**3. Spectral irradiance on the ground**

The sun is the source of energy in passive remote sensing; solar radiation carries the information of the natural environment for its intrinsic properties (wavelength, polarization, phase shift). Knowledge of the spectral distribution of the radiation that reaches the high atmosphere is very important for various applications. (Chadin, 1988).The solar spectrum has been the subject of several measures on the ground, air and satellite

Assuming that the atmosphere is transparent, the solar spectrum E0λ(w.cm-2µm-1) reaching the soil does not undergo any change in its trajectory.

The spectral irradiance in the upper atmosphere depends on the latitude of the location (latitude=ϕ), declination of the axis of rotation of the earth (δ) and time (h)

The solar spectrum on the ground is given by the following equation (Ratto, 1986 ):

$$\mathbf{E}\_{\lambda} = \mathbf{E}\_{0\lambda} \begin{pmatrix} 1+\mathbf{f} \end{pmatrix} \cos \left(\boldsymbol{\theta}\_{\mathbf{z}}\right) \tag{1}$$

E0λ : is the solar spectrum outside Earth's atmosphere, λ: wavelength of emission of radiation, 1: Astronomical Unit (1UA= 1.496x 108 km), f: is the correction factor of distance sun-soil (this factor depends on the number of days and cos (θz) is the zenith angle).

In clear sky atmosphere, the concentration of gases and aerosols varies with the changing weather conditions and geographical position. Gases and aerosols absorb and scatter solar radiation on a selective basis throughout the optical path. Gases, principally ozone, carbon dioxide and water vapor are the bodies responsible for absorption of the solar spectrum. Air molecules and aerosols are the body responsible for the dissemination of solar radiation in all directions. (Prieur & Morel, 1975). The effects of absorption and scattering functions are presented by the transmittance according to Bouguer's law (Bouguer, 1953):

$$\mathbf{T}\_{\lambda} = \mathbf{I}\_{\lambda} \Big/ \mathbf{I}\_{0\lambda} \tag{2}$$

Iλ is the spectral radiation output and I0λ is the radiation spectral λ input.

Diffusion occurs during the interaction between the incident radiation and particles or large gas molecules in the atmosphere (water droplets, dust, smoke ...). Where the suspended particles are negligible compared to the wavelength, the phenomenon that occurs is Rayleigh scattering. (Fröhlich & Brusa, 1981**)**

The diffusion of a particle occurs independently of other particles. The radiation will be distributed in all directions, the forward scattered radiation is equal to the radiation scattered backward.

#### **3.1 Model description of irradiance**

This model is to calculate the solar spectral irradiance (irradiance) direct normal and horizontal diffuse to the conditions of a cloudy sky not. This code calculates a range of 0.3 and 4.0 microns with a pitch of 10 nm. This code introduces a number of parameters such as solar zenith angle, the angle of inclination, atmospheric turbulence, the amount of water vapor precipitated amount of ozone, pressure and albedo (Guyot & Fagu ,1992).

Monochromatic distribution of a direct solar beam can be computed as a function of a number of variables, including optical mass and a wide variety of atmospheric parametersfor exemple, water-vapor content, ozone layer thickness, and turbidity parameters.

In the ultraviolet and visible region, it is essentially ozone absorption, Rayleigh scattering, and aerosols that control attenuation of the direct beam. The transmittance by aerosols is minimum at the short wavelengths and increases slowly as the wavelength increases. (Morel & Gentili, 1993)

#### **3.2 Direct spectral irradiance on the ground**

The equation of the light arriving directly from the sun at ground level for a wavelength λ is as follows:

$$\mathbf{I}\_{\mathrm{d}\lambda} = \mathbf{H}\_{\mathrm{o}\lambda} \mathbf{D} \mathbf{T}\_{\mathrm{r}\lambda} \mathbf{T}\_{\mathrm{a}\lambda} \mathbf{T}\_{\mathrm{w}\lambda} \mathbf{T}\_{\mathrm{o}\lambda} \mathbf{T}\_{\mathrm{u}\lambda} \tag{3}$$

Where

196 Atmospheric Model Applications

In this research, we are interested in applying the model to simulate the radiative transfer through the atmosphere under realistic conditions for assessing the significance of the effects of the atmosphere and conditions on shooting satellite images. The main objective of this application is the analysis of satellite measurements, along with their variations atmospheric parameters. The spectral signature of water is used here to simulate the action

