atmospheric effects and corrections

Atmospheric Effects and Corrections

Lecture 6

Terminology

• Radiant flux• Irradiance • Radiance• Reflection• Transmittance

Radiance (LT) from paths 1, 3, and 5 contains intrinsic valuable spectral information about the target of interest.

Conversely, the path radiance (Lp) from paths 2 and 4 includes diffuse sky irradiance or radiance from neighboring areas on the ground. This path radiance generally introduces unwanted radiometric noise in the remotely sensed data and complicates the image interpretation process.

Radiance received at a remote sensor

• Path 1 contains spectral solar irradiance ( Eo) that was attenuated very little before illuminating the terrain within the IFOV.

• We are interested in the solar irradiance from a specific solar zenith angle ( θo)

• The amount of irradiance reaching the terrain is a function of the atmospheric transmittance at this angle (Tθo).

• If all of the irradiance makes it to the ground, then the atmospheric transmittance equals one. If none of the irradiance makes it to the ground, then the atmospheric transmittance is zero.


• Path 2 contains spectral diffuse sky irradiance ( Ed ) that never reaches the the target study area because of scattering in the atmosphere.

• This energy is often scattered into the IFOV of the sensor system.

• Rayleigh scattering of blue light contributes much to this diffuse sky irradiance. Hence blue band image produced by a remote sensor system is often much brighter than any of the other bands and contains much unwanted diffuse sky irradiance that was scattered into the IFOV of the sensor system.

• Therefore, if possible, we want to minimize its effects. This quantity is referred to as the upward reflectance of the atmosphere (Edu).


• Path 3 contains modified energy from the Sun that has undergone some Rayleigh, Mie, and/or nonselective scattering and perhaps some absorption and reemission before illuminating the study area.

• Its spectral composition and polarization may be somewhat different from the energy that reaches the ground from path 1.

• This quantity is also referred to as the downward reflectance of the atmosphere (Edu).


• Path 4 contains radiation that was reflected or scattered by nearby terrain covered by snow, concrete, soil, water, and/or vegetation into the IFOV of the sensor system.

• The energy does not actually illuminate the study area of interest. Therefore, if possible, we would like to minimize its effects.

• Path 2 and Path 4 combine to produce what is commonly referred to as Path Radiance, Lp.


Path 5 is energy that was also reflected from nearby terrain into the atmosphere, but then scattered or reflected onto the study area.

Generally insignificant.


Images are arrays of pixels, where each pixel is represented by a brightness value or grey level, generally between 0 and 255. These values are called DNs.

We can determine the radiance at the sensor for any pixel from its DN value, between 0 and 255:

where

Lmax and Lmin are maximum and minimum measurable radiances of the sensor.

k and Lmin are also called gain and offset of the detector.

This information is provided by the sensor manufacturer.

min)( LkDNL pixpxl

max

minmax

DNLLk


Radiance received at a remote sensorBAND 1 2 3 4 5 7

Lmin (W/m2/sr/μm)

-1.5 -2.8 -1.2 -1.5 -0.37 -0.15

Lmax (W/m2/sr/μm)

152.1 296.8 204.3 206.2 27.19 14.38

Preflight TM-4 and TM-5 spectral range values (from NASA, 1986, Table C-8)

DN value of a pixel in bands 1 and 7 is 100 Maximum DN value in both bands is 255

Radiance at the pixel in band 1? In band 7??

For band 1, k = (152.1+1.5)/255 = 0.602353L pix = (100 x 0.602353 ) – 1.5 = 58.73 W/m2/sr/μm

For band 7, k = (14.38+0.15)/255 = 0.05698Lpix = (100 x 0.05698) – 0.15 = 5.54 W/m2/sr/μm

0cossunE

Remote sensing systems sense wavebands, rather than specific wavelengths. The available irradiance (Eo) in a specific wave band between λ1 and λ2 in the area of interest is

dEsun

2

1

0cos or2

0cosd

Esun

where Δλ = λ2- λ1 is very small and Esun Δ λ is the average irradiance in the band Δλ. d2 (in AU)accounts for varying distance of earth from the Sun. If the reflectance of the pixel of interest is R, then the radiant exitance of the pixel is:

