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TECHNICAL NOTE
Doc. no. : SRON/EPS/TN/09-002
Issue : 2.2
Date : 29 December 2012
EPSCat :
Page : 1 of 16
Colour Schemes
Prepared by: Paul Tol
51,34,136
332288
136,204,238
88CCEE
68,170,153
44AA99
17,119,51
117733
153,153,51
999933
221,204,119
DDCC77
204,102,119
CC6677
136,34,85
882255
170,68,153
AA4499
Document Change Record
Issue Date Changed Section Description of Change
1.0 18 November 2009 All Initial version
1.1 23 November 2009 Fig. 6 Improved green on grey background
2.0 17 January 2010 All Print-friendlier schemes
Added commands to simulate colour-blindness
2.1 17 August 2010 Fig. 3 Different choice of 8-colour set
p. 4 Remark added on background grey
p. 5 Remark added on NEN colour set
Section 5 Added section on palette check
2.2 29 December 2012 Section 4 Added a banded rainbow scheme
TECHNICAL NOTE
Doc. no. : SRON/EPS/TN/09-002
Issue : 2.2
Date : 29 December 2012
EPSCat :
Page : 2 of 16
Table of Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Distinct Colour Palettes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Best Colour Scheme for Different Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4 Rainbow Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
5 Colour-Scheme Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
6 Colour-Blindness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Reference Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1 Introduction
Graphics with scientific data become clearer when the colours are chosen carefully. It is convenient to have
a good default scheme ready for each type of data, with colours that are distinct for all readers, including
colour-blind people. This document shows such schemes as a function of the number of colours needed, with
some examples. It also gives a conversion of colour coordinates to simulate approximately how any colour is
seen if you are colour-blind.
51,34,136
332288
51,34,136
332288
136,204,238
88CCEE
136,204,238
88CCEE
68,170,153
44AA99
68,170,153
44AA99
17,119,51
117733
17,119,51
117733
153,153,51
999933
153,153,51
999933
221,204,119
DDCC77
221,204,119
DDCC77
204,102,119
CC6677
204,102,119
CC6677
136,34,85
882255
136,34,85
882255
170,68,153
AA4499
170,68,153
AA4499
Figure 1: Palette I of printable websmart colours that are as distinct as possible in both normal and colour-blind
vision, but also match well together. The same colours are shown on a white and a black background, marked
with their decimal RGB values and hexadecimal HTML colour codes.
TECHNICAL NOTE
Doc. no. : SRON/EPS/TN/09-002
Issue : 2.2
Date : 29 December 2012
EPSCat :
Page : 3 of 16
2 Distinct Colour Palettes
Palette I in Fig. 1 consists of colours that are as distinct from each other as possible, while also:
• distinct in colour-blind vision;
• distinct from black and white;
• distinct on computer screen and paper;
• matching well together.
Colour coordinates (R,G,B) are given in the RGB colour system (red R, green G and blue B), decimal at the
top and hexadecimal at the bottom. Alternative palette II in Fig. 2 is more regular: colours in each row have
the same shade (light, medium or dark) and in each column the same hue (azure, cyan, teal, yellow, orange,
red or pink). This palette has been optimized for the medium shades, so some combinations with light or
dark shades, shown in Table. 1, are best avoided. If palette I is used, colours can be chosen at random, but
17,68,119
114477
17,119,119
117777
17,119,68
117744
119,119,17
777711
119,68,17
774411
119,17,34
771122
119,17,85
771155
68,119,170
4477AA
68,170,170
44AAAA
68,170,119
44AA77
170,170,68
AAAA44
170,119,68
AA7744
170,68,85
AA4455
170,68,136
AA4488
119,170,221
77AADD
119,204,204
77CCCC
136,204,170
88CCAA
221,221,119
DDDD77
221,170,119
DDAA77
221,119,136
DD7788
204,153,187
CC99BB
Figure 2: Palette II with a more regular pattern of hues (columns) and shades (rows).
Table 1: Colour combinations from palette II (Fig. 2) that are least distinct in colour-blind vision. These should be
avoided, especially the top two.
