Graph workflow and defaults wreak havoc

For the past week or 10 days, every time I visited one news site, it insisted on showing me an article about precipitation in North Platte. It's baiting me to write a post about this lamentable bar chart (link):

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This chart got problems, and the problems start with the tooling, which dictates a workflow.

I imagine what the chart designer had to deal with.

For a bar chart, the tool requires one data series to be numeric, and the other to be categorical. A four-digit year is a number, which can be treated either as numeric or categorical. In most cases, and by default, numbers are considered numeric. To make this chart, the user asked the tool to treat years as categorical.

Many tools treat categories as distinct entities ("nominal"), mapping each category to a distinct color. So they have 11 colors for 11 years, which is surely excessive.

This happens because the year data is not truly categorical. These eleven years were picked based on the amount of rainfall. There isn't a single year with two values, it's not even possible. The years are just irregularly spaced indices. Nevertheless, the tool misbehaves if the year data are regarded as numeric. (It automatically selects a time-series line chart, because someone's data visualization flowchart says so.) Mis-specification in order to trick the tool has consequences.

The designer's intention is to compare the current year 2023 to the driest years in history. This is obvious from the subtitle in which 2023 is isolated and its purple color is foregrounded.

How unfortunate then that among the 11 colors, this tool grabbed 4 variations of purple! I like to think that the designer wanted to keep 2023 purple, and turn the other bars gray -- but the tool thwarted this effort.

The tool does other offensive things. By default, it makes a legend for categorical data. I like the placement of the legend right beneath the title, a recognition that on most charts, the reader must look at the legend first to comprehend what's on the chart.

Not so in this case. The legend is entirely redundant. Removing the legend does not affect our cognition one bit. That's because the colors encode nothing.

Worse, the legend sows confusion because it presents the same set of years in chronological order while the bars below are sorted by amount of precipitation: thus, the order of colors in the legend differs from that in the bar chart.

I can imagine the frustration of the designer who finds out that the tool offers no option to delete the legend. (I don't know this particular tool but I have encountered tools that are rigid in this manner.)

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Something else went wrong. What's the variable being plotted on the numeric (horizontal) axis?

The answer is inches of rainfall but the answer is actually not found anywhere on the chart. How is it possible that a graphing tool does not indicate the variables being plotted?

I imagine the workflow like this: the tool by default puts an axis label which uses the name of the column that holds the data. That column may have a name that is not reader-friendly, e.g. PRECIP. The designer edits the name to "Rainfall in inches". Being a fan of the Economist graphics style, they move the axis label to the chart title area.

The designer now works the chart title. The title is made to spell out the story, which is that North Platte is experiencing a historically dry year. Instead of mentioning rainfall, the new title emphasizes the lack thereof.

The individual steps of this workflow make a lot of sense. It's great that the title is informative, and tells the story. It's great that the axis label was fixed to describe rainfall in words not database-speak. But the end result is a confusing mess.

The reader must now infer that the values being plotted are inches of rainfall.

Further, the tool also imposes a default sorting of the bars. The bars run from longest to shortest, in this case, the longest bar has the most rainfall. After reading the title, our expectation is to find data on the Top 11 driest years, from the driest of the driest to the least dry of the driest. But what we encounter is the opposite order.

Most graphics software behaves like this as they are plotting the ranks of the categories with the driest being rank 1, counting up. Because the vertical axis moves upwards from zero, the top-ranked item ends up at the bottom of the chart.

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Moving now from the V corner to the D corner of the Trifecta checkup (link), I can't end this post without pointing out that the comparisons shown on the chart don't work. It's the first few months of 2023 versus the full years of the others.

The fix is to plot the same number of months for all years. This can be done in two ways: find the partial year data for the historical years, or project the 2023 data for the full year.

(If the rainy season is already over, then the chart will look exactly the same at the end of 2023 as it is now. Then, I'd just add a note to explain this.)

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Here is a version of the chart after doing away with unhelpful default settings:

Visual cues affect how data are perceived

Here's a recent NYT graphic showing California's water situation at different time scales (link to article).

It's a small multiples display, showing the spatial distribution of the precipitation amounts in California. The two panels show, respectively, the short-term view (past month) and the longer-term view (3 years). Precipitation is measured in relative terms,  so what is plotted is the relative ratio of precipitation in the reference period, with 100 being the 30-year average.