We know that

20cos

dREL sun

Pxl

The irradiance (Esunλ) of the sun in a specific length (λ) at a solar zenith angle of θ is

Radiance received at a remote

sensor

Rd

EE sunPxl

20cos

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2

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or 0cossunE

dsun

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R is the reflectance. If the atmospheric transmission in the direction θv is Tθv , then the radiance Lsensor arriving at the sensor after traversing the atmosphere is:

However the atmosphere scatters and absorbs a proportion of the solar irradiance. If the scattered or diffused sky irradiance is Ed and Tθo is the atmospheric transmission, i.e., the proportion of radiance transmitted by the atmosphere, in the direction θo, then the total irradiance at the pixel =

oT

The radiance from the pixel due to this irradiance =

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path

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Bidirectional Reflectance Distribution Function


The bidirectional reflectance distribution function (BRDF) is a theoretical concept that describes the relationship between 1) the geometric characteristics of the solar irradiance, and 2) the remote sensing system viewing geometry; hence the bidirectional terminology (Sandmeier, 1996; Jensen, 2000)

),();,;,();,;,(

ii

rriirrii dE

dLf


The accurate computation of BRDF required for:

• Making corrections to reflectance measurements of features measured from nadir or off-nadir pointing remote sensing systems.

• To identify bands that are least impacted by BRDF, recognize optimal sun/sensor angle-of-views, and provide insight into radiometrically adjusting remotely sensed data to minimize BRDF effects.

Objectives of atmospheric corrections

High goal of remote sensing:

To identify the composition of objects on ground from remote sensing data

Spectral reflectance curves are used for this purpose However, radiance-at-the-sensor is contaminated by path radiance due to the

atmosphere, hence spectral reflectance estimated from remote sensing data are incorrect

We have to correct the radiance-at-the-sensor to remove atmospheric effects

When is the atmospheric correction really required??

• Mono-temporal data : NO• Classification: NO• Change monitoring and detection: YES• Composition mapping, spectral analysis: YES

Sensor calibration • gain and offset

Atmospheric correction

• image measurement• ground measurements• atmospheric models• sensor view path atmospheric radiance• sensor view path atmospheric

transmittance

DN

Radiance at sensor

BRDF/Topographic correction

Radiance at ground

• solar angle, DEM

Surface reflectance

Radiometric calibration

Atmospheric corrections: Techniques

• Histogram minimum method aka dark object subtraction – the bootstrap approach

• Empirical line method

• Radiative transfer models – Physical-based approach

Estimation of LP : Dark object subtraction

• Dark-object subtraction techniques derive the corrected DN (digital number) values solely from the digital data with no outside information.

• This type of correction involves subtracting a constant DN value from the entire digital image.

• The assumption is that there is a high probability that at least a few pixels within an image which should be black (0% reflectance). If there are no pixels with zero values, that is the effect of atmospheric scattering

• For example, there are about 45 million pixels in a single TM band – so there very high probability that at least one of them should be black.

Water absorption

Water absorption

Water bodies have 0% reflectance in the IR region, hence zero DN

Non-zero values over water bodies in the IR consequence of path radiance.

Subtract the non-zero value over water bodies from all pixels. That would make water body perfectly non-reflecting.

In Visible bands, shadows should be black in absence of path radiance.

Hence non-zero values over shadowed areas can be used for dark pixel correction.


• Histograms of pixel values in all bands• pixel values of low reflectance areas near zero• exposures of dark colored rocks• deep shadows• clear water

• Lowest pixel values in visible and near-infrared are approximation to atmospheric path radiance

• Minimum values subtracted from image


Estimation of LP : Dark object subtractionEg Multispectral – can be applied to

hyperspectral as well

How will you calculate path radiance for all bands ??For example, calculate path radiance for a pixel whose DN value is 53 in band 1.


How will you calculate path radiance for all bands ??For example, calculate path radiance for a pixel whose DN value is 53 in band 1.

ETM+ Solar Spectral Irradiances Band watts/(m2 * μm)

1 19972 18123 15334 10395 230.87 84.90 8 1362.

