
[image]
We Will Write A Custom Essay Sample On ANY TOPIC SPECIFICALLY FOR YOU For Only $13.90/page
order now
vector representations of continuous data
helpful in 3 dimensions



created infinite numbers of points
line drawn on interpolated values between points
once drawn smooth
 when points are few
 interpolate additional point value
 then interpolate isolines



types of isolines = quantitative data types can be collected as points
many as specific names
Examples:
isobath
isocline
isohips



each line = 1 meter
context lines = multiples of isolines



[image]
spreadsheets
row & columns = forms cells
grid = rows
columns = tessellations
data unit = spatial (cell) — x,y = implicit
entity (object) info = explicity encoded
each cells must have numeral value
all about numbers
analytical modeling



natural world = continuous data
ideal spatial model to illustrate these surface


Natural Surfaces Examples
Raster


[image]
 Elevation
 Surfaces symbolized low & high using color ramps
 elevation
 ramp colors – rising & lowering elevation


Color Ramps & Continuous Surfaces 

Color Ramps = stretched data
stretched data organized values into 256 classes


Color Ramps & Continuous Surfaces
Examples


[image]
Hillshades = create classic cartographic product a shaded relief map
use as reference layer, to help ppl orient themselves within map



[image]
flat surface
appear 3D
Seldom
Digital
animated to different perspectives



nominal, ordinal, interval, ratio
numbers = data scale



telephone numbers
establish identity
race = individuals have numbers to identify him
not order & value


Ordinal Data Scale
Data Scale


establish order
1st place, 2nd place, 3rd place
phone number is NOT ordinal


Interval Scale
Data Scale


no absolute zero
negative values
degrees
100^{o}C
–50^{o}C


Ratio Scale Data
Data Scale


has absolute zero
no negative values
weight = 50 kg
direct composition


Why we should care?
Data Scale


different types of analysis
different cartographic symbols
different inappropriate values


nominal or categorical data
{data classifications}


qualitative: ordered but without a measurable range
no absolute values


ordinal data
{data classifications}


relative NOT absolute value
deals with quantitative but without a measurable range
using numbers label ordinal
data often confusing


interval data
{data classificitions}


quantitative: has NO absolute zero
subtraction works NOT division
class range = absolute zero
negative numbers


ratio scale data
{data classifications}


quantitative: absolute zero so both
subtraction & division work
no negative values in classification



sorting or arranging entities into groups or categories
number of classes usually between 5 & 10,
more likely 5 than 10
classifcation methods vary depending on data
ArcGIS = # of classification


Equal Interval
{data classification}


[image]
constant interval between classes # of observations will be different from class to class
Good = direct comparisons between different choropleth maps


Calculating Equal Interval


subtract minimum from maximum
divide result by # of classes
result = width of each class
add value with minimum value for first class
repeat until done


Quantile
{data classification}


[image]
equal # of observation per class
same class = interval between classes = different



divide count of features by # of classes
arrange features least to greatest
divide into classes = matches result of division equation


Jenks – Natural Breaks
{data classification}


[image]
minimizes variance within a class
by dividing classes in areas
different sized class &
different # of observations


Mean & Standard Deviations
{data classification}


[image]
classes = mean & deviations from the mean
best if data displays a nominal distribution


Calculating Mean and Standard Deviation 

 Calculate the mean of data
 Calculate the standard deviation of data
 Arrange your first class to straddle[stand] mean
 Then add classes at intervals of standard deviation both above and below the mean class


Quantile – 5 Classes using 7,1,18,20,6,14,19,13,21,25,2,23,1,15 

using 3 observation: (1,1,1) (2,2,6) (7,13,14) (15,18,19) (20,23,25) 

Equal Interval – 5 classes using 7,1,18,20,6,14,19,13,21,25,2,23,1,15 

(1,1,1,2,2) (6,7) (13,14,15) (18,19,20) (23,25) 


 diagram or abstract geographical to distorted proportionally value of an attribute
 NOT that useful
 Trade off between Area error and shape error
 Hard to make a real shapes
 Do not use cartograms to show average values, per capita, values, etc
 People look what’s on the map but comparing to what’s in their head
 CANNOT show mean, average
[image]


World Population
{Cartogram}


[image]
Area scale accurately represents selected variable
Contiguity is maintained
Shapes should remain recognized
World population is useful but not as continuity



[image]Look cool and artistic but hard to read
Election Count by counties NOT states



 Contiguous
 Non – Contiguous



Maintained Recognized = shapes
Area scale accurately selected
Advantages:
Easy to read
Disadvantage:
Distortion can confuse reader
Shapes of internal numeration may recognition impossible
Difficult to produce through commercial GIS software
The circle population = contiguity
[image]


Non – Contiguous
{Cartogram}


Not maintained
Area scale accurately recognized selected
Advantage:
Easy to construct GIS
True shapes of enumeration units
Disadvantage:
Separated
No compact
White spaces
Do not convey continuous nature of geographical space
Trade off between maintaining relative positive of enumeration unit and not overlapping
[image]


Restrictions on Cartogram 

Shape quality: cartograms useless? some approximation of true shape can be achieved
Each enumeration unit needs size, shape, orientation and contiguity…
Least important = communication


Data Limitation Cartogram 

Data must be ratio
Positive values in data sets with large range are problem.
Negative values cannot be mapped
Zero values eliminate the enumeration unit, creating map



Calculate total value for enumeration units based on single attribute
Compute proportional area of enumeration unit’s base on attribute value for each divided by total value
Draw, calculate and conform shapes and values

