copyright, 1998-2013 © qiming zhou geog1150/2015. cartography thematic mapping
TRANSCRIPT
Copyright, 1998-2013 © Qiming Zhou
GEOG1150/2015. Cartography
Thematic MappingThematic Mapping
Thematic Mapping 2
Thematic Mapping
Objectives of map design Data measurement Basic statistical concepts and processes Thematic map representations
Thematic Mapping 3
Objectives of map design
Geographical variables are so diverse and complex, we must understand their essential nature.
Geographical ordering - locational relationships. Discrete phenomena. Continuous phenomena.
Thematic Mapping 4
Data measurement
Scales of measurement Nominal Ordinal Interval Ratio
Use of the scales of measurement in thematic mapping
Thematic Mapping 5
Nominal scales of measurement
Point Line Area
Town River Swamp
Mine Road Desert
Church Graticule Forest
Bench mark
BoundaryCensus regions
Examples of differentiation of point, line and area features on a nominal scale of measurement.
After Robinson, et al., 1995
Thematic Mapping 6
Ordinal scales of measurement
Examples of differentiation of point, line and area features on an ordinal scale of measurement.
After Robinson, et al., 1995
Point Line (roads) Area
Large
Medium
Small
NationalProvincialCountyTownship
Industrial regions
Major Minor
Smoke pollution
Thematic Mapping 7
Interval-ratio scales of measurement
Examples of differentiation of point, line and area features on an interval or ratio scale of measurement.
After Robinson, et al., 1995
Point Line (roads) Area
Thematic Mapping 8
Basic statistical concepts and processes It is often necessary to manipulate raw
data prior to mapping. Pre-map data manipulation stage:
Making data to be mapped comparable.
Thematic Mapping 9
Absolute and derived data
Absolute qualities or quantities: “raw data” maps showing landuse categories, production of goods, elevations above sea level, etc.
Derived values. Summarisation or relationship between features. Four classes of relationships: averages, ratios,
densities and potentials.
Thematic Mapping 10
Averages
Measures of central tendency Three commonly used averages in
cartography: Arithmetic mean Median Mode
Thematic Mapping 11
Arithmetic mean
N
xx
n
ii
1
Arithmetic mean
Geographical mean
A
xax
n
iii
1
Thematic Mapping 12
Median and mode
Median - the attribute value in the middle of all ordered attribute values Geographic median - the attribute value
below which and above which half the total area occurs
Mode - the value that occurs most frequently in a distribution Area modal class - the class which
occupies the greatest proportion of an area
Thematic Mapping 13
Ratios
Something per unit of something else
Quantities that are not comparable should never be made the basis for a ratio
b
a
n
nx
Ratio or rate Proportion Percentage
N
nx a 100
N
nx a
Thematic Mapping 14
Densities
Relative geographical crowding or sparseness of discrete phenomena
A
nD
Thematic Mapping 15
Potentials
Individuals comprising a distribution (e.g. people or prices) interact or influence one another.
The gravity concept:
jiD
xxP
n
j ji
jii
1 ,
Thematic Mapping 16
Thematic map representations Indices of variation
Mode - variation ratio
Median - quantile range (quartiles, ceciles or centiles (percentiles))
Arithmetic mean - standard deviation
N
xxn
ii
1
2
A
aV
N
fV mm 1;1
Thematic Mapping 17
Scaling systems
Scale Average Index of Variation
Nominal Mode Variation ratio
Ordinal Median Decile range
Interval Arithmetic mean Standard deviation
Ratio Arithmetic mean Standard deviation
Thematic Mapping 18
Some basic statistical relations Regression analysis Correlation analysis
Spatial autocorrelation
n
ii
n
ii
n
iii
yyxx
yyxxr
1
2
1
2
1
Thematic Mapping 19
ExampleArea Per Capita Personal
Income ($)Per Capita Educational Expenditure ($)
Number of First-degree Graduates ($)
A 3882 273 330
B 4395 266 910
C 3870 240 500
D 5695 333 40
E 4282 273 870
F 4082 276 70
G 3952 210 240
H 5770 357 2920
J 5938 340 530
K 5550 390 1760
L 5304 314 460
M 4840 280 1670
N 4830 360 580
P 5745 376 0
Q 4570 287 2500
(Source: Robinson, et al., 1995)
Thematic Mapping 20
Regression analysis
200
220
240
260
280
300
320
340
360
380
400
3500 4000 4500 5000 5500 6000 6500
Per Capita Personal Income ($)
Per
Cap
ita E
du
catio
nal
Exp
end
iture
($)
85.0
5883.085.19ˆ
r
XY
Scattergrams with fitted linear regression line.