TECHNICAL NOTE
Doc. no. : SRON/EPS/TN/09-002
Issue : 2.2
Date : 29 December 2012
EPSCat :
Page : 4 of 16
68,119,170
4477AA
68,119,170
4477AA
204,102,119
CC6677
68,119,170
4477AA
221,204,119
DDCC77
204,102,119
CC6677
68,119,170
4477AA
17,119,51
117733
221,204,119
DDCC77
204,102,119
CC6677
51,34,136
332288
136,204,238
88CCEE
17,119,51
117733
221,204,119
DDCC77
204,102,119
CC6677
51,34,136
332288
136,204,238
88CCEE
17,119,51
117733
221,204,119
DDCC77
204,102,119
CC6677
170,68,153
AA4499
51,34,136
332288
136,204,238
88CCEE
68,170,153
44AA99
17,119,51
117733
221,204,119
DDCC77
204,102,119
CC6677
170,68,153
AA4499
51,34,136
332288
136,204,238
88CCEE
68,170,153
44AA99
17,119,51
117733
153,153,51
999933
221,204,119
DDCC77
204,102,119
CC6677
170,68,153
AA4499
51,34,136
332288
136,204,238
88CCEE
68,170,153
44AA99
17,119,51
117733
153,153,51
999933
221,204,119
DDCC77
204,102,119
CC6677
136,34,85
882255
170,68,153
AA4499
51,34,136
332288
136,204,238
88CCEE
68,170,153
44AA99
17,119,51
117733
153,153,51
999933
221,204,119
DDCC77
102,17,0
661100
204,102,119
CC6677
136,34,85
882255
170,68,153
AA4499
51,34,136
332288
102,153,204
6699CC
136,204,238
88CCEE
68,170,153
44AA99
17,119,51
117733
153,153,51
999933
221,204,119
DDCC77
102,17,0
661100
204,102,119
CC6677
136,34,85
882255
170,68,153
AA4499
51,34,136
332288
102,153,204
6699CC
136,204,238
88CCEE
68,170,153
44AA99
17,119,51
117733
153,153,51
999933
221,204,119
DDCC77
102,17,0
661100
204,102,119
CC6677
170,68,102
AA4466
136,34,85
882255
170,68,153
AA4499
Figure 3: Scheme examples for qualitative data. Each row is a scheme for a different number of colours.
even here some combinations are more distinct than others. Some of the most distinct subsets, depending
on the number of colours, are given in Fig. 3. When there are more than nine colours, some extra colours
outside palette I have been defined. For subsets of fewer than five colours, the dark blue has been replaced
by medium azure from palette II. Data gaps can be indicated with light grey DDDDDD (221, 221, 221). The
four-colour set in Fig. 3 is reasonably distinct when printed in grey, but a set optimized for this purpose is
shown in Figure 4.
TECHNICAL NOTE
Doc. no. : SRON/EPS/TN/09-002
Issue : 2.2
Date : 29 December 2012
EPSCat :
Page : 5 of 16
Figure 4: A four-colour subset of palette I that is optimized for printing in grey scale. Tip: if used for lines, also
use dashed and dotted lines.
B A C T G S Y O R P M V B A C T G S Y O R P M V
Figure 5: All websmart sRGB colours with vividness 0.4 with printable colours enclosed by a black line. Ini-
tials stand for blue, azure, cyan, teal, green, spring, yellow, orange, red, pink, magenta and violet. Colours in
palette I (left) and palette II (right) are indicated by white squares. Three light shades in palette II have been
made less vivid (out of the plane of the figure) to put them inside the CMYK gamut, and are therefore not in-
dicated. Geometric distance does not indicate perceptual colour distance, especially not if colour-blindness is
taken into account.
The design of these palettes involved four types of calculations:
• for the distance between colours the CIEDE2000 colour difference ΔE00 is used [1];
• red-blind and green-blind vision is simulated by the method described in section 6;
• colours with the same product of saturation S and value V in the HSV colour system (same ‘vividness’)
match well together;
• colours are called ‘printable’ if they are within the CMYK gamut provided by colour profile ‘ISO Coated v2
300%’ (discussed below).
To reduce the number of calculations without much loss of choice, only websmart colours were considered,
meaning the hexadecimal RGB coordinates are only 00, 11, . . . , FF. The vividness was chosen to be SV = 0.4.
