Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 1 Instrument Calibration and Atmospheric Corrections

Atmospheric and System Corrections Using Spectral Data

1Digital Imaging and Remote Sensing Laboratory

Instrument Calibration and Instrument Calibration and Atmospheric Corrections Atmospheric Corrections

Why calibrate ?– reference data

– temporal comparison



ELMELM

DCorL

DC

R() R()

Band 1 Band 2



Model Based Estimates of RModel Based Estimates of R

clouds

R predicted by model, e.g. Bio-optical model for R() as a function of coloring agents ([C], [CDOM], [TSS])

DCorL

R()



Standard SurfacesStandard Surfaces

Band 1

R()

DCorL

Clouds

Deep Vegetation

Significant potential for error if only limited samples are available or target, variability is high.



Atmospheric and System Corrections Atmospheric and System Corrections Using Spectral Data (cont’d)Using Spectral Data (cont’d)

• Note ELM can also be used with calibrated system

–Pros

• removes atmospheric and sensor artifacts

• simple and direct if good ground data available




– cons

• requires large known targets

• assumes uniform correction across image

• can introduce sizeable errors if reference

reflectance is not well-known or significantly

different than target reflectance




calibrating sensors

• laboratory calibration

–spectral calibration

–band center

– relative spectral response

–FW HM

–absolute calibration to radiance



AVIRISAVIRIS

Airborne Visible/Infrared Imaging Spectrometer

(AVIRIS)

Figure 3 shows a detail of the AVIRIS onboard

calibrator which is used for monitoring and

updating the laboratory calibration of AVIRIS.



AVIRIS (cont’d)AVIRIS (cont’d)

Figure 3. In-flight calibrator configuration




Figure 1. a) Laboratory spectral calibration set-up.




Figure 1. B) Typical spectral response function with error

bars and best fit Gaussian curve from which center

wavelength, FWHM bandwidth and uncertainties are

derived.




Figure 2. Derived center wavelengths for each AVIRIS

channel (bold line), read from left axis, and associated

uncertainty in center wavelength knowledge (normal

line), read from right axis.




Figure 7. Radiometric calibration laboratory setup.




(a) (b)

Figure 5.42 Integrating spheres used for sensor calibration: (a) sphere design, (b) sphere used in calibration of the AVIRIS Sensor. (Image courtesy of NASA Jet Propulsion Laboratory).




Figure 12. AVIRIS signal-to-noise for the 1995 in-

flight calibration experiment.




Figure 13. AVIRIS noise-equivalent-delta-radiance for

1995.




• radiometric calibration

–dark level

–intensity std with reflectance panel

–transfer through a detector std to sphere

–detector stds and spheres

–use of onboard reference – (laser line, spectral filters)

–use of onboard spectral reference




• inflight calibration and generation of model

mismatch spectral correction

–calibration sites

–MODTRAN prediction of sensed radiance



Adjustments to AVIRIS DataAdjustments to AVIRIS Data

At the start of a flight season, for a surface of

known reflectance, predict radiance reaching

AVIRIS using MODTRAN convolved with AVIRIS

spectral response. Call this LM(). N.B. This is for a

well-known study site with known radiosonde and

optical depth (Langley plot) values. Severe clear,

high and dry to minimize errors due to poor

characterization of any constituents.



Adjustments to AVIRIS Data (cont’d)Adjustments to AVIRIS Data (cont’d)

Generate a correction vector

(1)

where LA() is the observed AVIRIS radiance for the

target modeled in generating LM. The CM() vector is

the residual miscalibration error between MODTRAN and AVIRIS. In particular, any residual spectral miscalibration will be picked up by this process.

)()(

)(

M

AM L

LC




Fig. 4. Calibration ratio between AVIRIS and MODTRAN3 derived from the inflight calibration experiment on the 4th of April 1994.




For any spectra predicted by MODTRAN, the

equivalent AVIRIS spectra is then given by

(2)

Furthermore, the onboard calibrator senses slight

changes in detectors over time.

)()()( MMA CLL




Define a correction vector

(3)

where L1() = lamp radiance at time of inscene

correction used to generate equation 1 (Day 1), L2()

= lamp radiance at time of flight of current interest

(Day 2).

)()(

)(2

1

LL

CC




To correct AVIRIS radiance on Day 2 to equivalent

readings on Day 1,

(4))()()( 21

CCLL




Fig. 5. Calibration ratio of the on-board calibrator signal for the Pasadena flight to the signal for the inflight calibration experiment.




So radiance to be compared are

(5)

or to avoid changing all the image data

)()()(

vs.

