Visibility From Rh Calculator

Meteorological visibility is not a measure of how far light travels but of how far contrast survives. Light from a distant black target is progressively replaced by air light scattered into the line of sight, and the residual contrast decays exponentially as exp(-sigma * x), where sigma is the extinction coefficient in inverse kilometers. Setting the threshold contrast at 2 percent gives V = ln(50) / sigma = 3.912 / sigma, which is why that constant appears in every visibility formula. Extinction has two parts. Molecular Rayleigh scattering is nearly fixed at about 0.0116 per km at sea level for 550 nm light, and because it scales as the inverse fourth power of wavelength it sets a clean-air ceiling near 340 km that no real atmosphere reaches. The aerosol term dominates in practice and depends on both particle load and water uptake. The humidity dependence is the steep part. Hygroscopic particles - sea salt, ammonium sulfate, nitrate - deliquesce and swell as relative humidity climbs, and their scattering cross-section grows far faster than their dry mass would suggest. The growth is commonly parameterized as f(RH) = (1 - RH/100) raised to the power of negative gamma, with gamma near 0.3 for mixed continental aerosol. Below 60 percent RH the factor barely moves; between 90 and 99 percent it can triple or quadruple the aerosol extinction, which is why visibility collapses in the last hour before fog forms. The caveats are real: this power-law form diverges as RH approaches 100 percent and cannot represent fog itself, it assumes a single bulk gamma when composition actually varies, hydrophobic black carbon barely grows at all, and the relation breaks down entirely once droplets nucleate. Aviation thresholds sit at 5000 m for VFR-type operations and 1600 m for the low-IFR boundary, so errors in the humid regime carry operational weight.

The quantitative theory dates to Harald Koschmieder, who published Theorie der horizontalen Sichtweite in Beitraege zur Physik der freien Atmosphaere in 1924 while working at the Geophysical Institute in Danzig. Koschmieder derived the air-light equation showing that the apparent luminance of a distant dark object approaches that of the horizon sky exponentially with distance, and combined it with a threshold contrast to define a repeatable visual range. His work built on Lord Rayleigh, who in the 1870s explained molecular scattering and its inverse fourth-power wavelength dependence, and on Gustav Mie, whose 1908 solution for scattering by spheres comparable in size to the wavelength provided the physics of the aerosol term. The 2 percent contrast threshold was standardized internationally, and the World Meteorological Organization adopted meteorological optical range built on Koschmieder's framework as the definition used in synoptic and aviation reporting. Instrumentation followed the theory: transmissometers measuring beam attenuation over baselines of roughly 10 to 75 m came into airport use from the 1940s and 1950s, and forward-scatter meters, which infer sigma from light scattered at a fixed angle over a small sample volume, largely displaced them at automated stations from the 1980s onward because they are cheaper to site and maintain. The humidity growth factor entered the picture separately through aerosol physics: Christian Junge's work on atmospheric aerosol in the 1950s and 1960s, and later United States regional haze research culminating in the IMPROVE monitoring network established in 1987, produced the empirical f(RH) curves that let visibility be estimated from humidity and particulate loading rather than measured directly.