Green is much wetter than average while brown is much drier than average.

The key to making this chart work is a common color scheme across the two panels.

Also, the placement of major cities provides anchor points for our eyes to move back and forth between the two panels.

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The NYT graphic is technically well executed. I'm a bit unhappy with the headline: "Recent rains haven't erased California's long-term drought".

At the surface, the conclusion seems sensible. Look, there is a lot of green, even deep green, on the left panel, which means the state got lots more rain than usual in the past month. Now, on the right panel, we find patches of brown, and very little green.

But pay attention to the scale. The light brown color, which covers the largest area, has value 70 to 90, thus, these regions have gotten 10-30% less precipitation than average in the past three years relative to the 30-year average.

Here's the question: what does it mean by "erasing California's long-term drought"? Does the 3-year average have to equal or exceed the 30-year average? Why should that be the case?

If we took all 3-year windows within those 30 years, we're definitely not going to find that each such 3-year average falls at or above the 30-year average. To illustrate this, I pulled annual rainfall data for San Francisco. Here is a histogram of 3-year averages for the 30-year period 1991-2020.

For example, the first value is the average rainfall for years 1989, 1990 and 1991, the next value is the average of 1990, 1991, and 1992, and so on. Each value is a relative value relative to the overall average in the 30-year window. There are two more values beyond 2020 that is not shown in the histogram. These are 57%, and 61%, so against the 30-year average, those two 3-year averages were drier than usual.

The above shows the underlying variability of the 3-year averages inside the reference time window. We have to first define "normal", and that might be a value between 70% and 130%.

In the same way, we can establish the "normal" range for the entire state of California. If it's also 70% to 130%, then the last 3 years as shown in the map above should be considered normal.

 

 

Energy efficiency deserves visual efficiency

Long-time contributor Aleksander B. found a good one, in the World Energy Outlook Report, published by IEA (International Energy Agency).

The use of balloons is unusual, although after five minutes, I decided I must do some research to have any hope of understanding this data visualization.

A lot is going on. Below, I trace my own journey through this chart.

The text on the top left explains that the chart concerns emissions and temperature change. The first set of balloons (the grey ones) includes helpful annotations. The left-right position of the balloons indicates time points, in 10-year intervals except for the first.

The trapezoid that sits below the four balloons is more mysterious. It's labelled "median temperature rise in 2100". I debate two possibilities: (a) this trapezoid may serve as the fifth balloon, extending the time series from 2050 to 2100. This interpretation raises a couple of questions: why does the symbol change from balloon to trapezoid? why is the left-right time scale broken? (b) this trapezoid may represent something unrelated to the balloons. This interpretation also raises questions: its position on the horizontal axis still breaks the time series; and  if the new variable is "median temperature rise", then what determines its location on the chart?

That last question is answered if I move my glance all the way to the right edge of the chart where there are vertical axis labels. This axis is untitled but the labels shown in degree Celsius units are appropriate for "median temperature rise".

Turning to the balloons, I wonder what the scale is for the encoded emissions data. This is also puzzling because only a few balloons wear data labels, and a scale is nowhere to be found.

The gridlines suggests that the vertical location of the balloons is meaningful. Tracing those gridlines to the right edge leads me back to the Celsius scale, which seems unrelated to emissions. The amount of emissions is probably encoded in the sizes of the balloons although none of these four balloons have any data labels so I'm rather flustered. My attention shifts to the colored balloons, a few of which are labelled. This confirms that the size of the balloons indeed measures the amount of emissions. Nevertheless, it is still impossible to gauge the change in emissions for the 10-year periods.

The colored balloons rising above, way above, the gridlines is an indication that the gridlines may lack a relationship with the balloons. But in some charts, the designer may deliberately use this device to draw attention to outlier values.

Next, I attempt to divine the informational content of the balloon strings. Presumably, the chart is concerned with drawing the correlation between emissions and temperature rise. Here I'm also stumped.

I start to look at the colored balloons. I've figured out that the amount of emissions is shown by the balloon size but I am still unclear about the elevation of the balloons. The vertical locations of these balloons change over time, hinting that they are data-driven. Yet, there is no axis, gridline, or data label that provides a key to its meaning.

