Geodesy part3

Introduction to Geodesy and Cartography

  • Document targeted at UGent students, specifically for a course on UTM and UPS.

UTM (Universal Transverse Mercator)

Generalities

  • Origin: Military, developed during WWII and NATO.

  • Today: Primarily used as a civilian system.

  • Based on the Transversal Mercator projection, which is conformal (maintains angle).

  • The Earth is divided into 60 zones, with a limitation in latitude to minimize distortions.

  • Each zone is 6 degrees wide.

Earth's Division into Zones

  • 60 zones (strips) for managing geometric distortions. The UTM projection is useful for areas away from the central meridian, where distortions increase.

  • Central meridian: each zone has a particular central meridian to minimize distortion.

  • 1st strip: from 180° W to 174° W with a central meridian of 177° W.

  • Zones apply between 84°N and 80°S; upper areas are managed by the Universal Polar Stereographic (UPS) system.

UTM Coordinate System

  • Coordinates defined by Easting (X-axis) and Northing (Y-axis).

  • False Easting: E = E' + E_0 = E' + 500,000 ext{ m}.

  • False Northing is determined by hemisphere:

    • Northern Hemisphere: N = N' + N_0 = N' + 0 ext{ m},

    • Southern Hemisphere: N = N' + N_0 = N' + 10,000,000 ext{ m}.

  • Negative coordinates possible in certain situations.

Military System (MGRS)

  • Uses the same geographical division as UTM but for military purposes.

  • Divided into grids, rows, and columns with 100 km height in each row.

  • Columns are labeled with letters A-Z (excluding I and O).

UPS (Universal Polar Stereographic)

Overview

  • Used for polar regions, it uses Azimuthal (normal) projection.

  • Applies for latitudes greater than 84°N and less than 80°S.

  • Central point set at 0° longitude at 90°N/S.

Civil and Military Systems

  • Civil: Cartesian coordinates with false Easting at 2,000,000 m in both X and Y axes.

  • Military: Similar grid but differentiated between eastern/western partitions and has unique letter codes for different zones.

Distortions in Cartographic Projections

Generalities

  • Subject to various types of distortions: area, shape, distance, and direction.

  • Tissot’s indicatrix is a tool used for visualizing and quantifying distortions in projections.

Tissot's Indicatrix

  • Describes how points on the Earth morph when projected onto a plane.

  • Indicatrix shapes:

    • Unity circle transforms to an ellipse in projections.

    • Lengths and angles along the principal axes signify distortion rates.

    • The surface is projected as an ellipse, where the semi-axes reflect how distances are distorted in different directions.

Mathematical Projections

Transformation Formulas

  • Maps projections can be simplified through transformation equations:

    • For forward mapping: (x, y) = f( heta, ext{dist} ).

    • For inverse mapping: ( heta, ext{dist}) = g(x, y).

  • These equations are crucial for translating between geographic coordinates and projected coordinates.

Choosing the Right Projection

Essential Factors

  • Choosing projections greatly influences graphical representations.

  • Distortions can alter perceived information, crucial in contexts like navigation and thematic mapping.

  • Example: separate representations for Mercator (conformal) vs. Gall-Peters (equal-area).