**2. Modelling the interaction of the solar spectrum with the atmosphere** 

An analytical model for simulating radiative transfer in water coupled with an atmospheric model can adequately simulate the signal of a body of water to the attitude of the satellite to analyze the effects of atmospheric parameters and shallow water. This model determines the scattered radiation by a body of water in the software simulation of satellite data *SDDS* (Bachari, 1997), its main function is the calculation of the spectral radiance reflected from the

The purpose of modeling is to understand how different components of the measurement system combine to make a measurement. The form and content of a model depends on their purpose. The model is constructed to describe and characterize the measurement system to understand the phenomena which he is registered and to predict their behavior under the effect of an external action or as a result of a partial modification of the system itself same. The model developed is to break the middle-ground atmosphere into subsets in interaction

The source irradiates the object and the latter reflects the radiation in all directions, some of this radiation is captured. The radiation received by a radiometer on board the satellite, is composed of two main terms: brightness caused by the surface in the field of vision sensor and a brightness that is not caused by the surface in the field of vision. The first term is useful information, it is due to the direct and indirect solar radiation. The second term, considered the noise is due to the light scattered by the atmosphere. (Gordon & Clark, 1981;

The sun is the source of energy in passive remote sensing; solar radiation carries the information of the natural environment for its intrinsic properties (wavelength, polarization, phase shift). Knowledge of the spectral distribution of the radiation that reaches the high atmosphere is very important for various applications. (Chadin, 1988).The solar spectrum

Assuming that the atmosphere is transparent, the solar spectrum E0λ(w.cm-2µm-1) reaching

The spectral irradiance in the upper atmosphere depends on the latitude of the location

Eλ = E0λ (1+f) cos (θz) (1)

has been the subject of several measures on the ground, air and satellite

(latitude=ϕ), declination of the axis of rotation of the earth (δ) and time (h)

The solar spectrum on the ground is given by the following equation (Ratto, 1986 ):

with the solar spectrum and the sensor onboard the satellite.

of the satellites. (Gordon, 1974)

sea water level sensor.

Becker & Rffy, 1990)

**3. Spectral irradiance on the ground** 

the soil does not undergo any change in its trajectory.

Solar Radiation Modeling and Simulation of Multispectral Satellite Data 199

Fig. 1. Solar illumination for an area generally horizontal

Fig. 2. The solar irradiance for an area generally vertical

inclined surface we take the angle TILT = 60.0°;

illumination decreases with increasing solar zenith angle.



Figure 4 shows that the maximum solar irradiance is with a solar zenith angle of 0 °, which explains when the sun is overhead (the sun is at noon) solar intensity is high and second





The direct irradiation on a horizontal surface is obtained from the equation multiplied by cos (Z), or Z is the solar zenith angle:

$$\mathbf{I}\_{\mathrm{d}\lambda} = \mathbf{I}\_{\mathrm{d}\lambda} \cos(\mathbf{Z}) \tag{4}$$

#### **Spectral diffuse irradiance**

a. The diffuse irradiance on a horizontal surface

The diffuse irradiance on a horizontal surface is based on three components:


The total *Isλ* diffuse illumination is given by the sum.

$$\mathbf{I}\_{\rm s\lambda} = \mathbf{I}\_{\rm r\lambda} + \mathbf{I}\_{\rm a\lambda} + \mathbf{I}\_{\rm g\lambda} \tag{5}$$

The diffuse illumination on an inclined surface

The global spectral irradiance on an inclined surface is represented by:

$$\begin{aligned} \mathbf{I}\_{\rm IT}(\mathbf{t}) &= \mathbf{I}\_{\rm d\%} \cos(\theta) + \mathbf{I}\_{\rm s\%} \left\langle \left[ \mathbf{I}\_{\rm d\%} \cos(\theta) / \left[ \mathbf{H}\_{\rm ok} \mathbf{D} \cos(\mathbf{Z}) \right] \right] \right\rangle \\ &+ 0.5 \left[ 1 + \cos(\mathbf{t}) \right] \left[ 1 - \mathbf{I}\_{\rm d\%} / \left( \mathbf{H}\_{\rm ok} \mathbf{D} \right) \right] \end{aligned} \tag{6}$$

where


The angle of inclination to a horizontal surface is 0 ° and 90 ° to a vertical surface. The global irradiance on a horizontal surface is given by:

$$\mathbf{I}\_{\rm T\lambda} = \mathbf{I}\_{\rm d\lambda} \cos(\mathbf{Z}) + \mathbf{I}\_{\rm s\lambda} \tag{7}$$

Figures 1, 2, 3 shows the specter of global illumination DTOT, diffuse illumination DIF and direct illumination DIR.

