Visibility From Rh Calculator
Free Visibility rh Calculator for meteorology & atmospheric science. Enter variables to compute results with formulas and detailed steps.
Calculator
Adjust values & calculateFormula
Where V is meteorological visibility in km, sigma_dry is dry aerosol extinction, f(RH) is hygroscopic growth factor, and sigma_Rayleigh is molecular scattering.
Last reviewed: December 2025
Worked Examples
Example 1: Humid Coastal Evening
Example 2: Pre-Fog Urban Conditions
Background & Theory
The Visibility From Rh Calculator applies the following established principles and formulas. Earth science calculators draw on a wide range of measurement scales and physical principles that quantify natural phenomena across geological, atmospheric, and hydrological systems. Earthquake magnitude is most precisely described by the Moment Magnitude Scale (Mw), which replaced the original Richter scale for larger events. Mw is calculated as Mw = (2/3) log10(M0) − 10.7, where M0 is the seismic moment in dyne-centimeters. The Richter scale, while still referenced colloquially, is a local magnitude (ML) measurement derived from peak seismograph amplitude at a standard 100 km distance. Wind intensity is classified using the Beaufort Scale, a 13-point empirical scale (0–12) relating wind speed in knots to observable sea and land effects, with Beaufort 12 corresponding to hurricane-force winds above 64 knots. Tropical cyclone intensity is further categorized by the Saffir-Simpson Hurricane Wind Scale, which assigns Categories 1 through 5 based on sustained wind speed, correlating with expected structural damage. Mineral hardness is quantified on the Mohs scale (1–10), comparing scratch resistance relative to reference minerals from talc (1) to diamond (10). Soil composition analysis measures the proportions of sand, silt, and clay by particle size, alongside organic matter content, bulk density, and porosity, which together determine engineering and agricultural suitability. Seismic wave velocity in rock varies by material: P-waves travel at approximately 5–7 km/s in granite and 1.5 km/s in water, while S-waves travel at roughly 60% of P-wave speeds. Atmospheric pressure decreases with altitude according to the barometric formula: P = P0 × exp(−Mgh / RT), where M is molar mass of air, g is gravitational acceleration, h is altitude, R is the universal gas constant, and T is temperature in Kelvin. Standard sea-level pressure is 101,325 Pa. Tidal calculations use harmonic analysis of gravitational forcing by the Moon and Sun, with the principal lunar semidiurnal tidal constituent (M2) having a period of approximately 12.42 hours.
History
The history behind the Visibility From Rh Calculator traces back through the following developments. The systematic study of Earth's structure and processes spans millennia, but the scientific foundations were laid in the seventeenth century. In 1669, Danish naturalist Nicolas Steno published his principles of stratigraphy, establishing the laws of superposition, original horizontality, and lateral continuity — foundational rules for reading rock layers that remain in use today. Scottish geologist James Hutton introduced the concept of uniformitarianism in 1788, proposing that geological processes observable in the present have operated throughout Earth's history at broadly consistent rates. This idea of deep time challenged prevailing biblical chronologies and set the stage for modern geology. Charles Lyell systematized these ideas in his landmark three-volume work Principles of Geology, published beginning in 1830, which directly influenced Charles Darwin's thinking on biological evolution during the voyage of the Beagle. The nineteenth century saw growing curiosity about continental shapes, but a coherent theory awaited Alfred Wegener, a German meteorologist who proposed continental drift in 1912, arguing that the continents had once formed a supercontinent he called Pangaea. His evidence included matching fossil records and geological formations across the Atlantic, but his mechanism was disputed for decades. The theory gained acceptance in the 1960s when seafloor spreading was confirmed through paleomagnetic studies, and plate tectonics emerged as the unifying framework of modern geoscience. The United States Geological Survey was established by Congress in 1879 to classify public lands and examine the geological structure, mineral resources, and products of the national domain. The twentieth century brought instrumental advances, including the global seismograph network deployed after World War II, initially to monitor nuclear tests, which dramatically improved earthquake detection and characterization. Satellite Earth observation began in earnest with the Landsat program launched in 1972, enabling continuous global monitoring of land use, glacier retreat, and vegetation patterns. Today, GPS networks, LIDAR scanning, and ocean-floor mapping provide centimeter-scale precision for tracking tectonic motion, sea level rise, and volcanic deformation in near real time.
