What Meteorological Optical Range represents
Koschmieder's relationship fixes the contrast threshold at 0.02, whose negative natural logarithm is approximately 3.912. Dividing by uniform extinction returns MOR.
Meteorological Optical Range begins with atmospheric extinction coefficient. Mark each value as observed, remotely sensed, modeled, assumed, or derived, and preserve its valid time and spatial support.
Formula and convention
The working relationship is MOR = 3.912 ÷ σ. Meteorological Optical Range uses only the displayed entries and does not retrieve imagery, station observations, ephemerides, forecasts, or runway systems.
Keep percentages as percentages at entry and convert them to fractions only where the formula shows it. For Meteorological Optical Range, retain angle direction, optical threshold, height reference, and distance unit with the answer.
Checked numerical example
An extinction coefficient of 4 km⁻¹ gives exactly 0.978 km MOR.
Reset restores this Meteorological Optical Range example. Repeat it independently with the stated constants and rounding before replacing demonstration values with observations or scenarios.
Collecting compatible inputs
Use a representative atmospheric extinction coefficient for the path and instrument wavelength. Keep kilometres inverse and kilometres consistent.
Record site, coordinates, elevation, timestamp, time zone, path direction, wavelength or sensor band, target definition, cloud-layer method, solar-time convention, averaging period, and quality flags when relevant to Meteorological Optical Range.
Interpreting Meteorological optical range
MOR is the distance at which a black target against the horizon would fall to two-percent apparent contrast in the ideal model.
Compare Meteorological Optical Range outputs only after aligning reference height, sky footprint, path, illumination, contrast convention, and temporal average. Similar numbers can describe different optical or geometric quantities.
Continue the Meteorological Optical Range workflow with the related Cloud Base Height Calculator, keeping the same observation support and conventions.
Boundary and monotonic checks
Extinction must be positive. As extinction approaches zero, finite MOR grows beyond this formula's practical observational scope.
For Meteorological Optical Range, change one input at a time and predict whether the answer should rise, fall, or remain fixed. Unexpected behavior can expose percent-fraction, degree-radian, metre-kilometre, or layer-order mistakes.
Continue the Meteorological Optical Range workflow with the related Cloud Oktas from Percentage Calculator, keeping the same observation support and conventions.
Where the model stops
Night lights, runway systems, precipitation structure, terrain targets, variable backgrounds, and nonuniform fog are not captured by this daytime contrast definition.
Meteorological Optical Range is transparent educational arithmetic, not a cloud observation, weather forecast, solar-resource assessment, flight rule, runway visual range report, instrument calibration, or operational safety authority.
Uncertainty and sensitivity
Vary the least certain Meteorological Optical Range input over a credible range and retain the resulting spread in meteorological optical range. Display precision cannot overcome observer classification, retrieval uncertainty, spatial variability, or an empirical coefficient.
A Meteorological Optical Range sensitivity range is not automatically a probability interval. It omits correlations, model-form error, sampling mismatch, sub-grid cloud structure, nonuniform visibility paths, and uncertainty outside the entered variables.
Continue the Meteorological Optical Range workflow with the related Extraterrestrial Solar Radiation Calculator, keeping the same observation support and conventions.
Spatial and temporal representativeness
Cloud and visibility can change across seconds, kilometres, viewing directions, and vertical layers. One Meteorological Optical Range input set represents only its declared path, footprint, and interval.
When combining several Meteorological Optical Range samples, document weights and retain individual values so variability is not hidden by a single mean or total.
Cloud amount, overlap, and layers
Cloud fraction is an area or sky-dome proportion, while a ceiling is a height classification and optical depth is attenuation. Meteorological Optical Range should not substitute one quantity for another merely because each relates to cloud.
When layers enter Meteorological Optical Range, state whether overlap is random, maximum, observed, or ignored. Adding layer percentages directly can exceed 100% and double-count vertically aligned cloud.
Visibility and contrast conventions
Visibility from Meteorological Optical Range depends on the target contrast threshold and extinction units. Meteorological optical range fixes a two-percent contrast convention; a general contrast range or runway screening estimate may use another threshold.
Do not equate Meteorological Optical Range optical distance with prevailing visibility, slant range, night visual range, or official RVR without the required observation and processing conventions.
Continue the Meteorological Optical Range workflow with the related Runway Visual Range Estimate Calculator, keeping the same observation support and conventions.
Solar geometry and radiation conventions
Solar elevation is measured above the geometric horizon, while azimuth here is clockwise from true north. Meteorological Optical Range must retain whether radiation is normal to the rays or incident on a horizontal surface.
Civil time is not solar hour angle. Longitude, time zone, equation of time, atmospheric refraction, shading horizon, and surface tilt belong in Meteorological Optical Range only when the displayed model explicitly includes them.
Frequent clouds and visibility errors
Typical Meteorological Optical Range errors include mixing oktas and tenths, confusing AGL with MSL, adding overlapping layers, treating degrees as radians, using sea-level-reduced visibility, or applying a two-percent constant to a five-percent threshold.
Reject impossible Meteorological Optical Range combinations rather than forcing an answer. Keep a clear zero distinct from missing or obscured sky, preserve signs on hour angle, and verify every inverse distance and logarithm denominator before downstream use.
Questions about the sky model
Is this an operational visibility or aviation value?
No. Meteorological Optical Range does not replace official weather observations, RVR systems, flight procedures, warnings, or qualified judgment.
How should the result be rounded?
Keep full precision inside Meteorological Optical Range, then round no more finely than the least certain measurement or model assumption supports.
When should I recalculate?
Recalculate Meteorological Optical Range when its site, time, path, layer, sky footprint, illumination, source observation, or model assumption changes.