Visibility

 ( Meteorological Concepts ) 

The range over which the pilot of an aircraft on the centre line of a runway can see the runway surface markings or the lights delineating the runway or identifying its centre line.

In extremely clean air in Arctic or mountainous areas, the visibility can be up to 240 km (150 miles) where there are large markers such as mountains or high ridges. However, visibility is often reduced somewhat by air pollution and high humidity. Various report this as haze (dry) or mist (moist). Fog and smoke can reduce visibility to near zero, making driving extremely dangerous. The same can happen in a Dust storm in and near desert areas, or with . Heavy rain (such as from a thunderstorm) not only causes low visibility, but the inability to brake quickly due to hydroplaning. and ground blizzards (blowing snow) are also defined in part by low visibility.

$C\_\backslash text\{V\}(x)\; =\; \backslash frac\{F\_\backslash text\{B\}(x)-F(x)\}\{F\_\backslash text\{B\}(x)\}$

where F_B(x) and F(x) are the intensities of the background and the object, respectively. Because the object is assumed to be perfectly black, it must absorb all of the light incident on it. Thus when x=0 (at the object), F(0) = 0 and C_V(0) = 1.

Between the object and the observer, F(x) is affected by additional light that is scattering into the observer's line of sight and the absorption of light by gases and Particulate. Light scattered by particles outside of a particular beam may ultimately contribute to the irradiance at the target, a phenomenon known as multiple scattering. Unlike absorbed light, scattered light is not lost from a system. Rather, it can change directions and contribute to other directions. It is only lost from the original beam traveling in one particular direction. The multiple scatterings' contribution to the irradiance at x is modified by the individual particle scattering coefficient, the number concentration of particles, and the depth of the beam. The intensity change dF is the result of these effects over a distance dx. Because dx is a measure of the amount of suspended gases and particles, the fraction of F that is diminished is assumed to be proportional to the distance, dx. The fractional reduction in F is

$dF\; =\; -b\_\backslash text\{ext\}\; \{F\}\; dx$

where b_ext is the attenuation coefficient. The scattering of background light into the observer's line of sight can increase F over the distance dx. This increase is defined as b' F_B( x) dx, where b' is a constant. The overall change in intensity is expressed as

$dF(x)\; =\; \backslash leftb\text{'}\; dx$

Since F_B represents the background intensity, it is independent of x by definition. Therefore,

$dF\_\backslash text\{B\}(x)\; =\; 0\; =\; \backslash leftb\text{'}\; dx$

It is clear from this expression that b' must be equal to b_ext. Thus, the visual contrast, C_V( x), obeys the Beer–Lambert law

$\backslash frac\{dC\_\backslash text\{V\}(x)\}\{dx\}\; =\; -\; b\_\backslash text\{ext\}\; C\_\backslash text\{V\}(x)$

which means that the contrast decreases exponentially with the distance from the object:

$C\_\backslash text\{V\}(x)\; =\; \backslash exp(-\; b\_\backslash text\{ext\}\; x)$

Lab experiments have determined that contrast ratios between 0.018 and 0.03 are perceptible under typical daylight viewing conditions. Usually, a contrast ratio of 2% ( C_V = 0.02) is used to calculate visual range. Plugging this value into the above equation and solving for x produces the following visual range expression (the Koschmieder equation):

$x\_\backslash text\{V\}\; =\; \backslash frac\{3.912\}\{b\_\backslash text\{ext\}\}$

with x_V in units of length. At sea level, the Rayleigh atmosphere has an extinction coefficient of approximately 13.2 × 10⁻⁶ m⁻¹ at a wavelength of 520 nm. This means that in the cleanest possible atmosphere, visibility is limited to about 296 km.

Visibility perception depends on several physical and visual factors. A realistic definition should consider the fact that the human visual system (HVS) is highly sensitive to spatial frequencies, and then to use the Fourier transform and the contrast sensitivity function of the HVS to assess visibility.

With fog, occasional freezing drizzle and snow can occur. This usually occurs when temperatures are below . These conditions are hazardous due to ice formation, which can be deadly, particularly so because of the low visibility, which usually accompanies these conditions at under 1,000 yards. The combination of low visibility and ice formation can lead to accidents on roadways. These cold weather events are caused largely by low-lying .

Scattering by particulates impairs visibility much more readily. Visibility is reduced by significant scattering from particles between an observer and a distant object. The particles scatter light from the sun and the rest of the sky through the line of sight of the observer, thereby decreasing the contrast between the object and the background sky. Particles that are the most effective at reducing visibility (per unit aerosol mass) have diameters in the range of 0.1-1.0 μm. The effect of air molecules on visibility is minor for short visual ranges but must be taken into account for ranges above 30 km.

In geodesy the atmospheric refraction is always taken into account in the calculation, which increases the range of vision, so that even objects behind the horizon can still be seen.

• Coefficient of haze