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

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 medium.

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

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 inclination of the sun and time.

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

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

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, humidity, etc.).

Solar Radiation Modeling and Simulation of Multispectral Satellite Data 205

e atm o z <sup>a</sup> I ' I .cos L d

Based on this physical model, we developed a simulation system of satellite data to correct

A library of spectral signatures is introduced, it covers the main ground objects that have a reflectance in the bands of the electromagnetic spectrum. The combination of spectral signatures and different radiances allows us to calculate the spectral radiance reflected from the surfaces. The simulation results depend on the choice of input parameters. The software allows to show the influence of the effects of various parameters and geometric characteristics of the structures on the signal reaching the sensors onboard the satellite

To highlight the effect of a given parameter on the satellite measurement, are assigned fixed

The second part is from satellite SPOT, LANDSAT and IRS1C, applying the method of covariance matrix (a method that can provide a correction locally specific in the sense that it relates to the pixels of a given region of the image), one can estimate the atmospheric noise through a program to input data images from different channels and outputs the atmospheric noise of these channels.The physical quantity measured by the shooting system (sensor) is a solar radiation reflected by the soil-atmosphere averaged in some way in the spectral band considered the sensor. It depends on angle of illumination and shooting.

To determine the different radiation received at the satellite, the data input parameters are

Atmospheric correction is a major issue in visible or near-infrared remote sensing because the presence of the atmosphere always influences the radiation from the ground to the

As introduced before, the atmosphere has severe effects on the visible and near-infrared

**First**, it modifies the spectral and spatial distribution of the radiation incident on the surface.

**Third**, atmospheric scattered radiance, called path radiance, is added to the transmitted

data for all variables in the case of a clear sky and for geometrically well defined.

= + <sup>ρ</sup> δ λ π π (17)

τ ϑ

λ λ λ λ λ

2

λ

1

λ

with : Lλ : Radiation calculated in sea water for the canal λ.

Δλ : Spectral band of the channel.

δλ : Sensitivity of the channel.

**5. Simulation of satellite data for SDDS** 

the scattered radiation of atmospheric effects.

astronomical, geographical and atmospheric.

**Second**, radiance being reflected is attenuated.

**5.1 Atmospheric correction of remotely sensed data** 

SPOT, LANDSAT and IRS1C.

sensor.

radiance.

radiance.

#### **4.2 Total radiation reaching the satellite**

The luminance level of the satellite is the sum of the intrinsic brightness of the atmosphere and the luminance of the target which represents the sea water in our case. The radiation recorded at the satellite is given by the relation

$$\mathbf{B} = \begin{pmatrix} 1/\pi \end{pmatrix} \left[ \left( \mathbf{C}(\mathbf{x}, \mathbf{y}) \mathbf{T}\_k(\mathbf{b}) \mathbf{G}\_k(\mathbf{b}) \mathbf{p}\_k(\mathbf{x}, \mathbf{y}) (\mathbf{1} \cdot \mathbf{s} \mathbf{p}\_k(\mathbf{x}, \mathbf{y})) + \mathbf{H}\_k(\mathbf{b}) \right) \mathbf{S}\_k(\mathbf{b}) \mathbf{d} \lambda \right] \mathbf{S}\_k(\mathbf{b}) \, d\lambda \tag{11}$$

(1/π) is a normalization factor, Tλ(θv) transmittance of direct radiation toward the sensor, s : spherical albedo of the atmosphere et S(λ)sensitivity function optical sensor (Sturm, 1980).

The sensor has a spectral response δλ ,the recorded signal at the sensor is the luminance:

$$\mathbf{L} = \underset{\mathbf{0}}{\overset{\circ}{\mathrm{d}}} \left( \frac{\mathbf{I}\_{\lambda} \mathbf{\rho}\_{\lambda}}{\pi} \mathbf{T}\_{\mathrm{atm}} + \frac{\mathbf{I}\_{0\lambda} \cos \theta\_{\mathbf{z}}}{\pi} \mathbf{\rho}\_{\mathrm{a}\lambda} \right) \boldsymbol{\mathfrak{S}}\_{\lambda} \, \mathrm{d}\lambda \tag{12}$$

The luminance level of the satellite is the sum of the intrinsic brightness of the atmosphere and the luminance of the target which represents the sea water in our case. (Deschamps et al., 1983)

The radiation reflected from the water surface to the satellite passes through the atmosphere in a direct way with an angle θv and undergoes attenuation before being captured by the satellite.