The input parameters are:


• *Ho<sup>λ</sup>* : represents the irradiance in the upper atmosphere of Earth-Sun distance an

• *Tr<sup>λ</sup> , Taλ , Twλ ,To<sup>λ</sup>* et *Tu<sup>λ</sup>* are respectively the functions of the transmittance of the atmosphere for a wavelength λ of molecular diffusion (Rayleigh), mitigation of aerosols,

The direct irradiation on a horizontal surface is obtained from the equation multiplied by

• Component that takes into account multiple reflections of light between the ground and

[ ] ( )

The angle of inclination to a horizontal surface is 0 ° and 90 ° to a vertical surface. The global

Figures 1, 2, 3 shows the specter of global illumination DTOT, diffuse illumination DIF and

++ −

I (t) I cos( ) I I cos( ) / H Dcos(Z)

{ [ ]}

d o

λ λ

d d I I cos(Z) λ λ = (4)

srag IIII λλλλ =++ (5)

Td s I I cos(Z) I λλ λ = + (7*)*

(6)

the absorption of water vapor, the absorption of ozone and gas absorption

The diffuse irradiance on a horizontal surface is based on three components:

The global spectral irradiance on an inclined surface is represented by:

T d sd o

= θ+ θ

• θ is the angle of incidence of direct beam on an inclined surface

 0.5 1 cos(t) 1 I / H D λ λ λλ λ

average wavelength λ.

cos (Z), or Z is the solar zenith angle:

**Spectral diffuse irradiance** 

air

where

• D is the correction factor for Earth-Sun distance.

a. The diffuse irradiance on a horizontal surface

The total *Isλ* diffuse illumination is given by the sum.

The diffuse illumination on an inclined surface

• t is the angle of the inclined surface

direct illumination DIR. The input parameters are: - Optical thickness = 0.51. - Turbulence ALPHA = 1.14.

irradiance on a horizontal surface is given by:


• Component of Rayleigh scattering *Ir<sup>λ</sup>* • Release component aerosol *Ia<sup>λ</sup>*

Fig. 1. Solar illumination for an area generally horizontal

Fig. 2. The solar irradiance for an area generally vertical


Figure 4 shows that the maximum solar irradiance is with a solar zenith angle of 0 °, which explains when the sun is overhead (the sun is at noon) solar intensity is high and second illumination decreases with increasing solar zenith angle.

Solar Radiation Modeling and Simulation of Multispectral Satellite Data 201

Fig. 5*.* Variation of solar Irradiance according to the optical thickness

Fig. 6. Variation of illumination depending on the water vapor precipitated.

In this work, we determine the physical quantity measured by the system of shooting (sensor) which is sunlight reflected by the soil-atmosphere averaged in some way in the spectral band considered the sensor. For this, we described the various factors affecting a

**4. Modeling the radiation reflected by the ground** 

satellite measurement.

Fig. 3. The solar irradiance for an area generally inclined

Fig. 4. Variation of solar irradiance depending on the angle of incidence*.* 

Figure 5 shows a small optical thickness results in an intense light while a high optical thickness shows a low light, in other words, unlike the light varies with the optical thickness. (Kaufmann, and Sendra , 1992).

Figure 6 shows the variation of water vapor only affect the light weakly, but it is very important as if we compare it with the influence of the number of days in the year of the illumination.

Fig. 3. The solar irradiance for an area generally inclined

Fig. 4. Variation of solar irradiance depending on the angle of incidence*.* 

thickness. (Kaufmann, and Sendra , 1992).

illumination.

