Geospatial Data

1. Geospatial Data#

1.1. Topics#

  • Geospatial data

  • Measurement and reference systems

  • Mapping and measurement frameworks

  • Map as stored function

  • Types of maps

1.2. Geospatial/Geographic Data#

  • Data about things on or close to the Earth’s surface

  • Terminology: Spatial, geospatial, or geographic data

  • Scale: Operates at an Earth or planet scale

    • Spatial location

    • Spatial > geospatial

    • Geospatial = geographical

  • Three components

    • Attribute (what)

    • Location (where)

    • Time (when)

1.3. Why Do We Need Geospatial Data?#

  • Life is spatial

    • Life itself (matter) takes up space

    • It distinguishes itself from its environment

    • It interacts with the environment

    • It lives in space

  • Spatial intelligence

    • One of Howard Gardner’s multiple intelligences

    • Involves immediate sensory perception

  • Geographical intelligence

    • Insight beyond the line-of-sight

    • Insight beyond sensory perception

[Image of Howard Gardner’s multiple intelligences theory]

1.4. Life and Information#

  • What is life?

    • The basis of life is information processing

    • Life collects, stores, and uses information

    • Applies to biological and artificial life, organizations, and the economy

  • What is information?

    • Something that allows an observer to make predictions about the state of another system that are better than chance

  • Information vs. Data

    • Data becomes information when it enables better-than-chance predictions about another system

1.5. Measurement and Reference Systems#

  • Measurement

    • Classical physicist perspective: Provides a numerical relationship between a standard object and the object being measured

    • Representationalists perspective: Assignment of numbers to objects according to certain rules

    • Useful data includes both the numbers and the standard objects or rules used

  • Measurement reference systems

    • A set of rules for measurement or standard objects

    • Provides a means to compare a particular number to others measured under the same set of rules

1.6. Measurement Reference Systems#

  • Reference systems exist for attribute, time, and space

  • Temporal reference systems

    • Local vs. global time

    • Gregorian vs. lunar calendars

  • Attribute reference systems

    • Units (standard objects)

    • Levels of measurement: Nominal, Ordinal, Interval, and Ratio

  • Running race example

    • A number to wear (Nominal)

    • The order of finishing the race (Ordinal)

    • Arrival time (Interval)

    • Elapsed running time (Ratio)

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1.7. Spatial Reference Systems#

  • Location distinguishes geospatial data from other types of data

    • Specifying location on the Earth’s surface is essential

  • Geospatial coordinate systems are designed to:

    • Define locations on or close to the Earth’s irregular curved surface

    • Ensure each location is uniquely represented

    • Allow calculations of relationships such as distance and direction

1.8. Geographic Coordinate Systems (GCS)#

  • Based on a spheroid model of the Earth

  • Uses two angular measurements (latitude and longitude) to specify a location

  • Components of a GCS:

Geographic Coordinate System

Datum (Sphere or Ellipsoid)

Unit of Measure (DMS, DD, or Radian)

Prime Meridian

[Image of geographic coordinate system latitude and longitude]

1.9. (Horizontal) Datum#

  • A datum specifies a sphere or ellipsoid used to approximate the Earth’s shape and size

  • It defines how that model is aligned with the Earth

  • Latitude and longitude are defined based on specific datums

  • The same location may have different coordinates depending on the datum used

    • Earth-centered (WGS84) datum

    • Local (NAD27) datum

1.10. Projected Coordinate Systems (PCS)#

  • A PCS consists of:

Projected Coordinate System

A linear unit of measure (usually meters or feet)

A map projection with specific parameters

An underlying Geographic Coordinate System

1.11. GCS vs. PCS#

  • PCS is suitable for small areas

  • PCS always contains some form of distortion

  • GCS calculations for distance and area are more accurate but more complex

    • Uses spherical geometry

  • Most GIS analytical functions are implemented based on PCS

  • Use PCS primarily for printing or display on flat media

1.12. Height and Vertical Datum#

  • The vertical datum is the zero surface to which elevation refers

  • Geoids (equipotential surfaces) are standard zero surfaces

  • Ellipsoids can also be used, such as in GPS readings

  • The same location may have different elevation values based on different vertical datums

1.13. Mapping—Creating Geographic Data#

  • The process involves turning things on or near the Earth’s surface into data

    • Representing reality as numbers in a computer

  • What is measured:

    • Objects and fields on or close to the Earth’s surface

    • Location, attribute, and time components

  • Considerations and constraints:

