## Spatial Data Types and Spatial Reference System

Hui Hu Ph.D.

Department of Epidemiology

College of Public Health and Health Professions & College of Medicine

January 23, 2019

# Spatial Data Types and Spatial Reference System

### Spatial Data Types

• Geometry:
- the planar type
- the very first model and still the most popular type
- the foundation of the other types
- uses the Cartesian math

• Geography:
- the spheroidal geodetic type
- lines and ploygons drawn on the earth's curved surface

• Raster:
- the multiband cell type
- space as a grid of rectangular cells, each containing a numeric array of values

• Topology:
- the relational model type
- models the world as a network of connected nodes, edges, and faces
- network

• These four types can coexist in the same database:
- e.g. you can have a geometry that defines the boundaries of a plant, and a raster that defines the concentration of toxic waste along each part of the boundary

### Geometry Type

We can represent all geographical entities in 2D using 3 building blocks:

Point

Line

Polygon

• Simplified models of reality, and will never perfectly mimic the real thing

• Geometry type treats the world as a flat Cartesian grid

### Geography Type

Similar to geometry, but account for the curvature of the earth

### Shape of the earth

• Surface: The Earth's real surface
• Ellipsoid: Ideal, smooth surface
• Geoid: Bumpy surface, where gravity is equal for all locations

### Shape of the earth (cont'd)

• Gauss determined in the early 19th century that the surface of the earth can be defined using gravitational measurements
-  geoid: where gravity is equal for all locations

• Geoid is far from spherical
-  the core of the earth is not homogenous
-  mass is distributed unevenly

• Geoid is the foundation of both planar and
geodetic models

### Raster Type

Vector Model

- points, lines, polygons
- geometry and geography type

Raster Model
- exhaustive regular or irregular partitioning of space

Points

Lines

### Topology Type

• Network of points, lines, and polygons

• Not concerned with the exact shape and location of geographic features, but with how they're connected to each other

• Useful in many applications:
-  parcel (land lot) data, to ensure that the change of one parcel boundary adjusts all other parcels that share that boundary change as well
-  road management, water boundaries, etc.
-  architecture

### Spatial Reference System

• SRS is the production of geodetics and cartography
-  geodetics: the science of measuring and modeling the earth
-  cartography: the science of representing the earth on flat maps

• Why do we need SRS?
-  to bring in data from multiple sources and be able to overlay one atop another

• Many standards of SRS:
-  most common one is the European Petroleum Survey Group (EPSG) numbering system
-  take any two sources of data with the same EPSG number, and they will overlay perfectly

### SRID

• Spatial Reference IDentifier
-  It defines all the parameters of our data’s geographic coordinate system and projection.
-  An SRID is convenient because it packs all the information about a map projection (which can be quite complex) into a single number.

• http://spatialreference.org/ref/epsg/4326/

• EPSG is a very recent SRS numbering system
-  If you are using data from a few decades ago, you won't find EPSG number

• The constituent pieces that form an SRS:
-  ellipsoid
-  datum
-  projection

### Ellipsoid

• Simplifications of the geoid which are generally good enough for most geographic modeling needs

• An ellipsoid is merely a 3D ellipse

• Instead of one ellipsoid to rule us all, people on different continents wanted their own ellipsoids to better reflect the regional curvature of the earth

• Today, the world is settling on the World Geodetic System (WGS 84) and Geodetic Reference System (GRS 80) ellipsoids
- WGS 84 is the standard of choice, and is what all GPS systems are based on

### Common ellipsoids and their ellipsoidal parameters

• Lon/lat with different ellipsoid are not the same
-  they use different grounding points
-  it's important to not just call things lon/lat: you can have NAD27 lon/lat, NAD80 lon/lat, etc. Each will be subtly different

### Datum

• Ellipsoid only models the overall shape of the earth
-  after picking out an ellipsoid, you need to anchor it to use it for real-world navigation
-  even if two reference systems use the same ellipsoid, they can still have different anchors, or datum, on earth
• Defines the position of the spheroid relative to the center of the earth.

