MAP PROECTIONS AND COORDINATE SYSTEMS

MAP PROECTIONS AND COORDINATE SYSTEMS

Topics DiscJussed

  • Map Design

    • What is Cartography?

    • Scale of the map

    • Choosing a map design

    • Elements of Map Design

      • Definitions

      • Objective and Audience

      • Classification of Maps

      • Map Elements

    • Visual Variables

    • Visual Balance

    • Visual Hierarchy

    • Data Classification

    • Examples

    • Geovisualization

  • Where am I?

    • Recap on Scale

    • Absolute and Relative Geographic Location

    • Shape of the Earth:

      • Sphere

      • Ellipsoid

      • Geoid

    • Datum

    • Cartographic Projections

    • Choosing a Projection

    • Coordinate Systems

      • The Graticule and the Grid

      • Latitude and Longitude

      • Universal Transverse Mercator (UTM)

      • State Plane Coordinate System (SPCS)

Map Design

  • What is Cartography?

    • The science and art of creating maps.

  • Scale of the Map

    • Represents the ratio of a distance on the map to the corresponding distance on the ground.

    • Types of scales:

      • Representative Fraction (RF) (Ratio)

      • Verbal Scale

      • Graphical Scale

  • Choosing a Map Design

    • Depends on the purpose and audience of the map.

  • Elements of Map Design

    • Definitions: Key components that contribute to effective map representation.

    • Objective and Audience: Understanding the primary goal (informative, navigational, etc.) and who will use the map.

    • Classification of Maps: Different types of maps based on function (thematic, topographic, etc.).

    • Map Elements:

      • Title

      • Legend

      • Scale

      • North Arrow

  • Visual Variables

    • Attributes such as size, shape, color, texture, and orientation that convey information visually.

  • Visual Balance

    • The arrangement of elements to create a sense of harmony and proportion on the map.

  • Visual Hierarchy

    • The importance of elements shown through size, color, and placement to guide the viewer's attention.

  • Data Classification Examples

    • Methods for grouping data for better visualization on maps (natural breaks, equal intervals, quantiles, etc.).

  • Geovisualization

    • An advanced method combining visualization and geographic information to enhance understanding of spatial data.

Where Am I?

  • Recap on Scale

    • Understanding scale helps assess distance and size relationships on maps.

  • Absolute and Relative Geographic Location

    • Absolute Location: Defined by a fixed point on the Earth's surface (e.g., coordinates).

    • Relative Location: Describes locations in relation to others (e.g., "Building 215 is located just west of the Post Office").

  • Shape of the Earth

    • Sphere: Simplistic model

      • Radius: 6,371extkm6,371 ext{ km}

      • Circumference: 40,030extkm40,030 ext{ km}

    • Ellipsoid: More accurate representation

      • Circumference at poles: 39,940extkm39,940 ext{ km}

      • Circumference at equator: 40,075extkm40,075 ext{ km}

      • Flattening (f) ≈ rac1298.257rac{1}{298.257}

    • Geoid: A model of global mean sea level used to measure precise surface elevations. Defined as an undulating surface where gravity varies.

Earth Models

  • Why are ellipsoids used rather than geoids in developing map projections?

    • Map projections are typically derived from a single set of spherical trigonometry equations, which are simpler mathematically.

    • Geoids require complex geographic transformations, making them computationally intensive.

Datum

  • Definition: A datum is based on an ellipsoid and provides the base elevation for mapping.

  • Components of Datum:

    • Origin: Represented as DX,DY,DZDX, DY, DZ from the center of the Earth.

    • Orientation: Rotation angle of the datum.

    • Size and Shape: Defined by the semi-major and semi-minor axes of the ellipsoid.

    • Types of Datum:

      • Horizontal Datum: Used for determining locations and distances.

      • Vertical Datum: Used for determining geographic heights (elevation) or depths (bathymetry).

  • Important Datums for the USA:

    • 1927 North American Datum (NAD27)

      • Origin at Meades Ranch, KS

      • Based on Clarke 1866 ellipsoid

    • 1983 North American Datum (NAD1983)

      • Supersedes NAD27

      • Based on GRS 1980 ellipsoid, continuously updated with base stations of Continuously Operating Reference Stations (CORS).

    • World Geodetic System 1984 (WGS84)

      • Basis for the Global Positioning System (GPS); very close to NAD83.

Impact of Datum Mismatch

  • Mismatched datums can lead to significant positional errors.

    • Example: Position shifts due to datum differences can be as much as 500extmeters500 ext{ meters}.

What is a Map Projection?

  • Definition: A map projection is the systematic transformation of a 3-D spherical surface onto the 2-D planar surface of a flat map.

