CHAPTER 5CHAPTER 5

Atmospheric InfluenceAtmospheric Influenceand Radiometric Correctionand Radiometric Correction

PRE-PROCESSINGPRE-PROCESSING

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

Ideal situation:

- sun and sensorabove observed pixel,

- flat terrain,- no atmosphere.

Ideal situation:

- sun and sensorabove observed pixel,

- flat terrain,- no atmosphere.

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

Ideal situation:

- sun and sensorabove observed pixel,

- flat terrain,- no atmosphere.

Ideal situation:

- sun and sensorabove observed pixel,

- flat terrain,- no atmosphere.

E0 = incident irradiance

Er = reflected irradiance

ρ = reflectivity (caracterizes pixel class)

L0 = illuminance

(recorded at sensor)

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

Ideal situation:

- sun and sensorabove observed pixel,

- flat terrain,- no atmosphere.

Ideal situation:

- sun and sensorabove observed pixel,

- flat terrain,- no atmosphere.

E0 = incident irradiance

Er = reflected irradiance

ρ = reflectivity (caracterizes pixel class)

L0 = illuminance

(recorded at sensor)

π = solid angle of upper half spacewhere Er is diffused

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

Influence of atmosphere:

- Incident irradiance E0 reduced

by a factor T0,

- reflected illuminance L0 reduced

by a factor T0.

Influence of atmosphere:

- Incident irradiance E0 reduced

by a factor T0,

- reflected illuminance L0 reduced

by a factor T0.

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

Influence of atmosphere:

- Incident irradiance E0 reduced

by a factor T0,

- reflected illuminance L0 reduced

by a factor T0.

Influence of atmosphere:

- Incident irradiance E0 reduced

by a factor T0,

- reflected illuminance L0 reduced

by a factor T0.

0 0

0 00 0

,

S

E ρT E

ρT EEL T T

π π

=

= =

LS = illuminance

(recorded at sensor)

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

- sun at zenith angle θover observed pixel,

- sensor at zenith angle over observed pixel.

- sun at zenith angle θover observed pixel,

- sensor at zenith angle over observed pixel.

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

- sun at zenith angle θover observed pixel,

- sensor at zenith angle over observed pixel.

- sun at zenith angle θover observed pixel,

- sensor at zenith angle over observed pixel.

E = incident irradiance reducedby a factor Tθ > Τ0

(passing thicker layer) and by a factor cosθ(spread over larger area)

LT = illuminance

(recorded at sensor)reduced by a factor T > T0

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

- sun at zenith angle θover observed pixel,

- sensor at zenith angle over observed pixel.

- sun at zenith angle θover observed pixel,

- sensor at zenith angle over observed pixel.

E = incident irradiance reducedby a factor Tθ > Τ0

(passing thicker layer) and by a factor cosθ(spread over larger area)

LT = illuminance

(recorded at sensor)reduced by a factor T > T0

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

- sun at zenith angle θover observed pixel,

- sensor at zenith angle over observed pixel.

- sun at zenith angle θover observed pixel,

- sensor at zenith angle over observed pixel.

E = incident irradiance reducedby a factor Tθ > Τ0

(passing thicker layer) and by a factor cosθ(spread over larger area)

LT = illuminance

(recorded at sensor)reduced by a factor T > T0

0( )cosθE T E θ=0( )cosθ

T φ φ

ρ T E θρEL T T

π π= =

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

Additional incident irradiance EDdiffused from atmosphere(origin: sun and other earth pixels)

Additional incident irradiance EDdiffused from atmosphere(origin: sun and other earth pixels)

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

Additional incident irradiance EDdiffused from atmosphere(origin: sun and other earth pixels)

Additional incident irradiance EDdiffused from atmosphere(origin: sun and other earth pixels)

EG = incident irradiance

LT = illuminance

(recorded at sensor)

0cosG θ DE θT E E= +

(cos )

GT φ

θ G Dφ

ρEL T

π

ρ θT E ET

π

= =

+=

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

Additional illuminance LPdiffused from atmosphere(origin:

sun and other earth pixels)

Additional illuminance LPdiffused from atmosphere(origin:

sun and other earth pixels)

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

Additional illuminance LPdiffused from atmosphere(origin:

sun and other earth pixels)

Additional illuminance LPdiffused from atmosphere(origin:

sun and other earth pixels)

LS = illuminance

(recorded at sensor)

S φ T PL T L L= +

A. Dermanis

Atmospheric InfluenceAtmospheric Influence

Final situation:

E0 = incident irradiance from sun

Tθ = atmospheric absorbance on

incident irradiancecosθ = reduction factor for pixel

inclined to incident radiation ED = irradiance diffused from

atmosphereρ = pixel reflectanceπ = solid angle of

upper half spaceTφ = atmospheric absorbance on

reflected illuminanceLP = illuminance diffused from

atmosphere

Final situation:

E0 = incident irradiance from sun

Tθ = atmospheric absorbance on

incident irradiancecosθ = reduction factor for pixel

inclined to incident radiation ED = irradiance diffused from

atmosphereρ = pixel reflectanceπ = solid angle of

upper half spaceTφ = atmospheric absorbance on

reflected illuminanceLP = illuminance diffused from

atmosphere

A. Dermanis

00(cos ) cosS φ θ D P φ θ φ D P

Eρ ρL T θT E E L T θT ρ T E L

π π πé ùé ù= + + = + +ë û ê úë û

Radiometric CorectionRadiometric Corection

illuminance arriving at sensor:

A. Dermanis

00(cos ) cosS φ θ D P φ θ φ D P

Eρ ρL T θT E E L T θT ρ T E L

π π πé ùé ù= + + = + +ë û ê úë û

Radiometric CorectionRadiometric Corection

instead of ideal: 00

EL ρ

π=

illuminance arriving at sensor:

