**6. Analysis of variation in luminance**

The physical quantity measured in the system shooting (sensor) is a solar radiation reflected by the soil-atmosphere averaged in some way in the spectral band considered the sensor. It depends on the angle of illumination and shooting. (Bachari et al., 1997)

Fig. 8. Simulation of the scattered radiation as SDDS

Solar Radiation Modeling and Simulation of Multispectral Satellite Data 209

The zenith angle of observation determines the length of the journey made by atmospheric radiation. The simulation results show that the radiation collected is small if the angle of observation tends to a horizontal position. The growth of the zenith angle of observation leads to an increase in air mass and a decrease in transmittance. The following figure shows the contrast of the luminance for different sensors. In the case of surface spectral signature weak as water, atmospheric noise becomes important to the reflected radiation if the angle of observation believed to a horizontal position. The atmospheric contribution increases, therefore the luminance level of the sensor increases. The brightness peaks at a zenith angle

of observation [60°, 70°] and then begins to decrease if θV differs from 70°.

Fig. 12. The effect of the zenith angle of observation on the luminance.

Fig. 11. The effect of solar zenith angle on luminance.

**6.2 Effect of the zenith angle of observation** 

Fig. 9. Simulation of the spectral irradiance of water, ozone and gas as SDDS

Fig. 10. Simulation of the spectral irradiance on the ground as SDDS.

#### **6.1 Effect of solar zenith angle**

The zenith angle is involved in all aspects of calculation of the various transmittances and radiation, it depends on the latitude, the inclination of the sun and time.

$$
\cos(\theta\_z) = \cos(\delta)\cos(\text{latitude})\cos(15(12\text{-heure})) + \sin(\text{latitude})\sin(\delta) \tag{22}
$$

The zenith angle determines the illumination received by the ground and involved in all aspects of calculation of the various transmittances and radiation. Radiation received, for all satellite channels, decreases if the solar zenith angle tends to a horizontal position, and is maximum when the sun is at its zenith (Figure 11). The following figure shows the contrast angle (zenith-sun) radiances:

Fig. 9. Simulation of the spectral irradiance of water, ozone and gas as SDDS

Fig. 10. Simulation of the spectral irradiance on the ground as SDDS.

radiation, it depends on the latitude, the inclination of the sun and time.

The zenith angle is involved in all aspects of calculation of the various transmittances and

 cos(θz) = cos(δ).cos(latitude).cos(15(12-heure)) + sin(latitude)sin(δ) (22) The zenith angle determines the illumination received by the ground and involved in all aspects of calculation of the various transmittances and radiation. Radiation received, for all satellite channels, decreases if the solar zenith angle tends to a horizontal position, and is maximum when the sun is at its zenith (Figure 11). The following figure shows the contrast

**6.1 Effect of solar zenith angle** 

angle (zenith-sun) radiances:

Fig. 11. The effect of solar zenith angle on luminance.

#### **6.2 Effect of the zenith angle of observation**

The zenith angle of observation determines the length of the journey made by atmospheric radiation. The simulation results show that the radiation collected is small if the angle of observation tends to a horizontal position. The growth of the zenith angle of observation leads to an increase in air mass and a decrease in transmittance. The following figure shows the contrast of the luminance for different sensors. In the case of surface spectral signature weak as water, atmospheric noise becomes important to the reflected radiation if the angle of observation believed to a horizontal position. The atmospheric contribution increases, therefore the luminance level of the sensor increases. The brightness peaks at a zenith angle of observation [60°, 70°] and then begins to decrease if θV differs from 70°.

Fig. 12. The effect of the zenith angle of observation on the luminance.

Solar Radiation Modeling and Simulation of Multispectral Satellite Data 211

Fig. 14. The effect of atmospheric turbidity parameter Fc on the radiance.

For the same conditions of image capture, simulation of the observed brightness is determined by the relationship between apparent brightness and simulated the account

For the three channels of the HRV sensor, radiometric conversion is given by the relations:

 CNXS1 = 1.23 LXS1 + 0.22 (24) CNXS2 = 1.24LXS2 - 0.08 (25) CNXS3 = 1.32 LXS3 -0.59. (26)

The same method was applied directly to the accounts of digital Landsat 2003 and Spot 2004. The images are processed using the software to process satellite images PCSATWIN

Fig. 15. SPOT XS1 image before and after radiometric correction.

with factors a1 and a0 are calibration coefficients.

corresponding digital images processed.

