Latitude

Latitude is an angular coordinate that describes how far north or south a location lies relative to the equator of Earth. It ranges from $0^\circ$ at the equator to $90^\circ$ north at the North Pole and $90^\circ$ south at the South Pole. Together with longitude, it forms the latitude and longitude system used to specify geographic locations. In precise mapping, latitude normally means geodetic latitude, defined using a mathematical model of Earth’s shape rather than a perfect sphere. (oceanservice.noaa.gov)

Definition and notation

Latitude is conventionally represented by the Greek letter $\phi$. Northern latitudes are designated N and southern latitudes S; in signed numerical notation, north is positive and south is negative. A latitude therefore lies within the interval

Latitude is commonly expressed in decimal degrees or in degrees, minutes, and seconds. One degree contains 60 angular minutes, and one minute contains 60 angular seconds. These are subdivisions of angle, not units of time. (oceanservice.noaa.gov)

For a latitude whose absolute value is $D$ degrees, $M$ minutes, and $S$ seconds, conversion to decimal degrees follows directly from these subdivisions:

For example, $35^\circ 30' 00''\text{ S}$ is equivalent to $-35.5^\circ$. A hemisphere designation and a numerical sign are alternative ways of recording the same north–south distinction. (oceanservice.noaa.gov)

Parallels and distance

Lines joining locations of equal latitude are called parallels or circles of latitude. They run east–west around Earth, whereas meridians run north–south between the poles. On a spherical Earth, the equator is the largest parallel; other parallels become progressively smaller toward the poles, where they reduce to points. (oceanservice.noaa.gov)

Elementary geometry gives the radius $r$ and circumference $C$ of a parallel on a sphere of radius $R$:

Consequently, an east–west interval of one degree of longitude becomes shorter as absolute latitude increases. This differs from a degree of latitude, which corresponds to approximately 111 kilometres of north–south distance throughout the world. (en.wikipedia.org)

On the same spherical model, the distance along a meridian between latitudes $\phi_1$ and $\phi_2$ is

with the angular difference expressed in radians. Earth’s actual flattening means that equally spaced latitude angles do not correspond to exactly equal meridian distances. Precise distances are calculated on a specified ellipsoid rather than by treating the 111-kilometre approximation as exact. (oceanservice.noaa.gov)

Geodetic, geocentric, and astronomical latitude

Earth is approximately an oblate ellipsoid: its equatorial radius is greater than its polar radius. As a result, several definitions of latitude must be distinguished in geodesy, the science concerned with Earth’s shape, orientation, and positioning. (oceanservice.noaa.gov)

Geodetic latitude

Geodetic latitude, also called ellipsoidal latitude, is the angle between the equatorial plane and the normal, or perpendicular, to a reference ellipsoid. For a point above or below the ellipsoid, it is associated with the ellipsoidal normal passing through that point. This is the latitude ordinarily used on standard maps and in geodetic coordinate systems. It is not generally the angle measured at Earth’s centre. (ncei.noaa.gov)

Geocentric latitude

Geocentric latitude is the angle between the equatorial plane and a line connecting Earth’s centre to the point in question. Geodetic and geocentric latitude coincide on a sphere, but generally differ on an oblate ellipsoid. (ncei.noaa.gov)

For a point on an ellipsoid’s surface, their relationship is

where $\psi$ is geocentric latitude, $\phi$ is geodetic latitude, and $e$ is the ellipsoid’s first eccentricity. Away from the equator and poles, geocentric latitude has a smaller absolute value than geodetic latitude. The stated relationship applies to the ellipsoid’s surface; a point at nonzero ellipsoidal height requires that height to be included in the conversion. (en.wikipedia.org)

Astronomical latitude

Astronomical latitude is defined by the direction of the local vertical, established by gravity, rather than by the normal to a reference ellipsoid. It can be determined through observations of celestial objects. Because Earth’s gravity field is irregular, the local vertical and ellipsoidal normal need not coincide. Their angular separation is called the deflection of the vertical; its north–south component accounts for the difference between astronomical and geodetic latitude. (nweb.ngs.noaa.gov)

