Dr. Spencer responded with:

sort of… the ‘spirals’ display exaggerates linearly… the line segments increase in length with warming according to Pi*r.

But the ‘temperature circle” exaggeration causes the displayed area to increase nonlinearly,  by Pi*r-squared.

Dr. Spencer also added this during our discussion:

Imagine if the ‘spiral’ temperature scale was increasing inward. In that case the spirals would get smaller with warming, which would be much less dramatic. The perception of warming should not depend upon whether the scale is reversed, and is evidence that these new display techniques have been contrived to whip up alarm since (as the recent Gallup poll reminds us) most people aren’t very concerned about warming rates that are too small to feel in their lifetimes.

And that’s why you don’t see Hawkins produce the spiral in reverse. It would kill the effect of his visualization, making it far less alarming. Confirmation bias at work.

While Hawkins spiral graph uses colored line segments (much like Lipponen does), his are oriented perpendicular to the radius of the circle, with warmer temperatures being near the edge, and as the radius increases, the segments get longer. Hawkins also uses a temperature scale to color the lines, using a color scale called ‘viridis’ . Of course, the warmer temperatures tend to be depicted as yellows and oranges, and the cooler temperatures as blues and violets, as Hawkins states:

What do the colours mean? The colours represent time. Purple for early years, through blue, green to yellow for most recent years. The colour scale used is called ‘viridis’ and the graphics were made in MATLAB.

More on the color choice by Hawkins later (which has it’s own set of problems). For now, let’s concentrate on the geometry trick.

Here’s what we normally see – a linear graph, where all data points have the same weight:

Figure 1. Source: Met Office: https://ift.tt/2LBqmbi

Note that in the HadCRUT4 data shown above in a  linear fashion. most of the temperature increase comes after 1950. Hold that thought.

As Spencer pointed out about Lipponen’s circular graph, due to the way surface area increases exponentially with radius, far more surface area is given to the warmer temperatures than the cooler ones.

Anybody who has taken basic geometry in primary school knows this:

Figure 2. Source: A. Watts from plotted/calculated data

As seen in Figure 2, surface area increases exponentially with increasing radius.

To illustrate this with some basic geometry, I decided to take some measurements of Hawkins spiral graph. Since Hawkins spiral graph doesn’t have a reference scale on it, the only way I could get something to measure for radius was to import his graph into a graphics program and apply a pixel scale. I’ve done that in the image below from frame #1 of the animation and listed the values.

Figure 3. Ed Hawkins spiral global temperature graph ring values measured by pixels to give radius values. Due circle lines being multiple pixels wide, values are +/-  2 pixels. Image measured and annotated by: A. Watts Click to enlarge.

Because Hawkins didn’t provide 0.5°C and 1.0°C circle values, and because he offsets zero (to account visually for the possibility of negative anomaly values), it’s a bit different to work out, but I’ve done it in Table 1 below.

From Figure 3, the values are:

Temp in °C	Radius (pixels)		Surface area in pixels using πR2		Note
0.0°C	160		80424.7		(zero value offset is 160 px)
0.5°C	200		125663.7		(interpolated value)
1.0°C	240		180955.7		(interpolated value)
1.5°C	400		502654.8		(we aren’t there yet)
2.0°C	480		723822.9		(we aren’t there yet)

TABLE 1: Values of temperature, radius, offsets, and surface area from Hawkins spiral plot.

Clearly, as the lines expand and get longer in Hawkins spiral graph, they extend into larger surface areas because the lines themselves are longer. Humans, when viewing the lines all massed together, tend to average them visually, assigning more weight to them because they cover more surface area of the circle.

It’s a visual trick, and one that is peculiar to Hawkins, because nowhere else in climate science do we see a linear graph of temperature turned into an exponential representation. I suspect Lipponen’s representation might be inspired by Hawkins.

To illustrate, for a Hawkins spiral circle, here in Figure 4 is how the linear values and the exponentially increasing surface area value graph out using the pixel values measured, including the 160 pixel offset from zero to handle negative anomaly possibilities. A polynomial curve fit is also added to illustrate the exponential increase in surface area for the values closest to the circumference of the circle.