Day of Year Distance Day of Year Distance Day of Year Distance Day of Year Distance Day of Year Distance

1 .98331 74 .99446 152 1.01403 227 1.01281 305 .99253

15 .98365 91 .99926 166 1.01577 242 1.00969 319 .9891632 .98536 106 1.00353 182 1.01667 258 1.00566 335 .9860846 .98774 121 1.00756 196 1.01646 274 1.00119 349 .9842660 .99084 135 1.01087 213 1.01497 288 .99718 365 .98333

• DN values of correlated bands are plotted• Least square line fit using standard

regression methods• Resulting offset is approximation for

the atmospheric path radiance offset subtracted from image

Estimation of LP : Dark object subtractionRegression technique


Does it always work?

The key criterion of atmospheric correction algorithm - ….. Quantify atmospheric influences on satellite image radiometry but at the same time insensitive to surface reflection effects


So how to correct this image?

Manually select several clear and hazy area pixels in the image

Two spectral bands are selected based on the following criteria:

• The spectral responses of different land cover types, under clear atmospheric conditions, should be highly correlated in the two bands. This will result in a well-defined surface response vector in spectral space called “clear line” (CL)

• The effect of haze should be markedly different in the two bands so that increased atmospheric contamination manifests in increased shift away from the CL

• Typically we would select blue and red bands

Apply a transformation whose coefficients define a direction orthogonal to the CL and whose response magnitude is proportional to the deviation from this line

Estimation of LP : Haze Removal Algorithm Haze Optimization Transform (HOT)

Y. Zhang et al., 2002 (RSE)


Schematic diagram of the TM1 – TM3 spectral space illustrating the conceptual components of the HOT. Under clear sky conditions, radiances of common surface cover types, coded as A – K, exhibit high correlation and define a ‘clear line’ (CL). The effect of haze of increasing optical depth, illustrated by the numerical sequences 1 – 18, is to pixels to ‘migrate’ away from the CL. The HOT quantifies the atmospheric contamination level at a pixel location by its perpendicular distance, in spectral space, from the CL.

Y. Zhang et al., 2002 (RSE)


Y. Zhang et al., 2002 (Rem Sens Env)


1. Select two correlated bands (bands showing similar reflectance characteristics for all objects) but affected by scattering due to atmospheric components to different degrees.

Example: Bands 1 (Blue) and 3 (Red) of ETM/TM


2. Mask out areas with obvious haze3. Select some very clear areas that are unaffected by clouds/haze)


4. Plot DN (Blue band – X axis) vs DN (Red band – Y axis) of pixels from clear area

Band 1 (Blue)

Band

3 (R

ed)

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Clea

r line

5. Fit the pixel DNs to the clear line generated by linear regression (slope = α and offset β on x axis.

Haze vector

6. Haze vector is orthogonal to clearline


offset) theing(disregard

Or )(

CosDNSinDN

CosDNSinoffsetDN

redblue

redblue

10. Calculate HOT for all pixels as the offset of a pixel from the clear line in the haze vector direction

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8. Plot all DN (Blue) v/s DN(Red) for all pixels on the image

7. Plot clear line

α

Band 1 (Blue)

Band

3 (R

ed)

Clea

r line

β

9. Haze vector is orthogonal to clear line, hence you can identify haze pixels

. ... . . ... .. ... . . ... .

... . . ... .. ... . . .. ... . . ... .

. ... . . .... . . ... .. ... . . . Haze vector


11. Generate HOT Image and determine the HOT values for clear areas and hazy areas

(Not the same image as in the previous slide)


12. Plot HOT histogram for different HOT levels for clear and hazy areas

Clear areas

Haze areas

Increasing HOT = > Increasing Haze


13. histogram lower bound versus HOT for bands TM1–TM3

14. Estimate radiometric adjustment using a method similar to “dark object subtraction” to normalize the image to the radiometric level of the clearest areas.

From Step 13 plot, note that, for Band TM 1 (Blue), the histogram lower bound for clear pixels (i.e., HOT= 30) is approximately 20 DNs. Consider a hazy pixel with an observed HOT level of 40. It is a member of a histogram with a lower bound 27. This implies that this hazy pixel should have its band 1 DN level reduced by 7 during the radiometric adjustment phase. This procedure can be used to adjust all bands for which the histogram analysis has been done.