0SL A L B= +

( , , ) cosφ θA A θφ T θT= =a

( , , ) φ D Pρ

B B φ ρ T E Lπ

= = +aa = atmospheric condition parameters

A. Dermanis

00(cos ) cosS φ θ D P φ θ φ D P

Eρ ρL T θT E E L T θT ρ T E L

π π πé ùé ù= + + = + +ë û ê úë û

Radiometric CorectionRadiometric Corection

instead of ideal: 00

EL ρ

π=

illuminance arriving at sensor:

0SL A L B= +

( , , ) cosφ θA A θφ T θT= =a

( , , ) φ D Pρ

B B φ ρ T E Lπ

= = +a

recorded at sensor: Sx kL C= +

k0, C0 = nominal sensor parametersinstead of ideal: 0 0 0 0x k L C= +

a = atmospheric condition parameters

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00(cos ) cosS φ θ D P φ θ φ D P

Eρ ρL T θT E E L T θT ρ T E L

π π πé ùé ù= + + = + +ë û ê úë û

Radiometric CorectionRadiometric Corection

instead of ideal: 00

EL ρ

π=

illuminance arriving at sensor:

0SL A L B= +

( , , ) cosφ θA A θφ T θT= =a

( , , ) φ D Pρ

B B φ ρ T E Lπ

= = +a

recorded at sensor: Sx kL C= +

k0, C0 = nominal sensor parametersinstead of ideal: 0 0 0 0x k L C= +

Radiometric correction: Recovery of x0 from x

a = atmospheric condition parameters

A. Dermanis

Radiometric CorrectionRadiometric Correction

(a) Sensor Calibration: Computation of k and C

(b) Radiometric correction for sensor instability

(c) Determination of atmospheric influence parameters

(d) Radiometric correction for atmospheric influence

0SL B

LA-

= 0 0 0 0x k L C= +

Sx k

LC-

=

A. Dermanis

(a) Sensor Calibration: Computation of k and C

(b) Radiometric correction for sensor instability

(c) Determination of atmospheric influence parameters

Sx k

LC-

=

θ (flat terrain) = from astronomic ephemeris(replaced by ω for inclined terrain)

Radiometric CorrectionRadiometric Correction

A. Dermanis

(a) Sensor Calibration: Computation of k and C

(b) Radiometric correction for sensor instability

(c) Determination of atmospheric influence parameters

Sx k

LC-

=

θ (flat terrain) = from astronomic ephemeris(replaced by ω for inclined terrain)

φ = from satellite orbit

Radiometric CorrectionRadiometric Correction

A. Dermanis

(a) Sensor Calibration: Computation of k and C

(b) Radiometric correction for sensor instability

(c) Determination of atmospheric influence parameters

Sx k

LC-

=

θ (flat terrain) = from astronomic ephemeris(replaced by ω for inclined terrain)

φ = from satellite orbit

Tθ, Τφ = from atmospheric pressure, temperature, humidity

Radiometric CorrectionRadiometric Correction

A. Dermanis

(a) Sensor Calibration: Computation of k and C

(b) Radiometric correction for sensor instability

(c) Determination of atmospheric influence parameters

Sx k

LC-

=

θ (flat terrain) = from astronomic ephemeris(replaced by ω for inclined terrain)

φ = from satellite orbit

Tθ, Τφ = from atmospheric pressure, temperature, humidity

ED, LP = from atmospheric conditions related to scattering processes

(extremely difficult to access!)

Radiometric CorrectionRadiometric Correction

A. Dermanis

(a) Sensor Calibration: Computation of k and C

(b) Radiometric correction for sensor instability

(c) Determination of atmospheric influence parameters

Sx k

LC-

=

( , , ) cosφ θA A θφ T θT= =a ( , , ) φ D Pρ

B B φ ρ T E Lπ

= = +a

θ (flat terrain) = from astronomic ephemeris(replaced by ω for inclined terrain)

φ = from satellite orbit

Tθ, Τφ = from atmospheric pressure, temperature, humidity

ED, LP = from atmospheric conditions related to scattering processes

(extremely difficult to access!)

computation of:

Radiometric CorrectionRadiometric Correction

A. Dermanis

unknown !

(a) Sensor Calibration: Computation of k and C

(b) Radiometric correction for sensor instability

(c) Determination of atmospheric influence parameters

Sx k

LC-

=

( , , ) cosφ θA A θφ T θT= =a ( , , ) φ D Pρ

B B φ ρ T E Lπ

= = +a

θ (flat terrain) = from astronomic ephemeris(replaced by ω for inclined terrain)

φ = from satellite orbit

Tθ, Τφ = from atmospheric pressure, temperature, humidity

ED, LP = from atmospheric conditions related to scattering processes

(extremely difficult to access!)

computation of:

Radiometric CorrectionRadiometric Correction

A. Dermanis

unknown !

(a) Sensor Calibration: Computation of k and C

(b) Radiometric correction for sensor instability

(c) Determination of atmospheric influence parameters

(d) Radiometric correction for atmospheric influence

0SL B

LA-

= 0 0 0 0x k L C= +

Sx k

LC-

=

( , , ) cosφ θA A θφ T θT= =a ( , , ) φ D Pρ

B B φ ρ T E Lπ

= = +a

θ (flat terrain) = from astronomic ephemeris(replaced by ω for inclined terrain)

φ = from satellite orbit

Tθ, Τφ = from atmospheric pressure, temperature, humidity

ED, LP = from atmospheric conditions related to scattering processes

(extremely difficult to access!)

computation of:

Radiometric CorrectionRadiometric Correction

A. Dermanis