Mapping Techniques and Geographic Data Analysis

Classified in Mathematics

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Process of Contouring and Isolines

Isolines connect points of equal measurements. Contours indicate elevation and changes in elevation, such as slopes and hills. Isotherms connect points of equal temperature and tell us the current state of the atmosphere.

Rules for Drawing Isolines

  • Connect points of equal value.
  • Never cross one another.
  • Never touch.
  • The interval for isolines is the same for the whole map.

Contours show us slopes, valleys, and hills.

Topographic Profiles and Vertical Exaggeration

A profile is a topographic profile representing the lay of the land from the side. To draw a profile, a transect (straight line) is drawn between two points to show hills, valleys, and slopes.

Vertical Exaggeration is a mathematical representation used to ensure we see elevation changes, as horizontal distances often greatly exceed vertical distances.

GPS Systems and Signal Errors

The modern precursor to GPS was Transit (a military system), also called NAVSAT (Navy Navigation Satellite System), which was used to provide guidance to nuclear missile submarines.

Sources of GPS Error

  1. Ionosphere and troposphere delays: The signal slows as it passes through the atmosphere.
  2. Signal multipath: The GPS signal is reflected off objects like tall buildings or large rock surfaces.
  3. Orbital errors: Inaccuracies occur in the satellite's reported location.
  4. Number of satellites visible: Buildings, terrain, foliage, and electronic interference can block the signal.

Understanding Map Data and Charts

Levels of Data Measurement

Nominal Data divides a group into multiple subgroups. It is categorized based on qualitative criteria and does not necessarily imply importance. We can count the numbers in each group. For example, the colors of M&M candies are an example of nominal level data.

Ordinal Data uses a logical ordering criterion, ordering in a relative sense. Data is arranged based on size or another quality without specific measurement. Ordinal data are ranked; for example, movies on a certain TV show are classified as 2 thumbs up, 1 thumb up, or 0 thumbs up. There is an order here.

Ratio Data involves measurement using a regularly spaced scale. The scale begins at a non-arbitrary starting point (zero point) where no features or measurements exist at the start. Data can be added, subtracted, multiplied, and divided, allowing proportional differences to be understood. Examples of ratio level data include the ages of people, scores on exams (graded from 0 to 100), and hours of study for a test.

Interval Data is also arranged along a standard scale where values can be determined. However, the starting point is arbitrary. While addition or subtraction can be used, because the starting point is arbitrary, multiplication and subtraction cannot be used. Interval scales are rare. For example, the boiling temperatures of different liquids are listed as interval level data. We can tell whether a temperature is higher or lower than another, so we can put them in an order.

Common Chart Faults and Choropleth Maps

Chart Faults include the failure to start a vertical scale at 0, which compresses data and makes interpretation difficult. Multi-line graphs also present difficulty in interpreting several lines, especially if two different things are plotted (e.g., population is numbers of people, while GDP is monetary units) using different scales.

Choropleth Maps are quantitative maps where data within political boundaries are mapped and color-coded by amount or magnitude. An example would be the number of teachers in a county.

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