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Has anyone got good examples of where these changed?

PERSPECTIVE

The misuse of colour in science communication

Fabio Crameri

✉

, Grace E. Shephard

& Philip J. Heron

The accurate representation of data is essential in science communication. However, colour

maps that visually distort data through uneven colour gradients or are unreadable to those

with colour-vision deﬁciency remain prevalent in science. These include, but are not limited

to, rainbow-like and red–green colour maps. Here, we present a simple guide for the scientiﬁc

use of colour. We show how scientiﬁcally derived colour maps report true data variations,

reduce complexity, and are accessible for people with colour-vision deﬁciencies. We highlight

ways for the scientiﬁc community to identify and prevent the misuse of colour in science, and

call for a proactive step away from colour misuse among the community, publishers, and

the press.

ision is one of the most fundamental means of communication. It is (or should be) in

every scientist’s best intention to make ﬁgures and their content as accurate and easily

understandable as possible. One of the most powerful aspects of images is colour, which

in turn transforms information into meaning. The visual evaluation of a colour gradient is

important to a variety of different ﬁelds such as the ﬁrst direct impression of a black hole

, the

mapping of votes cast in political elections

2,3

, the planning of an expensive rover route on

Martian topography

, the essential communication of climate change

5,6

, or the critical diagnosis

of heart disease

. However, when colours are used incorrectly, this can lead to the effective

manipulation of data (e.g., by highlighting some data over others), the oversight of the needs of

those with colour vision deﬁciencies, and the removal of meaning when printed in black and

white (Supplementary Note 1).

As science has become more prevalent in mainstream culture, it is not only the scientiﬁc

community that suffers due to the use of poor colour choices, but also the wider public. Colour

maps, therefore, are a crucial intersection between science and society. For instance, weather

forecasts and hazard maps are two examples of immediately societal-relevant data sets that are

also repeat offenders for use of the rainbow-like colour maps. Given the (daily) importance of

these scientiﬁc topics, the underlying data should be conveyed in a universal manner. However,

the colour-vision deﬁcient fraction of the population is excluded and therefore unable to process

this critical information. Furthermore, zones of danger, such as the boundaries of a hurricane

track or current virus spread, are often based on uneven colour gradients to accentuate their

importance. Using an uneven colour gradient is not an action without consequences, including

those with signiﬁcant ﬁnancial or life-threatening consequences. Decisions based on data being

‘unfairly’ represented could produce, for instance, a Martian rover being sent over terrain that is

too steep as the topography was inaccurately visualised, or a medical worker making an

incomplete or inaccurate diagnosis based on uneven colour gradients.

Although some scientiﬁc communities have largely moved away from using distorting colour

maps, such as rainbow, there are numerous signs of bad habits returning en masse

. Unfortu-

nately, the previous efforts within speciﬁc disciplines to discredit rainbow-like maps appear to

https://doi.org/10.1038/s41467-020-19160-7

OPEN

Centre for Earth Evolution and Dynamics (CEED), University of Oslo, Postbox 1028, Blindern, 0315 Oslo, Norway.

Department of Earth Sciences, Durham

University, Durham, UK.

✉

email: fabio.crameri@geo.uio.no

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1234567890():,;

have not trickled through to all scientiﬁc leaders, publishers, and

software designers. For most scientists, the choice of colour maps

has become almost passive, with the unscientiﬁc rainbow-like

colour palette being commonplace. Similarly, colour maps that

pair red–green are also problematic, but remain widely used. At

one point, most of the common software programmes applied

rainbow as their default palette (e.g., MatLab, Paraview, VisAd,

IrisExplorer) despite issues surrounding colour maps like rain-

bow, and variations thereof, being known for some time

9–20

So, what’s the problem with these colour maps? Even though

rainbow colour maps might reﬂect aesthetic attractiveness, the

extreme values in the standard Red-Green-Blue (RGB) are very

dominant and can, therefore, distract from the underlying visual

message

. In rainbow colour maps, the yellow is the brightest

colour and attracts the eye the most

22,23

(see Box 1), but it is

neither at the end nor the centre of the colour map, while its

greenish shades form a wide band with low perceived colour

contrast (Supplementary Fig. 1). Hence, such an arrangement of

colours can unfairly highlight a particular section of the para-

meter space while obscuring other parts (Fig. 1). Building a colour

map on a purely physical rather than a perceptual basis sig-

niﬁcantly alters how we perceive data; it adds artiﬁcial boundaries

to some parts of the data range, hiding small-scale variations

elsewhere, it prevents any visual intuitive order occurring in the

data set, and renders the data unreadable for readers with com-

mon colour-vision deﬁciencies (Fig. 2).

Colour maps that include both red and green colours with

similar lightness cannot be read by a large fraction of the read-

ership (Fig. 2). The general estimate is that worldwide 0.5% of

women and 8% of men are subject to a colour-vision deﬁciency

(CVD; e.g., refs.

24,25

, and references therein). While these

numbers are lower and almost disappear in populations from

sub-Saharan Africa, they are likely signiﬁcantly higher in popu-

lations with a larger fraction of white (Caucasian) people as, for

example, in Scandinavia

. It is needless to state that scientiﬁc

results should be accessible to as many people as possible. CVD-

friendliness is, therefore, an aspect that should be important to all

researchers, as well as publishers

18,27,28

For the casual reader, it might appear curious that the com-

munity of scientists, a group of people who are usually more

critically inclined, fail to condemn the proliferation among

themselves of rainbow and other, similarly unﬁt, colour maps.

Based on this prevalence of unscientiﬁc colour maps, a basic

understanding of their nature (Supplementary Fig. 2) and their

dynamics seems to be missing in the academic community.

