Visibility/Haze Metric

Visibility is a measure of how well an observer can view a scene.  This includes how far one can see in the atmosphere as well as the ability to see the textures and colors of the scene.  Haze is the inverse of visibility, that is the measure of the inability to view a scene.  Visibility is reduced, or haze increased, by the absorption and scattering of gases and aerosols (particles) in the atmosphere.  Therefore, visibility involves both the physical interaction of light with the gases and particles as well as psychophysical processes and concurrent value judgments of visual impacts by the human observers.  The fact that visibility involves both physical and psychophysical processes makes it difficult to quantify with a single metric.  Hence, a number of metrics are used depending on the situation at hand.  Below, four common visibility/haze metrics are defined, the common situation for their use, and the mathematical relationships between the various metrics are also provided.

Visual Range (V.R.):The greatest distance at which an observer can just see a black object viewed against the horizon sky.   

Units:  Distance, e.g. kilometers (km)

Benefit:  This metric is most useful in situation where only the distance that one can see is important, such as for aviation.

Drawback:  Does not account for changes in scene, such as loss of textures and discoloration as haze increases.

Relationships:

V.R. = K/b_ext
Where K is the Koschmieder Coefficient – the log of the contrast threshold of the human eye,  K = 3 – 3.9

Light Extinction (b_ext): The attenuation of light due to scattering and absorption as it passes through a medium.

Units: inverse distance, e.g. inverse mega meters (Mm^-1)

Benefit:  Light extinction can be directly related to gaseous and aerosol concentrations.

Drawback:  Light extinction is non-linearly related to a person perception of changes in haze.  For example, a 10 Mm^-1 increase in b_ext will have a larger perceived impact on a scene at b_ext = 20 Mm^-1 than at b_ext = 100 Mm^-1

Relationships:

b_ext = K/V.R. 
Where K is the Koschmieder Coefficient – the natural log of the contrast threshold of the human eye,  K = 3 – 3.9

b_ext = 10*exp(DV/10) 

Deciview (DV): A metric of haze proportional to the logarithm of the atmospheric extinction (b_ext).

Units: Unitless

Benefit: Under many circumstances a change in one deciview will be perceived to be the same on clear and hazy days.

Drawback:  Deciview is not easily related to gaseous and aerosol concentrations

Relationships:

DV = 10*ln(b_ext/10)

DV = 10*ln(K/V.R./10) 

Perceived Visual Air Quality (PVAQ): An index that relates directly to how human observers perceive changes in visual air quality.

Units:  Unitless

Benefit: Quantitatively, measures haze or visibility impairment to how human observers perceive changes in visual air quality.