0
500
1000
1500
2000
2500
3000
3500 4000 4500 5000 5500 6000 6500
Per Capita Personal Income ($)
Nu
mb
er o
f F
irst
-deg
ree
Gra
du
ates
($) 21.0
2533.067.335ˆ
r
XY
Thematic Mapping 21
Areal units
Thematic Mapping 22
Observed, predicted and residuals
Maps showing observed per capita educational expenditures, predicted per capita educational expenditures based on per capita income, and residuals from the regression.
From Robinson, et al., 1995
Thematic Mapping 23
Observed, predicted and residuals (cont.)
Maps showing observed numbers of first-degree graduates, predicted numbers of first-degree graduates based on per capita income, and residuals from the regression.
From Robinson, et al., 1995
Thematic Mapping 24
Classification
Natural breaks Equal interval Equal area Quartile Standard deviation
Thematic Mapping 25
1
23
34
42
7
16
8 24 33 43 9 48 2 18 10 28 37 13 52 15 54 17 6 19 35 46
3 25 26 27 11 29 30 31 32
4 20 1236 41 50
38 5 49
4753 44
2114
22
4540
51
39
ID Density Area ID Density Area ID Density Area
1 4728 1 19 2471 1 37 21 1
2 7945 1 20 486 9 38 157 16
3 1288 4 21 369 36 39 1692 5
4 38 9 22 4428 2 40 285 8
5 404 16 23 204 4 41 494 9
6 7668 1 24 630 1 42 304 16
7 523 25 25 391 4 43 4432 1
8 275 1 26 418 4 44 1414 25
9 1336 1 27 618 4 45 343 12
10 4017 1 28 5366 1 46 8597 1
11 175 4 29 943 4 47 243 25
12 393 9 30 15 4 48 4172 1
13 2883 1 31 1981 4 49 336 16
14 286 36 32 1195 4 50 1683 9
15 2113 1 33 1244 1 51 74 18
16 272 36 34 140 9 52 5241 1
17 445 1 35 2539 1 53 191 25
18 3719 1 36 628 9 54 723 1
Classification data set
Thematic Mapping 26
Natural break
ID Density Class ID Density Class ID Density Class
30 15 1 25 391 2 50 1683 3
37 21 1 12 393 2 39 1692 3
4 38 1 5 404 2 31 1981 3
51 74 1 26 418 2 15 2113 3
34 140 2 17 445 2 19 2471 3
38 157 2 20 486 2 35 2539 3
11 175 2 41 494 2 13 2883 3
53 191 2 7 523 2 18 3719 4
23 204 2 27 618 2 10 4017 4
47 243 2 36 628 2 48 4172 4
16 272 2 24 630 2 22 4428 4
8 275 2 54 723 2 43 4432 4
40 285 2 29 943 3 1 4728 4
14 286 2 32 1195 3 52 5241 4
42 304 2 33 1244 3 28 5366 4
49 336 2 3 1288 3 6 7668 5
45 343 2 9 1336 3 2 7945 5
21 369 2 44 1414 3 46 8597 5
0
2000
4000
6000
8000
10000
1
23
34
42
7
16
8 24 33 43 9 48 2 18 10 28 37 13 52 15 54 17 6 19 35 46
3 25 26 27 11 29 30 31 32
4 20 1236 41 50
38 5 49
4753 44
2114
22
4540
51
39
15 - 74
140 - 723
943 - 2883
3719 - 5366
7668 - 8597
Thematic Mapping 27
Equal Interval
Max = 8597
Min = 15
Interval = (8597 – 15) / 5 = 1716.4
ID Density Class ID Density Class ID Density Class
30 15 1 25 391 1 50 1683 1
37 21 1 12 393 1 39 1692 1
4 38 1 5 404 1 31 1981 2
51 74 1 26 418 1 15 2113 2
34 140 1 17 445 1 19 2471 2
38 157 1 20 486 1 35 2539 2
11 175 1 41 494 1 13 2883 2
53 191 1 7 523 1 18 3719 3
23 204 1 27 618 1 10 4017 3
47 243 1 36 628 1 48 4172 3
16 272 1 24 630 1 22 4428 3
8 275 1 54 723 1 43 4432 3
40 285 1 29 943 1 1 4728 3
14 286 1 32 1195 1 52 5241 4
42 304 1 33 1244 1 28 5366 4
49 336 1 3 1288 1 6 7668 5
45 343 1 9 1336 1 2 7945 5
21 369 1 44 1414 1 46 8597 5
0
2000
4000
6000
8000
10000
1
23
34
42
7
16
8 24 33 43 9 48 2 18 10 28 37 13 52 15 54 17 6 19 35 46