Colour map choice is often made passively and is not subject to

the same scrutiny as other data methodologies. Rainbow’s eye-

grabbing nature, ease of use, and the inertia of both software

products and scientiﬁc group leaders, allows the scientiﬁc com-

munity to remain attached to this unscientiﬁc colour map

.Asa

result, pointing out colour map ﬂaws to the science community

through scientiﬁc peer-review remains a challenging task, as

BOX 1:

Human colour perception

Colour is not inherent in objects. A perceived colour is the portion of light that is reﬂected from a surface and translated into a speciﬁc colour by our

eyes and brain (Box Fig. 1). A certain colour is perceived via its hue, the true tint (i.e., yellow, orange, red, violet, blue or green), and its luminosity (the

measure of how bright or dark a hue is). Within the eye, one type of light receptors, the rod cells, process achromatic information (i.e., lightness or grey-

scale vision), which is derived mostly from the light’s energy. The other type, the cone cells, handle chromatic information (the hue) mostly from the

light’s wavelength. The latter transmit information to the brain and create the sensation of colour that is so familiar to most of us.

Two thirds of all cone cells process longer wavelengths of light (i.e., colours like red, orange, yellow), which allows the human eye to perceive more

colour detail across warmer colours than for cooler colours

. Greenish colour gradients tend to under-represent a given data variation compared to

yellow-red gradients. Three types of cone cells (for short, medium and, long wavelengths) build the trichromatic visual system that can, as a whole,

represent all colours in our visual spectrum

55–58

The physiological prerequisites for perceiving colour suggest that there is no uniform colour perception among individuals

; several physiological

deviations can lead to a shift in colour perception, which, in general, is hardly measurable

. However, it is not unlikely that at least one of the cone cell

types is altered, defect, or even absent, which induces a signiﬁcant shift in colour vision. Such a shift is commonly referred to as colour-vision deﬁciency

(CVD), or colour blindness, and can be modelled by a given combination of the three fundamental spectral sensitivity functions representing short,

medium and long wavelengths of the light

(as represented in Fig. 2). The most common form of colour-vision deﬁciency is the red–green

dichromatism, called deuteranomaly, concerning the M-cone and causing red and green to appear indistinguishable. Protanomaly, concerning the L-

cone, and tritanomaly, concerning the S-cone cause reduced sensitivity to red and blue light, respectively. Total colour blindness is, fortunately, very

rare, but does exist.

Box Fig. 1: Simpliﬁed schematic of human colour perception. The perception of a certain colour, or colour gradient, by the optical cortex depends not

only on the optical properties of the object, but also on the optical properties of both light source and object background, and the eye’s light receptors

(rod and cone cells for short, medium and long wavelengths).

“Coloured”

object

Object

Background

Light source Optical cortex

Optical nerveEye lens

Cone cells

(S, M, L)

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jet

Original

batlow

Fig. 1 The superiority of scientiﬁcally derived colour maps. By knowing what something looks like in advance, the distortion by unscientiﬁc colour maps,

like jet or rainbow, becomes instantly obvious. The look of scientiﬁc data is, however, usually unknown a priori, which makes the distortion of an

unscientiﬁc colour map, and the true data representation of a scientiﬁcally derived colour map, like batlow

, less apparent. Marie Skłodowska-Curie, as

originally photographed by Henri Manuel around 1920, the Earth from space, and an apple are shown a in their original images and b in distorted and c in

undistorted colour versions. Inferring the true picture from an unscientiﬁcally (e.g., jet) coloured data set is incomparably harder than from a data set

represented in a perceptually uniform and ordered colour map, like batlow

viridis

Colour-vision deficient (CVD)

Colour-blind

Deuteranopia

Protanopia Tritanopia

CVD-friendly

Grey scale

cividis

kry

thermal

batlow

jet

Fig. 2 Colour vision tests. Available perceptually uniform colour maps versus the non-uniform rainbow (i.e., jet; bottom row) as seen with either of the

three common forms of human colour-vision deﬁciency (deuteranopia, protanopia, and tritanopia), and for grey-scale (representing total colour-blindness

or simple black-and-white prints). Rainbow, the most-widely used colour map, fails to reproduce a meaningful smooth gradient, yet the other colour

maps (see Box 2) are all universally readable.

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requests or suggestions to change the colour palette are often met

with rebuttal, misunderstanding, or are simply ignored.

Here, we highlight the importance of the scientiﬁc use of colour

in data visualisation. We summarise methods to generate colour

maps that deliver equal colour gradients all along the colour axis,

to prevent data distortion. Various types of scientiﬁcally derived

colour maps are readily and freely available (Box 2), and are the

only way to intuitively and inclusively represent data without any

blind interpretation. We outline key guidelines for choosing sci-

entiﬁc colour maps that most accurately represent your data, and

highlight how to spot common unscientiﬁc colour maps so they

can be avoided. Finally, we call for a universal switch by the

science community to adopt scientiﬁcally derived colour maps.

Individuals, publishers and press should take a proactive

approach to spot unscientiﬁc use of colour and so prevent the

dissemination of visually distorted data.