Major parallels and sunlight

Several named parallels have particular astronomical and geographic significance:

The tropical and polar circles are linked to Earth’s axial tilt, approximately $23.5^\circ$. In idealized geometry, the tropics lie at latitudes equal in magnitude to the tilt, and the polar circles at its complement, approximately $90^\circ-23.5^\circ$. The rounded values in the table are not exact surveyed positions. (oceanservice.noaa.gov)

Between the tropics, the Sun can reach the zenith, directly overhead, on particular dates. Poleward of the polar circles, there are periods when the Sun’s centre remains above or below the horizon throughout a complete daily rotation. Actual observed sunrise and sunset also depend on atmospheric refraction, the Sun’s apparent size, and the observer’s horizon. (pwg.gsfc.nasa.gov)

Latitude and climate

Latitude strongly influences climate because it helps determine the angle of incoming sunlight and the seasonal duration of daylight. Averaged over a year, low latitudes receive more solar energy per unit area than polar regions. At higher latitudes, seasonal differences in daylight and solar elevation become much greater. These patterns contribute to Earth’s broad tropical, temperate, and polar climatic zones. (science.nasa.gov)

The resulting imbalance in heating drives exchanges of energy through the atmosphere and the ocean. Latitude alone, however, does not determine local temperature or rainfall: ocean heat storage, atmospheric circulation, and proximity to the sea also influence regional conditions. Places at similar latitudes can therefore have substantially different climates. (science.nasa.gov)

Measurement and historical development

Latitude has long been determined through astronomical observations. Measuring the elevation of a suitable celestial object above the horizon allows an observer to infer latitude, provided the object’s position in the sky is known. Observations of the Sun and the North Star were especially important in navigation. Reliable latitude measurement at sea preceded reliable longitude measurement by centuries. (oceanservice.noaa.gov)

In ancient Greek mathematical geography, Eratosthenes and Hipparchus developed systems for describing north–south position using parallels, angular measurements, and related astronomical quantities. In the second century CE, Ptolemy used a geographic coordinate system in his Geography. Surviving ancient coordinates reflect differing observational methods, precision, and transmission histories, rather than the uniform accuracy of a modern survey. (arxiv.org)

Terrestrial surveying subsequently established networks in which positions were mathematically connected through measured angles and distances. Satellite methods, including the Global Positioning System, made it possible to determine positions within global reference systems rather than relying solely on local astronomical observations or connected ground surveys. (nweb.ngs.noaa.gov)

Reference systems and practical use

A precise latitude is meaningful only within an identified geodetic datum or reference frame. Such a system specifies how coordinates and a reference surface are related to Earth. Different datums may assign different numerical coordinates to the same physical location; changing between them is a coordinate transformation, not merely a change from degrees–minutes–seconds to decimal notation. (geodesy.noaa.gov)

Latitude and longitude are widely used in digital mapping and geographic information systems. They are angular coordinates, unlike projected eastings and northings expressed as linear distances. Spatial datasets therefore record coordinate-system and datum information so that locations can be interpreted and combined correctly. (usgs.gov)

References

1. What is latitude?oceanservice.noaa.gov
2. NOAA KLM User’s Guidencei.noaa.gov
3. API for NGS Data Explorergeodesy.noaa.gov
4. Longitudeen.wikipedia.org
5. INVERSE and FORWARDgeodesy.noaa.gov
6. Geodesy for the Laymannweb.ngs.noaa.gov
7. Datums and Reference Framesgeodesy.noaa.gov
8. Latitudeen.wikipedia.org
9. Geodetic Astronomy at NGS: Past and Presentgeodesy.noaa.gov
10. Global Climate, Global Wind Flowpwg.gsfc.nasa.gov
11. Circle of latitudeen.wikipedia.org
12. Climate and Earth’s Energy Budgetscience.nasa.gov