With a smaller value colours become too grey, with a larger value there is not enough range of shades for
palette II and in general there are fewer printable colours.
All colours in this document are defined in sRGB colour space, the default used by most software and
displays. Printers work in a different colour space that also varies from model to model. When they con-
form to international standard ISO 12647-2 and the exact printing conditions are not known beforehand, it
is recommended to assume the CMYK colour space provided by colour profile ‘ISO Coated v2 300%’ [2]. All
palette colours are taken from the overlap between this and the sRGB colour spaces. More specifically, the
two colour blocks in Fig. 5 show all sRGB colours with vividness 0.4, while the colours enclosed by a black
line are also in the CMYK colour space defined above and therefore printable. Pure blue of this vividness (col-
umn above B) is not printable. Magenta, green and light cyan are also problematic for printers. The palette
colours are indicated by squares. They are not equally spread over the figure within the black lines, because
geometric distance in this figure does not correspond to perceptual colour distance, even in normal vision.
The Netherlands Standardization Institute NEN has issued a code of practice which includes a recom-
mended palette with eight colours, three greys and white [3]. Differences between them are often much
smaller than the smallest difference in palette I, two colours are not printable and they cannot be quoted
without infringing copyright.
This section ends on an SRON-specific topic: PowerPoint presentations on a dark grey background. In
this case the light shades (top row) in palette II could be used. However, the original SRON template already
TECHNICAL NOTE
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Issue : 2.2
Date : 29 December 2012
EPSCat :
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255,255,255
FFFFFF
255,255,204
FFFFCC
255,204,102
FFCC66
128,155,200
809BC8
100,194,4
64C204
255,102,102
FF6666
66,66,66
424242
Figure 6: SRON PowerPoint colours on a dark grey background, with the left four taken from the original tem-
plate. Colours from the top row in Fig. 2 also work on this background.
defines three colours: white for titles, light yellow for normal text and orange for highlighted text. If the light
blue from the footer is added, two extra hues are green and red. The complete palette optimized for projec-
tion is shown in Fig. 6. The red is rather pale, because it becomes darker on a projection screen. The green is
carefully chosen so it differs from orange in red-blind vision and differs from red in green-blind vision.
3 Best Colour Scheme for Different Data Types
A colour scheme should reflect the type of data shown. There are three basic types of data:
1. Qualitative data—nominal or categorical data, where magnitude differences are not relevant. This includes
text in presentations and lines in plots. Use palette I (Fig. 3) or different hues (colours from a row) in palette II
(Fig. 2).
2. Sequential data—data ordered from low to high.
255,247,188
FFF7BC
254,196,79
FEC44F
217,95,14
D95F0E
255,251,213
FFFBD5
254,217,142
FED98E
251,154,41
FB9A29
204,76,2
CC4C02
255,251,213
FFFBD5
254,217,142
FED98E
251,154,41
FB9A29
217,95,14
D95F0E
153,52,4
993404
255,251,213
FFFBD5
254,227,145
FEE391
254,196,79
FEC44F
251,154,41
FB9A29
217,95,14
D95F0E
153,52,4
993404
255,251,213
FFFBD5
254,227,145
FEE391
254,196,79
FEC44F
251,154,41
FB9A29
236,112,20
EC7014
204,76,2
CC4C02
140,45,4
8C2D04
255,255,229
FFFFE5
255,247,188
FFF7BC
254,227,145
FEE391
254,196,79
FEC44F
251,154,41
FB9A29
236,112,20
EC7014
204,76,2
CC4C02
140,45,4
8C2D04
255,255,229
FFFFE5
255,247,188
FFF7BC
254,227,145
FEE391
254,196,79
FEC44F
251,154,41
FB9A29
236,112,20
EC7014
204,76,2
CC4C02
153,52,4
993404
102,37,6
662506
Figure 7: Scheme for sequential data [4]. The smooth version at the bottom is produced with Eq. (1).