Frequently Asked Questions
Formula
V = 3.912 / (sigma_dry * f(RH) + sigma_Rayleigh)
Where V is meteorological visibility in km, sigma_dry is dry aerosol extinction, f(RH) is hygroscopic growth factor, and sigma_Rayleigh is molecular scattering.
Worked Examples
Example 1: Humid Coastal Evening
Problem: RH is 92% at 18 C with aerosol concentration 60 at standard pressure and 550nm.
Solution: Growth=(1-0.92)^(-0.33)=2.32, dryExt=60*0.002=0.12, wetExt=0.278, total=0.290, V=3.912/0.290=13.5km
Result: Visibility: 13.5 km (8.4 mi) | Clear | Fog Risk: Moderate
Example 2: Pre-Fog Urban Conditions
Problem: RH has risen to 98% at 8 C with high aerosol loading of 120.
Solution: Growth=(1-0.98)^(-0.33)=3.68, dryExt=0.24, wetExt=0.883, total=0.895, V=3.912/0.895=4.37km
Result: Visibility: 4.37 km (2.72 mi) | Moderate | Fog Risk: Very High
Frequently Asked Questions
How does relative humidity affect visibility?
Relative humidity has a profound and nonlinear effect on atmospheric visibility. As RH increases, hygroscopic aerosol particles absorb water and swell in size, dramatically increasing their ability to scatter and absorb light. The relationship becomes especially steep above 80 percent RH, where small increases cause large visibility drops. At 95 percent RH, aerosol particles can grow to several times their dry diameter. This is why visibility often deteriorates rapidly in the hours before fog formation as the air approaches saturation.
What causes low visibility besides fog?
Several atmospheric phenomena beyond fog can significantly reduce visibility. Haze consists of dry aerosol particles from pollution, dust, or biomass burning that scatter light even at moderate humidity levels. Smog combines photochemical pollution with haze, particularly in urban areas. Blowing dust and sand in arid regions can reduce visibility to near zero during strong wind events. Volcanic ash plumes from eruptions can travel thousands of kilometers degrading visibility. Heavy precipitation including rain, snow, and sleet scatter light proportional to their intensity.
How is visibility measured at weather stations?
Weather stations measure visibility using several methods depending on automation level and required accuracy. Traditional observations involve a human observer estimating the distance at which known landmarks become indistinguishable. Automated stations use transmissometers measuring light beam attenuation over a fixed baseline of 10 to 75 meters, then extrapolate using the Koschmieder equation. Forward scatter meters send a light beam and detect the amount scattered at a specific angle, correlating with extinction coefficient. Modern lidar-based ceilometers can also provide visibility profiles through the atmosphere.
How does temperature affect visibility calculations?
Temperature affects visibility through several physical mechanisms. Lower temperatures reduce saturation vapor pressure, meaning less moisture is needed to reach high relative humidity and potential fog formation. Temperature inversions trap pollutants and aerosols near the surface, increasing extinction and reducing visibility. The Rayleigh scattering contribution increases slightly at lower temperatures due to higher air density. Temperature also controls photochemical reaction rates producing secondary aerosols like sulfates and organic particles, indirectly affecting visibility in polluted regions.
What is the relationship between visibility and PM2.5?
There is a strong inverse relationship between atmospheric visibility and PM2.5 particulate matter concentration. PM2.5 particles in the size range that most efficiently scatters visible light, particularly at wavelengths around 550 nanometers. Empirical studies show visibility in kilometers can be roughly estimated as V = K / PM2.5 where K depends on humidity and aerosol composition, typically 800 to 1500 for dry conditions. As PM2.5 increases from clean air levels of 5 micrograms per cubic meter to polluted levels of 100, visibility can drop from 30 kilometers to under 2.
How do aviation visibility categories work?
Aviation uses specific visibility categories to determine flight rules and operational requirements. Visual Flight Rules require visibility of at least 3 statute miles and ceiling of 1000 feet or higher. Marginal VFR applies when visibility is between 3 and 5 miles or ceilings are 1000 to 3000 feet. Instrument Flight Rules are required when visibility drops below 3 miles or ceilings below 1000 feet. Low IFR conditions exist when visibility is below 1 mile or ceilings below 200 feet. These categories are critical for flight safety and airport capacity.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy