View source for Visibility

{{short description|Measure of the distance needed to visually discern an object}}
{{other uses}}

{{More footnotes needed|date=March 2010}}

In [[meteorology]], '''visibility''' is the measure of the [[distance]] at which an object or light can be clearly discerned. It depends on the [[Transparency and translucency|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 observation]]s and [[METAR]] code either in [[Metre|meters]] or [[statute miles]], depending upon the country. Visibility affects all forms of traffic: [[road 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===
[[File:Plane flying into clouds.jpg|thumb|right|upright=0.75|Airplane flying into clouds on descent for landing]]
[[ICAO]] Annex 3 ''Meteorological Service for International Air Navigation'' <ref name=":0">{{Cite web|url=https://www.wmo.int/pages/prog/www/ISS/Meetings/CT-MTDCF-ET-DRC_Geneva2008/Annex3_16ed.pdf|title=ICAO Annex 3 Meteorological Service for International Air Navigation|date=July 2007|publisher=International Civil Aviation Organization|access-date=2018-03-09|edition=16th}}</ref> 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 [[candela]]s can be seen and identified against an unlit background.
:Note.— The two distances have different values in air of a given [[Attenuation coefficient|extinction coefficient]], and the latter b) varies with the background illumination. The former a) is represented by the meteorological optical range (MOR).
Annex 3 <ref name=":0" /> also defines [[Runway visual range|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.

[[File:Foggy morning road - visibility at 200 ft.jpg|thumb|upright=1.2|[[Fog]]gy morning road]]
[[File:Tel Aviv Carmel Panorama.jpg|thumb|upright=2.4|On clear days, Tel Aviv's skyline is visible from the Carmel mountains, 80 km north]]

In extremely clean air in Arctic or mountainous areas, the visibility can be up to 240&nbsp;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 [[weather station]]s 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|sandstorm]] in and near [[desert]] areas, or with [[forest fire]]s.  Heavy [[rain]] (such as from a [[thunderstorm]]) not only causes low visibility, but the inability to [[brake]] quickly due to [[Hydroplaning (tires)|hydroplaning]].  [[Blizzard]]s and ground blizzards (blowing snow) are also defined in part by low visibility.

===History===
{{Expand section|date=May 2022}}

===Derivation===
To define visibility the case of a [[Black body|perfectly black]] object being viewed against a perfectly white background is examined. The [[Contrast (vision)|visual contrast]], ''C''<sub>V</sub>(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

:<math>C_\text{V}(x) = \frac{F_\text{B}(x)-F(x)}{F_\text{B}(x)}</math>

where ''F''<sub>B</sub>(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<sub>V</sub>''(0) = 1.

Between the object and the observer, ''F''(x) is affected by additional light that is [[scattering|scattered]] into the observer's line of sight and the [[Absorption (electromagnetic radiation)|absorption]] of light by gases and [[Particulate|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

:<math>dF = -b_\text{ext} {F} dx</math>

where ''b''<sub>ext</sub> 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''<sub>B</sub>(''x'') ''dx'', where ''b''' is a constant. The overall change in intensity is expressed as

:<math>dF(x) = \left[b' F_\text{B}(x) - b_\text{ext} F(x)\right] dx</math>

Since ''F''<sub>B</sub> represents the background intensity, it is independent of ''x'' by definition.  Therefore,

:<math>dF_\text{B}(x) = 0 = \left[b' F_\text{B}(x) - b_\text{ext} F_\text{B}(x)\right] dx</math>

It is clear from this expression that ''b''' must be equal to ''b''<sub>ext</sub>. Thus, the visual contrast, ''C''<sub>V</sub>(''x''), obeys the [[Beer–Lambert law]]

:<math>\frac{dC_\text{V}(x)}{dx} = - b_\text{ext} C_\text{V}(x)</math>

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

:<math>C_\text{V}(x) = \exp(- b_\text{ext} x)</math>

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''<sub>V</sub> = 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):

:<math>x_\text{V} = \frac{3.912}{b_\text{ext}}</math>

with ''x''<sub>V</sub> in units of length.  At sea level, the [[Rayleigh scattering|Rayleigh atmosphere]] has an extinction coefficient of approximately 13.2 × 10<sup>−6</sup> m<sup>−1</sup> at a [[wavelength]] of 520&nbsp;nm.  This means that in the cleanest possible atmosphere, visibility is limited to about 296&nbsp;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.<ref>{{cite journal|last1 = Moreno|first1 = Ivan|last2 = Jauregui-Sánchez|first2 = Y.|last3 = Avendaño-Alejo|first3 = Maximino|year = 2014|title = Invisibility assessment: a visual perception approach|url = http://fisica.uaz.edu.mx/~imoreno/Publicaciones/JOSA2014.pdf|journal = Journal of the Optical Society of America A|volume = 31|issue = 10|pages = 2244–2248|doi = 10.1364/josaa.31.002244|pmid = 25401251|bibcode = 2014JOSAA..31.2244M|access-date = 2017-01-10|archive-date = 2017-08-08|archive-url = https://web.archive.org/web/20170808173026/http://fisica.uaz.edu.mx/~imoreno/Publicaciones/JOSA2014.pdf|url-status = dead}}</ref>