TECHNICAL NOTE
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Issue : 2.2
Date : 29 December 2012
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153,199,236
99C7EC
255,250,210
FFFAD2
245,162,117
F5A275
0,139,206
008BCE
180,221,247
B4DDF7
249,189,126
F9BD7E
208,50,50
D03232
0,139,206
008BCE
180,221,247
B4DDF7
255,250,210
FFFAD2
249,189,126
F9BD7E
208,50,50
D03232
58,137,201
3A89C9
153,199,236
99C7EC
230,245,254
E6F5FE
255,227,170
FFE3AA
245,162,117
F5A275
210,77,62
D24D3E
58,137,201
3A89C9
153,199,236
99C7EC
230,245,254
E6F5FE
255,250,210
FFFAD2
255,227,170
FFE3AA
245,162,117
F5A275
210,77,62
D24D3E
58,137,201
3A89C9
119,183,229
77B7E5
180,221,247
B4DDF7
230,245,254
E6F5FE
255,227,170
FFE3AA
249,189,126
F9BD7E
237,135,94
ED875E
210,77,62
D24D3E
58,137,201
3A89C9
119,183,229
77B7E5
180,221,247
B4DDF7
230,245,254
E6F5FE
255,250,210
FFFAD2
255,227,170
FFE3AA
249,189,126
F9BD7E
237,135,94
ED875E
210,77,62
D24D3E
61,82,161
3D52A1
58,137,201
3A89C9
119,183,229
77B7E5
180,221,247
B4DDF7
230,245,254
E6F5FE
255,227,170
FFE3AA
249,189,126
F9BD7E
237,135,94
ED875E
210,77,62
D24D3E
174,28,62
AE1C3E
61,82,161
3D52A1
58,137,201
3A89C9
119,183,229
77B7E5
180,221,247
B4DDF7
230,245,254
E6F5FE
255,250,210
FFFAD2
255,227,170
FFE3AA
249,189,126
F9BD7E
237,135,94
ED875E
210,77,62
D24D3E
174,28,62
AE1C3E
Figure 8: Scheme for diverging data [4]. The smooth version at the bottom is produced with Eq. (2).
(a) If there are two or three classes, it is possible to use different intensities of the same hue (colours
from a column) in palette II (Fig. 2).
(b) For three or more classes, use a scheme as given in Fig. 7.
3. Diverging data—data ordered between two extremes where the midpoint is important, e.g. positive and
negative deviations from zero or a mean. Use a scheme as given in Fig. 8.
Plot examples of qualitative data, sequential data and a combination are given in Figs. 9, 10 and 11, respec-
tively. An example of diverging data is shown in Fig. 12. The smooth version of the yellow-orange-brown
scheme in Fig. 7 is produced by
R/255 = 1− 0.392(1+ erf[(− 0.869)/0.255]) , (1a)
G/255 = 1.021− 0.456(1+ erf[(− 0.527)/0.376]) , (1b)
B/255 = 1− 0.493(1+ erf[(− 0.272)/0.309]) , (1c)
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Date : 29 December 2012
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-1.0 -0.5 0.0 0.5 1.0
-1.0
-0.5
0.0
0.5
1.0 blue
green
yellow
red
Figure 9: A qualitative colour scheme: distinct colour hues with modest intensity differences for data where
magnitude differences are not relevant. Left: four curves and labels that are distinguishable from each other
and clear on a white background. Right: members (red), associate members (green), observers (blue) and as-
sociate partners (yellow) of the Western European Union. The four-colour set from Fig. 3 is used.
0
50
100
150
200
250
300
350
400
po
pu
latio
nd
en
sity@k
m-
2D
Figure 10: A sequential colour scheme: variation of colour intensity for data that are ordered from low to high,
in this case the population density. The hue can also vary to some extent, as long as the intensity differences
dominate. (On this map there are no countries in the class 250–300 km−2.)
Figure 11: A combination of a qualitative and a sequential colour scheme. As in Fig. 9, different categories have
different hues: European Football Championship winners are red. As in Fig. 10, within each category, data are
ordered from low to high by different intensities: the suicide rate per 100,000 is < 10 (light), 10–15 (medium)
or > 15 (dark). Three shades of two hues from Fig. 2 are used.
