In meteorology, visibility is the measure of the distance at which an object or light can be clearly discerned. It depends on the transparency of the surrounding air and as such, it is unchanging no matter the ambient light level or time of day. It is reported within surface weather observations and METAR code either in meters or statute miles, depending upon the country. Visibility affects all forms of traffic: roads, railways, sailing and aviation. The geometric range of vision is limited by the curvature of the Earth and depends on the eye level and the height of the object being viewed. In geodesy, the atmospheric refraction must be taken into account when calculating geodetic visibility.
Meteorological visibility
Definition
ICAO Annex 3 Meteorological Service for International Air Navigation contains the following definitions and note:
a) the greatest distance at which a black object of suitable dimensions, situated near the ground, can be seen and recognized when observed against a bright background; b) the greatest distance at which lights of 1,000 candelas can be seen and identified against an unlit background. Note.— The two distances have different values in air of a given extinction coefficient, and the latter b) varies with the background illumination. The former a) is represented by the meteorological optical range (MOR). Annex 3 also defines Runway Visual Range (RVR) as:
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 (e.g., in Arctic areas), the visibility can be up to 240 km (150 miles). Distant observable visibility requires large markers such as mountains or high ridges; however, visibility is often reduced somewhat by air pollution and high humidity. Various weather stations report this as haze (dry) or mist (moist). Heavy rain (such as from a thunderstorm) can impair visibility. Blizzards and ground blizzards (blowing snow) are also defined in part by low visibility. These conditions, as well as Fog and smoke, can reduce visibility to near zero, making driving extremely dangerous. The same can happen in a sandstorm or with forest fires.
History
Derivation To define visibility the case of a perfectly black object being viewed against a perfectly white background is examined. The visual contrast, CV(x), at a distance x from the black object is defined as the relative difference between the light intensity of the background and the object
C V ( x ) = F B ( x ) − F ( x ) F B ( x ) {\displaystyle C_{\text{V}}(x)={\frac {F_{\text{B}}(x)-F(x)}{F_{\text{B}}(x)}}}
where FB(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 CV(0) = 1. Between the object and the observer, F(x) is affected by additional light that is scattered into the observer's line of sight and the absorption of light by gases and particles. 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
d F = − b ext F d x {\displaystyle dF=-b_{\text{ext}}{F}dx}
where bext 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' FB(x) dx, where b' is a constant. The overall change in intensity is expressed as
d F ( x ) = [ b ′ F B ( x ) − b ext F ( x ) ] d x {\displaystyle dF(x)=\left[b'F_{\text{B}}(x)-b_{\text{ext}}F(x)\right]dx}
Since FB represents the background intensity, it is independent of x by definition. Therefore,
d F B ( x ) = 0 = [ b ′ F B ( x ) − b ext F B ( x ) ] d x {\displaystyle dF_{\text{B}}(x)=0=\left[b'F_{\text{B}}(x)-b_{\text{ext}}F_{\text{B}}(x)\right]dx}
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