Now I focus my attention on the trapezoids. I notice the labels "NZE", "APS", etc. The red section says "Pre-Paris Agreement" which would indicate these sections denote periods of time. However, I also understand the left-right positions of same-color balloons to indicate time progression. I'm completely lost. Understanding these labels is crucial to understanding the color scheme. Clearly, I have to read the report itself to decipher these acronyms.

The research reveals that NZE means "net zero emissions", which is a forecasting scenario - an utterly unrealistic one - in which every country is assumed to fulfil fully its obligations, a sort of best-case scenario but an unattainable optimum. APS and STEPS embed different assumptions about the level of effort countries would spend on reducing emissions and tackling global warming.

At this stage, I come upon another discovery. The grey section is missing any acronym labels. It's actually the legend of the chart. The balloon sizes, elevations, and left-right positions in the grey section are all arbitrary, and do not represent any real data! Surprisingly, this legend does not contain any numbers so it does not satisfy one of the traditional functions of a legend, which is to provide a scale.

There is still one final itch. Take a look at the green section:

What is this, hmm, caret symbol? It's labeled "Net Zero". Based on what I have been able to learn so far, I associate "net zero" to no "emissions" (this suggests they are talking about net emissions not gross emissions). For some reason, I also want to associate it with zero temperature rise. But this is not to be. The "net zero" line pins the balloon strings to a level of roughly 2.5 Celsius rise in temperature.

Wait, that's a misreading of the chart because the projected net temperature increase is found inside the trapezoid, meaning at "net zero", the scientists expect an increase in 1.5 degrees Celsius. If I accept this, I come face to face with the problem raised above: what is the meaning of the vertical positioning of the balloons? There must be a reason why the balloon strings are pinned at 2.5 degrees. I just have no idea why.

I'm also stealthily presuming that the top and bottom edges of the trapezoids represent confidence intervals around the median temperature rise values. The height of each trapezoid appears identical so I'm not sure.

I have just learned something else about this chart. The green "caret" must have been conceived as a fully deflated balloon since it represents the value zero. Its existence exposes two limitations imposed by the chosen visual design. Bubbles/circles should not be used when the value of zero holds significance. Besides, the use of balloon strings to indicate four discrete time points breaks down when there is a scenario which involves only three buoyant balloons.

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The underlying dataset has five values (four emissions, one temperature rise) for four forecasting scenarios. It's taken a lot more time to explain the data visualization than to just show readers those 20 numbers. That's not good!

I'm sure the designer did not set out to confuse. I think what happened might be that the design wasn't shown to potential readers for feedback. Perhaps they were shown only to insiders who bring their domain knowledge. Insiders most likely would not have as much difficulty with reading this chart as did I.

This is an important lesson for using data visualization as a means of communications to the public. It's easy for specialists to assume knowledge that readers won't have.

For the IEA chart, here is a list of things not found explicitly on the chart that readers have to know in order to understand it.

• Readers have to know about the various forecasting scenarios, and their acronyms (APS, NZE, etc.). This allows them to interpret the colors and section titles on the chart, and to decide whether the grey section is missing a scenario label, or is a legend.
• Since the legend does not contain any scale information, neither for the balloon sizes nor for the temperatures, readers have to figure out the scales on their own. For temperature, they first learn from the legend that the temperature rise information is encoded in the trapezoid, then find the vertical axis on the right edge, notice that this axis has degree Celsius units, and recognize that the Celsius scale is appropriate for measuring median temperature rise.
• For the balloon size scale, readers must resist the distracting gridlines around the grey balloons in the legend, notice the several data labels attached to the colored balloons, and accept that the designer has opted not to provide a proper size scale.

Finally, I still have several unresolved questions:

• The horizontal axis may have no meaning at all, or it may only have meaning for emissions data but not for temperature
• The vertical positioning of balloons probably has significance, or maybe it doesn't
• The height of the trapezoids probably has significance, or maybe it doesn't

 

 

Following this pretty flow chart

Bloomberg did a very nice feature on how drought has been causing havoc with river transportation of grains and other commodities in the U.S., which included several well-executed graphics.

I'm particularly attracted to this flow chart/sankey diagram that shows the flows of grains from various U.S. ports to foreign countries.

It looks really great.

Here are some things one can learn from this chart:

• The Mississippi River (blue flow) is by far the most important conduit of American grain exports
• China is by far the largest importer of American grains
• Mexico is the second largest importer of American grains, and it has a special relationship with the "interior" ports (yellow). Notice how the Interior almost exclusively sends grains to Mexico
• Similarly, the Puget Sound almost exclusively trades with China

The above list is impressive for one chart.