Clear pixel

DN


Results

One dark (X1) and one bright (X2) object selected on the image which can be clearly identified on the ground also

Ground reflectance of X1 and X2 measured using field radiometer (R X1 and R X2).

Radiance-at-the-sensor of X1 and X2 measured using field radiometer (L X1 and L X2).

The two points plotted on a graph, joined by a line, and the slope (s) and intercept (a) of the line measured.

Equation of the line derived, used for converting all radiance values into reflectance valuesR = (L-a)*s R - Reflectance

a - Offsets - Slope

Empirical line method

Advantages and disadvantages of bootstrap techniques??

Model-based atmospheric corrections -Visibility

The farthest distance at which one can see a large, black object against the sky at the horizon. It is determined by:• optical properties of the atmosphere; • amount and distribution of light; • characteristics of the objects observed; • properties of the human eye.

Visibility is reduced by the absorption and scattering of light by both gases and particles. However, light scattering by particles is the most important phenomenon responsible for visibility degradation.In clean (background) atmospheric conditions, one can see over distances up to several hundred kms; in polluted atmospheric conditions, visibility is up to 10 km.

(Koschmieder equation)

where is the extinction coefficient (per sq km) at 550 nm. It is the sum of extinction coefficients of all gases and particles, which attenuate light, and is therefore a measure of the loss of radiation per unit distance

ext

VIS912.3

ext

Optical thicknessOptical thickness (δ) is defined as the product of the extinction coefficient and the path length, x, e.g., from the sea level to space in a vertical path:

Optical thickness due to molecular scattering (mainly due to N2 and O2) depends only on the pressure level and can be calculated for a given ground elevation.

Optical thickness due to molecular absorption due to O3 and CO2 can be averaged over large areas. Optical thickness due to water vapour absorption is significant and varies with time and space.

Therefore, the total optical thickness can be considered a function of aerosol optical thickness (AOT),and water vapour absorption which varies strongly in time and space.

xext

absorptionMolecularaerosolscatteringMolecular

Atmospheric transmittance

e

Algorithms for atmospheric corrections

• ATmospheric CORrection (ATCOR)• ATmosphere REMoval (ATREM)• Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes

(FLAASH)

All the above algorithms use radiative transfer models of atmosphere such as MODerate resolution atmospheric TRANsmission (MODTRAN)

0

102

cos})({

ETLDNccd

Ro

path

where d2 takes into account the sun-to-earth distance (in AU), because the LUTs for path radiance and global flux are calculated for d=1 in ATCOR

ATCOR (ATmospheric CORrection) algorithm for atmosphere corrected reflectance estimation

ATCOR

What is needed?

• An accurate radiometric calibration

• An accurate estimate of the values of the LP and . o

T

0

102

cos})({

ETLDNccdR

o

P

RADIATIVE TRANSFER MODELS: used for modeling the transfer of electromagnetic energy through different layers of the atmosphere

PROBLEMS : 1. Atmosphere is not homogenous vertically nor horizontally 2. Wavelength dependent3. Viewing and illumination geometry dependence

INPUTS TO RADIATIVE TRANSFER MODELS: • Solar azimuth • Location of the scene • Wavelength (bands) • Ground elevation • Sensor view angle • Atmospheric transmittance• Atmospheric scattering

WITH ABOVE PARAMETERS, RADIATIVE TRANSFER MODELS YIELD PATH RADIANCE AND TRANSMITTANCE FOR ESTIMATING SURFACE REFLECTANCE

ATCOR: Estimation of Atmospheric transmittance and Atmospheric scattering


• Not realistically possible to estimate radiative transfer models for all variations in atmospheric conditions

• Therefore, radiative transfer models defined for standard atmospheric conditions, which include vertical profiling of: • air pressure, • air temperature, • O2, O3, N2, CO2 , O3 concentrations

• The standard atmospheres typically used are:• mid-latitude summer atmosphere• US standard atmosphere 1976• standard tropical atmosphere• desert tropical (arid) atmosphere• fall (autumn) atmosphere• mid-latitude winter• subarctic winter

Atmospheric scattering (Path radiance)

• Mainly due to:• Nitrogen • Oxygen • Carbon dioxide• Aerosols

• The optical properties of N2 and O2 are well-known; their concentration varies insignificantly over time and space. Measured values for different standard atmospheres are used.