The importance of colour to prevent data distortion. Scientiﬁc

data should be displayed without the addition of visually artiﬁcial

features or subtraction of real details, while also being universally

readable and intuitive. A perceptually uniform colour map

weights the same data variation equally all across the dataspace,

while other colour maps (such as rainbow) interpret some small

data variation to be more important than others (Fig. 3). For such

unscientiﬁc, perceptually non-uniform colour maps (like rain-

bow), the interpretation is performed blindly (i.e., by the colour

map instead of by the author) as the author or reader is not aware

of the exact visual distortion that is introduced by the colour map

(Fig. 3). Any scientiﬁc study drawing conclusions from a given set

of data is, therefore, strongly dependent on the perceptual uni-

formity of the colour palette applied and, with it, author and

reader become captive to a blind interpretation (for various

examples, see Supplementary Note 1). Such a colour-introduced

blind interpretation can diverge from an objective representation

by more than seven percent of the displayed data variation

(Fig. 3e–f). A ﬂat slope on Mars can become visually distorted by

the most prominent local gradients in colour rather than data,

and then appears like rough terrain, while rough terrain con-

versely might be interpreted as a ﬂat slope (compare Supple-

mentary Fig. 7a, b), which is suboptimal with regards to a

Martian exploration.

Scientiﬁcally derived colour maps are perceptually uniform.

This means the same data variation is weighted equally across the

dataspace, and so the true data variation is accurately represented

without unnecessary visual error (Fig. 3a, c, e, g, i). Just like a

spatial x-, y-, or z-axis needs to have equal spacing between all

axis tick marks (Fig. 3g, h), a colour axis (commonly termed

colour bar; Supplementary Fig. 1) needs to have equidistant

colour gradients. In other words, a certain data variation (e.g., a

5 °C temperature drop) should appear the same no matter

whether it occurs at low temperatures (–10 °C) or high

temperatures (30 °C).

Design and implementation of scientiﬁcally derived colour

maps. While understanding the importance of perceptually uni-

form colour maps is simple, creating them can be complicated.

Quantifying perceptual colour gradients is challenging because

the complex nature of the human eye and brain has to be con-

sidered (Box 1). However, extensive research has been conducted

to understand and provide guidelines for an optimal colour map

design (see description in ‘Methods’ and refs.

18–20,29,31–35

), and

today, various freely available tools exist to create perceptually

uniform colour palettes. In Box 2, we have compiled freely

available scientiﬁc colour map toolkits, and described the beneﬁts

BOX 2

Freely available scientiﬁcally derived colour maps and toolkits

Scientiﬁcally derived colour maps should be easily recognisable, and also be freely and readily available. While there are many online sources to

download pre-made colour maps, and toolboxes to create colour maps, only few offer all the aspects required for use in science communication. Below,

we mention the most accessible and/or robustly documented sources of scientiﬁcally derived colour maps, and outline their individual properties.

●

Colorbrewer: The Colorbrewer colour maps (available at ref.

) developed by Cynthia Brewer are provided through an online tool to manually

produce and export a variety of discrete colour maps, which can, optionally, be colour-vision deﬁciency friendly and exported to a given a variety of

formats. With the main aim being cartography, the online tool offers sequential, diverging and categorical (or in other words, qualitative) colour

maps, but does not currently offer them in a continuous type.

●

MPL (Matplotlib): The MPL colour maps (available at ref.

) developed by Stéfan van der Walt and Nathaniel Smith. MPL maps aim for the most

accurate perceptual uniformity with its widely applied colour maps being: viridis, magma, plasma and inferno. These maps have spearheaded the way

towards more scientiﬁc colour mapping. The MPL colour maps are all sequential and continuous only. The MPL colour maps are openly available

(currently for use with Python) and often built into software.

●

Cividis: The cividis colour map

(available at ref.

), developed by Jamie R. Nuñez and colleagues, aims to represent an almost identical

appearance for red–green colour-vision deﬁciencies, the closest of all currently available colour maps, while also being perceptually uniform. The

colour-vision deﬁciency friendly, sequential and continuous colour map is currently available as a standard colour array.

●

CMOcean (colormaps inspired by oceanography): The CMOcean colour maps

(available at ref.

), developed by Kristen M. Thyng and

colleagues, aim to provide the most intuitive colours for a given suite of physical parameters, while now also being perceptually uniform. A variety of

continuous sequential, diverging and cyclic colour maps are provided to allow for an intuitive, true representation of a given physical parameter ﬁeld.

The CMOcean colour maps are available in a large variety of ﬁle formats.

●

CET (Centre for Exploration Targeting): The CET colour maps

(available at ref.

), developed by Peter Kovesi, aim to offer a large choice of the

most common colour combinations in a wide variety of data formats. Many of the offered colour maps feature perceptual uniformity, although not all

of them to the highest standards. The CET colour maps are continuous and cover sequential, diverging, and cyclic classes.

●

Scientiﬁc colour maps: The Scientiﬁc colour maps

(available at ref.

, and permanently archived at ref.

) are perceptually uniform (based on the

underlying methodology of the CET colour maps

), perceptually ordered, colour-vision deﬁciency and colour-blind friendly, readable in black and

white prints, and, if applied properly, also data set speciﬁc and parameter intuitive. The Scientiﬁc colour maps include sequential, diverging, and

cyclic palettes, which are also provided as discrete and categorical palettes, and are available in a multitude of different ﬁle formats. They are also

available through external routines and as built-in versions in a variety of software programmes. In contrast to others, the Scientiﬁc colour map

package includes individual colour map diagnostics, and is versioned on a long-term online repository so individual versions can be accurately cited,

which allows active developments from the community (e.g., improve their perceptual uniformity to the latest standards), and aids overall scientiﬁc

reproducibility.

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and limitations of each toolkit, to aid users in designing and/or

selecting the most appropriate and accurate colour map for

their data.

Perceptual uniformity is a crucial property for colour maps

used in science, but by no means the only property to care about.