Figure 5 shows a small optical thickness results in an intense light while a high optical thickness shows a low light, in other words, unlike the light varies with the optical

Figure 6 shows the variation of water vapor only affect the light weakly, but it is very important as if we compare it with the influence of the number of days in the year of the

Fig. 5*.* Variation of solar Irradiance according to the optical thickness

Fig. 6. Variation of illumination depending on the water vapor precipitated.

#### **4. Modeling the radiation reflected by the ground**

In this work, we determine the physical quantity measured by the system of shooting (sensor) which is sunlight reflected by the soil-atmosphere averaged in some way in the spectral band considered the sensor. For this, we described the various factors affecting a satellite measurement.

Solar Radiation Modeling and Simulation of Multispectral Satellite Data 203

• Variation in the average radiation in the area surrounding the pixel observed at all

It is therefore necessary to analyze different types of information in order to quantify and qualify. (Becker,1978). To do this, we should dissect the process of taking an image, estimate its multiple components and determine at what level the various categories of information

This model is followed by a detailed study of factors affecting the optical properties of sea water. To correctly interpret satellite data, we must solve the equation of radiative transfer soil-atmosphere. Solving the transfer equation is based on atmospheric models at several levels that require a considerable mass of meteorological data generally not available.

The first test is performed to explain the blue sky, was made by Lord Rayleigh that the assumptions of his theory are: the particles are small compared to the wavelength, the scattering particles and the medium does not contain free charges (not conductive), therefore, the dielectric constant of the particles is almost the same as that of the

In vertical viewing, then the reflectance is lower than when the sun is at its zenith . The set of simulated data depends on the reflectance and the spectral amplitude of the radiation that reaches the ground is maximum at the zenith, so the measure is more affected by radiation

The zenith angle determines the illumination received by the target surface and is involved in all elements of calculating the various transmittances and radiation. Radiation received, for all channels, decreases if the solar zenith angle tends to a horizontal position; it is maximum when the sun is at its zenith . The zenith angle is involved in all elements of calculating the various transmittances and radiation, it depends on the latitude, the

The information spectral radiometers are determined by the wavelengths recorded by the sensor. The width of each spectral band radiometer defined spectral resolution. We consider

Solar radiation travels through space as electromagnetic waves. In the case where the wave propagates in a medium refractive index and suddenly she meets any other medium characterized by a different index of refraction, part of the wave is then transmitted into the second medium and the other part is reflected in the first medium. The amplitude of the

Part of the global radiation reaching the ground is reflected to the sensor by the coefficient of reflectance. The major problem in determining the reflected radiation is the development of a model that generates all the soil properties affecting in a direct spectral signature (lighting condition, roughness, soil type,....) or indirect (color , salinity,

that the observation is made in a plane perpendicular to the direction of the grooves.

reflected wave depends on the nature of the medium, shape and lighting conditions.

can be determined follow atmospheric correction models . (Bukata et *al*.,1995)

• Change in weather conditions across an image.

times.

medium.

inclination of the sun and time.

humidity, etc.).

• Change of observation relative to the position of the sun.

**4.1 Simulation analysis of the reflectance of sea water** 

than because of the dependence of reflectance of the zenith angle.

Thus, after characterization data on the spectrum of electromagnetic radiation, reflection, emission and atmospheric transmission is determined and developed by the optical properties of the elements of natural surfaces, radiation reflected by the surface water and radiation captured by satellites. (Houma and *al*.,2004)

The methods used in atmospheric modeling can be divided into direct method and indirect method. Generally, direct methods are represented by the development of a model of interaction of the solar spectrum with the various elements that are in the path of solar radiation the sun-ground and ground sensor. The radiance Lsat captured by the satellite is the sum of the three luminances:


$$\mathbf{L}\_{\text{sat}} = \mathbf{L}\_{\text{a}} + \mathbf{L}\_{\text{sol}} + \mathbf{L}\_{\text{v}} \tag{8}$$

Either a pixel image coordinate (x, y) and a spectral band b, the radiation that excites the sensor λ K (x, y, b) (w.cm-2 µm-1 sr-1) according to Teillet (Teillet , 1986) is written as follows:

$$\mathbf{K\_{k}(x,y,b)} = \mathbf{C(x,y)} \cdot \mathbf{R\_{k}(x,y,b)} + \mathbf{H\_{k}(b)} + \Delta\_{\mathbf{b}}(x,y,b) \tag{9}$$

C(x,y) is a multiplicative constant that describes the form factor that is the orientation of the surface topography relative to the sun's position during the shooting; R(x, y, b) is the radiation reflected by the ground is proportional to the average reflectance of the pixel (x, y) in the spectral band b; Hλ (b) is the distribution of soil-atmosphere (noise) by considering the earth as a black body and Δλ (x, y, b) represents a residual variable that creates the effect of neighborhood.