    • The act of projecting inherently introduces distortions in one or more of the following properties: area, distance, direction, and shape.

  • Distortion Patterns:

    • Area, Distance, Direction, Shape - it all contributes to the overall projection result.

  • Developable Surfaces:

    • Surfaces onto which the Earth can be projected include:

      • Cone

      • Plane (Azimuthal)

      • Cylinder

Types of Projections Based on Developable Surfaces

  • Tangent Projection:

    • The projection surface is tangent to the globe at one point (standard point).

    • Distortion increases as one moves away from the point of tangency.

  • Secant Projection:

    • The projection surface intersects the globe, forming standard lines where distortion is minimized.

Aspects of Map Projections

  • Aspect Types:

    • Equatorial

    • Transverse

    • Oblique

Properties of Different Map Projections

  • Conformal Projections:

    • Preserve shape; typically used for large scale maps.

    • Example projections: Lambert Conformal, Mercator.

  • Equivalent Projections:

    • Preserve area; size on the map corresponds to actual size on the earth.

    • Useful in maps where area comparison is critical (e.g., choropleth maps).

    • Example projections: Albers Equal Area, Sinusoidal.

  • Distance/Direction Preserving Projections:

    • Azimuthal: True direction maintained from any two points on the map; useful for navigation.

    • Example: Azimuthal Equidistant.

  • Compromise Projections:

    • Minimize distortion in all properties but do not preserve any one property; often used for world maps.

    • Examples: Goode's Homolosine, Winkel Tripel.

Choosing a Projection

  • Factors to consider:

    • Which properties to preserve: Area, Distance, Direction, or Shape?

    • Size and shape of the study area: Is it large or small? Is the orientation N-S or E-W?

    • Conventions and regulatory standards for maps.

  • Example of Projections:

    • Different map types such as Mercator and Lambert Conformal can be centered at specific geographic coordinates and serve distinct purposes.

Coordinate Systems

  • Definition: A coordinate system describes how locations are defined on a plane with respect to a reference system.

  • Common Coordinate Systems:

    • Cartesian (x and y)

    • Latitude and Longitude: Involves Easting and Northing designations.

    • Universal Transverse Mercator (UTM)

    • State Plane Coordinate System (SPCS)

  • Spherical vs. Cartesian Coordinates:

    • Disadvantages of Spherical Coordinates (Latitude/Longitude):

    • Units can be cumbersome (e.g., degrees).

    • Inconvenient for spatial calculations.

    • Advantages of Cartesian Coordinates:

    • Logical and straightforward for mapping

    • Units are in meters or feet.

Latitude and Longitude

  • Definitions:

    • Longitude (λ) (Meridian): Range from 180extoW180^ ext{o} W to 180extoE180^ ext{o} E.

    • Latitude (φ) (Parallel): Range from 90extoS90^ ext{o} S to 90extoN90^ ext{o} N.

    • Equator and Prime Meridian are key reference lines (0°).

  • Coordinate Formats:

    • Decimal Degrees (DD) (e.g., 29.890661extoLat,−97.911530extoLong29.890661^ ext{o} Lat, -97.911530^ ext{o} Long)

    • Degrees Minutes Seconds (DMS) (e.g., 29exto53′26.3976′′N,97exto54′41.5080′′W29^ ext{o} 53' 26.3976'' N, 97^ ext{o} 54' 41.5080'' W ).

    • Conversion from DMS to DD involves manipulation of values in degrees and minutes.

The Graticule and the Grid

  • The Graticule:

    • A network of latitude parallels and longitude meridians forming a spherical coordinate system.

  • The Grid:

    • Consists of evenly spaced horizontal and vertical lines representing projected coordinates.

  • Combination:

    • The graticule can be overlaid on a grid to provide multi-dimensional context on maps.

Universal Transverse Mercator (UTM)

  • Introduction:

    • UTM divides the earth into 6° horizontal zones and uses a central meridian as the reference for projection.

  • Zone Basics:

    • Each zone has unique numbers and covers a specific section of the earth.

    • UTM measurements involve Northing and Easting starting from a defined origin.

State Plane Coordinate System (SPCS)

  • Unique Parameters:

    • Each U.S. state has particular projections based on its shape (e.g., elongated north-south may use Transverse Mercator).

  • Components Include:

    • Easting and Northing origins, standard parallels, and false origins.

Warnings in Mapping

  • Unprojected/Geographic (“GCS”):

    • Based on spherical coordinates (latitude/longitude); can distort representation heavily when plotted on a flat map.

  • Projected Maps:

    • These are preferred to reduce distortion, represented mathematically.

Readings

  • To learn more, explore Bolstad (2022), Chapters 2 and 3.