Perceptual colour order is another important aspect in scientiﬁc

colour map design, as it ensures the colour gradient is easily and

intuitively understandable and allows qualitative understanding

of a data set (Fig. 4). To achieve perceptual order, both lightness

and brightness should increase linearly to avoid the perception of

artiﬁcial gradients and to easily discern and compare signiﬁcant

values. The heated black-body radiation palette, for which the

colours can be easily ordered from black-red-orange-yellow (or

vice versa), is one example. Perceptual order is, therefore, a great

asset to a colour map by emphasising gradients and pattern(s) in

data. Moreover yet, colour maps speciﬁcally created for certain

data sets (e.g., ref.

) by no means guarantee their perceptual

uniformity. Perceptual uniformity and intuitive colour order are

both needed to prevent bias percolating into colour maps. This is

also the case for so-called ‘improved’ rainbow-like maps such as

Google’s Turbo

. Although Turbo appears to meet perceptual

order, the perceptual uniformity requirement of a science-ready

colour map is not met due to its non-uniform lightness spectra.

In addition, colour maps should be universally readable, and

they can be mathematically optimised to account for colour-

vision deﬁciency using modern colour appearance models

(Fig. 2 and Box 1). As well as making colour palettes readable

for readers with variable vision capabilities, it is also advantageous

to make them readable for completely colour-blind readers. In

contrast to other colour palettes, a colour map for scienti ﬁc use

should feature a uniform gradient across the whole colour axis.

With an even, monotonic lightness gradient (Supplementary

Fig. 1a), a colour palette remains readable (as well as perceptually

uniform and ordered) even after a conversion to grey scale,

assuming no complicated grey-scale ﬁlter is used.

To ach ieve the best possible data representation, colour

palettes need to effectively convey the underlying data and its

nature. This can be achieved by choosing the most appropriate

colourmapclassandtype(Fig.5 and outlined in detail

in Supplementary Notes 2 and 3). If the data is divergent about

a central value (e.g., centred about zero), a divergent or a multi-

sequential colour map should be c hosen that clearly and

intuitively distinguishes either side of the axis (Fig. 5,andFig.6

for a detailed user guide).

An intuitive colour gradient becomes imperative if data are

displayed without the provision of the colour bar (the axis relating

colours to data values). Unfortunately, missing colour bars are

more common than most would expect, as scales are sometimes

cropped out or omitted during reproduction or subsequent

dissemination (e.g., refs.

1,4,39

). It is imperative to ensure the

batlow jet

1.5

0.5

CIEDE2000

10.0

200

150

100

Cumulative

0123

batlow represented as a position axis

batlow representing a linear graph jet representing a linear graph

456789

0123

jet represented as a position axis

45 678 9

Visual error %

Colour bar index Colour bar index

0.2

8.15

1.5

0.5

Fig. 3 Colour map measure, distortion, and error. a, b The incremental lightness difference, ΔE, here using the CIEDE2000 formulation (see ‘Methods’), is

a measure for the perceptual colour difference along the colour map. For a perceptually uniform colour map, ΔE

CIEDE2000

should be equal all along the

colour map (i.e., a ﬂat graph; a). Using c, d the cumulative colour lightness difference, ΔE

Cumulative

, it is possible to extract e, f the resulting visual error in

percentage of total data variation. For scientiﬁcally derived colour maps like batlow

, the resulting error introduced to the data by the colouring is

negligibly small as g the incremental data variation is represented equally all along the axis, and a linear data gradient, therefore, appears linear. Put

differently, i a ﬂat line looks ﬂat. For non-scientiﬁc colour maps, like jet, h data gradients are unevenly represented and f visual error can be >7% of the

displayed data variation such that j a linear graph (e.g., a ﬂ at line), for example, becomes unrecognisable.

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colour bar is included on all ﬁgures where a colour scale is used, as

even the most intuitive colour map could be rendered useless with

no colour bar for the reader to refer to. Excluding a colour bar

would be equivalent to not including the axis labels and tick marks

on the x-ory-axis of a plot. Additionally, attention has to be paid

to the lightness (i.e., light or dark) of the background on which the

colours are displayed. Background creates contrast, in lightness

and colour, to the displayed data (Supplementary Fig. 3 and

Supplementary Movie 1).

To optimise the use of the currently available perceptually

uniform colour maps listed in Box 2, t here are certain

requirements to prevent them from becoming distorted (e.g.,

ref.

). As the colour bar has to be handled similarly to the

position axis, parts of a scientiﬁcally derived colour map cannot

AA′

A′

Colour & lightness

Lightness

Colour

Colour & lightness

Incremental contrast

Intuitive order

Variable

Unique

Unclear

Uniform

B′

C′

CDEF

ABCDEFGHI

A′ BB′ CC′

C′

A′

B′

C′

Fig. 4 Perceptual uniformity and order. A constant incremental colour and lightness contrast along a colour map is a proxy for its perceptual uniformity.

a While a certain incremental data variation is either under- or strongly overrepresented with jet (a.k.a. rainbow) depending on the colour map segment, it

is instead b evenly represented all along a colour bar when using a scientiﬁc colour map like batlow

, due to its uniform colour and lightness contrast.

Perceptual order is given when individual colours of a colour map can be sequentially ordered effortlessly without consulting the colour bar. While c a

sequential ordering is not intuitively possible for jet (a.k.a. rainbow), it is d possible to sequentially order individual colours of a scientiﬁcally derived colour

map like batlow

, thanks to its constant lightness gradient.

Class

batlow

roma

romao romao10

oleron oleron10

roma10

batlow10

batlows

Continuous

Sequential

Diverging

Multi-sequential

Cyclic

Discrete Categorical

Type

Fig. 5 Colour map classes and types. The various classes of colour maps (sequential; diverging; multi-sequential; cyclic) and types (continuous; discrete;

categorical). Only sequential colour maps can be faithfully applied to categorical types of data.