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Some key questions are not as easy to see from this layout:

• What proportion of the total exports does the Mississippi River account for? (Turns out to be almost exactly half.)
• What proportion of the total exports go to China? (About 40%. This question is even harder than the previous one because of all the unlabeled values for the smaller countries.)
• What is the relative importance of different ports to Japan/Philippines/Indonesia/etc.? (Notice how the green lines merge from the other side of the country names.)
• What is the relative importance of any of the countries listed, outside the top 5 or so?
• What is the ranking of importance of export nations to each port? For Mississippi River, it appears that the countries may have been drawn from least important (up top) to most important (down below). That is not the case for the other ports... otherwise the threads would tie up into knots.

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Some of the features that make the chart look pretty are not data-driven.

See this artificial "hole" in the brown branch.

In this part of the flow, there are two tiny outflows to Myanmar and Yemen, so most of the goods that got diverted to the right side ended up merging back to the main branch. However, the creation of this hole allows a layering effect which enhances the visual cleanliness.

Next, pay attention to the yellow sub-branches:

At the scale used by the designer, all of the countries shown essentially import about the same amount from the Interior (yellow). Notice the special treatment of Singapore and Phillippines. Instead of each having a yellow sub-branch coming off the "main" flow, these two countries share the sub-branch, which later splits.

 

 

 

Finding the right context to interpret household energy data

Bloomberg's recent article on surging UK household energy costs, projected over this winter, contains data about which I have long been intrigued: how much energy does different household items consume?

A twitter follower alerted me to this chart, and she found it informative.

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If the goal is to pick out the appliances and estimate the cost of running them, the chart serves its purpose. Because the entire set of data is printed, a data table would have done equally well.

I learned that the mobile phone costs almost nothing to charge: 1 pence for six hours of charging, which is deemed a "single use" which seems double what a full charge requires. The games console costs 14 pence for a "single use" of two hours. That might be an underestimate of how much time gamers spend gaming each day.

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Understanding the design of the chart needs a bit more effort. Each appliance is measured by two metrics: the number of hours considered to be "single use", and a currency value.

It took me a while to figure out how to interpret these currency values. Each cost is associated with a single use, and the duration of a single use increases as we move down the list of appliances. Since the designer assumes a fixed cost of electicity (shown in the footnote as 34p per kWh), at first, it seems like the costs should just increase from top to bottom. That's not the case, though.

Something else is driving these numbers behind the scene, namely, the intensity of energy use by appliance. The wifi router listed at the bottom is turned on 24 hours a day, and the daily cost of running it is just 6p. Meanwhile, running the fridge and freezer the whole day costs 41p. Thus, the fridge&freezer consumes electricity at a rate that is almost 7 times higher than the router.

The chart uses a split axis, which artificially reduces the gap between 8 hours and 24 hours. Here is another look at the bottom of the chart:

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Let's examine the choice of "single use" as a common basis for comparing appliances. Consider this:

• Continuous appliances (wifi router, refrigerator, etc.) are denoted as 24 hours, so a daily time window is also implied
• Repeated-use appliances (e.g. coffee maker, kettle) may be run multiple times a day
• Infrequent use appliances may be used less than once a day

I prefer standardizing to a "per day" metric. If I use the microwave three times a day, the daily cost is 3 x 3p = 9 p, which is more than I'd spend on the wifi router, run 24 hours. On the other hand, I use the washing machine once a week, so the frequency is 1/7, and the effective daily cost is 1/7 x 36 p = 5p, notably lower than using the microwave.

The choice of metric has key implications on the appearance of the chart. The bubble size encodes the relative energy costs. The biggest bubbles are in the heating category, which is no surprise. The next largest bubbles are tumble dryer, dishwasher, and electric oven. These are generally not used every day so the "per day" calculation would push them lower in rank.

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Another noteworthy feature of the Bloomberg chart is the split legend. The colors divide appliances into five groups based on usage category (e.g. cleaning, food, utility). Instead of the usual color legend printed on a corner or side of the chart, the designer spreads the category labels around the chart. Each label is shown the first time a specific usage category appears on the chart. There is a presumption that the reader scans from top to bottom, which is probably true on average.

I like this arrangement as it delivers information to the reader when it's needed.

