## Introduction

Vision 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 hole1, the mapping of votes cast in political elections2,3, the planning of an expensive rover route on Martian topography4, the essential communication of climate change5,6, or the critical diagnosis of heart disease7. 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 masse8. Unfortunately, the previous efforts within specific disciplines to discredit rainbow-like maps appear to 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 rainbow, and variations thereof, being known for some time9,10,11,12,13,14,15,16,17,18,19,20.

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 message21. In rainbow colour maps, the yellow is the brightest colour and attracts the eye the most22,23 (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 parameter space while obscuring other parts (Fig. 1). Building a colour map on a purely physical rather than a perceptual basis significantly 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 common 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 readership (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 populations with a larger fraction of white (Caucasian) people as, for example, in Scandinavia26. 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 publishers18,27,28.

For the casual reader, it might appear curious that the community 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 community to remain attached to this unscientific colour map29. As a result, pointing out colour map flaws to the science community through scientific peer-review remains a challenging task, as 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 scientific 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 rainbow), 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 uniformity 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 variation30 (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 conversely might be interpreted as a flat slope (compare Supplementary 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 uniform 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 considered (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. 18,19,20,29,31,32,33,34,35), 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 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. 36) 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 Turbo37. 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 models38 (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 scientific 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 achieve 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 colour map class and type (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 chosen that clearly and intuitively distinguishes either side of the axis (Fig. 5, and Fig. 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 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- or y-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, there are certain requirements to prevent them from becoming distorted (e.g., ref. 30). As the colour bar has to be handled similarly to the position axis, parts of a scientifically derived colour map cannot 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 graph 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 directly connected colour tiles, as opposed to tiles with gaps in between, can alter individual colours significantly40 (Supplementary Fig. 3).

### How to recognise an unscientific colour map

It is the responsibility of individuals, publishers, and the press to prevent the dissemination of visually distorted data and to take a proactive approach in spotting the unscientific use of colour. There are straightforward checks to recognise the unscientific use of colour that are handy for users, readers, reviewers and editors:

1. 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).

2. 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. 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. 32).

4. 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

It is 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 significant 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 hole1, for which a lajolla-like colour map41 was used, and the effective visualisation of climate change on a local, regional, and global level39, which applied a vik-like colour map41. However, 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 importance 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 Intergovernmental 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 accessible 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 UCS42,43,44. CIELAB UCS (also abbreviated from Uniform/Unified Colour Scale, Chromaticity Scale, Chromaticity Space) describes the complete range of colours in a perceptually uniform rectangular coordinate system45 and allows the creation of perceptually uniform colour palettes32,35,46,47.

The colour appearance model CIECAM0248,49, and the perceptually uniform colour space CIECAM02-UCS50 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 vision into account.

Here, the CIELAB UCS colour difference metric ΔECIEDE 200051 is used (Fig. 3a, b) and allows the calculation of a local lightness gradient between two colours by

$$\Delta {\mathrm{E}_{\it{CIEDE}2000}} = [(L_1 - L_2)^2 + (a_1 - a_2)^2 + (b_1 - b_2)^2]^{1/2},$$
(1)

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. 20) and calculate the effective, perceptual error that is added to the underlying data by uneven colour gradients along a colour map30. 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).