$$\mathbf{G}\_{\lambda(\text{sat})} = \mathbf{I}\_{\text{e}\lambda}.\mathbf{\mathcal{T}}\_{\lambda} \tag{13}$$

eI <sup>λ</sup> : radiation reflected from the surface of the water; ' <sup>λ</sup> τ : total spectral transmittance

The amount of energy that reaches the satellite sensor is the sum of that from the ground and scattered by the atmosphere. The radiation emitted by the sea water that reaches the sensor is:

$$\mathbf{R}\_{\text{(sol}-\text{atm})} = \left[\mathbf{I}\_{\text{e}\lambda} \left(\mathbf{\pi}\_{\lambda}^{\prime} + \mathbf{\pi}\_{\text{da}\lambda}^{\prime} + \mathbf{\pi}\_{\text{dr}\lambda}^{\prime}\right)\right] / \pi \tag{14}$$

The radiation scattered by the atmosphere:

$$\mathbf{R}\_{\text{(atm-sat)}} = \frac{\mathbf{I}\_{\text{o}\lambda.} \cos \vartheta\_x}{\pi} \mathbf{\rho}\_{\text{a}\lambda} \tag{15}$$

Radiation reaching the satellite is composed of spectral global radiation reflected from the sea water passing through the atmosphere R(sol-atm)) and part of the radiation scattered by the atmosphere R(atm-sat) . (Bricaud ,1988)

So the radiation that reaches the sensor is expressed:

$$\mathbf{R}\_{\lambda} = \mathbf{R}\_{\text{(sol-atm)}} + \mathbf{R}\_{\text{(atm-sat)}} \tag{16}$$

The signal of sea water recorded at the sensor is:

$$\mathcal{L}\_{\lambda} = \bigwedge\_{\lambda\_1}^{\lambda\_2} \left( \frac{\mathbf{I}\_{\rm e\lambda} \mathbf{t}\_{\rm atm}^\dagger}{\pi} + \frac{\mathbf{I}\_{\rm c\lambda} \cdot \cos \theta\_x}{\pi} \rho\_{\rm a\lambda} \right) \mathfrak{S}\_{\lambda} \mathbf{d}\lambda \tag{17}$$

with : Lλ : Radiation calculated in sea water for the canal λ.

Δλ : Spectral band of the channel.

δλ : Sensitivity of the channel.

204 Atmospheric Model Applications

The luminance level of the satellite is the sum of the intrinsic brightness of the atmosphere and the luminance of the target which represents the sea water in our case. The radiation

 B= (1/π) [( C(x,y)Tλ(b)Gλ(b)ρλ(x,y)(1-sρλ(x,y))+Hλ(b))Sλ(b)dλ/ Sλ(b) dλ (11) (1/π) is a normalization factor, Tλ(θv) transmittance of direct radiation toward the sensor, s : spherical albedo of the atmosphere et S(λ)sensitivity function optical sensor (Sturm,

0 z atm <sup>a</sup>

λ λ

π π (12)

G I .' λ( ) sat = τ <sup>e</sup>λ λ (13)

(14)

RR R <sup>λ</sup> ( )( ) sol atm atm sat − − = + (16)

<sup>λ</sup> τ : total spectral transmittance

(15)

I I cos L T d

ρ θ = + <sup>ρ</sup> δ λ

The luminance level of the satellite is the sum of the intrinsic brightness of the atmosphere and the luminance of the target which represents the sea water in our case. (Deschamps et

The radiation reflected from the water surface to the satellite passes through the atmosphere in a direct way with an angle θv and undergoes attenuation before being captured by the

The amount of energy that reaches the satellite sensor is the sum of that from the ground and scattered by the atmosphere. The radiation emitted by the sea water that reaches the

( ) R I'' ' / sol atm <sup>−</sup> <sup>e</sup>λλ λ λ ( ) da dr = τ +τ +τ π

( ) o z atm sat a I .cos <sup>R</sup> <sup>λ</sup>

Radiation reaching the satellite is composed of spectral global radiation reflected from the sea water passing through the atmosphere R(sol-atm)) and part of the radiation scattered by

− λ <sup>ϑ</sup> <sup>=</sup> <sup>ρ</sup> π

The sensor has a spectral response δλ ,the recorded signal at the sensor is the luminance:

λλ λ

**4.2 Total radiation reaching the satellite** 

recorded at the satellite is given by the relation

0

eI <sup>λ</sup> : radiation reflected from the surface of the water; '

The radiation scattered by the atmosphere:

the atmosphere R(atm-sat) . (Bricaud ,1988)

So the radiation that reaches the sensor is expressed:

The signal of sea water recorded at the sensor is:

∞

1980).

al., 1983)

satellite.

sensor is:
