Functions: Atmospheric Refraction

Functions for computing atmospheric refraction corrections using Bennett’s (1982) empirical formula. Earth’s atmosphere bends light from celestial objects, making them appear higher above the horizon than their true geometric position. Near the horizon, refraction is approximately 0.57 degrees --- enough to extend satellite visibility windows by roughly 35 seconds at AOS and LOS, and to make the Sun appear above the horizon when it has already geometrically set.

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atmospheric_refraction

Computes the atmospheric refraction correction in degrees for a given geometric elevation using Bennett’s (1982) formula under standard atmosphere conditions (pressure 1010 mbar, temperature 10 C). The domain is clamped at -1 degree to avoid singularity in the cotangent term.

Signature

atmospheric_refraction(elevation_deg float8) → float8

Parameters

Parameter	Type	Unit	Description
elevation_deg	float8	degrees	Geometric elevation of the object above the horizon

Returns

Refraction correction in degrees. Always positive --- add this value to the geometric elevation to get the apparent elevation. At the horizon (0 degrees), refraction is approximately 0.57 degrees. It drops rapidly with increasing elevation and is negligible above 45 degrees.

Note

The domain guard at -1 degree prevents numerical blowup in the cotangent. Objects below -1 degree geometric elevation are deeply below the horizon and refraction is not physically meaningful there.

Example

-- Refraction at various elevations
SELECT elevation,
       round(atmospheric_refraction(elevation)::numeric, 4) AS refraction_deg
FROM unnest(ARRAY[-1, 0, 5, 10, 20, 45, 90]) AS elevation;

-- How much does refraction shift the Sun at sunset?
SELECT round(atmospheric_refraction(0)::numeric, 4) AS horizon_refraction_deg;

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atmospheric_refraction_ext

Computes atmospheric refraction with a pressure and temperature correction factor applied to Bennett’s formula, following the Meeus formulation. Useful for high-altitude observatories or extreme weather conditions where standard atmosphere assumptions break down.

Signature

atmospheric_refraction_ext(elevation_deg float8, pressure_mbar float8, temp_celsius float8) → float8

Parameters

Parameter	Type	Unit	Description
elevation_deg	float8	degrees	Geometric elevation of the object above the horizon
pressure_mbar	float8	mbar	Atmospheric pressure at the observer
temp_celsius	float8	C	Air temperature at the observer

Returns

Refraction correction in degrees, adjusted for the given pressure and temperature. The correction factor is (P / 1010) * (283 / (273 + T)) applied to the standard Bennett formula result.

Example

-- Refraction at Mauna Kea summit (4205m, ~620 mbar, -2C)
SELECT round(atmospheric_refraction_ext(5.0, 620.0, -2.0)::numeric, 4) AS refraction_mauna_kea,
       round(atmospheric_refraction(5.0)::numeric, 4) AS refraction_standard;

-- Compare standard vs corrected refraction across a range of elevations
SELECT elevation,
       round(atmospheric_refraction(elevation)::numeric, 4) AS standard,
       round(atmospheric_refraction_ext(elevation, 850.0, -10.0)::numeric, 4) AS high_altitude_cold
FROM unnest(ARRAY[0, 2, 5, 10, 30]) AS elevation;

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topo_elevation_apparent

Convenience function that returns the apparent elevation of an object by adding the atmospheric refraction correction to the geometric elevation stored in a topocentric value. The result is in degrees.

Signature

topo_elevation_apparent(topocentric) → float8

Parameters

Parameter	Type	Description
(unnamed)	topocentric	A topocentric observation result from any *_observe function

Returns

Apparent elevation in degrees --- the geometric elevation plus the Bennett refraction correction under standard atmosphere. Always higher than the geometric topo_elevation() value.

Example

-- Compare geometric vs apparent elevation for the Moon
SELECT round(topo_elevation(t)::numeric, 3) AS geometric_el,
       round(topo_elevation_apparent(t)::numeric, 3) AS apparent_el,
       round(topo_elevation_apparent(t) - topo_elevation(t)::numeric, 4) AS refraction_correction
FROM moon_observe('40.0N 105.3W 1655m'::observer, now()) AS t;

-- Find objects that are geometrically below horizon but visible due to refraction
SELECT norad_id,
       round(topo_elevation(o)::numeric, 3) AS geometric_el,
       round(topo_elevation_apparent(o)::numeric, 3) AS apparent_el
FROM satellite_catalog,
     observe_safe(tle, '40.0N 105.3W 1655m'::observer, now()) AS o
WHERE o IS NOT NULL
  AND topo_elevation(o) < 0
  AND topo_elevation_apparent(o) > 0;

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predict_passes_refracted

Predicts satellite passes using a refracted horizon threshold instead of the geometric horizon. The geometric threshold is set to -0.569 degrees, which corresponds to the apparent horizon after atmospheric refraction. This means satellites become visible approximately 35 seconds earlier at AOS and remain visible approximately 35 seconds later at LOS compared to predict_passes.

Signature

predict_passes_refracted(
  tle tle,
  obs observer,
  start_time timestamptz,
  end_time timestamptz,
  min_el float8 DEFAULT 0.0
) → SETOF pass_event

Parameters

Parameter	Type	Default	Description
tle	tle		Satellite TLE
obs	observer		Observer location
start_time	timestamptz		Start of the search window
end_time	timestamptz		End of the search window
min_el	float8	0.0	Minimum peak elevation in degrees. Passes whose maximum elevation is below this threshold are excluded.

Returns

A set of pass_event records, ordered by AOS time. Each pass will show slightly earlier AOS and later LOS times compared to predict_passes due to the refracted horizon.

Tip

The refracted threshold of -0.569 degrees geometric matches what visual observers actually experience --- the atmosphere bends satellite light so it is visible even when the satellite is geometrically below the horizon. Use this function for scheduling visual observations, antenna pointing, or any application where the physical visibility window matters.

Example

-- Compare geometric vs refracted pass predictions for the ISS
WITH iss AS (
  SELECT '1 25544U 98067A   24001.50000000  .00016717  00000-0  10270-3 0  9025
2 25544  51.6400 208.9163 0006703  30.1694  61.7520 15.50100486 00001'::tle AS tle
)
SELECT pass_aos_time(p)      AS rise,
       pass_max_elevation(p) AS max_el,
       pass_los_time(p)      AS set,
       pass_duration(p)      AS dur
FROM iss,
     predict_passes_refracted(tle, '40.0N 105.3W 1655m'::observer,
                              now(), now() + interval '24 hours', 10.0) AS p;

-- How much extra visibility does refraction add?
WITH iss AS (
  SELECT '1 25544U 98067A   24001.50000000  .00016717  00000-0  10270-3 0  9025
2 25544  51.6400 208.9163 0006703  30.1694  61.7520 15.50100486 00001'::tle AS tle
),
geo AS (
  SELECT pass_duration(p) AS dur
  FROM iss, predict_passes(tle, '40.0N 105.3W 1655m'::observer,
                           now(), now() + interval '24 hours') AS p
  LIMIT 1
),
refr AS (
  SELECT pass_duration(p) AS dur
  FROM iss, predict_passes_refracted(tle, '40.0N 105.3W 1655m'::observer,
                                     now(), now() + interval '24 hours') AS p
  LIMIT 1
)
SELECT geo.dur AS geometric_duration,
       refr.dur AS refracted_duration
FROM geo, refr;