)()()(

21

C

MMA

CLL

CLL




(6)

where LA2 is the day 2 radiance that AVIRIS is

predicted to observe using ground reflectance estimates and the MODTRAN code.

)( vs. )(

)()()( 22

LC

CLL

C

MMA




If we want to correct using MODTRAN then we

would want to convert day two spectral radiance

to LM values, i.e.

)(C)(C)(L

)(LM

C2M



Critical Atmospheric ParametersCritical Atmospheric Parameters

• density of the atmosphere (pressure depth)

• aerosols type and number

• water – column water vapor



Pressure Depth

Modtran derived radiance vs. wavelength plots for sensor reaching radiance for different target elevations.



Pressure Depth (cont’d)



Aerosol Number Density

Retrieved spectra for straight 60% reflector

0.5

0.52

0.54

0.56

0.58

0.6

0.62

0.64

0.66

0.3 0.5 0.7 0.9 1.1

wavelength

Ret

riev

ed S

pec

tra

case 1

case 2

Visibility Elevation Water vaporCase 1 10.0 0.315 0.05Case 2 70 0.315 0.05

Typical particle size distribution curves for a rural aerosol type.

DRY TROPO AEROSOLSRH = 80% TROPO MODELRH = 95% TROPO MODELRH = 99% TROPO MODEL



Modtran derived sensor reaching radiance for identical targets viewed through two atmospheres where only the column water vapor amount differs.

0 g/cm2 1.0 g/cm2

Column Water Vapor



Water Vapor EstimationWater Vapor Estimation

• CIBR (Continuum Interpolated Band Ratio)

–spectral prediction of sensed radiance with

MODTRAN

–computation of a continuum interpolated band

ratio

–per pixel corrections to reflectance



A

B

D

C

Water Vapor EstimationWater Vapor Estimation

compare to

LUT of MODTRAN

predicated

C

D

LL

C

D

LL



Water Vapor Estimation (cont’d)Water Vapor Estimation (cont’d)

• ATREM

–use of bands in ATREM to adjust for

material reflectance spectra



Atmospheric CalibrationAtmospheric Calibration

In general, Scattering dominates below 1 μm;

absorption above 1 μm, Top of atm reflectance

Tanré 1960 claims

cos

sE

Lp

ssussd

ag

1

)((1)




rearranging (1) yields:

1

a

gsdsua

g

s

(2)

2)14.1(

2

)94.0(

14.1

94.0

EDE

CAB

g

g

where A - F are expressed in apparent reflectance (TOA) averaged over a predefined set of AVIRIS bands designed to characterize the absorption feature and its wings.

(3)

An apparent reflectance spectrum with relevant positions and widths of spectral regions used in three channel rationing being illustrated.

0.85 1.20wavelength

Ap

par

ent

refl

ecta

nce

A

B

C D

E

F

0

2

Comparing the average of the mean effective transmission in the two absorption regions with theoretical values predicted using radiation propagation models, you can use LUT to obtain an estimate of water vapor concentration on a pixel-by-pixel basis.

Step 1. from lat, long, T.O.D. and D.O.Y.Step 2. g calculated based on models and atm path. For H2O, several spectra computed as function of total column H2O range 0 - 10 cm. So we end up with many g spectra. The band ratio transmittances can be calculated for each spectra.Step 3. a, s, us and ud are calculated using 5s (now 6S) which assumes no absorption for these calculations.Step 4. AVIRIS radiance converted to apparent reflectance spectrum (TOA reflectance).Step 5. Calculate channel ratios at 0.94 and 1.14 µm regions using Equation 3 on the results of Step 4. Compare Step 5 to results of Step 2 and estimate column H2O and corresponding g.Step 6. g from 5 and inputs from 3 and 4 are used with Equation 2 to estimate reflectance spectra.



Band ratio assumes uniform slope in reflectance spectra over 3 bands. This is compensated for vegetation, snow, and ice by adjusting bands to more closely approximate for errors introduced by non linearity. i.e., band ratios use 3 sets of bands, 1 for vegetation, 1 for snow, and 1 for non vegetation or snow.




Equation 1 can be expressed as:

as compared with the manner we normally express radiance

])(1[coscoscos 2ss

EEEL susdgsgass

uds LrLrE

L

221cos

)()()(

)()(coscos

)()(

cos

)()(

2123

212

21221

212

21

rssrr

rE

rL

E

Lr

E

L

adga

s

d

s

u

s

if atmosphere is very clear. From radiative transfer 1 2 () are calculated for different H2O content.




