Geovisualization and Geographic Information Systems (GIS)

Posted on Oct 29, 2024 in Other subjects

Geovisualization: traditionally been called Cartography

Steven’s Scales of Measurement

Nominal – Equality; name, ID, gender; determination of equality; # of cases, mode

Ordinal – Greater than; grade, standing; median, percentile

Interval – How much greater; temperature (C); +, – ; mean, standard deviation

Ratio – How many times greater (true zero point); population, area, temperature (K); /, * ; coefficient of variation.

How to Visualize GIS Data?

By giving each geometric entity a symbol representing its location and attribute(s) according to certain rule(s)

Georeferencing

The process of assigning a geographic object one or more values that specify its location on Earth.

Specify Location on Earth

Coordinates on a certain reference frame.

Reference Frame

Spherical/ellipsoidal (longitude & latitude) or Cartesian (Easting, x & Northing, y) coordinate system.

Map Projections

A process of transforming the curved (3D) surface of the Earth to a flat (2D) surface.

Projection Types

• Equivalent (preserve area)
• Equidistant (preserve distance)
• Conformal (preserves shapes and angles)

Projection Distortions

• Area
• Angle
• Distance
• Direction

Cartographic Scale

Ratio of a distance on the map corresponding to a distance on Earth. A smaller-scale map covers a larger area and shows less detail of that area. The reverse is true for a larger scale map.

Problems with Scale

• Congestion: Too many objects in a small area.
• Coalescence: Objects falsely touch each other.
• Conflict: Impossible relations among objects.
• Complication: Difficult to comprehend.

Cartographic Generalization

The process of selecting and representing coordinate data to reduce the complexity of a map and enhance its readability.

Douglas-Peucker Algorithm

Method used in Geographic Information Systems (GIS) to simplify polylines (lines made of connected points) while preserving their overall shape. This is particularly useful for reducing data complexity in mapping and spatial analysis.

Analog vs. Digital

For digital maps, the data storage medium is not the same as the data presentation medium. An analog map is static, while a digital map is dynamic.

General Reference Map

Visualizes the location of selected features for general reference.

Thematic Map

Visualizes a spatial pattern of selected attributes, e.g., election results, statistical data.

Chloropleth Mapping

Visualizes the spatial variation of an attribute by assigning each spatial unit a color or visual variable according to its value or class.

Advantages

• Easy to produce and read.
• Easy to recognize distribution patterns.
• Good for nominal and statistical data.

Disadvantages

• All units are not the same scale.
• Cannot show variability within units.
• Misleading if not standardized.
• False impression of abrupt change at boundaries.
• Color scheme or units might not be appropriate.

Standardization

Divide an attribute by any other attribute, e.g., percentage or density.

Modifiable Area Unit Problem (MAUP)

Affects results when point-based measures of spatial phenomena (e.g., population density) are aggregated into districts. Resulting summary values are influenced by the choice of district boundaries. Different aggregations can create different visual representations.

Choice of Color Scheme

1. Color association (e.g., red is hot, blue is cold, green is OK, red is danger).
2. Type of audience (e.g., age, background, color blindness).
3. Aesthetics (e.g., dark colors for small regions, bright colors for something negative may not be good).
4. Type of data (e.g., hue for nominal, lightness for others may be good).
5. Available resources (e.g., digital vs. analog media, black and white vs. color printers).

Proportional Symbols Mapping

Assigns each spatial unit a graphic symbol whose size is proportional to its value or its class.

• True point: True location of a point in a polygon.
• Conceptual point: Location of the symbol in the center of the polygon.

Cartogram Mapping

Scales the size of each spatial (normally area) unit in proportion to its value.

Dot Mapping

Assigns each spatial (normally area) unit a set of dots whose number is proportional to its value.

Parameters

1. Unit value: The value represented by each dot.
2. Dot size: The size of each dot in the output medium.

Flow Mapping

Assigns each line unit a visual variable representing the direction and/or magnitude of flow from one end to the other.

Spatially Continuous Data

Represent the spatial distribution of attribute values that can be measured at any location in a study area.

Interpolation

A method of estimating values at arbitrary points from known values at sample points. Can increase resolution but not accuracy.

Inverse Distance Weighting Interpolation (IDW)

Compute the value of a new point as a weighted average of those of its neighboring sample points.

Strategies for Selecting a Neighboring Point Set

• Simple
• Quadrant
• Octant

If we increase n, does it make the interpolation more accurate?

No, we do not know which n is the correct n.

If we increase the radius, does it make the interpolation more accurate?

Yes, we get more information.

Triangulated Irregular Network (TIN)

Approximates a surface with a set of triangles generated from a set of observed points.

TIN Uses Delaunay Triangulation, What Does That Mean?

Avoids skinny triangles or makes triangles as equilateral as possible by maximizing the minimum angle.

Is a TIN Created from a Raster Unique?

No, the triangles can be angled in different ways.

Advantages of TIN

• Efficient sampling (fewer points sampled in less varying regions).
• Efficient computation of geomorphologic characteristics (slope, aspect, volume, etc.).
• Can easily take into account abrupt interruptions in surface smoothness (rivers, roads, etc.).

Kriging

A statistical method to estimate a function from sample points.