• The concentration of CO2 varies slowly over time and space, and therefore the variability can be ignored. Measured values for different standard atmospheres are used.

• Aerosols……??? Will come back to aerosols


Atmospheric transmittance:

• Function of optical depth:

• δmolecular scattering mainly due to scattering by N2, O2, CO2 .• Predictable, see previous slide. Measured for standard atmospheres.

• δmolecular absorption mainly by O3, H2O and CO2, • their absorption behaviours well-known, predictable. • the concentration of O3 and CO2 can be assumed constant. Measured for standard atmospheres. • the concentration of H2O (water vapour) varies significantly… how to estimate…??

• δmolecular absorption due to aerosols ??? Will come back..

aerosolabsorptionMolecularscatteringMolecular

eT


• Aerosol type and concentration• Water vapour concentration

The unkown parameters …..


Water vapour concentrationMust have bands in one of the following bands:

• 1.05 – 1.21 μm• 0.87 – 1.02 μm• 0.77 – 0.87 μm

The band depth can be used to estimate the water vapor content (pixel wise)


Aerosol : nature and concentration

• Not critical if the visibility is high (>40 km)

• Difficult to estimate for every atmospheric condition, therefore standard types are used:• rural• urban• desert• maritime

• The amounts of aerosols measured for different visibility ranges


MODTRAN is a computer program designed to model atmospheric propagation of EM radiation (radiative transfer models) in the 0.2 to 100 um spectral range.

• ATCOR contains a catalogue (LUT) of atmospheric correction values compiled for different input values.

• These parameters are calculated using MODTRAN.

• Typical inputs values are:• sensor type (LANDSAT/ASTER/etc etc) • solar azimuth• sensor viewing angle• standard atmosphere in the image• visibility• aerosol type• average ground elevation

• The most recently released version of the code, MODTRAN5, provides a spectral resolution of 0.2 cm-1 using its 0.1 cm-1 band model algorithm.

MODTRAN


The catalogue (LUT) consists atmospheric correction functions for:1. Different standard atmospheres (altitude profile of pressure, air temperature, gases (O2, N2, CO2, O3) concentration)

• mid-latitude summer atmosphere• US standard atmosphere 1976• standard tropical atmosphere• desert tropical (arid) atmosphere• fall (autumn) atmosphere• mid-latitude winter• subarctic winter.

2. Different aerosol types: rural, urban, desert, maritime3. Different aerosol concentrations (aerosol optical depth) defined by the visibility. The range provided is 5-40 km, calculated

values are: 5, 7, 10, 15, 23, 40 km. Values for 4 and 80 km are obtained by linear extrapolation. The conditions range from hazy to very clear.

ATCOR-2 LUT derived using MODTRAN

4. Water vapour concentrations (calculated from absorption bands depths – optionally user defined)5. Different ground elevations ranging from 0 to 1 km (calculated values are for 0, 0.5, and 1km ASL; other values interpolated.)6. Solar zenith angles ranging from 0o - 70o in the steps of 10o

7. Different functions for each sensor and each band - the atmospheric correction functions depend on the spectral response of the sensor, thus there are different functions for each sensor and each band

8. Different sensor view angle

The above parameters can be specified by the user, or are read from the image header.For illustration - in ATCOR-2, the number of entries in the look-up tables for the six reflective bands of Landsat TM is about 9000, i.e. 12 x 7 x 6 x 3 x 6 = 9072, including 12 atmospheres, 7 solar zenith angles, 6 visibilities, 3 ground elevations, and 6 bands.

Measured atmospheric data can also be used to calculate new files of look-up tables for the catalogue.

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path

ETLDNccd

Ro

})*({ 102

After estimation of path radiance, global flux and atmospheric transmission, apply the following equation to derive surface reflectance

atmospheric effects and corrections

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