Lecture 7: Map Projections

Introduction

  • Geographic Information Systems (GIS) are distinct from other information systems.

    • They include spatial data, which consists of coordinates that define the location and extent of geographic objects.

    • Effective usage of GIS necessitates an understanding of:

    • How coordinate systems are established.

    • How coordinates are measured.

Challenges in Defining Coordinates

  • Defining a coordinate system for the Earth's surface is complicated by two primary factors:

    1. Common Understanding of Geography:

    • Most individuals comprehend geography using the Cartesian coordinate system that represents a flat surface.

    • The Cartesian system establishes two or three orthogonal axes for representation.

    1. Shape of the Earth:

    • Defining a coordinate system must also take into account the irregular shape of the Earth.

Geodesy

  • Geodesy is crucial for GPS and GIS systems, involving multiple scientific and engineering disciplines.

  • Definition of Geodesy:

    • The study of the Earth's shape, size, and gravity field.

    • The Earth is predominantly spherical, but it is essential to understand its actual shape for making accurate maps and elevation measurements.

Shape of the Earth

  • General Perception of Earth:

    • Commonly viewed as a sphere.

    • Reality is more complex; it resembles a potato's surface rather than a uniform sphere.

  • The Earth's shape is classified as a spheroid, which is slightly larger in radius at the equator compared to the poles.

Earth’s Topographic Features

  • Inquiry into Earth's features notable for their geographical significance:

    • Hills, valleys, mountain ranges, and oceanic trenches contribute to the Earth's overall shape.

    • These topographic variations represent a rough surface.

    • Elevation differences are significant:

    • Highest point (Mount Everest): Approximately 9 km above sea level.

    • Deepest point (Mariana Trench): Approximately 12 km below sea level.

    • Variation in gravitational strength across the Earth arises from the presence of diverse materials, though these variations tend to be minute.

Geodetic Coordinate System

  • Geodesy emphasizes understanding the Earth's dimensions and gravity fields, while also addressing the need for unique addressing of places and objects on Earth's surface.

  • Introduction of Geodetic Coordinate System:

    • This system employs latitude, longitude, and height to denote positions on Earth's surface:

    • Latitude (Parallels):

      • Runs east to west, ranging from 0° at the Equator to 90° at the poles.

    • Longitude (Meridians):

      • Extends north to south, starting at 0° at the Prime Meridian and ranges to 180°.

Geodetic Latitude, Longitude, and Height

  • Geodetic Measurements:

    • Latitude and longitude measurements account for the Earth’s ellipsoidal shape, contrasting with early spherical models.

    • Height definition:

    • Refers to the vertical distance above or below a reference, typically described using an ellipsoid.

    • Differentiation between:

      • Ellipsoidal Height: Distance above or below the defined ellipsoid surface.

      • Elevation: Generally refers to distances above mean sea level.

    • Different reference surfaces exist:

    • Ellipsoid reference for Geodesy.

    • Mean sea level for elevation measurement.

The Geoid

  • Description and Characteristics of the Geoid:

    • Serves as the equivalent of mean sea level in geodesy.

    • Envisioned as an imaginary sea that engulfs the Earth's surface, unaffected by external forces (e.g., wind, waves, lunar effects) other than gravity.

    • Not directly modelable due to its complexity.

Ellipsoids vs Geoid

  • Ellipsoids are utilized as mathematical approximations to model the Earth's shape:

    • Ellipsoid Characteristics:

    • Simple geometric shape defined by two parameters.

    • Cannot be directly sensed by instruments.

    • Geoid Characteristics:

    • Physically defined, with a complex surface described by an infinite number of parameters.

    • Can be measured or sensed by appropriate instruments.

Mapping and Height Measurements

  • The ellipsoidal shape that best fits the geoid is employed in mapping efforts.

    • Measurements:

    • Height above the ellipsoid is denoted as Height Above the Ellipsoid (HAE).

    • Orthometric Height (H):

    • Vertical distance above the geoid; distinct from ellipsoidal height (h).

    • Orthometric height emerges from the difference between ellipsoidal height and geoidal height at a specified location (denoted as N).

Geoidal Variation

  • Geoidal variations in the Earth's shape dictate the implementation of different ellipsoids worldwide.