Area

Area
- What?
  - area is the 2-dimensional space occupied by a polygon ...
  - ... can be of any shape (circle, triangle, rectangle or irregular)
  - ... for us is typically irregular in shape
  - area is measured 'square units' (i.e. m2 ... or, more typically, in hectares)
  - thus we measure area of forest stands, wetlands, etc. in ha
- How?
  - square/rectangle ... = length * width
  - irregular shapes ... we reduce them to many smaller squares (or rectangles)
  - methods
    - planimeter
      - tracing instrument
        
        mechanical (very old)
        
        digital (still old)
      - you are not responsible for this skill
    - break into "regular shapes"
      - break into rectangles, squares and triangles
      - you are not responsible for this skill
    - squares (graph paper / dot grid)
      - determine the length of the edge (side) of a square
        
        simply use your ruler
        
        measure to nearest 1/2 mm
        
        best to measure across several (10, 15, 20) squares
        
        and simply divide by number of squares
        
        gives you a better answer
        
        example
        
        I measured across 10 squares and got 7.35cm
        
        divide by 10
        
        1 square measures 0.735cm on one side
      - convert to 'real world' (ground) distance
        
        map scale is 1:10,000
        
        ground distance = 7350 cm
        
        = 73.5 m
      - calculate 'ground area' of one square
        
        this is simply length * width
        
        example
        
        73.5m * 73.5m
        
        = 5,402 m2
      - count the squares / dots within the polygon
        
        pretend I count 85 dots
      - determine area
        
        = ground area of one square * # of dots
        
        = 5,402 m2 per dot * 85 dots
        
        = 459,170 m2
        
        we want hectares (ha) ...
        
        ... so divide by 10,000
        
        ... = 45.9 ha
        
        ... tada
    - strips
      - determine the width of line spacing
        
        simply use your ruler
        
        measure to nearest 1/2 mm
        
        best to measure across several (10, 15, 20) lines
        
        and simply divide by number of squares
        
        gives you a better answer
        
        example
        
        I measured across 10 line spaces and got 7.35cm
        
        divide by 10
        
        1 line width measures 0.735cm
      - measure the lengths of all strips and sum
        
        4 lines: 2.30cm, 5.65cm, 6.00cm, 3.20cm
        
        = 17.15cm
      - convert to 'real world' (ground) distance
        
        map scale is 1:10,000
        
        WIDTH ground distance = 7350 cm = 73.5 m
        
        LENGTH ground distance = 171,500 cm = 1,715 m
      - determine area
        
        area = L * W = 73.5m * 1,715m = 126,052 m2
        
        = 12.6 ha
        
        ... tada
    - iPad
      - shown in class with PDF Maps
      - assume you now have the skill
      - if not ... you might want to get it :)
    - GIS
      - use computer mapping software
      - you are not responsible for this skill
      - until next year :)
- Errors?
  - simply put - each step has potential for error
    - poor job measuring the edge of a square (or width & length of a strip)
    - incorrect coversion to real world distance
    - incorrect calculation of real world area of square (or strip)
    - miscounting the squares (more of an issue with smaller squares)
    - incorrect calculation of final area
  - other issues
    - relative size of line spacing to polygon size
      - small polygons need small spacing
      - larger polygons "are OK" with larger spacing
    - skinny and very irregular shapes are prone to "variable answers"
- Improving the Answer
  - large squares (line spacing)
    - do more than once and average
    - "variability depends on placement"
  - very small squares (line spacing)
    - "count/measure" more than once and average
    - "block off" large areas for a quicker count
    - "variability depends on our counting (measuring) ability"