80.

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Page 17

(1.6)

Consider a sensor that is receiving the reflectance from the ground target. The reflectance is generated by two main sources: one is the contribution of the total solar radiation reflected by the ground target and directly transmitted from the surface to the sensor, while the other is the contribution from the target neighbourhood, which is scattered into the field of view of the sensor. The reflectance received by the sensor can thus expressed by:

(1.7)

In this equation, θ_v is the sensor view zenith angle, and Equation (1.4) can be again applied to express T(θ_v) as:

(1.8)

The sensor also receives a fraction of the solar radiation that has been scattered out of the downward solar beam into the sensor’s field of view without interaction with the ground target, as shown in Figure 1.8b. This component is the atmospheric reflectance, denoted by the function ρ_a(θ_s,θ_v, Φ), where Φ is the relative azimuth between the Sun and the sensor. Therefore, the apparent reflectance ρ* at the sensor is:

(1.9)

Equation (1.9) is a linear equation which specifies the relationship between the apparent reflectance ρ* and the surface reflectance ρ_s. The term T(θ_s)·T(θ_v) is the total atmospheric transmittance along the Sun-target-sensor path.

A second atmospheric interaction should be considered, namely, the process of absorption. In the solar (optical) spectrum, atmospheric gaseous absorption is principally due to the presence of ozone (O₃), oxygen (O₂), water vapour (H₂O) and carbon dioxide (CO₂). Both O₂ and CO₂ are uniformly mixed in the atmosphere and are constant in terms of their concentrations, whereas H₂O and O₃ concentrations vary with time and geographical location. If T_g(θ_s, θ_v) denotes atmospheric gas transmittance after absorption, then Equation (1.9) can be modified to give:

(1.10)

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