• Global datum:
- uses the earth's center of mass as the origin

• Local datum:
- aligns its spheroid to closely fit the earth's surface in a particular area
- a point on the surface of the spheroid is matched to a particular position on the surface of the earth
- the coordinate system origin of a local datum is not at the center of the earth

### Coordinate Reference System

• A coordinate reference system is only one necessary ingredient that goes into the making of an SRS and isn't SRS itself
-  used to identify a point on your reference ellipsoid

• Most popular coordinate reference system for use is the geographical coordinate system
-  also known as geodetic coordinate system or simply lon/lat
• Longitude and latitude
• Units: Degrees (DMS or DD)

### Projection

Taking an ellipsoidal earth and squashing it onto a flat surface

• Projection has distortion built in
- because geodetic and 3D globes are ellipsoidal, they by definition do not refer to a flat surface

• Why do we need to have 2D projections?
-  the mathematical and visual simplicity that comes with planar (Euclidean) geometry

### Distortion

• How exactly you squash an ellipsoidal earth on a flat surface depends on what you are trying to optimize for

• In creating a projection, we try to balance four conflicting features:
-  measurement
-  shape: how accurately does it represent angles
-  direction: is north really north
-  range of area supported

• E.g. if you want to span a large area, you have to either give up measurement accuracy or deal with the pain of maintaining multiple SRSs and some mechanisms to shift among them

### Projection Types

Cylindrical projections

Conic projections

Azimuthal projections

### Main classes of planar coordinate systems

• Lambert Azimuthal Equal Area (LAEA)
-  good for measurement and can cover large areas, but not great for shape
-  US National Atlas (EPSG:2163)

• Lambert Conformal Conic (LCC)
-  preserve shape more than area, good for measurement for the regions they serve, and distort poles
-  best used for middle latitudes with east-west orientation

• Universal Trans Mercator (UTM)
-  good for measurement, shape, and direction, but only span six-degree longitudinal strips, cannot be used for the polar regions

• Mercator
-  good for preserve shape and direction, and spanning the globe, but not good for measurement
-  common favorites for web map display since we only need to maintain one SRID

• National grid systems
-  variant of UTM or LAEA, but are used to define a restricted region, such as a country

• State plane
-  US spatial reference systems, usually designed for a specific state
-  most are derived from UTM

### Universal Transverse Mercator Coordinate System

• World divided into 60 six-degree-wide zones
• From 80S to 84N
• Zones numbered 1-60 (N&S), W to E, starting at 180W

### What spatial reference system is appropriate?

• Excellent: covers the globe
• Good: covers a large country like the US; the measurements for the area served are usually within a meter for length, area, and distance calculations
• Medium: covers several degrees or a large state; measurements are accurate within meters, but can be as much as 10 meters off
• Bad: measurements don't have useful units

# git pull

### Type Modifiers

``geometry(POINT,4326)``

data type

subtype type modifier

SRID type modifier

### Geometry: Points and Linestrings

``````POINT
POINTZ
POINTM

POINTZM

LINESTRING
LINESTRINGZ
LINESTRINGM

LINESTRINGZM``````
• A point in 2D space specified by its X and Y coordinates
• A point in 3D space specified by its X, Y, and Z coordinates
• A point in 2D space with a measured value specified by its spatial X and Y coordinates plus an M value
• A point in 3D space with a measured value specified by its X, Y, and Z coordinates plus an M value
• A linestring in 2D specified by two or more distinct POINTs
• A linestring in 3D specified by two or more distinct POINTZs
• A linestring in 2D specified by two or more distinct POINTMs
• A linestring in 3D specified by two or more distinct POINTZMs

### Geometry: Polygons

• Closed linestrings are the building block of polygons

• A polygon contains all the enclosed area, and its boundary is the linestring that forms it

• The enclosed linestring outlining the boundary of the polygon is called the ring of the polygon. More specifically, it's the exterior ring.
``POLYGON``

### Collection of Geometries

• A collection of geometries groups separate geometries that logically belong together:
-  multipoints
-  multilinestrings
-  multipolygons

• geometrycollection
-  can contain any kind of geometry as long as all geometries in the set have the same spatial reference system and the same coordinate dimensions

### Geography

• In PostGIS, geography starts by assuming that all your data is based on a geodetic coordinate system, specifically the WGS 84 lon/lat SRID of 4326

• Only include support for basic subtypes of points, linestrings, and polygons, and no support for anything above 2D space

• The structure of the geography data mimic those of geometry
-  everything you know about geometry applies to geography with no changes except for swapping out the term geometry for geography in both data type and function names

By Hui Hu

# PHC6194-Spring2019-Lecture3

Slides for Lecture 3, Spring 2019, PHC6194 Spatial Epidemiology

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