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Date : 29 December 2012
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-100 -80 -60 -40 -20 0 20 40 60 80
geoid height @mD
Figure 12: A diverging colour scheme: the middle of the legend is emphasized with light colours and low and
high extremes are emphasized with dark colours that have contrasting hues. Distance between the WGS84
ellipsoid and the geoid calculated with the EGM96 gravity model.
with 0 ≤ ≤ 1 and error function erf. The smooth blue-yellow-red scheme in Fig. 8 is given by:
R/255 = 0.237− 2.13+ 26.922 − 65.53 + 63.54 − 22.365 , (2a)
G/255 =
0.572+ 1.524− 1.8112
1− 0.291+ 0.15742
!2
, (2b)
B/255 = 1�
�
1.579− 4.03+ 12.922 − 31.43 + 48.64 − 23.365�
. (2c)
The quantitative (sequential and diverging) schemes in Fig. 7 and 8 were taken from the ColorBrewer
website [4], where many others can be found. The qualitative schemes there do not have the characteristics
of palettes I and II, which was the reason I designed these two.
4 Rainbow Schemes
Quantitative data should not be shown with a rainbow scheme, because the spectral order of visible light car-
ries no inherent magnitude message. In addition, most rainbow schemes contain bands of almost constant
hue with sharp transitions in-between, which are perceived as jumps in the data. Finally, colour-blind people
have difficulty distinguishing some colours of the rainbow.
However, if you have tried schemes as discussed in the previous section and still want a rainbow, Fig. 13
shows such a scheme that is continuous and reasonably clear in colour-blind vision. The colours in each row
are equidistant in normal vision using the CIEDE2000 colour difference [1] as a distance measure. The smooth
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64,64,150
404096
87,163,173
57A3AD
222,167,58
DEA73A
217,33,32
D92120
64,64,150
404096
82,157,183
529DB7
125,184,116
7DB874
227,156,55
E39C37
217,33,32
D92120
64,64,150
404096
73,140,194
498CC2
99,173,153
63AD99
190,188,72
BEBC48
230,139,51
E68B33
217,33,32
D92120
120,28,129
781C81
63,96,174
3F60AE
83,158,182
539EB6
109,179,136
6DB388
202,184,67
CAB843
231,133,50
E78532
217,33,32
D92120
120,28,129
781C81
63,86,167
3F56A7
75,145,192
4B91C0
95,170,159
5FAA9F
145,189,97
91BD61
216,175,61
D8AF3D
231,124,48
E77C30
217,33,32
D92120
120,28,129
781C81
63,78,161
3F4EA1
70,131,193
4683C1
87,163,173
57A3AD
109,179,136
6DB388
177,190,78
B1BE4E
223,165,58
DFA53A
231,116,47
E7742F
217,33,32
D92120
120,28,129
781C81
63,71,155
3F479B
66,119,189
4277BD
82,157,183
529DB7
98,172,155
62AC9B
134,187,106
86BB6A
199,185,68
C7B944
227,156,55
E39C37
231,109,46
E76D2E
217,33,32
D92120
120,28,129
781C81
64,64,150
404096
65,108,183
416CB7
77,149,190
4D95BE
91,167,167
5BA7A7
110,179,135
6EB387
161,190,86
A1BE56
211,179,63
D3B33F
229,148,53
E59435
230,104,45
E6682D
217,33,32
D92120
120,28,129
781C81
65,59,147
413B93
64,101,177
4065B1
72,139,194
488BC2
85,161,177
55A1B1
99,173,153
63AD99
127,185,114
7FB972
181,189,76
B5BD4C
217,173,60
D9AD3C
230,142,52
E68E34
230,100,44
E6642C
217,33,32
D92120
Figure 13: Continuous rainbow scheme. The smooth version at the bottom is produced with Eq. (3).