**Application to images**

developed by (Bachari et al, 1997)

#### **6.3 Effect of relative humidity**

The presence of water vapor in the atmosphere depends on the location and altitude above the ground. Analysis of simulated data shows the insensitivity of the channels XS1, XS2, TM1, TM2, TM3, MSS4 to increase or decrease of water vapor in the atmosphere.The transition from a dry to a humid atmosphere causes a slight decrease in the extent to channel XS3 and TM4. Constructors radiometers onboard satellites SPOT and LANDSAT have avoided the windows of absorption of radiation by water vapor.

The following figure shows the change in apparent radiance between the two extreme amounts of water vapor. (Figure 13)

The apparent radiance level of the system SPOT, LANDSAT is practically independent of the wet state of the atmosphere because the spectral bands used do not contain the total absorption window of radiation by water vapor.

Fig. 13. The effect of relative humidity on the radiance.

### **6.4 Effect of diffusion parameter Fc**

Mie scattering has a significant influence on the measured signal at the sensor described by the diffusion parameter Fc. The atmosphere absorbs in the field of short wavelength and becoming more transparent. The information is degraded in the channels depending on the diffusion parameter Fc. (Figure14). The following figure shows that for low surface reflectance as the case of water degradation in the channel becomes more comparable, especially for channels XS1 and MSS4.

#### **7. Correction of satellite images**

Each pixel of an image is a digital count from 0 to 255, which translates into a color using an editable pre-selected distribution in image processing. Generally the relationship between digital count and the luminance is linear:

$$K(\mathbf{x}, y) = \mathbf{a}\_1 \text{ . } \text{CN} + \mathbf{a}\_0 \tag{23}$$

Fig. 14. The effect of atmospheric turbidity parameter Fc on the radiance.

with factors a1 and a0 are calibration coefficients.

For the same conditions of image capture, simulation of the observed brightness is determined by the relationship between apparent brightness and simulated the account corresponding digital images processed.

For the three channels of the HRV sensor, radiometric conversion is given by the relations:

$$\text{CN}\_{\text{NSI}} = 1.23 \text{ L}\_{\text{NSI}} + 0.22 \tag{24}$$

$$\text{CN}\_{\text{NS2}} = 1.24 \text{L}\_{\text{NS2}} \text{ - 0.08} \tag{25}$$

$$\text{CN}\_{\text{MS3}} = 1.32 \text{ L}\_{\text{MS3}} \text{ -0.59.} \tag{26}$$

#### **Application to images**

210 Atmospheric Model Applications

The presence of water vapor in the atmosphere depends on the location and altitude above the ground. Analysis of simulated data shows the insensitivity of the channels XS1, XS2, TM1, TM2, TM3, MSS4 to increase or decrease of water vapor in the atmosphere.The transition from a dry to a humid atmosphere causes a slight decrease in the extent to channel XS3 and TM4. Constructors radiometers onboard satellites SPOT and LANDSAT

The following figure shows the change in apparent radiance between the two extreme

The apparent radiance level of the system SPOT, LANDSAT is practically independent of the wet state of the atmosphere because the spectral bands used do not contain the total

Mie scattering has a significant influence on the measured signal at the sensor described by the diffusion parameter Fc. The atmosphere absorbs in the field of short wavelength and becoming more transparent. The information is degraded in the channels depending on the diffusion parameter Fc. (Figure14). The following figure shows that for low surface reflectance as the case of water degradation in the channel becomes more comparable,

Each pixel of an image is a digital count from 0 to 255, which translates into a color using an editable pre-selected distribution in image processing. Generally the relationship between

1 0 *K(x,y)* = + a . CN a (23)

have avoided the windows of absorption of radiation by water vapor.

**6.3 Effect of relative humidity** 

amounts of water vapor. (Figure 13)

absorption window of radiation by water vapor.

Fig. 13. The effect of relative humidity on the radiance.

**6.4 Effect of diffusion parameter Fc** 

especially for channels XS1 and MSS4.