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be subsequently deformed by being partly squeezed or

elongated. If the spacing between a position axis’ ticks were

squeezed or elongated, it would visually distort the data in the

ﬁgure. Simply put, a linear grap h would no longer appear linear

(Fig. 3h, j). Therefore, altering any available scientiﬁcally

derived colour map is not recommended. Additionally,

avoiding certain types of graphs and plots is important to not

alter the local perception of individual colours. Common

heatmaps with dire ctly connected colour tiles, as opposed to

tiles with gaps in between, can alter individual colours

signiﬁcantly

(Supplementary Fig. 3).

How to recognise an unscientiﬁc colour map.Itisthe

responsibility of individuals , publisher s, and the press to

prevent the dissemination of visually distorted data and to take

a proactive approach in spotting the unscientiﬁcuseofcolour.

There are straightforward checks to recognise the unscientiﬁc

use of colour that are handy for users, readers, reviewers and

editors:

1. The colour bar should be perceptually uniform to prevent

data distortion and visual error. This means the perceptual

colour differences between all neighbouring colours should

appear the same. If two neighbouring colours have a

different variation compared to other neighbouring colours

(e.g., two greenish versus two yellowish-reddish colours in

rainbow colour maps), the colour bar is perceptually non-

uniform and not scientiﬁc (as shown in Fig. 4).

Given dataset

Ordered

Centric value

TYPE

CLASS

Diverging/

converging

Important small

variations?

Empty values

The data parameter

has intuitive colours

Centric value

Light figure

background

Light figure

background

Diverging

Continuous

Use light

coloured

centre

colour map

Use dark

coloured

centre

colour map

Use light

part for

high values

Use dark

part for

high values

Use colour

map with

parameter-

intuitive

colours

Discrete

Prevent colour map

containing the figure

background colour

Categorical

Multi-

sequential

Cyclic

Sequential

Circular/

periodic

Has the data an order?

(e.g., temperature range)

Has the data a central value?

(e.g., zero in vertical velocity)

Is the data ordered

relative to a central value?

(e.g., residual temperature)

Is the data periodic

(e.g., orientation)

Should small data

variations be visible?

Does the data contain

empty values like NaNs?

(e.g., measured surface

temperature)

Is there an intuitive

colouring for the

parameter? (e.g., blue to

red for temperature)

Has the data a central

value? (e.g., zero in

vertical velocity)

Is the plot

background

light?

Ye s

CHOOSING COLOUR MAP CLASS AND TYPE

CHOOSING COLOUR COMBINATION

Ye s

Fig. 6 Guideline for choosing the right scientiﬁc colour map. For effective data representation, the nature of a given data set has to be matched by a

suitable colour map class, type, and colour combination.

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2. The colour map should not contain red and green at a

similar luminosity (Box 1 for deﬁnitions). If this is the case,

it can be assumed that these two colours cannot be

distinguished by a large fraction of the readership and,

therefore, fails as a scientiﬁc way of displaying data.

3. The common rainbow colour map should not be used in

data visualisation. There is not a single rainbow colour map

with similarly bright colours across the colour bar that

comes close to being scientiﬁc (e.g., ref.

4. The most secure test is to discard any colour map that is not

described as scientiﬁcally derived (for example, is not listed

in Box 2), as it should be both perceptually uniform and

CVD friendly.

A proactive step forward for the science community.Itis

important to maintain the progress that has already been made

across the scientiﬁc community (in particular in the ﬁelds of

Earth, Space, and Climate science). Recently, a number of sig-

niﬁcant scientiﬁc achievements have been based upon non-

distorting and universally readable scientiﬁcally derived colour

maps, such as the ﬁrst ever observation-based visualisation of a

black hole

, for which a lajolla-like colour map

was used, and

the effective visualisation of climate change on a local, regional,

and global level

, which applied a vik-like colour map

. How-

ever, there are danger signs that this progress could be lost.

Unscientiﬁc colour maps are still often set as the default in

software packages, which in turn also renders them a prevalent

choice among many academic group leaders. Furthermore,

unscientiﬁc colour maps are still accepted and published by

academic journals. This combination leads users, students, and

readers into believing that these choices are based on informed

decisions, and that there are no fundamental issues with

unscientiﬁc colour maps. Given this current landscape, it is an

instructive reminder that new generations of scientists have to be

made aware of the importance of scientiﬁcally derived colour

maps and the pitfalls of those that are not.

Transferring the knowledge and awareness about the impor-

tance of scientiﬁcally derived colour maps to new generations of

scientists is, therefore, a key goal. Teaching is a frontline tool in

building solid visualisation skills. Indeed, learning and applying

scientiﬁc data visualisation should be a requirement to receive

BSc, MSc, and PhD degrees. Here, we provide an instructive user

guide for choosing and applying a suitable scientiﬁc colour map

(Fig. 6), which should be part of every research ofﬁce, and

possibly even desk space. We provide a poster (Supplementary

Data 1) that can be placed in communal areas, like near a printing

station, coffee machine or restroom, that highlights the key

advantages of scientiﬁcally derived colour maps and serves as a

conversation starter.

Recommendations to colleagues via peer-review is another

critical tool to ensure the quality of our ongoing scientiﬁc visual

communication. While editors could certainly provide guiding

recommendations, it is also critical that scientiﬁcally derived

colour maps are being applied already during the early diagnosis

of the data, and not just applied for publication only. Set

instructions by scientiﬁc journals or conference organisers could

remind researchers to fulﬁl the graphical standards that science

needs to be built upon. It might even be useful to limit researchers

to using only a handful of hand-picked, suitable colour maps for

speciﬁc types of data and data parameters to streamline and

enhance data visualisation. This type of approach is being

developed for the next assessment reports of the Intergovern-

mental Panel on Climate Change (IPCC), in collaboration with

Melissa Gomis (Graphics and Science Communication ofﬁcer,

IPCC WGI Technical Support Unit, Université Paris-Saclay,

France).