 

 

 

Speedometer charts: love or hate

Pie chart hate is tired. In this post, I explain my speedometer hate. (Also called gauges,  dials)

Next to pie charts, speedometers are perhaps the second most beloved chart species found on business dashboards. Here is a typical example:

 

For this post, I found one on Reuters about natural gas in Europe. (Thanks to long-time contributor Antonio R. for the tip.)

The reason for my dislike is the inefficiency of this chart form. In classic Tufte-speak, the speedometer chart has a very poor data-to-ink ratio. The entire chart above contains just one datum (73%). Most of the ink are spilled over non-data things.

This single number has a large entourage:

- the curved axis
- ticks on the axis
- labels on the scale
- the dial
- the color segments
- the reference level "EU target"

These are not mere decorations. Taking these elements away makes it harder to understand what's on the chart.

Here is the chart without the curved axis:

Here is the chart without axis labels:

Here is the chart without ticks:

When the tick labels are present, the chart still functions.

Here is the chart without the dial:

The datum is redundantly encoded in the color segments of the "axis".

Here is the chart without the dial or the color segments:

If you find yourself stealing a peek at the chart title below, you're not alone.

All versions except one increases our cognitive load. This means the entourage is largely necessary if one encodes the single number in a speedometer chart.

The problem with the entourage is that readers may resort to reading the text rather than the chart.

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The following is a minimalist version of the Reuters chart:

I removed the axis labels and the color segments. The number 73% is shown using the dial angle.

The next chart adds back the secondary message about the EU target, as an axis label, and uses color segments to show the 73% number.

Like pie charts, there are limited situations in which speedometer charts are acceptable. But most of the ones we see out there are just not right.

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One acceptable situation is to illustrate percentages or proportions, which is what the EU gas chart does. Of course, in that situation, one can alo use a pie chart without shame.

For illustrating proportions, I prefer to use a full semicircle, instead of the circular sector of arbitrary angle as Reuters did. The semicircle lends itself to easy marks of 25%, 50%, 75%, etc, eliminating the need to print those tick labels.

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One use case to avoid is numeric data.

Take the regional sales chart pulled randomly from a Web search above:

These charts are completely useless without the axis labels.

Besides, because the span of the axis isn't 0% to 100%, every tick mark must be labelled with the numeric value. That's a lot of extra ink used to display a single value!

Superb tile map offering multiple avenues for exploration

Here's a beauty by WSJ Graphics:

The article is here.

This data graphic illustrates the power of the visual medium. The underlying dataset is complex: power production by type of source by state by month by year. That's more than 90,000 numbers. They all reside on this graphic.

Readers amazingly make sense of all these numbers without much effort.

It starts with the summary chart on top.

The designer made decisions. The data are presented in relative terms, as proportion of total power production. Only the first and last years are labeled, thus drawing our attention to the long-term trend. The order of the color blocks is carefully selected so that the cleaner sources are listed at the top and the dirtier sources at the bottom. The order of the legend labels mirrors the color blocks in the area chart.

It takes only a few seconds to learn that U.S. power production has largely shifted away from coal with most of it substituted by natural gas. Other than wind, the green sources of power have not gained much ground during these years - in a relative sense.

This summary chart serves as a reading guide for the rest of the chart, which is a tile map of all fifty states. Embedded in the tile map is a small-multiples arrangement.

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The map offers multiple avenues for exploration.

Some readers may look at specific states. For example, California.

Currently, about half of the power production in California come from natural gas. Notably, there is no coal at all in any of these years. In addition to wind, solar energy has also gained. All of these insights come without the need for any labels or gridlines!

Browsing around California, readers find different patterns in other Western states like Oregon and Washington.

Hydroelectric energy is the dominant source in those two states, with wind gradually taking share.

At this point, readers realize that the summary chart up top hides remarkable state-level variations.

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There are other paths through the map.

Some readers may scan the whole map, seeking patterns that pop out.

One such pattern is the cluster of states that use coal. In most of these states, the proportion of coal has declined.

Yet another path exists for those interested in specific sources of power.

For example, the trend in nuclear power usage is easily followed by tracking the purple. South Carolina, Illinois and New Hampshire are three states that rely on nuclear for more than half of its power.

I wonder what happened in Vermont about 8 years ago.

The chart says they renounced nuclear energy. Here is some history. This one-time event caused a disruption in the time series, unique on the entire map.