**7. Correction of satellite images** 

digital count and the luminance is linear:

The same method was applied directly to the accounts of digital Landsat 2003 and Spot 2004. The images are processed using the software to process satellite images PCSATWIN developed by (Bachari et al, 1997)

Fig. 15. SPOT XS1 image before and after radiometric correction.

Solar Radiation Modeling and Simulation of Multispectral Satellite Data 213

**Image CNmin CNmax CNmax- CNmin Ecart-type (**σ**) Moyenne (m) V=(**σ**/m)\*100**  XS1 Brute 38 254 216 18,23 65,10 28 XS1 Corrigée 29 255 226 24,99 38,76 64 XS2 Brute 25 235 210 21,04 55,26 38 XS2 Corrigée 11 255 244 32,80 58,58 56 XS3 Brute 17 213 206 26,40 57,85 46 XS3 Corrigée 14 255 241 37,28 67,39 55

graph defining the linear relationship between the reflectance calibration and account for two-channel digital SPOT XS1 and XS2 for images corrected and uncorrected images

0 50 100 150 200 250 300

C o m p te N u m é r iq u e

Fig. 17. The digital count –reflectance at ground level

Table 2. Statistical data of radiometric channels SPOT HRV.

1 ,4 xs 1 n c

 xs 1 c o r xs 2 n c xs 2 c o r

Fig. 18. Linear calibration reflectance before and after atmospheric correction.

(Figure18).

R é fle c ta n c e

0 ,0

0 ,2

0 ,4

0 ,6

0 ,8

1 ,0

1 ,2

Fig. 16. Landsat TM1 image before and after radiometric correction.

#### **Calculation of the reflectance**

The luminance is happening to global satellite is expressed by the relation:

$$L = a\overline{\rho} + b \,. \tag{27}$$

With ρλ is the reflectance at the sea surface, E is the total illumination received by the surface. The average reflectance is connected to the luminance by the following equation:

$$
\overline{\mathfrak{p}} = \mathbf{a} \, \mathbf{C} \mathbf{N} + \mathbf{b} \, \tag{28}
$$

The conversion factors obtained by modeling of radiation on SPOT satellite channels (XS1, XS2, XS3 and) and Landsat (TM1, TM2, TM3 and TM4) are given in the table below: (Bachari,2006)


Table 1. Conversion factors accounts simulated digital reflectance.

#### **Quality of radiometric corrections**

According to the criterion Rouquet, we can estimate the quality of the correction by comparing the properties of the raw images and corrected. (Morel & Prieur, 1977) For a given image, the atmospheric effect is minimum if the contrast and the ratio of standard deviation is the average maximum, this quantitative criterion is also applied systematically for the selection of good quality data and is also a primary method of atmospheric correction, which tends to minimize atmospheric effects.

There is also a primary method of atmospheric correction, which tends to minimize atmospheric effects. The properties of the images are combined and corrected in the following table ( Bachari,1999)

For a simple analysis of the results expressed in Table 2, we note that the criterion used is justified for the corrected images. The application of atmospheric corrections is shown in the

With ρλ is the reflectance at the sea surface, E is the total illumination received by the surface. The average reflectance is connected to the luminance by the following equation:

The conversion factors obtained by modeling of radiation on SPOT satellite channels (XS1, XS2, XS3 and) and Landsat (TM1, TM2, TM3 and TM4) are given in the table below:

**Channel XS1 XS 2 XS 3 TM1 TM2 TM3 TM4 a** 0. 0024 0,0025 0,0031 0,0017 0,0033 0,0026 0,0036 **b** − 0,05 −0,0433 −0,0217 − 0,099 − 0,0723 − 0,0416 − 0,0295

According to the criterion Rouquet, we can estimate the quality of the correction by comparing the properties of the raw images and corrected. (Morel & Prieur, 1977) For a given image, the atmospheric effect is minimum if the contrast and the ratio of standard deviation is the average maximum, this quantitative criterion is also applied systematically for the selection of good quality data and is also a primary method of atmospheric

There is also a primary method of atmospheric correction, which tends to minimize atmospheric effects. The properties of the images are combined and corrected in the

For a simple analysis of the results expressed in Table 2, we note that the criterion used is justified for the corrected images. The application of atmospheric corrections is shown in the

*L = a ρ+ b* . (27)

ρ a CN b = + (28)

Fig. 16. Landsat TM1 image before and after radiometric correction.