Presently, scientiﬁcally derived colour maps are easily acces-

sible and applicable across various tools and platforms and

suitable palettes exist for any given data (Box 2). The open

availability of such colour maps ultimately leaves little legitimate

room to continue using colour maps that cause visual distortion,

are unreadable in some circumstances, or exclude readers from

understanding them.

The wider scientiﬁc community needs to accept that colour

maps are a pivotal tool in scientiﬁc discovery, data visualisation

and science communication. Non-scientiﬁc colour maps require

scrutiny and rejection from the community to preserve academic

integrity. The evidence is clear, there are no more reasons to

continue using unscientiﬁc colour maps.

Methods

Deﬁning colour spaces. Various methods and tools based on different metrics and

colour spaces (Supplementary Note 4) exist to diagnose the uniformity of a colour

palette (e.g., refs.

32,34,38

). A widely used example is the International Commission

on Illumination’s uniform colour space named CIELAB UCS

42–44

. CIELAB UCS

(also abbreviated from Uniform/Uniﬁed Colour Scale, Chromaticity Scale, Chro-

maticity Space) describes the complete range of colours in a perceptually uniform

rectangular coordinate system

and allows the creation of perceptually uniform

colour palettes

32,35,46,47

The colour appearance model CIECAM02

48,49

, and the perceptually uniform

colour space CIECAM02-UCS

based on it, is the current gold standard to

describe how we perceive colour and colour differences. CIECAM02-UCS describes

a certain colour by its lightness (L) and its red–green (a) and yellow-blue (b)

correlates (Supplementary Figs. 4 and 5), and it represents a certain perceptual

colour variation on equal Euclidean distances across the whole space. Colour

spaces like CIECAM02-UCS make it possible to design perceptually uniform

colour maps and, also, to take colour-deﬁcient visio n into account.

Here, the CIELAB UCS colour difference metric ΔECIEDE 2000

is used

(Fig. 3a, b) and allows the calculation of a local lightness gradient between two

colours by

ΔE

CIEDE2000

¼½ðL

 L

þða

 a

þðb

 b



1=2

;

ð1Þ

where L is the lightness of one speciﬁc colour, and a its red–green and b its yellow-

blue correlative (Supplementary Figs. 4 and 5). This lightness difference metric can

be used to diagnose any colour map (e.g., ref.

) and calculate the effective,

perceptual error that is added to the underlying data by uneven colour gradients

along a colour map

. These errors and the resulting visual data distortion can be

signiﬁcant and make, for example, linear data gradients look like a wobbly graph

(Fig. 3).

Data availability

The scientiﬁc colour maps are openly available from ref.

and archived on Zenodo

(https://doi.org/10.5281/zenodo.1243862). All other additional information related to the

article is provided in the Supplementary Information and Box 2.

Received: 17 January 2020; Accepted: 1 October 2020;

References

1. Akiyama, K. et al. First M87 event horizon telescope results. IV. Imaging the

central supermassive black hole. Astrophys. J. Lett. 875, L4 (2019).

2. Long, E. Election Data Visualisation (University of Plymouth, 2013).

3. Cox, A., Bostock, M., Watkins, D. & Shan, C. The Most Detailed Maps You’ll

See from the Midterm Elections., https://www.nytimes.com/interactive/2014/

11/04/upshot/senate-maps.html (2014).

4. Lemoine, F. G. et al. An improved solution of the gravity ﬁeld of Mars (GMM-

2B) from Mars Global Surveyor. J. Geophys. Res.: Planets 106, 23359–23376

(2001).

5. Hawkins, E. Scrap rainbow colour scales. Nature 519, 291 EP (2015).

6. IPCC. Global Warming of 1.5° C: An IPCC Special Report on the Impacts of

Global Warming of 1.5° C Above Pre-industrial Levels and Related Global

Greenhouse Gas Emission Pathways, in the Context of Strengthening the Global

Response to the Threat of Climate Change, Sustainable Development, and

Efforts to Eradicate Poverty. (Intergovernmental Panel on Climate Change,

2018).

PERSPECTIVE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-19160-7

8 NATURE COMMUNICATIONS | (2020) 11:5444 | https://doi.org/10.1038/s41467-020-19160-7 | www.nature.com/naturecommunications

7. Borkin, M. et al. Evaluation of artery visualizations for heart disease diagnosis.

IEEE Trans. Vis. Computer Graph. 17, 2479–2488 (2011).

8. McNeall, D. How many Rainbows at EGU 2018,<https://betterﬁgures.org/

2018/04/16/how-many-rainbows-at-egu-2018> (2020).

9. Bertin, J. Graphics and Graphic Information Processing. (Walter de Gruyter,

2011).

10. Bertin, J. Semiology of graphics; diagrams networks maps. (University of

Wisconsin, Press, Madison, 1983).

11. Tufte, E. R. Envisioning Information. Vol. 126 (Graphics Press, 1990).

12. Travis, D. Effective Color Displays: Theory and Practice. Vol. 1991 (Academic

press London, 1991).

13. Brewer, C. A. Color use guidelines for mapping. Vis. Mod. Cartogr. 1994,

123–148 (1994).

14. MacEachren, A. M. How Maps Work: Representation, Visualization, and

Design. (Guilford Press, 2004).

