Geography - Map Projections

Geography - Map Projections

0. 有用的网站

[1] I Hate Coordinate Systems!, 地址

[2] EPSG, 地址

[3] The True Size of, 地址

1 Coordinate Reference System (CRS)

Coordinate Reference System (CRS) or Spatial Reference System (SRS)

1.1 Geographic Coordinate Systems 地理坐标系

• Latitude and longitude: Degrees Minutes Seconds (DMS), decimal degrees

• World Geodetic System 1984 (WGS-84):

  • EPSG:4326

  • Google Map, GPS

1.2 Projected Coordinate Systems 投影坐标系

• Properties of geographic objects that are distorted:

  • Area

  • Scale

  • Shape

  • Direction

• Three families of map projections

  • Cylindrical Projection: preserve distances or areas

  • Conical Projection: preserve angles

  • Planar Projections: preserve distances

• Examples of compromise projections

  • Robinson Projection: Compromises distortions of area, angular conformity and distance.

  • Winkel Tripel Prokection

1 Projections with angular conformity

• Conformal or orthomorphic projections:

  • Mercator projection

  • Lambert Conformal Conic projection

• Results in distortion of areas

• Lager the area the larger the distortion

• Used by USGS topographical maps

• Used for navigation, meteorology

Universal Transverse Mercator (UTM)

• a global map projection

2 Projections with equal distance

• Equidistant projection

• Constant scale

• Maintains accurate distances from the centre of the projection or along give lines

• Examples:

  • Plate Carree Equidistant Cylindrical Projection

  • Equirectangular Projection

  • Azimuthal Equidistant Projection: United State logo

• Use: radio and seismic, mapping, navigation

3 Projections with equal area

• Equal area projection

• Preserves proportions of areas

• Results in distortions in angular conformity

• Examples:

  • Alber's Equal Area Projection

  • Lambert's Equal Area Projection

  • Mollweide Equal Area Cylindrical Projection

• Use: general reference, education

1.3 Some terminology

• Datum (基准): Localised approximation of earth's ellipsoid

• spheroid

• geoid

• False Northing, False Easting

1.4 Use EPSG codes

EPSG (European Petroleum Survey Group)

1.5 On-the-fly reprojection (OTF)

• All layers visualised in a GIS application need to be in the same projection

• Instead of reprojecting all layers to the same projection, GIS applications use on-the-fly reprojection.

• Beware: OTF reprojection does not change the projection of layers!

2 Practice by Python

2.1 pyproj 库

pyproj 主要通过 pyproj.crs.CRS 类型处理 CRS，site。可以使用以下格式直接初始化：

• PROJ strings

• EPSG codes

• Well-Known-Text (WKT): Shapefile 文件中的 .prj 文件使用此格式记录 CRS

• JSON

实例： 通过 EPSG code 初始化

import pyproj
crs_1 = pyproj.CRS(4326)
crs_2 = pyproj.CRS.from_epsg(4326)
crs_3 = pyproj.CRS("epsg:4326")
crs_4 = pyproj.CRS(("epsg", "4326"))
print(crs_1.equals(crs_2), crs_1.equals(crs_3), crs_1.equals(crs_4))

crs_1 = pyproj.crs.CRS(4326)
crs_2 = pyproj.crs.CRS.from_epsg(4326)
crs_3 = pyproj.crs.CRS("epsg:4326")
crs_4 = pyproj.crs.CRS(("epsg", "4326"))

实例： 通过 WKT 初始化

wkt_str = ''
crs_1 = pyproj.CRS(wkt_str)
crs_2 = pyproj.CRS.from_wkt(wkt_str)
crs_3 = pyproj.CRS.from_string(wkt_str)

pyproj.crs.CRS 对象常用属性和方法

.is_bound

.is_derived

.is_engineering

.is_geocentric

.is_geographic：CRS 是否为地理坐标系

.is_projected: CRS 是否为投影坐标系

.is_vertical

2.2 坐标投影，坐标系之间转换

实例：相同坐标系的不同坐标格式之间的转化

from pyproj import CRS
# PROJ dictionary
crs_dict = data_gdf.crs   
# pyproj CRS object
crs_object = CRS(crs_dict)  
# EPSG code
crs_epsg = CRS(crs_dict).to_epsg(min_confidence=25)   
# PROJ string
crs_proj4 = CRS(crs_dict).to_proj4()  
# Well-Known Text (WKT)
crs_wkt = CRS(crs_dict).to_wkt(pretty=True)

在 geopandas 库中，geopandas.Series 和 geopandas.GeoDataFrame 数据对象，可以直接使用 .to_crs() 方法实现，返回的类型为 pyproj.crs.crs.CRS。参考官方文档 site 和 Tutorial：Managing Projections

Case: CRS in Singapore

DataMall 中数据 Geospatial Data 的位置信息均采用以下投影坐标系统，其单位为米

wkt_str = '''
PROJCS["SVY21",GEOGCS["GCS_WGS_1984",DATUM["D_WGS_1984",SPHEROID["WGS_1984",6378137.0,298.257223563]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Transverse_Mercator"],PARAMETER["False_Easting",28001.642],PARAMETER["False_Northing",38744.572],PARAMETER["Central_Meridian",103.833333333333],PARAMETER["Scale_Factor",1.0],PARAMETER["Latitude_Of_Origin",1.36666666666667],UNIT["Meter",1.0]]
'''
crs_1 = pyproj.CRS.from_string(wkt_str)
print(crs_1.is_geographic, crs_1.is_projected)

EPSG Dataset 中，与 Singapore 有关的 CRS 主要有：

• EPSG:4757，SVY21，地理坐标系

• EPSG:3414，SVY21 / Singapore TM，投影坐标系，单位为米

crs_2 = pyproj.CRS("EPSG:4757")
crs_3 = pyproj.CRS("EPSG:3414")
print(crs_2.is_geographic, crs_2.is_projected)  # True False
print(crs_3.is_geographic, crs_3.is_projected)  # False True

注意： crs_1 和 crs_3 并不完全相同，区别在于其 datum 不相同：

print(crs_1.datum)  # World Geodetic System 1984
print(crs_3.datum)  # SVY21

Reference

8 Coordinate Reference Systems in QIGS Document, 地址

Map projections in GIS (theory), Yotube, 地址

Map projections, Automating GIS-processes 2021, ite