[image]

vector representations of continuous data

helpful in 3 dimensions

created infinite numbers of points

line drawn on interpolated values between points

once drawn smooth

1. when points are few
2. interpolate additional point value
3. 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 Surfaces

Raster

natural world = continuous data

ideal spatial model to illustrate these surface

Natural Surfaces Examples

Raster

[image]

• Elevation
• Contours
• Rasters
• Surfaces symbolized low & high using color ramps
• elevation
• ramp colors - rising & lowering elevation

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

Nominal Scale

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^oC

-50^oC

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

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

1. diagram or abstract geographical to distorted proportionally value of an attribute
2. NOT that useful
3. 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

1. Contiguous
2. Non - Contiguous

Contiguous

{Cartogram}

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]

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 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