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**Atmospheric effect in the solar spectrum**

Vermote et al. University of Maryland/ Dept of Geography and NASA/GSFC Code 614.5

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Solar Energy Paths

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**atmospheric contribution**

direct + direct diffuse + direct direct + diffuse multiple scattering

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**Solar (reflective) spectral domain**

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**Observation Geometry Solar zenith angle View zenith angle**

Relative azimuth angle

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Solution of the Radiative Transfer in the reflective domain for non absorbing atmosphere and lambertian ground Ground reflectance (= albedo for lambertian) Atmospheric reflectance Atmospheric Transmissions Apparent reflectance at satellite level Atmosphere spherical albedo

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**Perfect Lambertian Reflector**

Radiance of the Perfect Lambertian Reflector Es Isotropic radiation

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**Simple Radiative Transfer Equation**

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SRTE (cont.) Absorbing ground

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SRTE (cont.) Ei Et

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SRTE (cont.)

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SRTE (cont.) v E0 Er 40

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**SRTE 1 interaction (cont.)**

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SRTE 2 interactions

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**SRTE Multiple Interactions**

groundSatm < 1 so when n->∞ then (groundSatm)n ->0 Therefore

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**STRE for non absorbing atmosphere and lambertian ground**

Ground reflectance (= albedo for lambertian) Atmospheric reflectance Atmospheric Transmissions Apparent reflectance at satellite level Atmosphere spherical albedo

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**The composition of the atmosphere**

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**Gaseous Absorption (H2O)**

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**Modified SRTE to account for absorption**

In case of a pure molecular atmosphere (no aerosol) we can write: m is the air mass = 1/cos(s)+1/ cos(v) Ugaz is the gaz concentration 10

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**Final SRTE approximation**

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**Water vapor effect for different sensors in the near infrared**

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Scattering angle , The scattering angle, is the relative angle between the incident and the scattered radiation Incident Radiation Particle scattered radiation

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Phase function The phase function, P() describe the distribution of scattered radiation for one or an set of particles. It is normalized such as: since we have

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**Rayleigh/molecular scattering 1/4**

Rayleigh or molecular scattering refers to scattering by atmospheric gases, in that case:

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**Rayleigh/molecular scattering 2/4**

The concentration in scatterer is better described by the efficiency they scatter at a certain wavelength or the proportion of direct transmission which is related to the spectral optical thickness E0( Et()/ E0()=e- Et( For Rayleigh is proportional to -4 and for standart pressure is ~ at 0.45 m

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**Rayleigh/molecular scattering 3/4**

The rayleigh reflectance, R, could be crudely approximated by:

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**Rayleigh/molecular scattering 4/4**

Compute the reflectance of the sky (assumed clear no aerosol) at solar noon at 45degree latitude at vernal equinox looking straight up at 0.45m, 0.55m, 0.65m

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Aerosol scattering 1/5 aerosol scattering refers to scattering by particles in suspension in the atmosphere (not molecules). The MIE scattering theory could be applied to compute the aerosol phase function and spectral optical depth, based on size distribution, real and imaginary index.

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Aerosol scattering 2/5 Continental aerosol phase function

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**Aerosol scattering 3/5 single scattering albedo**

( ) to account for absorbing particles

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Aerosol scattering 4/5 Continental aerosol optical thickness spectral variation 60

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Aerosol scattering 5/5 Continental aerosol single scattering albedo spectral variation

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**Atmospheric effect: Vegetation 1/3**

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**Atmospheric effect: Vegetation 2/3**

No absorption, Continental aerosol

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**Atmospheric effect: Vegetation 3/3**

Absorption tropical atmosphere, Continental aerosol

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**Atmospheric effect: Ocean 1/2**

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**Atmospheric effect: Ocean 2/2**

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**Perfect Lambertian Reflector**

Isotropic radiation

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**Different Types of Reflectors**

diffuse reflector (lambertian) Specular reflector (mirror) Nearly Specular reflector (water) nearly diffuse reflector Hot spot reflection

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**Sun glint as seen by MODIS**

Gray level temperature image

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**MODIS data illustrating the hot-spot over dense vegetation**

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**BRDF atmosphere coupling correction**

Lambertian infinite target approximation BDRF atmosphere coupling approximation

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**Adjacency effect correction**

Lambertian infinite target approximation adjacency effect approximation

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**Adjacency effect correction (practical implementation)**

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**Adjacency effect correction (testing)**

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**Adjacency effect correction (testing)**

Reflectance’s observed over a horizontal transect on the checkerboard. The red bars are the “true” surface reflectance, the blue bars correspond to the top of the atmosphere signal including adjacency effect. The green bars correspond to the corrected data using the infinite target assumption. The open square correspond to the data corrected for the adjacency effect using the operational method developed.

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**Adjacency effect correction (validation)**

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Conclusions Review of atmospheric effect including the BRDF-coupling and the adjacency effect Current version of MOD09 (Collection 4) does not include the BRDF-coupling or adjacency effect correction Collection 5 (start scheduled in Jan06), will include adjacency correction for 250m bands. BRDF-coupling correction is still being evaluated.

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