12

if 2

)()(

)(

2

)()(

)(

2

Model RT FromAVIRIS From

32321221

121

321221

121

32

1

rr

r

rr

r




wavelength0.4 2.4

RA

TIO

0

1.2

Ratio of one atmospheric water vapor transmittance spectrum with more water vapor against another water vapor transmittance spectrum with 5% less water vapor.




wavelength0.4 2.4

RA

TIO

0

1.2 Ratio of one atmo-spheric transmittance spectrum of CO2, N20, CO, CH4, and O2

in a sun-surface-sensor path with a surface elevation at sea level against another similar spectrum but with a surface elevation at 0.5 km.




• APDA

–correction to 940 ratio for upwelled radiance

using a column water dependent upwelled

radiance




APDA Chart



The APDA TechniqueThe APDA Technique

The single channel/band Rapda:

)LL()LL(

)PW(LLR

r2,atmr2r2r1,atmr1r1

m,atmmAPDA

which can be extended to more channels:

im][jm,atmmjr

im,atmmAPDA |)]LL[,]([LIR

]LL[R




Relate R ratio with the corresponding water vapor amount (PW)

Solving for water vapor:

)(PW)(-APDAWV eR(PW)

1

APDAAPDA

)Rln()R(PW




))(( PWAPDALnR

)(

1

PWLnR



Compute LUTw/ LT(wv,h,)@=0.4 and Latm (wv,h,

Calculate RAPDA foreach MODTRAN runby applying APDAequation to the LUT.

Fit ratio values toPW and store theregressionparameters.

Assume startingPW1 and subtractheight dependentLu from image.

Calculate APDA ratioand transform RAPDA

values to PW2 usinginverse mapping eq.

Substitute the Latm

in eq. with newPW dpndt valuesderived from LUT.

Calculate RAPDA a2nd time and trans-form to final PW3(x,y).

General APDA ProcedureGeneral APDA Procedure



APDA SolutionsAPDA Solutions

Channel #10 from an AVIRIS image of the Los Angeles/Pasadena area.

Preliminary water vapor density image generated using the ATREM algorithm (the darker the pixels, the more water vapor).



APDA SolutionsAPDA Solutions

Channel #25 from the cropped AVIRIS image of the Los Angeles/Pasadena area.

Preliminary water vapor density image generated using the APDA algorithm (the darker the pixels, the more water vapor).




• Multi parameter approach

–NLLSSF



Atmospheric InversionAtmospheric Inversion

Oxygen - pressure elevation

To estimate the effective height (surface pressure

elevation) the strength of the oxygen absorption

band (760 nm) in the AVIRIS spectrum is fitted to

MODTRAN data.

1. To increase sensitivity, average (e.g., 5x5

pixels) to generate AVIRIS spectrum.



Atmospheric Inversion (cont’d)Atmospheric Inversion (cont’d)

2. Iteratively predict oxygen spectra in AVIRIS

radiance units using pressure elevation. Use non

linear least squares to control the iteration process.

Parameters adjusted were pressure elevation,

reflectance magnitude (a), and reflectance slope (b).

)(baR




Fig. 4. The fit with residual between the MODTRAN2 nonlinear least

square fit spectrum and the AVIRIS measured spectrum for the

estimation of surface pressure elevation from the oxygen band at

760 nm.




The resulting surface pressure elevation can be

constrained in subsequent calculations (e.g.,

aerosol optical depth).

Aerosol optical depth - AVIRIS data averaged over

11X11 pixels

Select aerosol type in MODTRAN




Adjust parameters describing:

– aerosol optical depth (visibility parameter)

– reflectance magnitude

– reflectance spectral slope

– leaf chlorophyll absorption

(parametric description of location and shape of spectrals

feature)

Fit run over visible region 410 - 680

vegRbaR γ)(




Fig. 7. Spectral fit for aerosols at the Rose Bowl parking lot.




Fig. 3. The nonlinear least squares between the AVIRIS measured

radiance and the MODTRAN2 modeled radiance for estimation of

aerosol optical depth. The modeled reflectance required for this fit

in the 400 to 600 nm spectral region is also shown as is the

resulting AVIRIS calculated reflectance.




Water vapor determination (940 absorption feature)

for each pixel

Fits parameters for

– column water vapor and

– 3 parameters that describe surface reflectance with

leaf water.

)()( vegRbaR




Fig. 7. Fit with residual between the AVIRIS measured radiance

and the MODTRAN2 modeled radiance in the 940 nm spectral

region for an area of green grass in the Jasper Ridge AVIRIS

data set.




Fig. 8. Surface reflectance with leaf water absorption required

to achieve accurate fit between the measured radiance and

modeled radiance for the spectrum in Fig. 4.