136,46,114
882E72
177,120,166
B178A6
214,193,222
D6C1DE
25,101,176
1965B0
82,137,199
5289C7
123,175,222
7BAFDE
78,178,101
4EB265
144,201,135
90C987
202,224,171
CAE0AB
247,238,85
F7EE55
246,193,65
F6C141
241,147,45
F1932D
232,96,28
E8601C
220,5,12
DC050C
17,68,119
114477
68,119,170
4477AA
119,170,221
77AADD
17,119,85
117755
68,170,136
44AA88
153,204,187
99CCBB
119,119,17
777711
170,170,68
AAAA44
221,221,119
DDDD77
119,17,17
771111
170,68,68
AA4444
221,119,119
DD7777
119,17,68
771144
170,68,119
AA4477
221,119,170
DD77AA
119,17,85
771155
170,68,136
AA4488
204,153,187
CC99BB
17,68,119
114477
68,119,170
4477AA
119,170,221
77AADD
17,119,119
117777
68,170,170
44AAAA
119,204,204
77CCCC
119,119,17
777711
170,170,68
AAAA44
221,221,119
DDDD77
119,68,17
774411
170,119,68
AA7744
221,170,119
DDAA77
119,17,34
771122
170,68,85
AA4455
221,119,136
DD7788
119,17,85
771155
170,68,136
AA4488
204,153,187
CC99BB
17,68,119
114477
68,119,170
4477AA
119,170,221
77AADD
17,119,119
117777
68,170,170
44AAAA
119,204,204
77CCCC
17,119,68
117744
68,170,119
44AA77
136,204,170
88CCAA
119,119,17
777711
170,170,68
AAAA44
221,221,119
DDDD77
119,68,17
774411
170,119,68
AA7744
221,170,119
DDAA77
119,17,34
771122
170,68,85
AA4455
221,119,136
DD7788
Figure 14: Banded rainbow schemes with a large number of steps. It is better to use all colours in a smaller
scheme than to pick colours from a larger scheme.
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-100 -50 0 50 100 150
longitude @degreesD
-60
-40
-20
0
20
latitu
de@d
eg
ree
sD
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
1018 molecules�cm2
Figure 15: The smooth, continuous rainbow scheme from Fig. 13 used for sequential data. SCIAMACHY CO total
column in October 2004 [5].
-100 -50 0 50 100 150
longitude @degreesD
-60
-40
-20
0
20
latitu
de@d
eg
ree
sD
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
1018 molecules�cm2
Figure 16: Top banded rainbow scheme from Fig. 14 used for the same sequential data as in Fig. 15.
version at the bottom is given by:
R/255 =0.472− 0.567+ 4.052
1+ 8.72− 19.172 + 14.13, (3a)
G/255 = 0.108932− 1.22635+ 27.2842 − 98.5773 + 163.34 − 131.3955 + 40.6346 , (3b)
B/255 = 1�
�
1.97+ 3.54− 68.52 + 2433 − 2974 + 1255�
. (3c)
If more than 10 steps are needed, the colours become difficult to discern. In that case consider using the
smooth version or (part of) one of the banded schemes in Fig. 14. The top banded scheme is based on the
temperature map of the weather forecast in newspaper de Volkskrant, tweaked to make the colours more dis-
tinct. The other banded schemes are based on distinct colour palette II and a reoptimization with 15 colours.
Examples of all types are shown in Figs. 15, 16 and 17. Figure 15 shows an advantage of the continuous
rainbow scheme over the earlier quantitative schemes when data is missing: because the whole range of
colours is equally saturated, there is a clear distinction between data and non-data. The other schemes have
pale colours at the low end or middle of the range. With a banded scheme as in Fig. 16, it is easier to deter-
mine the value at a particular location.
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
albedo
Figure 17: Bottom banded scheme from Fig. 14 used for sequential data. Albedo of snow- and cloud-free land at
2.1 µm at a resolution of 7.5 km, using MODIS data from 4–19 July 2007.
5 Colour-Scheme Robustness
Figure 18 shows most schemes defined in this document used in a variation of the diagnostic map used by
the ColorBrewer website [4]. A scheme works if the following can be done without much effort:
• in the random section at the left, distinguish every colour;
• in each section with one main colour, find the outliers (one per colour) and distinguish them from each
other.
All schemes are shown with nine colours; in cases where fewer colours are used, the data will be clearer.
6 Colour-Blindness
People usually find out at an early age whether they are colour-blind. However, there are subtle variants of
colour-vision deficiency. The two main types are:
• Green-blindness – the cone cells in the retina that are sensitive to medium wavelengths are absent or have
their response shifted to the red (6% of men, 0.4% of women);
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Figure 18: Check for colour-scheme robustness: can all colours be distinguished in a random pattern and when
surrounded by another colour.
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Figure 19: The readable text in this image is the colour-vision diagnosis of the reader. It is not a puzzle: there is
no hidden message that requires much effort to see. The clarity of the text is not important, only whether it is
readable at all. Please do not make life-changing decisions based only on this test.