15. Dent, B. D., Torguson, J. S. & Hodler, T. W. Cartography: Thematic Map

Design. Vol. 5 (WCB/McGraw-Hil l New York, 1999).

16. Robinson, A. Elements of Cartography. (John Wiley and Sons, New York,

1960).

17. Monmonier, M. How to Lie with Maps (University of Chicag o Press, 2018).

18. Light, A. & Bartlein, P. J. The end of the rainbow? Color schemes for

improved data graphics. Eos Trans. AGU 85, 385–391 (2004).

19. Stauffer, R., Mayr, G. J., Dabernig, M. & Zeileis, A. Somewhere over the

rainbow: how to make effective use of colors in meteorological visualizations.

Bull. Am. Meteorological Soc. 96, 203–216 (2015).

20. Thyng, K. M., Greene, C. A., Hetland, R. D., Zimmerle, H. M. & DiMarco, S.

F. True colors of oceanography: guidelines for effective and accurate colormap

selection. Oceanography 29,9–13 (2016). Introducing the scientiﬁcally

derived cmocean colour maps for better data visualisation in oceanography

that also underline the importance of intuitive colour palettes given a certain

data parameter.

21. Cairo, A. The Functional Art: An Introduction to Information Graphics and

Visualization. (New Riders, 2012).

22. Wolfe, J. M. & Horowitz, T. S. Five factors that guide attention in visual

search. Nat. Hum. Behav. 1, 0058 (2017).

23. Alexander, K. R. & Shansky, M. S. Inﬂuence of hue, value, and chroma on the

perceived heaviness of colors. Percept. Psychophys. 19,72–74 (1976).

24. Sharpe, L. T., Stockman, A., Jägle, H. & Nathans, J. Opsin Genes, Cone

Photopigments, Color Vision, and Color Blindness. Vol. 351 (Cambridge

University Press, 1999).

25. Neitz, J. & Neitz, M. The genetics of normal and defective color vision. Vis.

Res. 51, 633–651 (2011).

26. Drummond-Borg, M., Deeb, S. S. & Motulsky, A. G. Molecular patterns of X

chromosome-linked color vision genes among 134 men of European ancestry.

Proc. Natl Acad. Sci. 86, 983–987 (1989).

27. Albrecht, M. Color blindness. Nat. Methods 7, 775 EP (2010).

28. Wong, B. Reply to \“More on color blindness\“. Nat. Methods 8, 891 EP

(2011).

29. Moreland, K. Why we use bad color maps and what you can do about it.

Electron. Imaging 2016,1–6 (2016). The widespread use of the rainbow is the

main reason scientists propagate it further, which must therefore be

considered if a scientiﬁc alternative is to be effective.

30. Crameri, F. Geodynamic diagnostics, scientiﬁc visualisation and StagLab 3.0.

Geoscientiﬁc Model Dev. 11, 2541–2562 (2018).

31. Silva, S., Sousa Santos, B. & Madeira, J. Using color in visualization: a survey.

Computer Graph. 35, 320–333 (2011).

32. Kovesi, P. Good colour maps: how to design them. CoRR abs/1509.03700

(2015). Provides a set of colour map diagnostics and shows that the most

important factor designing a colour map is perceptually uniform lightness,

allowing to construct more consistent and reliable ternary base colours to

replace the problematic RGB primaries red, green, and blue.

33. Szaﬁr, D. A. Modeling color difference for visualization design. IEEE Trans.

Vis. Computer Graph. 24, 392–401 (2018).

34. Bujack, R. et al. The Good, the bad, and the ugly: a theoretical framework for

the assessment of continuous colormaps. IEEE Trans. Vis. Computer Graph.

24, 923–933 (2018).

35. Ware, C. et al. Measuring and modeling the feature detection threshold

functions of colormaps. IEEE Trans. Vis. Computer Graph. 25, 2777–2790

(2019).

36. Zeller, S. & Rogers, D. Visualizing science: How color determines what we see.

Eos Trans. AGU Vol. 101 (American Geophysical Union, 2020). https://doi.

org/10.1029/2020EO144330

37. Mikhailov, A. in Google AI Blog Vol. 2020 (Google, https://ai.googleblog.com/

2019/08/turbo-improved-rainbow-colormap-for.html, 2019).

38. Nuñez, J. R., Anderton, C. R. & Renslow, R. S. Optimizing colormaps with

consideration for color vision deﬁciency to enable accurate interpretation of

scienti

ﬁc data. PLoS ONE 13, e0199239 (2018). Developed the mathematically

optimal colour map for readers with different colour-vision deﬁciencies

named Cividis, which allows most accurate perception of data by as many

viewers as possible.

39. Hawkins, E. (http://www.climate-lab-book.ac.uk/2018/2018-visualisation-

update/, 2019).

40. Wong, B. Color coding. Nat. Methods 7, 573 EP (2010).

41. Crameri, F. Scientiﬁc Colour Maps, http://www.fabiocrameri.ch/colourmaps

(2020).

42. Smith, T. & Guild, J. The CIE colorimetric standards and their use. Trans.

Optical Soc. 33, 73 (1931).

43. C. I. E. Technical Report Colorimetry. (Commission Internationale de

l’Eclairage Central Bureau Vienna, Austria, 2004).

44. CIE. Part 4: CIE 1976 L* a* b* Colour space, http://www.cie.co.at/

publications/colorimetry-part-4-cie-1976-lab-colour-space (2011).

45. Hunter Associates Laboratory Inc. Brief Explanation of Delta E or Delta E*,

http://support.hunterlab.com/hc/en-us/articles/%20203023559-Brief-

Explanation-of-delta-E-or-delta-E -> (2019).