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This work is wonderful. Enjoy it!

Funnel is just for fun

This is part 2 of a review of a recent video released by NASA. Part 1 is here.

The NASA video that starts with the spiral chart showing changes in average global temperature takes a long time (about 1 minute) to run through 14 decades of data, and for those who are patient, the chart then undergoes a dramatic transformation.

With a sleight of hand, the chart went from a set of circles to a funnel. Here is a look:

What happens is the reintroduction of a time dimension. Imagine pushing the center of the spiral down into the screen to create a third dimension.

Our question as always is - what does this chart tell readers?

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The chart seems to say that the variability of temperature has increased over time (based on the width of the funnel). The red/blue color says the temperature is getting hotter especially in the last 20-40 years.

When the reader looks beneath the surface, the chart starts to lose sense.

The width of the funnel is really a diameter of the spiral chart in the given year. But, if you recall, the diameter of the spiral (polar) chart isn't the same between any pairs of months.

In the particular rendering of this video, the width of the funnel is the diameter linking the April and October values.

Remember the polar gridlines behind the spiral:

Notice the hole in the middle. This hole has arbitrary diameter. It can be as big or as small as the designer makes it. Thus, the width of the funnel is as big or as small as the designer wants it. But the first thing that caught our attention is the width of the funnel.

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The entire section between -1 and + 1 is, in fact, meaningless. In the following chart, I removed the core of the funnel, adding back the -1 degree line. Doing so exposes an incompatibility between the spiral and funnel views. The middle of the polar grid is negative infinity, a black hole.

For a moment, the two sides of the funnel look like they are mirror images. That's not correct, either. Each width of the funnel represents a year, and the extreme values represent April and October values. The line between those two values does not signify anything real.

Let's take a pair of values to see what I mean.

I selected two values for October 2021 and October 1899 such that the first value appears as a line double the length of the second. The underlying values are +0.99C and -0.04C, roughly speaking, +1 and 0, so the first value is definitely not twice the size of the second.

The funnel chart can be interpreted, in an obtuse way, as a pair of dot plots. As shown below, if we take dot plots for Aprils and Octobers of every year, turn the chart around, and then connect the corresponding dots, we arrive at the funnel chart.

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This NASA effort illustrates a central problem in visual communications: attention (what Andrew Gelman calls "grabbiness") and information integrity. On the one hand, what's the point of an accurate chart when no one is paying attention? On the other hand, what's the point of a grabby chart when anyone who pays attention gets the wrong information? It's not easy to find that happy medium.

What do I think about spirals?

A twitter user asked how I feel about this latest effort (from NASA) to illustrate global warming. To see the entire video, go to their website.

This video hides the lede so be patient or jump ahead to 0:56 and watch till the end.

Let's first describe what we are seeing.

The dataset consists of monthly average global temperature "anomalies" from 1880 to 2021 - an "anomaly" is the deviation of the average temperature that month from a reference level (seems like this is fixed at the average temperatures by month between 1951 and 1980).

A simple visualization of the dataset is this:

We see a gradual rise in temperature from the 1980s to today. The front half of this curve is harder to interpret. The negative values suggest that the average temperatures prior to 1951 are generally lower than the temperature in the reference period. Other than 1880-1910, temperatures have generally been rising.

Now imagine chopping up the above chart into yearly increments, 12 months per year. Then wrap each year's line into a circle, and place all these lines onto the following polar grid system.

Close but not quite there. The circles in the NASA video look much smoother. Two possibilities here. First is the aspect ratio. Note that the polar grid stretches the time axis to the full circle while the vertical axis is squashed. Not enough to explain the smoothness, as seen below.

The second possibility is additional smoothing between months.

The end result is certainly pretty:

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Is it a good piece of scientific communications?

What is the chart saying?

I see red rings on the outside, white rings in the middle, and blue rings near the center. Red presumably means hotter, blue cooler.

The gridlines are painted over. The 0 degree (green) line is printed over again and again.

The biggest red circles are just beyond the 1 degree line with the excess happening in the January-March months. In making that statement, I'm inferring meaning to excess above 1 degree. This inference is purely based on where the 1-degree line is placed.

I also see in the months of December and January, there may have been "cooling", as the blue circles edge toward the -1 degree gridline. Drawing this inference actually refutes my previous claim. I had said that the bulge beyond the +1 degree line is informative because the designer placed the +1 degree line there. If I applied the same logic, then the location of the -1 degree line implies that only values more negative than -1 matter, which excludes the blue bulge!