Visualization Techniques (Spatially Continuous Data)

• Extrusion
• Chloropleth mapping
• Isopleth mapping (contour lines)
• Hillshading (or shaded relief)
• Fishnet (or Wire Frame)
• Drape Image (3D rendering)

What Does 2.5D Mean?

Each location is defined by two coordinates (x, y) and characterized by only one value (z) of a chosen attribute (may be visualized as height). The z-value may also represent a point in time (normally it’s elevation).

Vector Data in 3D GIS

Advantages

• Quick and direct access to data points.
• Explicit modeling.
• Can achieve a detailed level of geometry.

Disadvantages

• Difficult automation.
• Big and complex models are hard to visualize.

Raster Data in 3D GIS

Advantages

• Easily automated processes.
• The data is highly compressible.

Disadvantages

• Computational requirements increase on a quadratic scale with size.
• Slow data processing time.
• Cannot see the data completely without manipulation.

City Models

A scalable spatio-semantic digital representation of urban areas by 3D geospatial data.

Ways of Visualizing 3D Rasters

• Voxel
• Points
• Wireframe
• Glyphs
• Cross-section
• Threshold

Examples of Applications of 3D GIS

• Coastal modeling
• Disaster modeling
• Underground applications
• Underwater applications
• Applications in the air

Spatio-Temporal Data

Change in location with discrete time (also called MOTION). Has attributes, location, and time values.

Frame

Smallest unit of an animation.

Duration of a Frame

The length of time for which it is displayed.

Rate of Change of a Pair of Successive Frames

The magnitude of change (in position or attribute) divided by the duration of each frame.

A Sequence of Frames Has

• An order, which is likely but not necessarily chronological.

Change of Attribute with Time

The attribute of each object is a function of time. Success depends on:

1. Symbols used.
2. Interactivity.
3. User’s expertise.

Tobler’s First Law of Geography

“Everything is related to everything else, but near things are more related than distant things.”

Classification Methods

Ways to reduce a given set of measurements into a smaller set of classes.

Equal Intervals

All classes have the same range. (Highest value – lowest value) / number of classes.

Quantiles

All classes have the same number of observations; number of observations / number of classes.

Mean-Standard Deviation

Mean +/- 1, 2, 3,… standard deviations.

Maximum Breaks

Breaks at the largest differences between two measurements.

Natural Breaks

Variance within a class is minimized, variance among classes is maximized.

If the highest value increases, it will affect equal intervals and mean-standard deviation calculations. Maximum breaks will only be affected if the new difference is larger than another difference that is currently a limit. If the temperature is linearly transformed (Celsius to Fahrenheit), it will not change the appearance of the maps, only the values within the intervals themselves.

Subtraction of Temperatures

A difference in temperature provides new information, such as which place has the highest difference between seasons.

Division (Ratio) of Temperatures

Does not provide new information as the values are in the interval scale and therefore do not have a true zero point. A ratio would not have any meaning; for example, 20°C is not twice as hot as 10°C.

Map to Use on Standardized Data

Chloropleth mapping should be used. Cartograms and dot maps are used to show the standardization, not when the values are already standardized.

Geographic Phenomena in Respect to Time

• Location changes with time (hurricanes, animal migration).
• Attribute changes with time (unemployment levels).
• Both change with time (traffic congestion where the number of cars changes as well as the location of cars).

How to Visualize Spatiotemporal Phenomena (Hurricane)

Vector

Points for hurricane centers that are color-coded for wind speed are animated by the temporal data with an appropriate lag. This allows us to track movement prior to its present location and find out if the winds will be problematic.

Raster

Assign each cell a value based on wind speed and color-code them. When animating by temporal data, the highest wind speeds will show the hurricane’s movement.

MAUP for Line Units (Roads)

If the line segment is very long, it might be misleading to aggregate the data to the whole segment; instead, use smaller segments. For example, when visualizing accidents on roads, a long segment might have a lot of accidents on just a small part. This would either show a lot of accidents on the whole road or, when standardized by length, show very low density.

Path in 2D Space (Space-Time Path)

It is only possible to go upwards in the diagram. Sideways movement means teleportation, and downwards movement means movement in negative time.

Chrisman

Would define population density on the log-interval scale since we might use an exponent instead of a unit to define the intervals.

Equilateral Triangles

Are useful in surface approximation because they provide a consistent and uniform tessellation of a surface. They are more predictable and visually pleasing.

Convert a 100×200 Raster Surface to a TIN

The minimal number of triangles is one if we were to have the triangle be a lot bigger than the raster and encompass the entire raster. If we were to limit the triangle size to be within the raster, four would be the smallest amount if we want to avoid skinny triangles.

DEM Types

• Aspect = nominal
• Visibility = ordinal
• Slope = ratio

Animations

Used to visualize change, emphasize locations, and emphasize the spatial distribution of an attribute.

Three Types of Distribution of Dots

• Random
• Clustered
• Uniform

IDW Follows Tobler’s First Law

By giving higher priority to measurements that are closer to the point of interest. If Tobler’s law were worded differently as to have higher priority to measurements further away, we could use d_jⁿ instead of 1/d_jⁿ. See the next image for calculation.