46. Meier, B. J., Spalter, A. M. & Karelitz, D. B. Interactive color palette tools.

IEEE Computer Graph. Appl. 24,64–72 (2004).

47. Moreland, K. in Advances in Visual Computing (eds George Bebis et al.)

92–103 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2009).

48. Moroney, N. et al. in Color and Imaging Conference Vol. 2002 23–27 (2002).

49. International Commission on Illumination. Technical Committee TC 8-01. in

Colour Appearance Modeling for Colour Management Systems (2004).

50. Luo, M. R., Cui, G. & Li, C. Uniform colour spaces based on CIECAM02

colour appearance model. Color Res. Appl. 31, 320– 330 (2006).

51. Lindbloom, B. Delta E (CIE 1976). http://www.brucelindbloom.com/index.

html?Eqn_DeltaE_CIE76.html (2019).

52. Crameri, F. Scientiﬁc colour maps: perceptually uniform and colour-vision

deﬁciency friendly. Zenodo, https://doi.org/10.5281/zenodo.1243862 (2018).

53. Crameri, F. DiVA: effective design for any MatLab ﬁgure. Zenodo

, https://doi.

org/10.5281/zenodo.3596368 (2020).

54. Curcio, C. A. et al. Distribution and morphology of human cone

photoreceptors stained with anti‐blue opsin. J. Comp. Neurol. 312, 610–624

(1991).

55. Meyer, G. W. & Greenberg, D. P. Color-defective vision and computer

graphics displays. IEEE Computer Graph. Appl. 8,28–40 (1988).

56. Lennie, P., Pokorny, J. & Smith, V. C. Luminance. J. Optical Soc. Am. A: Opt.

Image Sci., Vis. 10, 1283–1293 (1993).

57. Kaiser, P. & Boynton, R. Human Color Vision. 2nd edn, (Optical Society of

America, 1996).

58. Roorda, A., Metha, A. B., Lennie, P. & Williams, D. R. Packing arrangement of

the three cone classes in primate retina. Vis. Res. 41, 1291–1306 (2001).

59. Lafer-Sousa, R., Hermann, K. L. & Conway, B. R. Striking individual

differences in color perception uncovered by ‘the dress’ photograph. Curr.

Biol. 25, R545–R546 (2015).

60. Emery, K. J. & Webster, M. A. Individual differences and their implications for

color perception. Curr. Opin. Behav. Sci. 30,28–33 (2019).

61. Brewer, C. A. Colorbrewer Colour Maps, https://colorbrewer2.org/ (2020).

62. van der Walt, S. & Smith, N. MPL Colour Maps, https://bids.github.io/

colormap (2020).

63. Nuñez, J. R., Anderton, C. R. & Renslow, R. S. Cividis colour map, PLoS ONE,

https://www.doi.org/10.1371/journal.pone.0199239.s002 (2020).

64. Thyng, K. M., Greene, C. A., Hetland, R. D., Zimmerle, H. M. & DiMarco, S.

F. CMOcean Colour Maps, http://matplotlib.org/cmocean (2020).

65. Kovesi, P. CET Colour Maps, http://peterkovesi.com/projects/colourmaps

(2020).

Acknowledgements

We thank Melissa Gomis for valuable feedback on the user guide and Stefan Scherrer for

contributing the Supplementary Movie 1. The open-access ﬁgure design routine DiVA

was used. F.C. and G.E.S. acknowledge support from the Research Council of Norway

through its Centres of Excellence funding scheme, Project Number 223272. P.J.H.

receives funding from the European Union’s Horizon 2020 research and innovation

programme under the Marie Skłodowska-Curie Grant Agreement 749664.

Author contributions

F.C. designed the Scientiﬁc colour maps and the ﬁgures, G.E.S. contributed to the

development and software compatibility of the Scientiﬁc colour maps, P.J.H. designed the

outreach poster. All authors conceived the study, evaluated the use of and promoted

scientiﬁcally derived colour maps, and contributed to the scientiﬁc discussion and pre-

paration of the manuscript.

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Competing interests

The authors declare no competing interests.

Additional information

Supplementary information is available for this paper at https://doi.org/10.1038/s41467-

020-19160-7.

Correspondence and requests for materials should be addressed to F.C.

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This is all too common in scientific communication... >> Coulour maps that visually distort data through uneven colour gradients or are unreadable to those with colour-vision deﬁciency remain prevalent in science. Another major problem is "chartjunk"- coined by Edward Tufte to describe visual elements in graphs that aren't necessary to comprehend the information presented and could actually distract from the information: https://en.wikipedia.org/wiki/Chartjunk Most readers will only read the title, abstract and figures of a scientific paper, making it crucial that the figures capture the information as accurately as possible. More on color vision... >>"Isaac Newton discovered that white light after being split into its component colors when passed through a dispersive prism could be recombined to make white light by passing them through a different prism. Photopic relative brightness sensitivity of the human visual system as a function of wavelength (luminosity function). The visible light spectrum ranges from about 380 to 740 nanometers. Spectral colors (colors that are produced by a narrow band of wavelengths) such as red, orange, yellow, green, cyan, blue, and violet can be found in this range. These spectral colors do not refer to a single wavelength, but rather to a set of wavelengths: red, 625–740 nm; orange, 590–625 nm; yellow, 565–590 nm; green, 500–565 nm; cyan, 485–500 nm; blue, 450–485 nm; violet, 380–450 nm. Wavelengths longer or shorter than this range are called infrared or ultraviolet, respectively. Humans cannot generally see these wavelengths, but other animals may." Source: https://en.wikipedia.org/wiki/Color_vision Has anyone got good examples of where these changed?

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