3 25 26 27 11 29 30 31 32
4 20 1236 41 50
38 5 49
4753 44
2114
22
4540
51
39
15 - 1731
1732 - 3448
3449 - 5164
5165 - 6881
6882 - 8597
Thematic Mapping 28
Equal area
ID Density Class ID Density Class ID Density Class
30 15 1 25 391 4 50 1683 5
37 21 1 12 393 4 39 1692 5
4 38 1 5 404 4 31 1981 5
51 74 1 26 418 4 15 2113 5
34 140 1 17 445 4 19 2471 5
38 157 1 20 486 4 35 2539 5
11 175 1 41 494 4 13 2883 5
53 191 1 7 523 4 18 3719 5
23 204 2 27 618 5 10 4017 5
47 243 2 36 628 5 48 4172 5
16 272 2 24 630 5 22 4428 5
8 275 2 54 723 5 43 4432 5
40 285 2 29 943 5 1 4728 5
14 286 3 32 1195 5 52 5241 5
42 304 3 33 1244 5 28 5366 5
49 336 3 3 1288 5 6 7668 5
45 343 3 9 1336 5 2 7945 5
21 369 4 44 1414 5 46 8597 5
0
2000
4000
6000
8000
10000
1
23
34
42
7
16
8 24 33 43 9 48 2 18 10 28 37 13 52 15 54 17 6 19 35 46
3 25 26 27 11 29 30 31 32
4 20 1236 41 50
38 5 49
4753 44
2114
22
4540
51
39
Total area = 441
Classes = 5
Area interval = 88.2
15 - 191
204 - 285
286 - 343
369 - 523
618 - 8597
Thematic Mapping 29
Quintile
ID Density Class ID Density Class ID Density Class
30 15 1 25 391 2 50 1683 4
37 21 1 12 393 2 39 1692 4
4 38 1 5 404 2 31 1981 4
51 74 1 26 418 3 15 2113 4
34 140 1 17 445 3 19 2471 4
38 157 1 20 486 3 35 2539 4
11 175 1 41 494 3 13 2883 4
53 191 1 7 523 3 18 3719 5
23 204 1 27 618 3 10 4017 5
47 243 1 36 628 3 48 4172 5
16 272 2 24 630 3 22 4428 5
8 275 2 54 723 3 43 4432 5
40 285 2 29 943 3 1 4728 5
14 286 2 32 1195 3 52 5241 5
42 304 2 33 1244 4 28 5366 5
49 336 2 3 1288 4 6 7668 5
45 343 2 9 1336 4 2 7945 5
21 369 2 44 1414 4 46 8597 5
0
2000
4000
6000
8000
10000
1
23
34
42
7
16
8 24 33 43 9 48 2 18 10 28 37 13 52 15 54 17 6 19 35 46
3 25 26 27 11 29 30 31 32
4 20 1236 41 50
38 5 49
4753 44
2114
22
4540
51
39
Total units = 54
Classes = 5
Unit Interval = 10.8
15 - 243
272 - 404
418 - 1195
1244 - 2883
3719 - 8597
Thematic Mapping 30
Standard Dev
ID Density Class ID Density Class ID Density Class
30 15 -1 25 391 -1 50 1683 -1
37 21 -1 12 393 -1 39 1692 -1
4 38 -1 5 404 -1 31 1981 0
51 74 -1 26 418 -1 15 2113 0
34 140 -1 17 445 -1 19 2471 0
38 157 -1 20 486 -1 35 2539 0
11 175 -1 41 494 -1 13 2883 0
53 191 -1 7 523 -1 18 3719 0
23 204 -1 27 618 -1 10 4017 1
47 243 -1 36 628 -1 48 4172 1
16 272 -1 24 630 -1 22 4428 1
8 275 -1 54 723 -1 43 4432 1
40 285 -1 29 943 -1 1 4728 1
14 286 -1 32 1195 -1 52 5241 1
42 304 -1 33 1244 -1 28 5366 1
49 336 -1 3 1288 -1 6 7668 2
45 343 -1 9 1336 -1 2 7945 2
21 369 -1 44 1414 -1 46 8597 3
0
2000
4000
6000
8000
10000
1
23
34
42
7
16
8 24 33 43 9 48 2 18 10 28 37 13 52 15 54 17 6 19 35 46
3 25 26 27 11 29 30 31 32
4 20 1236 41 50
38 5 49
4753 44
2114
22
4540
51
39
Mean = 1721.8
Sta Dev = 2169.8
15 - 1692
1981 - 3719
4017 - 5366
7668 - 7954
8957
Thematic Mapping 31
Example: world population density
0
5000
10000
15000
20000
25000
30000
Po
pu
lati
on
Den
sity
(p
erso
ns/
sqkm
)
Maximum = 30127Minimum = 0Mean = 291.3Std = 1947.1
Thematic Mapping 32
Natural breaks
Thematic Mapping 33
Equal interval
Thematic Mapping 34
Equal area
Thematic Mapping 35
Quartile
Thematic Mapping 36
Standard deviation
Mean = 291.3
SD = 1947.1