Introduction to PROJ in Earth Statistics
Build-up
The Earth is round, and more precisely, it is considered an ellipsoid. A ‘globe’, which is a scaled-down model of the Earth, is an accurate model but not very widely used since, after all, humanity is still more comfortable with flat pictures. Thus, various coordinate systems have been devised, and there are… quite a variety of them.
For example, the world map we commonly see uses the Mercator Projection, where the longitude and latitude are accurate, although the area is distorted,2 and other methods were designed with their own advantages and reasons.
Given that these projections are about ’enclosing a curved surface within a plane’, there will inevitably be some distortion and loss in some aspects. Or they could be accurate but too complex to use, or they might work well globally but lose their finesse in very small specific areas.
This is not only a problem with Earth but also with celestial bodies that we can call planets. While there might be a mainstream or dominant system, ultimately, a variety of coordinate systems proliferate. The key now is how to navigate between these coordinate systems.
Introduction
PROJ is a geospatial coordinate transformation software that performs the task of converting from one CRS to another CRS, which is hard to ignore if you are dealing with spatial statistics, and you’re bound to encounter it at least once. Its implementation or wrapping is easily found regardless of programming language or framework:
Example
How PROJ is used varies with each implementation, so it’s neither meaningful nor possible to explain each one in detail. Regardless of the language, let’s take a look at how it is used in Julia.
using Proj
trans = Proj.Transformation("EPSG:4326", "+proj=utm +zone=32 +datum=WGS84")
trans(55, 12)
# -> (691875.632137542, 6.098907825129169e6)
In Julia, the Proj.Transformation function allows for
- mapping a coordinate in the EPSG:4326 coordinate system
- to a coordinate in the coordinate system using the UTM method, in zone 32 with datum WGS84,
- and returns the transformation (function itself), resulting in converting the EPSG:4326 coordinate (55, 12) into (691875.632137542, 6.098907825129169e6).
What +proj, +zone, and +datum actually mean should be discovered by consulting the official documentation. The definition of these coordinate systems is carried out through strings, and must be understood as a unique syntax used in the field of geostatistics.
Major Coordinate Systems in Korea
The list of major coordinate systems can be found on the OSGeo Korean Division Official Website.
Archive as of January 27, 2023
Global Coordinate Systems
These coordinate systems are widely used when representing the entire world at once.
- WGS84 Latitude and Longitude: The coordinate system used by GPS
EPSG:4326, EPSG:4166 (Korean 1995)
+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs
- Bessel 1841 Latitude and Longitude: A coordinate system using the regional ellipsoid that fits well in Korea and Japan
EPSG:4004, EPSG:4162 (Korean 1985)
+proj=longlat +ellps=bessel +no_defs +towgs84=-115.80,474.99,674.11,1.16,-2.31,-1.63,6.43
- GRS80 Latitude and Longitude: Almost identical to WGS84
EPSG:4019, EPSG:4737 (Korean 2000)
+proj=longlat +ellps=GRS80 +no_defs
- Google Mercator: The coordinate system used by Google Maps/Bing Maps/Yahoo Maps/OSM, etc.
EPSG:3857(공식), EPSG:900913(통칭)
+proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k=1.0 +units=m +nadgrids=@null +no_defs
UTM
A standard TM dividing the world into 6-degree units, widely used in military maps.
- UTM52N (WGS84): Used between longitudes 120-126 degrees
EPSG:32652
+proj=utm +zone=52 +ellps=WGS84 +datum=WGS84 +units=m +no_defs
- UTM51N (WGS84): Used between longitudes 126-132 degrees
EPSG:32651
+proj=utm +zone=51 +ellps=WGS84 +datum=WGS84 +units=m +no_defs
Unadjusted Old Topographic Standard
These coordinate systems are registered with EPSG, but due to problems with the lon_0 value, they are hardly used in practice. The Old Topographic Standard was actually used in the field.
- East Origin (Bessel): For eastern regions like Gangwon-do
EPSG:2096
+projtmerc +lat_0=38 +lon_0=129 +k=1 +x_0=200000 +y_0=500000 +ellps=bessel +units=m +no_defs +towgs84=-115.80,474.99,674.11,1.16,-2.31,-1.63,6.43
- Central Origin (Bessel): For central regions like Seoul
EPSG:2097
+proj=tmerc +lat_0=38 +lon_0=127 +k=1 +x_0=200000 +y_0=500000 +ellps=bessel +units=m +no_defs +towgs84=-115.80,474.99,674.11,1.16,-2.31,-1.63,6.43
- West Origin (Bessel): For western regions like the West Sea islands
EPSG:2098
+proj=tmerc +lat_0=38 +lon_0=125 +k=1 +x_0=200000 +y_0=500000 +ellps=bessel +units=m +no_defs +towgs84=-115.80,474.99,674.11,1.16,-2.31,-1.63,6.43
Old Topographic Standard
This describes the coordinate systems used by the National Geographic Information System (KLIS) and topographic maps from the Geographic Information Institute before 2002.
