FAQs on fog Last updated on 1997-11-12 Started on 1997-01-29 Content 0. What is this fog FAQ all about 0.1. Why a fog FAQ ? 0.2. Who are the contributors ? 0.3. Where should the contributions be sent ? 0.4. Why is this FAQ so grammatically incorrect ? 0.5. How comes this FAQ is in English ? 1. What is fog 1.1. What is the definition for fog ? 1.2. What is fog composed of ? 1.3. Are there different types of fog ? 1.4. What is fog microstructure ? 2. How does fog form 2.1. How does fog form ? 2.2. How does fog dissipate ? 3. What are the effects of fog on light propagation 3.1. What are the optical effects of fog ? 4. What are the visual effects of fog 4.1. How does fog affect the intensity of a distant light ? 4.2. How does fog affect the luminance of a distant object ? 4.3. How does fog affect the contrast of a distant object ? 4.4. What is the meteorological visibility range ? 4.5. How does fog affect colors ? 5. How do you render fog 5.1. What is the easiest way to render fog ? 5.2. What are the fog rendering techniques ? ---------------------------------------------------------------------------- 0. What is this fog FAQ all about ? 0.1. Why a fog FAQ ? I've been studying fog for some time now, mainly trying to figure out in what ways it lowers visibility, for road security issues. I spent quite an amount of energy looking for facts on the WWW, through search engines. But I found the information was scarce. So I decided to pack all the material I gathered on fog issues, and make it available for everybody to use. I'm just starting this FAQ, and far from omniscience on fog matters. But hopefully I'll get plenty of remarks and contributions (to dumont@lcpc.fr), which will all be welcome. 0.2. Who are the contributors ? Anyone is welcome to contribute to this FAQ. Here's the list of the contributors so far: * Dr. Steve Ackerman (CIMSS) * Bill Maier 0.3. Where should the contributions be sent ? All questions, answers, facts, dreams, pictures, insults, comments, critics, or anything else you can think of, should be sent to eric Dumont address: Laboratoire Central des Ponts & Chaussées 58, boulevard Lefèbvre 75732 PARIS Cedex 15 FRANCE URL: http://www.lcpc.fr/LCPC/Bottin/Alphabetique/Eric.DUMONT 0.4. Why is this FAQ so grammatically incorrect ? That's an easy one. Because the author is French ;-) 0.5. How comes this FAQ is in English ? Because the author has no intention in doing twice as much work maintaining, but still wants maximum people to have access to this FAQ. English is the Net's native language. Sorry. ---------------------------------------------------------------------------- 1. What is fog ? 1.1. What is the definition for fog ? Webster definition (1a): vapor condensed to fine particles of water suspended in the lower atmosphere that differs from cloud only in being near the ground. Fog is often described by its thickness, or ability to cut off vision. Fog is when the visibility range is under 1km. Otherwise it's haze, or mist. 1.2. What is fog composition ? Usually, fog isn't just composed of plain water droplets. The condensation process occurs more easily with the presence of hygroscopic condensation nuclei in the atmosphere (e.g. dust or salt particles, often caused by pollution). In case of a high concentration of nuclei, the fog will be called smog. Fog is often considered to be composed only of water. 1.3. Are there different types of fog ? The types of fog are named with reference to the method by which they form: * radiation (ground) fog, * advection fog, * upslope fog, * evaporation (or mixing) fog, * steam fog. But the way a fog formed is no clue concerning its microstructure. 1.4. What is fog microstructure ? The microstructure describes the shape and concentration of the water (mainly) droplets in the atmosphere causing the fog. The droplets are usually considered to be spheres. There can be droplets of many different diameters, with different concentrations. The distribution mode varies from 1µm to 20µm (droplets are usually bigger within clouds). The microstructure of a fog depends on the place (nature of hygroscopic condensation nuclei), the time, and the atmospheric conditions. The droplets are small when the fog forms, then grow bigger as condensation occurs. ---------------------------------------------------------------------------- 2. How does fog form ? from Dr. Steve Ackerman 2.1. How does fog form ? Fog forms in either one or combinations of three ways: * by cooling the air, * by evaporation of water