Table 1. Conversion factors accounts simulated digital reflectance.

correction, which tends to minimize atmospheric effects.

The luminance is happening to global satellite is expressed by the relation:

**Calculation of the reflectance** 

**Quality of radiometric corrections**

following table ( Bachari,1999)

(Bachari,2006)

Fig. 17. The digital count –reflectance at ground level


Table 2. Statistical data of radiometric channels SPOT HRV.

graph defining the linear relationship between the reflectance calibration and account for two-channel digital SPOT XS1 and XS2 for images corrected and uncorrected images (Figure18).

Fig. 18. Linear calibration reflectance before and after atmospheric correction.

Solar Radiation Modeling and Simulation of Multispectral Satellite Data 215

Corrected images and spectra of radiation have a greater spread and therefore a high

XS BRUTE

Fig. 22. Coefficient of variation of the three images corrected for atmospheric effects.

123

Fig. 23. Radiometric correction in the SPOTXS1 channel of the bay of Algiers.

Fig. 24. Radiometric correction in the SPOTXS2 channel of the bay of Algiers.

contrast, this justifies the first condition of Rouquet.

This simple method of correction amounts to replacing the linear calibration another linear relationship applied to both SPOT images, this new relationship calibration results to correct the measured reflectances.

Fig. 19. XS1 image of the Bay of Oran

Fig. 20. XS1 corrected image of the Bay of Oran

The statistical properties of the corrected images are presented in the following histograms:

Fig. 21. Histogram spread between raw images and images corrected SPOT.

This simple method of correction amounts to replacing the linear calibration another linear relationship applied to both SPOT images, this new relationship calibration results to correct

The statistical properties of the corrected images are presented in the following histograms:

123

Fig. 21. Histogram spread between raw images and images corrected SPOT.

XS BRUTE

the measured reflectances.

 Fig. 19. XS1 image of the Bay of Oran

Fig. 20. XS1 corrected image of the Bay of Oran

Corrected images and spectra of radiation have a greater spread and therefore a high contrast, this justifies the first condition of Rouquet.

Fig. 22. Coefficient of variation of the three images corrected for atmospheric effects.

Fig. 23. Radiometric correction in the SPOTXS1 channel of the bay of Algiers.

Fig. 24. Radiometric correction in the SPOTXS2 channel of the bay of Algiers.

Solar Radiation Modeling and Simulation of Multispectral Satellite Data 217

with Ss<sup>λ</sup> a specular reflection at the surface, Sf<sup>λ</sup> is a reflectance of the bottom in shallow

e s s0 a z v

with ρλ a reflectance of the sea water, Ra, a reflectance of the bottom, k, is attenuation coefficient, z, a depth, ω0 albedo of diffusion of water molecules, θz a zenith angle and θv a

> 0 5 10 15 20 25 30 35 **Profondeur (m)**

> > TM1 TM2 TM3 TM4

0 510 15 20 25 30 35 **Profondeur (m)**

= ρ+ ρω − − − − ϑ+ ϑ

ρ ρ

1 1 S G G . 1 1 R exp( kz cos cos

s s

( )

XS1 XS2 XS3 (31)

waters, Sdλ a component owed to the diffuse reflection by volume water.

s a z v

G 1 R exp kz(cos cos )

+ −ρ − ϑ + ϑ

Fig. 26. A variation a luminance's of a SPOT XS with a depth

Fig. 27. A variation a luminance's of a LANDSAT TM with a depth.

( )

λ

viewer angle of the sensor.

0,00

0

10

20

30

40

**LUminance W m**

50

60

70

10,00

20,00

30,00

40,00

**Luminance W m**

50,00

60,00

70,00

λλ λ

Fig. 25. Radiometric correction in the SPOT XS3 channel of the bay of Algiers.

In the histogram of the coefficient of variation we wish to point out that the first channel has a high coefficient corrected this can be explained as the effect of correction is more experienced in this channel than in the other two channels. In the third channel (NIR), Mie scattering and Rayleigh are less experienced.

Images are acquired by satellite sensors (HRV pour SPOT 2) (B1 (green: 0.50 – 0.59 microns), B2 (red: 0.61 – 0.68 microns), and B3 (near infrared: 0.78 – 0.89 microns).