    • Purpose and resources/cost

    • Resolution and precision

    • Limitations of finite computing systems

1.14. Mapping and Measurement Frameworks#

  • Geospatial data consists of location, attribute, and time components

    • All three components cannot be measured simultaneously

  • Measurement frameworks provide rules for ignoring or controlling some components to measure one

    • One component must be fixed (irrelevant)

    • Another component serves as control (imposes discrete divisions)

  • Discrete divisions constrain the resolution and accuracy of the measurement

1.15. Common Mapping Measurement Frameworks#

  • Time is fixed: Measured at a specific point in time or during a period

  • Location as control: Space is divided into cells, polygons, or administrative boundaries

    • Attributes are then measured for these divisions

  • Attribute as control: Specific attributes (e.g., land cover types or elevations) are chosen

    • Locations are then measured for these attributes

1.16. Mapping Surface Elevation—Raster Map#

  • Location serves as the control

    • Space is systematically divided into cells

  • Attributes are measured at each cell

    • Rules like min, max, or mean may be applied

  • Cell values are typically stored as a matrix

1.17. Mapping Surface Elevation—Vector Map#

  • Attribute serves as the control

    • Focuses on discrete elevations (e.g., every 100m)

  • Locations are measured for each elevation (e.g., contour lines)

  • Location-value pairs are stored as rows in a table

ID

Location/Geometry

Elevation

1

(x1,y1), (x2,y2) … (xn, yn)

100

2

(x1,y1), (x2,y2) … (xm, ym)

200

10

(x1,y1), (x2,y2) … (xk, yk)

1000

1.18. Vector Census Map#

  • Location serves as the control

    • Uses census blocks or aggregated boundaries

  • Population is counted based on set rules

1.19. Function and Map#

  • A function associates each element x of a domain to a single element y of a codomain

  • Analogy for maps: Location represents the domain, and the measured attribute represents the codomain

1.20. Stored Function#

  • Relations are explicitly stored when they cannot be represented mathematically

  • A stored function acts as a lookup table

  • Locations must be discretized (mapping units) due to finite computing power

1.21. Map as Stored Function#

  • Relation between location and attribute: \(Attribute = f(location)\)

  • Domain: Location on Earth

  • Codomain: Any measured attributes/variables

  • Map is a stored function because location-value relations usually lack mathematical formulas

1.22. Raster Map#

  • Matrix serves as a stored function

    • Each cell is located by its row and column

  • Each cell represents a location-value relation

  • Usually, the upper-left corner cell is georeferenced; other locations are derived

1.23. Zone Raster Map#

  • Cells with the same value form a “zone”

  • The zone serves as the mapping unit location

  • Typically includes an attribute table with counts/histograms

Zone ID

Count

Value

0

50

200

1

50

325.6

1.24. Predicting Attribute Value at a Location#

  • Map as a function: Prediction is a fundamental capability (\(v = m(l)\))

  • Estimation/Interpolation is necessary when the target mapping unit differs from stored units

1.25. Interpolating Attribute Value#

  • Land cover interpolation: Uses majority types for target polygons

  • Population interpolation: Uses areal interpolation

  • Attribute types:

    • Intensive: Magnitude independent of size (e.g., density)

    • Extensive: Magnitude is additive (e.g., mass, population)

  • Spatially intensive: Value is the same everywhere within a mapping unit

  • Spatially extensive: Value changes if the mapping unit is modified

1.26. Multi-valued Vector Map#

  • Results from combining multiple single-valued maps (e.g., Soil + Land Cover)

  • Each mapping unit represents a set of homogeneous attributes

Map

Attributes

Soil

A, B

Land cover

C, D

Combined

(A, C), (A, D), (B, C), (B, D)

1.27. Multi-Valued Raster#

  • Each cell contains a set of attribute values (e.g., multi-band remote sensing)

  • Storage methods: Band sequential (BSQ), Band interleaved by line (BIL), and Band interleaved by pixel (BIP)

1.28. Meta-map: Map of Spatial Relationships#

  • Spatial relationship involves the exchange of matter, energy, and information between locations

    • Examples include watersheds and viewsheds

  • Types of map relations:

    • Single-valued: {Location, value}

    • Multi-valued: {Location, {values}}

    • Meta-map: {Location, {(location, {values})}} (a map of maps)

1.29. Flood Inundation Relations#

  • Floodplain pixels (FPP) can be flooded by flood source pixels (FSP) through backfill and spillover

  • Depth to flood (DTF): The minimum depth at an FSP required to flood a specific FPP

  • The FLDPLN model identifies these relations and DTFs through an iterative process

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