into the air, * mixing of two air parcels. Radiation (ground) fog Produced by the radiational cooling at the surface. Favorable conditions: * clear nights, * shallow layer of moist air near the ground, * long nights, * light winds. Radiation fogs are common over land in late fall and winter. Radiation fogs also form in low-lying areas (valley fog). Cold air and high moisture content in river valleys make them susceptible to radiation fog. Radiation fogs form at the ground and are deepest around sunrise - sometimes an increase in thickness at sunrise due to the evaporation of dew supplying moisture to the fog. Advection fog Air is cooled to saturation by having warm moist air moving over a cold surface. Pacific Coast has a lot of advection fog since the surface water near the coast is much colder than the water farther off shore. Warm moist air from the Pacific Ocean is advected over the cold coastal waters, chilling the advected air from below. Advection fog, unlike radiation fog always involves the movement of air. Fog, while a traffic hazard, is very important water source for some plants and animals. Upslope fog Forms as moist air flows up an elevated plain, hill or mountain. Upslope fogs may last for several days. (The above methods of forming a fog all require cooling the air.) Evaporation (or mixing) fog Formed by mixing two unsaturated air masses. Moist air coming out of your mouth is an example of mixing fog. Contrails are another example. Saturation vapor pressure depends on the temperature - the higher the temperature the higher the saturation vapor pressure. Warm rain falling into a cool air mass near the surface can form a fog. An example of such a fog is the type that forms in the vicinity of warm fronts. Steam fog Forms when cold air moves over warm water (heated outside swimming pool) water evaporates from the pool into the air, increasing the dew point and if mixing is sufficient the air above becomes saturated. The colder air directly above the water is heated from below and rises forming what appears to be steam. Observed over unfrozen lakes in autumn or winter. Steam fog also forms above a wet surface on a sunny day - over a road after a summer rain shower. 2.2. How does fog dissipate ? Fogs do not "burn off", the sun warms the ground. The air near the ground warms lowering the relative humidity. This warmer drier air mixes upwards destroying the fog. Sometimes the fog does not totally dissipate, but forms a stratus cloud. ---------------------------------------------------------------------------- 3. What are the effects of fog on light propagation ? 3.1. What are the optical effects of fog ? When incident light hits a particle in fog, part of the energy is absorbed, and the rest is scattered. When going from one point to another through fog, light will meet many particles that will cause multiple scatterings. The extinction of light is the combined effect of absorption and scattering. Scattering coefficient ks [m-1] describes the part of incident light that's scattered by the turbid medium. It is a function of the microstructure of the fog: [ks = Sum[0..inf](n(r).r^2.qs(r).dr)] where r is the droplet radius, n(r) is the fog droplet size distribution, qs(r) is the scattering efficiency, computed by Mie theory (qs -> 2 when r > 2µm). Extinction coefficient ke [m-1] describes the part of incident light that is not transmitted by the turbid medium, due to the combined effects of absorption and scattering. [ke = Sum[0..inf](n(r).r^2.qe(r).dr)] where r is the droplet radius, n(r) is the fog droplet size distribution, qe(r) is the extinction efficiency, computed by Mie theory (ke = ks when the fog particles are only water droplets). Absorption coefficient ka [m-1] describes the part of incident light that's absorbed by the turbid medium. ke = ka + ks When the fog particles are only water droplets, the absorbed energy is less than 0.5%, and is not accounted for (ka = 0). Albedo a is the fraction of incident light that is scattered by the turbid medium. a = ks / ke (a = 1 when the fog particles are only water droplets) Phase function (or scattering function) P describes the fractions of incident light that are scattered in any given direction by a particle (goniometric distribution). If the particle if a sphere, the symmetry about the incident axis allows the description of the whole phase function with only one parameter: the scattering angle, between 0° (forth-scattering) and 180° (back-scattering). The phase function can be obtained from the particle size distribution using Mie electromagnetic equations. Otherwise it is often approximated by the Henyey-Greenstein (1941) expression: [P(tetha) = (1 - g*g) / (1 + g*g - 2*cos(tetha))^1.5] where g is the asymmetry factor: g=-1 for backward scattering, g=0 for isotropic scattering, and g=1 for forward scattering. [g = .5*SUM[-1..