1. Mapping Geographical Volumes: The Isarithmic Map SP 240 Cartography Alex Chaucer

2. Spatial Information Technology Center The Nature of Isarithmic Mapping: Fundamental Concepts Isarithmic map a planimetric graphic representation of a three-dimensional volume Isoline mapping the creation of a system of quantitative line symbols that attempt to portray the undulating surface of a three dimensional volume If this mapping technique is used, there must be a 3 rd Dimension, or an implied 3 rd Dimension

3. Spatial Information Technology Center The Nature of Isarithmic Mapping: Fundamental Concepts May be a real or imaginary surface Topographic surface: real Population density surface: abstract mental construct Must be continuous surface Temperature Population (can be assumed to exist everywhere) Frequency Polygon Joining the tops of a histogram with a line

4. Spatial Information Technology Center Isarithmic Forms and Terminology Isometric Map map from data that occur at points actual: temp, elevation derived: meaures of dispersion, proportions, ratios Isoplethic Map constructed from geographic data that occur over area these areas are called unit areas ie. Population density, crop yield per acre

5. Spatial Information Technology Center The Basis for Isarithmic Construction Imagine a series of pins constructed at data points. The tops of the pins represent the the surface of the new volume. The bottom of the pins is the datum. Connect the pin tops to form the volume’s surface. Hypothetical planes are passed through the volume. The traces of the intersections of the planes and the surface form the isarithms.

6. Spatial Information Technology Center A Brief History of Isarithmic Mapping Isobaths (1584) used as far back as 1584 for ocean depths Isohypse (1777) proposed by Meusnier as a way to depict surface features (1782) Map made by du Carla-Dupain-Triel Isogones (1630) lines showing equal magnetic declination, used by Borri, an Italian Jesuit (1701) used on a thematic map by Edmond Halley Isotherms Used to measure areas of equal temperature Isopleth (1845) used by Leon Lalanne

7. Spatial Information Technology Center When to Select the Isarithmic Method 1.Data must be a geographical volume 2.Must be continuous 3.Understand the distribution Advantages: 1.Shows the total form of spatially varying phenomenon 2.Commensurable and graphic at same time 3.Flexible, easily adapted 4.Easily rendered by computers

8. Spatial Information Technology Center Isarithmic Practices: Elements of Isarithmic Mapping Placing the isarithms Locating data points Unit areas Interpolation Methods manual automated Computer-Generated Isarithmic Maps The Selection of Isarithmic Intervals

9. Spatial Information Technology Center Placing the Isarithms- The General Case Uses methods of projective geometry Choose horizontal planes “thread” the data points Smooth the straight line segments

10. Spatial Information Technology Center Locating Data Points Aka “control points” Easy to specify in isometric mapping, because instrument location is known. Ie. Weather station for temperature. More difficult in isopleth data data point usually selected for enumeration district, usually the geographic center.

11. Spatial Information Technology Center Unit Areas in Isopleth Mapping Enumeration districts Political area units, states, towns Hexagonal shape yields better patterns

12. Spatial Information Technology Center Interpolation Methods Interpolation procedure for the careful positioning of isolines between adjacent data points 1. Manual 2. Automated

13. Spatial Information Technology Center Manual Interpolation Tracing a line that falls between data points “linear interpolation” Line placed at a certain value between control points

14. Spatial Information Technology Center Automated Interpolation Conceptually the same as Manual method Two Step Process 1. Primary Interpolation Calculation of data values to a grid matrix 2. Secondary Interpolation Positions the isarithms SURFER is a software that has been used for this.

15. Spatial Information Technology Center Computer Generated Isarithmic Maps Lessens the burden of doing it manually SURFER is a software used to do this TOPO is a part of SURFER http://www.goldensoftware.com/products/surfer/surfer.shtml

16. Spatial Information Technology Center The Selection of Isarithmic Intervals Decisions must be made regarding isarithmic intervals Select a uniform interval and try it Intervals should show most abrupt changes, not to wide and interval, and not too narrow

17. Spatial Information Technology Center Sources of Error in Isarithmic Mapping CRM Errors Collection, recording, manipulation errors From Instrumentation to inappropriate statistics Method Produced Errors Error from the technique, bad placement Production Errors Errors in drafting or graphics Map reading and analysis errors Map reader interpretation incorrect

18. Spatial Information Technology Center Preparing the Finished Isarithmic Map Lines, labeling, and Legend Designs Isolines should be dominant Label, but don’t over label Legends should be clear