R (x, y, b) is given by the following equation:

$$\mathbf{R\_{A}(x,y,b)} = \mathbf{S\_{A}(b)} \mathbf{T\_{A}(b)} \mathbf{G\_{A}(b)} \ \mathbf{p\_{A}(x,y)} \tag{10}$$

Sλ(b) : represents the gain factor of the system in the channel b (sensor sensitivity),

Tλ(b) is the atmospheric transmittance of the earth to the satellite in channel b,

Gλ(b) : is the global radiation and ρλ(x,y,b) : reflectance of the pixel (x, y) (assumed Lambertian) in the channel b.

Using a database of spectral signatures and spectral extinction coefficients to model parameters. A numerical code to track the signal in the solar sun-trip ground and ground sensor.

The energy quantity Rλ(x,y,b) is transformed into a numbered account, which includes all information about the Earth-atmosphere system, the geometric conditions of shooting and optical properties of the sensor.

It is obvious that the atmospheric absorption and scattering vary across an image due to three effects:

• Change in weather conditions across an image.

202 Atmospheric Model Applications

Thus, after characterization data on the spectrum of electromagnetic radiation, reflection, emission and atmospheric transmission is determined and developed by the optical properties of the elements of natural surfaces, radiation reflected by the surface water and

The methods used in atmospheric modeling can be divided into direct method and indirect method. Generally, direct methods are represented by the development of a model of interaction of the solar spectrum with the various elements that are in the path of solar radiation the sun-ground and ground sensor. The radiance Lsat captured by the satellite is

1. The luminance of the system from the ground - atmosphere considering the ground as a

3. Lv luminance reflected from nearby objects but observed in the direction of the ground

Either a pixel image coordinate (x, y) and a spectral band b, the radiation that excites the sensor λ K (x, y, b) (w.cm-2 µm-1 sr-1) according to Teillet (Teillet , 1986) is written as follows:

C(x,y) is a multiplicative constant that describes the form factor that is the orientation of the surface topography relative to the sun's position during the shooting; R(x, y, b) is the radiation reflected by the ground is proportional to the average reflectance of the pixel (x, y) in the spectral band b; Hλ (b) is the distribution of soil-atmosphere (noise) by considering the earth as a black body and Δλ (x, y, b) represents a residual variable that creates the effect of

Sλ(b) : represents the gain factor of the system in the channel b (sensor sensitivity),

Gλ(b) : is the global radiation and ρλ(x,y,b) : reflectance of the pixel (x, y) (assumed

Using a database of spectral signatures and spectral extinction coefficients to model parameters. A numerical code to track the signal in the solar sun-trip ground and ground

The energy quantity Rλ(x,y,b) is transformed into a numbered account, which includes all information about the Earth-atmosphere system, the geometric conditions of shooting and

It is obvious that the atmospheric absorption and scattering vary across an image due to

Tλ(b) is the atmospheric transmittance of the earth to the satellite in channel b,

**Lsat = La + Lsol +Lv** (8)

**K**λ**(x,y,b) = C(x,y) R**λ**(x,y, b) + H**λ**(b) +** Δλ**(x,y,b)** (9)

**R**λ**(x,y,b)=S**λ**(b)T**λ**(b)G**λ**(b)** ρλ**(x,y)** (10)

radiation captured by satellites. (Houma and *al*.,2004)

2. Lsol luminance reflected from the ground toward the sensor

the sum of the three luminances:

black body

neighborhood.

sensor.

three effects:

R (x, y, b) is given by the following equation:

Lambertian) in the channel b.

optical properties of the sensor.


It is therefore necessary to analyze different types of information in order to quantify and qualify. (Becker,1978). To do this, we should dissect the process of taking an image, estimate its multiple components and determine at what level the various categories of information can be determined follow atmospheric correction models . (Bukata et *al*.,1995)
