Reference spheroid/geoid and datum: e.g. GRS80-NAD83, WGS84, NATR2022
Projection and its parameters, e.g. :
Lambert Conformal Conic (LCC): states in US
Universal Transverse Mercator (UTM): USGS, military
Albers Equal Area (conic): USGS national map
Vertical datum: e.g. NAVD88, NAPGD2022
NAD83 and NAVD88 to be replaced
with North American Terrestrial Reference Frame (NATR2022) and North American-Pacific Geopotential Datum of 2022 (NAPGD2022)
CRS standards
CRS have standardized definition with assigned EPSG codes
(initiated by European Petroleum Survey Group)
Transition to ISO 19111:2019
international standard notation in WKT:well known text (text markup language)
Popular Visualization CRS
World map in Pseudo Mercator with massive distortions farther from the equator,
compared with Winkel-Tripel projection with more realistic representation
Although the EPSG committee stated that they will not devalue the EPSG dataset by
including such inappropriate geodesy and cartography, Pseudo Mercator was eventually included as
EPSG 3857
- it is not recommended for professional work
Coordinate transformations
Geospatial data often come in different CRS, e.g.:
Federal agencies: Geodetic CRS (WGS84), Albers equal area, UTM
State agencies: State Plane CRS
Older data may have different datums (NAD27, NAD83)
Coordinate transformations
x,y -> longitude, latitude -> x’,y’
often performed on-fly, may be inaccurate and time consuming
first reproject all data into a suitable common CRS
then perform analysis and modeling
Geospatial data models
Mapped data, results of modeling or analysis are represented in GIS using
raster (regular grid) data model
vector (feature) data model
specialized representations: meshes
Geospatial phenomena
Continuous fields
elevation surfaces
temperature, precipitation
concentration of chemicals in soil or water bodies
Discrete features: lines, points or areas with attributes
roads, buildings, cell towers
land use types, administrative units
Some phenomena can be treated as both types
agricultural fields (crop type vs. crop height), soil properties
population densities
Continuous fields
each point in space is assigned a distinct value,
change in values between neighboring points is small
mathematical representation: bi-variate or multi-variate
continuous functions $w=f(x,y), w=f(x,y,z), w=f(x,y,z,t)$
often represented by a raster data model
vector model is also used: isolines, meshes, or points.
Discrete objects / features
points, lines, or areas (polygons) with attributes
represented by vector data model as geometry(shape) with attribute table
raster representation is also used
Raster data model: 2D
header: spatial extent and resolution, followed by matrix of values (INT, FP, DP),
continuous field : value assigned to a grid point
discrete object : category value assigned to pixel (area)
Raster data model: continuous fields
Elevation, 10m resolution (combined with shaded relief)
Precipitation, 500m resolution (color map draped over shaded relief)
Raster data model: discrete features
Land use classes at 30m resolution, qualitative data
Raster data model: discrete features
Roads: Speed limits for roads and walking speed for off-road areas, 30m resolution, quantitative data
Raster data model: 3D hybrid
vertical stack of 2D raster layers
can be used to represent soil horizons or geological layers
combined representation:
continuous (horizontally)
discrete (vertically)
Cross-sections through 3D model of soil horizons
Raster data model: 3D grid
header + 3D matrix of values, voxel model
spatial extent N,S,E,W,Top, Bottom
vertical resolution is usually much finer than horizontal
often used for 3D continuous representation $w=f(x,y,z)$