Illumination Dependent Aerosol Optical Properties n Volume scattering function n Path function n Path radiance n Atmospheric modulation transfer function

gainloss Radiation Transfer Equation

When N r has some special value, N q, such that b ext N q =, then dN q /dr = 0. N q is independent of r and is commonly referred to as the equilibrium radiance. Equilibrium Radiance

If N q is constant, the previous equation can be integrated to yield where Radiance Difference

Rearranging yields The second term is the path radiance (airlight),, which results from scattering processes throughout the sight path. The parameter is the sky radiance Path Radiance

If T  is approximately zero, then N q = =N s (sky radiance) and: Path Radiance Approximation

In general:

.. Radiance Difference and Real World

Apparent and Inherent Contrast Define: Apparent Contrast: Inherent Contrast:

Radiance Difference Transmittance

Contrast Transmittance

If background is sky then: and

If background is sky, N s : Estimating Extinction and, which yields

The distance at which C r approaches a threshold contrast of between or defines the visual range, V r. If  C o  = 1 (black object) and is taken to be a threshold contrast, then the previous equation becomes The Visual Range Concept

Visibility Metrics n Apparent contrast: C r = C o e -b ext r n Visual Range: vr = 3.912/ b ext n decView: dv = 10 ln(b ext /.01)

Contrast Sensitivity Surface (back)

Contrast Sensitivity Surface (forward)

Forward Scattering

Back Scattering

Optics of Visibility

La Sals –Forward Scattering

La Sals – Backward Scattering

La Sals -- 30km

Mt Trumbull km

North Rim of Grand Canyon Through Smoke Plume

Easterly View of Grand Canyon from Desert View Watch Tower

Westerly View from Desert View Watch Tower

Clouds Evaporate Leaving Sulfate Haze

Clouds Evaporated Leaving Sulfate Haze

Sulfate Haze Trapped Below Rim

Next Day After Haze is Blown Out

Path Radiance Absent Because of Clouds

Nitrogen Dioxide Haze

Nitrogen Dioxide Plume

Illumination Effects