The water content, aerosol optical depth, and

pressure elevation can all be fixed on a pixel- by-

pixel basis and a radiative transfer equation solved

of the form.

Sr

rr

EL

g

ga

s

1cos 21




where Es is exoatmospheric irradiance, is solar

declination angle, ra is the effective reflectance of the

atmosphere, rg is the reflectance of the ground 1 and

2 are sun-target and target-sensor transmissions, S

is the single spherical scattering albedo of

atmosphere above the target (rgS accounts for

multiple scattering adjacency effects).




Solving for rg yields

SrEL

Er

aO

Og

)/cos(cos

1

21



Non-Linear Least-Squared Spectral Non-Linear Least-Squared Spectral Fit (NLLSSF) TechniqueFit (NLLSSF) Technique

g: Lambertian ground reflectance

Minimize the difference between the sensor radiance and the MODRAN-derived sensor radiance by changing parameters in the governing radiative transfer equation:

)(

])cos([g

g2d21OgenvUsensor

S1LELLLLSE



NLLSSF Flex ParametersNLLSSF Flex Parameters

0.760µm Oxygen Band

, , surface

elevation

0.94µm

H2O Band water

, , vapor

0.4 - 0.70 µm

Aerosol Band , ,

visibility



In the .760µm oxygen band, the target reflectance is

assumed linear with

In the case of the aerosol and water vapor bands the

equation includes a non-linearity for liquid water:

NLLSSF Model of ReflectanceNLLSSF Model of Reflectance

=++(H2Ol

)

= +



Using all Solved Parameters, Invert Governing Radiometric Equation and Calculate Ground Reflectance.

Input ConstantParameters(i.e geometry,particle density,etc)

General Flow Chart of General Flow Chart of AlgorithmAlgorithm

Solve for TotalColumn Water Vapor Using the .94µm band.

Input Image Pixel:Solve for SurfacePressure Depth in.76µm O2 band.

Solve for AtmosphericVisibility Given an Aerosol Type Using.4-7µm bands



Surface Pressure ElevationSurface Pressure Elevation

0.015

0.0175

0.02

0.0225

0.025

0.0275

0.03

0.745 0.75 0.755 0.76 0.765 0.77 0.775 0.78 0.785

HYDICE Channel Center Wavelength (micron)

Rad

ian

ce (

W/c

m^

2/s

r/m

icro

n)

HYDICE Sensor

MODTRAN Calculated



NLLSSF Curve FitNLLSSF Curve Fit

0

0.005

0.01

0.015

0.02

0.025

0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 1.02

HYDICE Channel Center Wavelength (microns)

Rad

ian

ce

(W

/cm

^2

/sr/

mic

ron

)

HYDICE Sensor

MODTRAN Calculated




–Pressure depth

• 760 feature

• spectral model prediction and LUT generation

• model match – amoeba algorithm




–aerosol number density/visibility


• model match

–column water vapor


• model match




–products

• reflection spectra

• water vapor map

• pressure depth map

• vegetation moisture map

RIM to generate spectral upwelled radiance estimate

Per image or per region model match to spectral estimate of upwelled radiance from RIM

Per pixel model over visible region NLLSSF

Per pixel atmospheric coefficients for computing inversion equations

or

APDA per pixel iterative ratio match

or

Pressure depth(elevation)

aerosol number density (visibility)

water vapor

wavelength

Rad

ianc

e

MeasuredModeledResidualslocal met

station visibility

radio-sonde

or

elevationand

pressure

Per pixel model match on 760nm oxygen feature

6

Per pixel model match on 940nm water feature NLLSSF

Radiative TransferModel MODTRAN



Average Image-Wide Reflectance Error for HYDICE Run cr08m33 from NLLSSF 2nd Pass

(average of Old panel reflectances less than 18%)

-0.05

-0.045

-0.04

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

Wavelength (nm)

Av

g R

efl

ec

tan

ce

Err

or

Estimated image-wide reflectance Estimated image-wide reflectance error for ground targets of 18% error for ground targets of 18%

reflectance or less.reflectance or less.



Estimated Image-Wide Reflectance Error for HYDICE Run cr15m50 from NLLSSF 2nd Pass (average of Old panel reflectances less than 18%)

-0.05

-0.045

-0.04

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

Wavelength (nm)

Av

g R

efl

ec

tan

ce

Err

or

Estimated image-wide reflectance Estimated image-wide reflectance error for ground targets of 18% error for ground targets of 18% reflectance or less.reflectance or less.

Documents

Digital Imaging and Remote Sensing Laboratory Atmospheric and System Corrections Using Spectral Data 1 Instrument Calibration and Atmospheric Corrections