• Red-blindness – the cone cells in the retina that are sensitive to long wavelengths are absent or have their
response shifted to the green (2.5% of men).
Figure 19 is a test on these types. It works on a computer screen (when looking straight at it), projected with
a beamer and sometimes even in unfaded print, although this will depend on the quality of the equipment.
To simulate green-blindness [6, 7], all RGB colours in an image are converted to R’G’B’ colours with
R′ =�
4211+ 0.677G2.2 + 0.2802R2.2�1/2.2
, (4a)
G′ =�
4211+ 0.677G2.2 + 0.2802R2.2�1/2.2
, (4b)
B′ =�
4211+ 0.95724B2.2 + 0.02138G2.2 − 0.02138R2.2�1/2.2
, (4c)
with parameters R, G and B in the range 0–255 and the output values rounded. To simulate red-blindness,
colours are shifted as follows:
R′ =�
782.7+ 0.8806G2.2 + 0.1115R2.2�1/2.2
, (5a)
G′ =�
782.7+ 0.8806G2.2 + 0.1115R2.2�1/2.2
, (5b)
B′ =�
782.7+ 0.992052B2.2 − 0.003974G2.2 + 0.003974R2.2�1/2.2
. (5c)
These conversions should be applied in sRGB colour space, i.e. they work on a standard video display, but
not necessarily on paper. The conversion can be performed with the free software suite ImageMagick. The
following two commands make green-blind and red-blind versions of original image original.png, respec-
tively:1
convert original.png \( +clone -channel RG -fx "(0.02138+0.6770*G^2.2+0.2802*R^2.2)^(1/2.2)" \) \
+swap -channel B -fx "(0.02138(1+v.G^2.2-v.R^2.2)+0.9572*v.B^2.2)^(1/2.2)" greenblind.png
convert original.png \( +clone -channel RG -fx "(0.003974+0.8806*G^2.2+0.1115*R^2.2)^(1/2.2)" \) \
+swap -channel B -fx "(0.003974(1-v.G^2.2+v.R^2.2)+0.9921*v.B^2.2)^(1/2.2)" redblind.png
Figure 20 shows the result when they are applied to a triangle of normal colours (top): the green-blind simula-
tion is at bottom left, the red-blind simulation at bottom right. Contrary to popular belief, pure red and green
1These are Unix-style commands, for Windows replace \( and \) by ( and ), and use a caret (ˆ) instead of a backslash to end the first line.
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gree
n-bl
ind
visi
on
red-
blin
dvi
sion
norm
alvi
sion
Figure 20: Colour scale in normal vision (top), green-blind vision (bottom left) and red-blind vision (bottom
right). These conversions are only approximate and are designed for a computer screen.
Table 2: Colours in Fig. 1 as seen in normal and colour-blind vision.
Palette I in normal vision.
Approximate green-blind simulation of palette I.
Approximate red-blind simulation of palette I.
can be distinguished. Instead, yellow/green and purple/blue combinations are problematic. However, there are
more unexpected pairs of colours that look the same, as used in Fig. 19. Table 2 shows colour-blind vision simu-
lations of distinct colour palette I.
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Reference Documents
[1] Gaurav Sharma, Wencheng Wu, and Edul N. Dalal. The CIEDE2000 color-difference formula: implementation
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colour—accommodating colour vision disorders. Code of practice NPR 7022, Netherlands Standardization
Institute, Delft, April 2006.
[4] Cynthia A. Brewer. ColorBrewer, a web tool for selecting colors for maps, 2009. http://colorbrewer2.org.
[5] A.M.S. Gloudemans, M.C. Krol, J.F. Meirink, A.T.J. de Laat, G.R. van der Werf, H. Schrijver, M.M.P. van den
Broek, and I. Aben. Evidence for long-range transport of carbon monoxide in the southern hemisphere from
SCIAMACHY observations. Geophysical Research Letters, 33:L16807, 2006.
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displays by dichromats. Color Research and Application, 24:243–252, 1999.
[7] Hans Brettel, Françoise Viénot, and John D. Mollon. Computerized simulation of color appearance for dichro-
mats. Journal of the Optical Society of America A, 14:2647–2655, 1997.