- Adjusted West Origin (Bessel) - Used in KLIS for western regions
EPSG:5173
+projtmerc +lat_0=38 +lon_0=125.0028902777778 +k=1 +x_0=200000 +y_0=500000 +ellps=bessel +units=m +no_defs +towgs84=-115.80,474.99,674.11,1.16,-2.31,-1.63,6.43
- Adjusted Central Origin (Bessel): Used in KLIS for central regions
EPSG:5174
+proj=tmerc +lat_0=38 +lon_0=127.0028902777778 +k=1 +x_0=200000 +y_0=500000 +ellps=bessel +units=m +no_defs +towgs84=-115.80,474.99,674.11,1.16,-2.31,-1.63,6.43
- Adjusted Jeju Origin (Bessel): Used in KLIS for the Jeju region
EPSG:5175
+proj=tmerc +lat_0=38 +lon_0=127.0028902777778 +k=1 +x_0=200000 +y_0=550000 +ellps=bessel +units=m +no_defs +towgs84=-115.80,474.99,674.11,1.16,-2.31,-1.63,6.43
- Adjusted East Origin (Bessel): Used in KLIS for eastern regions
EPSG:5176
+proj=tmerc +lat_0=38 +lon_0=129.0028902777778 +k=1 +x_0=200000 +y_0=500000 +ellps=bessel +units=m +no_defs +towgs84=-115.80,474.99,674.11,1.16,-2.31,-1.63,6.43
- Adjusted East Sea (Ulleung) Origin (Bessel): Used in KLIS for the Ulleung region
EPSG:5177
+proj=tmerc +lat_0=38 +lon_0=131.0028902777778 +k=1 +x_0=200000 +y_0=500000 +ellps=bessel +units=m +no_defs +towgs84=-115.80,474.99,674.11,1.16,-2.31,-1.63,6.43
KATEC Series
A coordinate system widely used to represent the entire Korean peninsula as one coordinate system.
- UTM-K (Bessel): Used in the new address system
EPSG:5178
+proj=tmerc +lat_0=38 +lon_0=127.5 +k=0.9996 +x_0=1000000 +y_0=2000000 +ellps=bessel +units=m +no_defs +towgs84=-115.80,474.99,674.11,1.16,-2.31,-1.63,6.43
- UTM-K (GRS80): The coordinate system used by Naver maps
EPSG:5179
+proj=tmerc +lat_0=38 +lon_0=127.5 +k=0.9996 +x_0=1000000 +y_0=2000000 +ellps=GRS80 +units=m +no_defs
// Added by Shin Sang-hee on January 21, 2014
- KATEC coordinate system for navigation (KOTI-KATEC)
EPSG 없음. 비공식 좌표계임.
+proj=tmerc +lat_0=38 +lon_0=128 +k=0.9999 +x_0=400000 +y_0=600000 +ellps=bessel +units=m +no_defs +towgs84=-115.80,474.99,674.11,1.16,-2.31,-1.63,6.43
Ellipsoid-Changed Old Topographic Standard
These are coordinate systems where problems with ellipsoids and lon_0 have been corrected, and were briefly widely used in the early 2000s.
- West origin (GRS80)-falseY:50000
EPSG:5180
+projtmerc +lat_0=38 +lon_0=125 +k=1 +x_0=200000 +y_0=500000 +ellps=GRS80 +units=m +no_defs
- Central origin (GRS80)-falseY:50000: The coordinate system used by Daum maps
EPSG:5181
+proj=tmerc +lat_0=38 +lon_0=127 +k=1 +x_0=200000 +y_0=500000 +ellps=GRS80 +units=m +no_defs
- Jeju origin (GRS80)-falseY:55000
EPSG:5182
+proj=tmerc +lat_0=38 +lon_0=127 +k=1 +x_0=200000 +y_0=550000 +ellps=GRS80 +units=m +no_defs
- East origin (GRS80)-falseY:50000
EPSG:5183
+proj=tmerc +lat_0=38 +lon_0=129 +k=1 +x_0=200000 +y_0=500000 +ellps=GRS80 +units=m +no_defs
- East Sea (Ulleung) origin (GRS80)-falseY:50000
EPSG:5184
+proj=tmerc +lat_0=38 +lon_0=131 +k=1 +x_0=200000 +y_0=500000 +ellps=GRS80 +units=m +no_defs
Current National Geographic Information Institute Standard
Coordinate systems used in the National Geographic Information Institute maps since 2002.
- West origin (GRS80)-falseY:60000
EPSG:5185
+proj=tmerc +lat_0=38 +lon_0=125 +k=1 +x_0=200000 +y_0=600000 +ellps=GRS80 +units=m +no_defs
- Central origin (GRS80)-falseY:60000
EPSG:5186
+proj=tmerc +lat_0=38 +lon_0=127 +k=1 +x_0=200000 +y_0=600000 +ellps=GRS80 +units=m +no_defs
- East origin (GRS80)-falseY:60000
EPSG:5187
+proj=tmerc +lat_0=38 +lon_0=129 +k=1 +x_0=200000 +y_0=600000 +ellps=GRS80 +units=m +no_defs
- East Sea (Ulleung) origin (GRS80)-falseY:60000
EPSG:5188
+proj=tmerc +lat_0=38 +lon_0=131 +k=1 +x_0=200000 +y_0=600000 +ellps=GRS80 +units=m +no_defs
흥미롭게도 이 근사한 짤은 지구 평평론자가 만들었다: https://flatearth.ws/map-projection ↩︎