+1](P(m).m.dm)] where [m = cos(theta)]. ---------------------------------------------------------------------------- 4. What are the visual effects of fog ? 4.1. How does fog affect the intensity of a distant light ? Allard's empirical law (1876): E = I exp(-ked) / d² where I is the light intensity, d is the distance between the source and the observer, ke is the extinction coefficient of the fog, and E is the illuminance in the eye of the viewer. 4.2. How does fog affect the luminance of a distant object ? Koschmieder's theory (1924): L = L0exp(-ked) + Lv(1 - exp(-ked)) where L0 is the initial luminance, d is the distance between the object and the observer, ke is the extinction coefficient of the fog, Lv is the veiling luminance, and L is the observed luminance. 4.3. How does fog affect the contrast of a distant object ? The classic theory of contrast, derived from Koschmieder's law, gives a simple expression of the apparent contrast of an object on its background. C = C0exp(-ked) where C0 is the initial contrast, d is the distance between the object and observer, ke is the extinction coefficient of the fog, and C is the observed contrast. We can see this expression is a simplification, because it does not account for the microstructure of the fog (two fogs with the same ke but particles of different sizes will have the same effect on contrast according to this theory). 4.4. What is the meteorological visibility range ? The meteorological visibility range (V) is the parameter meteorologists use to describe the thickness of fog. It is often abusively shortened to visibility range. It is computed using the above theory of contrast applied to a black object with an arbitrary 5% contrast detection threshold, given by the CIE: V = - log(0.05) / ke = 3 / ke where ke is the extinction coefficient of the fog. Some people use 2% as a threshold (Koshmieder did). 4.5. How does fog affect colors ? Fog has no effect on colors if we consider the particles to be only water droplets, except the desaturation. ---------------------------------------------------------------------------- 5. How do you render fog ? 5.1. What is the easiest way to render fog ? You can easily create atmospheric effects by blending the color of the objects in the scene with fog color, based on their distance from the viewer (like depth-cueing). COL = COL0.exp(-ked) + COLf.(1 - exp(-ked)) where COL0 is the color of an object, COLf is the fog color, ke is the fog extinction coefficient and d is the distance between the object and the viewer. This function is now taken care of by graphics chips, which makes it very fast. from Bill Maier You can use another easy trick to simulate the materialization of the cone from a car headlight, for example. Make a set of cones, perhaps 5 or so, with the same vertex (point of the cone) at the headlight itself. Have the base of the cone out in front of the vehicle where the light is shining, perhaps 20 meters out. Design the cones with slightly different radii at the base, for example, 0.5 meters, 0.75 m, 1.0 m, 1.25, etc. Assign each cone a transparency value so it is translucent. Then when you look at the outer edges of the light cones, you will see only the outermost cone and the light will appear dimmer. At the center of the beam you will see the combined effect of all 5 cones, so it will appear denser. Of course you won't get shadows in the beam, but if you can live with that limitation it's a good method. If you think about it, this is really a sort of cheap way to do volumetric rendering. The more cones you have, the better your resolution (and the more CPU power required!). Here's an example: http://home1.gte.net/ciric/basket.htm 5.2. What are the rendering techniques dealing with fog ? Any CG technique that deals with participating media will do : distributed ray tracing, Monte Carlo light tracing, zonal radiosity... [Working on it...] ---------------------------------------------------------------------------- © ED [Commentaires (Comments)...] ---------------------------------------------------------------------------- According to SiteFlow the number of visitors since 14/08/1997 is