance
πLλ
Gλ
E sλ =
=
πLλ
µ s Esλ
ESUN λ
2
ds
Esλ : Exo - stomospheric Solar Spectral Irradiance W / m 2 ⋅ µm
ESUN λ : Average Exo - atmospheric Spectral Irradiance W / m 2 ⋅ µm
ESUNλ for ETM+
http://modarch.gsfc.nasa.gov/MODIS/ATM/solar.html
http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11/chapter11.html
Sun Earth Distance ds
E sλ =
1
ESUN λ
2
ds
d s : Earth - Sun distance in astronomical units
Relative Solar Irradiance 1/(ds*ds)
1.10
1.05
1.00
0.95
0.90
0
30
60
90
120
150
180
210
240
270
300
330
360
http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11/chapter11.html
7
Solar Zenith Angle
|
LANDSAT: Use Zenith Angle ( 90deg – Sun
Elevation) at the centre of the image for the
whole image
180km -> +- 0.81 deg
z If Zenith Angle < 20deg, difference < 1%
z
Or
|
Calculate the angle from Lat, Lon, Julian day
and time ( i.e POSSOL of 6S ).
http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11/chapter11.html
Atmospheric Correction
|
|
|
|
The reflectance we have obtained here is Apparent
Reflectance or Reflectance at TOA
Atmospheric correction is needed to obtain Reflectance at
Ground Level
You may run 6S with appropriate parameters
Some products are Reflectance at Ground Surface, such as
MODIS, SPOT VEGETAION…
8
References
|
Landsat 7 Science Data Users Handbook
z
Chapter6
z
Chapter 11
•
•
|
http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11/chapter11.html
Dr. Kawamura's page DN->Refelctance for
Landsat ( Japanese )
z
|
http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter6/chapter6.html
http://www.geocities.jp/kensuke_kawamura/Others/LandsatCal
ibration/LandsatCalibration.html
6S Manual
9