===Fog, mist, haze, and freezing drizzle===
The international definition of [[fog]] is a visibility of less than {{cvt|1|km|ft}}; [[mist]] is a visibility of between {{cvt|1|km|mi}} and {{cvt|2|km|mi}} and [[haze]] from {{cvt|2|km|mi}} to {{cvt|5|km|mi}}. Fog and mist are generally assumed to be composed principally of water droplets, haze and smoke can be of smaller particle size. This has implications for sensors such as [[thermographic camera|thermal imagers]] (TI/[[forward-looking infrared|FLIR]]) operating in the [[far infrared|far-IR]] at wavelengths of about 10 μm, which are better able to penetrate haze and some smokes because their particle size is smaller than the wavelength; the IR radiation is therefore not significantly deflected or absorbed by the particles.{{Citation needed|date=March 2010}}

With fog, occasional [[freezing drizzle]] and [[snow]] can occur. This usually occurs when temperatures are below {{cvt|0|C|F}}. 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 [[stratus cloud]]s.

===Very low visibility===
Visibility of less than {{convert|100|m|ft}} is usually reported as zero.  In these conditions, roads may be closed, or automatic warning lights and signs may be activated to warn drivers.  These have been put in place in certain areas that are subject to repeatedly low visibility, particularly after [[traffic collision]]s or  [[pile-up]]s involving multiple vehicles.

===Low visibility warnings===
In addition, an advisory is often issued by a government weather agency for low visibility, such as a dense fog advisory from the U.S. [[National Weather Service]].  These generally advise motorists to avoid [[travel]] until the fog dissipates or other conditions improve.  [[Airport]] travel is also often delayed by low visibility, sometimes causing long waits due to [[Instrument approach#Decision height or altitude|approach visibility minimums]] and the difficulty of safely moving aircraft on the ground in low visibility.<ref>{{cite web|title=Why fog can play havoc with your travel plans|url=http://www.newcastleairport.com.au/blog/why-fog-can-play-havoc-with-your-travel-plans#.WayUZciGOUk|website=www.newcastleairport.com.au|access-date=3 September 2017}}</ref><ref>{{cite web|title=Project AS 07/13 - Regulation of Low Visibility Operations|url=https://www.casa.gov.au/standard-page/project-0713-regulation-low-visibility-operations?WCMS%3APWA%3A%3Apc=PC_93101|website=www.casa.gov.au|publisher=Australian Civil Aviation Safety Authority|access-date=3 September 2017|language=en|date=21 March 2009}}</ref>

===Visibility and air pollution===
A visibility reduction is probably the most apparent symptom of [[air pollution]].  Visibility degradation is caused by the [[Absorption (electromagnetic radiation)|absorption]] and [[scattering]] of light by particles and gases in the [[Atmosphere of Earth|atmosphere]]. Absorption of [[electromagnetic radiation]] by gases and particles is sometimes the cause of discolorations in the atmosphere but usually does not contribute very significantly to visibility degradation.

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&nbsp;μm. The effect of air molecules on visibility is minor for short visual ranges but must be taken into account for ranges above 30&nbsp;km.

[[File:20240204 Monte_Cimone.jpg|thumb |upright=2.4|From the summit of Mount Summano (1296 m Vicenza Italy), it is possible to see (dark blue sky line) the Tuscan-Emilian Apennines and Mount Cimone (2165 m Modena Italy) in good visibility. The distance is about 180 km. Note the fog present throughout the Po Valley in the lower layers.]]

== Geodetic visibility ==
{{More citations needed section|date=June 2022}}
[[File:Visibility 1.png|thumb|]]
[[File:Visibility 2.png|thumb|]]

The geographical visibility depends on the altitude of the observation site and the topology of its surroundings. Planes and water surfaces provide a maximum range of vision, but vegetation, buildings and mountains are geographical obstacles that limit the geographical visibility. When the sky is clear and the meteorological visibility is high, the [[curvature of the earth]] limits the maximum possible geodetic visibility. The visibility from an elevated observation point down to the surface of the sea can be calculated using the [[Pythagorean theorem]], since the [[Sightline|line of sight]] and the [[Earth radius|radius of the Earth]] form the two legs of a [[right triangle]]. The height of the elevated point plus the Earth radius form its [[hypotenuse]]. If both the eyes and the object are raised above the reference plane, there are two right-angled triangles. The tangent touching the surface of the Earth or water consists of the two short legs of the two right triangles, which are added together to calculate the geometric range of vision.

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.

==See also==
*[[Coefficient of haze]]
*[[Interferometric visibility]]

==References==
{{Reflist}}

==Further reading==

{{Meteorological variables}}
{{Authority control}}

[[Category:Visibility| ]]
[[Category:Meteorological concepts]]
[[Category:Meteorological quantities]]