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The Earth and Its Coordinate System
Published in Terry A. Slocum, Robert B. McMaster, Fritz C. Kessler, Hugh H. Howard, Thematic Cartography and Geovisualization, 2022
Terry A. Slocum, Robert B. McMaster, Fritz C. Kessler, Hugh H. Howard
Although latitude was defined in general terms at the beginning of this chapter, it should be recognized that the same location can take on different latitude values, depending on the chosen reference ellipsoid. Figure 7.13A shows geodetic and geocentric latitudes on a reference ellipsoid. Geodetic latitude computed on a reference ellipsoid is measured by an angle that results when a perpendicular line at the ellipsoid's surface is drawn toward Earth's center. In every instance, except when the location in question is directly over the Equator or one of the poles, the perpendicular line will never intersect Earth's center. Rather, the line will pass through the equatorial plane at some other location. This result occurs because an ellipsoid does not have a constant radius. The angle measured at the intersection of the line and the equatorial plane is called the geodetic latitude. On the other hand, geocentric latitude computed on a reference ellipsoid is measured by an angle that results when a line at Earth's surface is drawn intersecting the plane of the Equator at Earth's center. Given the same point on any given reference ellipsoid, the geocentric and geodetic latitudes will be off by a small amount.8 This amount is significant for creating accurate maps (e.g., large-scale topographic maps) of local areas. For instance, surveyors commonly use geodetic latitude when referencing their survey positions because their surveys are tied to a specific reference ellipsoid for the country in which they are surveying. Geocentric latitudes are commonly used for global phenomena, such as satellite ground tracking maps.
Chapter 3
Published in Pearson Frederick, Map Projections:, 2018
The geocentric latitude is the angle between a vector from a center of the ellipse to a point P on the ellipse, or meridian, and the semimajor axis. The geodetic latitude is the angle between a line through the given point, normal to the ellipse, and the semimajor axis. The normal to the ellipse is the line defined by a surveyor’s plumb line if all gravity anomalies are ignored. Thus, geocentric latitude is defined by angle POB. Geodetic latitude is given by angle PQW, where line OB is parallel to line QW.
Generation of global 1-km daily top-of-atmosphere outgoing longwave radiation product from 2000 to 2021 using machine learning
Published in International Journal of Digital Earth, 2023
The MODIS sensor, onboard the Terra/Aqua satellites, contains 20 visible and shortwave infrared (VSWIR) bands and 16 TIR bands with resolutions from 250 m to 1 km. The twin sensors provide at least two daytime observations for most areas of the Earth (Wang and Liang 2016). In this study, three MODIS C6 products provided by the NASA Goddard Space Flight Center Level 1 and atmosphere archive and distribution system are used: MOD021KM/MYD021KM, MOD03/MYD03, and MOD35_L2/MYD35_L2. The MOD021KM/MYD021KM products are Earth-view level_1B data with 1-km resolution at nadir, which contain radiances and reflectances measured at the TOA. The MOD03/MYD03 products are geolocation field’s data consisting of geodetic latitude, longitude, solar zenith and azimuth angles, as well as satellite zenith and azimuth angles for each 1-km sample. The MOD35_L2/MYD35_L2 products contain cloud mask data that assign a clear sky confidence level (i.e. clear, probably clear, uncertain, and cloudy) to each instantaneous field of view (Barnes, Pagano, and Salomonson 1998).
Mapping the spatio-temporal visibility of global navigation satellites in the urban road areas based on panoramic imagery
Published in International Journal of Digital Earth, 2021
Ruixiong Kou, Bisheng Yang, Zhen Dong, Fuxun Liang, Shuwen Yang
Let the coordinate of the satellite in the geocentric coordinate system be , and the coordinate of the station in the geocentric coordinate system be , then the coordinate of the satellite in the station-centric coordinate system is calculated by the Bursa model, which is written by where is the geodetic latitude of the station and is the geodetic longitude of the station. Hence, the elevation (degree) and azimuth (degree)of the satellite are calculated by and if or , ; if , .
Monitoring the deformation of a concrete dam: a case study on the Deriner Dam, Artvin, Turkey
Published in Geomatics, Natural Hazards and Risk, 2020
Berkant Konakoglu, Leyla Cakir, Volkan Yilmaz
The commercial Magnet Tools 5.1 software developed by the Topcon Inc. was used to process the recorded GNSS data. The software automatically selects the processing frequency. Since the baseline length of the vector did not exceed 10 km, it automatically selected the L1/L2 mode for processing static vectors. The broadcast ephemeris was used as the satellite orbit. The Magnet Tools 5.1 software is able to provide geocentric cartesian coordinates in the World Geodetic System 1984 (WGS84) datum. Since the geocentric cartesian coordinates cannot be used in structural health monitoring applications, they should be transformed into local topocentric coordinates (Yigit 2016). Hence, all geocentric cartesian coordinates and their cofactor matrices were transformed into a local topocentric coordinate system for each period. The equations are given as follows: where and are the geodetic latitude and longitude of the topocentric origin, respectively. and are derived from their geocentric cartesian coordinates and