Now what years are represented by these circles? Test your intuition. Are you tempted to think that the red lines are the most recent years, and the blue lines are the oldest years? If you think so, like I do, then we fall into a trap. We have now imputed two meanings to color -- temperature and recency, when the color coding can only hold one.

The only way to find out for sure is to rewind the tape and watch from the start. The year dimension is pushed to the background in this spiral chart. Instead, the month dimension takes precedence. Recall that at the start, the circles are white. The bluer circles appear in the middle of the date range.

This dimensional flip flop is a key difference between the spiral chart and the line chart (shown again for comparison).

In the line chart, the year dimension is primary while the month dimension is pushed to the background.

Now, we have to decide what the message of the chart should be. For me, the key message is that on a time scale of decades, the world has experienced a significant warming to the tune of about 1.5 degrees Celsius (35 F2.7 F). The warming has been more pronounced in the last 40 years. The warming is observed in all twelve months of the year.

Because the spiral chart hides the year dimension, it does not convey the above messages.

The spiral chart shares the same weakness as the energy demand chart discussed recently (link). Our eyes tend to focus on the outer and inner envelopes of these circles, which by definition are extreme values. Those values do not necessarily represent the bulk of the data. The spiral chart in fact tells us that there is not much to learn from grouping the data by month. 

The appeal of a spiral chart for periodic data is similar to a map for spatial data. I don't recommend using maps unless the spatial dimension is where the signal lies. Similarly, the spiral chart is appropriate if there are important deviations from a seasonal pattern.

 

 

Speaking to the choir

A friend found the following chart about the "carbon cycle", and sent me an exasperated note, having given up on figuring it out. The chart came from a report, and was reprinted in Ars Technica (link).

The problem with the chart is that the designer is speaking to the choir. One must know a lot about the carbon cycle already to make sense of everything that's going on.

We see big and small arrows pointing up or down. Each arrow has a number attached to it, plus a range inside brackets. These numbers have no units, and it's not obvious what they are measuring.

The arrows come in a variety of colors. The colors are explained by labels but the labels dexcribe apparently unrelated concepts (e.g. fossil CO2 and land-use change).

Interspersed with the arrows is a singular dot. The dot also has a number attached to it. The number wears a plus sign, which signals it's being treated differently than the quantities with up arrows.

The singular dot is an outcast, ostracized from the community of dots in the bottom part of the chart. These dots have labels but no numbers. They come in different sizes but no scale is provided.

The background is divided into three parts, showing the atmosphere, the land mass, and the ocean. The placement of the arrows and dots suggests each measured quantity concerns one of these three parts. Well... except the dot labeled "surface sediments" that sit on the boundary of the land mass and the ocean.

The three-way classification is only one layer of the chart. A different classification is embedded in the color scheme. The gray, light green, and aquamarine arrows in the sky find their counterparts in the dots of the land mass, and the ocean.

What's more, the boundaries between land and sky, and between land and ocean are also painted with those colors. These boundary segments have been given different colors so that the lengths of these segments seem to contain data but we aren't sure what.

At this point, I noticed thin arrows which appear to depict back and forth flows. There may be two types of such exchanges, one indicated by a cycle, the other by two straight arrows in opposite directions. The cycles have no numbers while each pair of straight thin arrows gets two numbers, always identical.

At the bottom of the chart is a annotation in red: "Budget imbalance = -1.0". Presumably some formula ties the numbers shown above to this -1.0 result. We still don't know the units, and it's unclear if -1.0 is a bad number. A negative number shown in red typically indicates a bad number but how bad is it?

Finally, on the top right corner, I found a legend. It's not obvious at first because the legend symbols (arrows and dots) are shown in gray, a color not used elsewhere on the chart. It appears as if it represents another color category. The legend labels do little for me. What is an "anthropogenic flux"? What does the unit of "GtCO2" stand for? Other jargon includes "carbon cycling" and "stocks". The entire diagram is titled "carbon cycle" while the "carbon cycling" thin arrows are only a small part of the diagram.

The bottom line is I have no idea what this chart is saying to me, other than that the earth is a complex system, and that the designer has tried valiantly to impregnate the diagram with lots of information. If I am well read in environmental science, my experience is likely different.