Figure 4: Values of temperature -vs- surface area (blue) calculated from radii measured in Hawkins base spiral from Figure 3. Polynomial curve fit to data points added (red).

It looks a lot like a hockey stick, doesn’t it?

When first I plotted Figure 4, and saw that the blue line didn’t follow the plotted path of a pure circle as seen in Figure 2, I thought I had made some sort of mistake. I looked at the data again, couldn’t find any errors in the way I measured it, then threw it out and started over again. I came up with the same result, again and again.

My conclusion? Hawkin’s 0.0, 1.5, and 2.0 reference circles aren’t accurate. I suspect they were some hand generated overlay, because they certainly don’t follow the surface area from increasing radii of a pure circle seen in figure 2. Either that, or he’s used some sort of non-linear scale for temperature that isn’t obvious when trying to reverse engineer his work. Not having his original MatLAB data and plots, I can’t say for sure. If I’ve erred someplace in measuring the original graph, please point it out in comments.

But one thing IS certain: by plotting HadCRUT 4.6 data using the circle/spiral method, he’s weighted post 1950 data far more heavily that data from 1850 to 1950, both in line length, as well as the surface area the pixels that make up those lines cover in the circle. Knowing this now, it is clearly obvious looking at his spiral graph endpoint in 2017:

Figure 5. Hawkins spiral graph, end frame at 2017. Note how the earlier lighter blues and pastel magentas are covered up by the more recent temperatures. Note also how the greenish yellows are the most prominent visual elements, both by color, and by surface area covered.

In figure 5 above, note how the earlier lighter blues and pastel magentas are covered up by the more recent temperatures. Note also how the greenish yellows are the most prominent visual elements, both by color, and by surface area covered.

It’s basically “Mike’s Nature Trick” all over again.

The more recent graphic elements (post 1950) cover up the ones that the really didn’t want you to see. PLUS..the spiral presentation visually weights the more recent temperature data far more heavily than earlier data due to the increased surface area of the lines created by the most recent data. It’s a double-whammy of visualization bias.

Finally, remember earlier I said: “More on the color choice by Hawkins later (which has it’s own set of problems). ”

The problem is that the human eye does not perceive colors linearly, as this graph clear illustrates:

Figure 6. The three curves in the figure above shows the normalized response of an average human eye to various amounts of ambient light. The shift in sensitivity occurs because two types of photoreceptors called cones and rods are responsible for the eye’s response to light. The curve on the right shows the eye’s response under normal lighting conditions and this is called the photopic response. The cones respond to light under these conditions. Source: Robinson, S. J. and Schmidt, J. T., Fluorescent Penetrant Sensitivity and Removability – What the Eye Can See, a Fluorometer Can Measure, Materials Evaluation, Vol. 42, No. 8, July 1984, pp. 1029-1034

More on Figure 6 here: https://www.nde-ed.org/EducationResources/CommunityCollege/PenetrantTest/Introduction/lightresponse.htm

From colors in figure 6, we can clearly see that the end-frame of Hawkin’s spiral graph is mostly in the green to yellow range, and that the cooler blues and magentas aren’t just covered up, they don’t have the same visual color impact.

This is why fire trucks and other emergency vehicles are now painted a yellowish-green; it makes them more visible in traffic and easier to avoid.

Figure 7. Fire trucks are now painted to match the color sensitivity of the human eye.

The red fire trucks of days past weren’t as easy to see. It’s documented by a study: http://www.apa.org/action/resources/research-in-action/lime.aspx

So due to the color scale choice, there’s a TRIPLE-WHAMMY of visualization bias in Hawkins graph.

In summary, Ed Hawkins spiral graph does the following.

1. It gives post 1950 data far more visual weight due to increased line length and surface area of pixels that make up those lines.
2. It it covers up older data with newer data, making it unavailable for visual comparison
3. The color scale choice visually weights the present data far more than the older data, shrinking it’s impact.

This isn’t good science, it’s simple visual propaganda, and Ed Hawkins should retract it, in my opinion. As Dr. Spencer said:

I consider this very deceptive.

Hawkins probably won’t retract it since we’ve learned time and again that climate science often doesn’t care much about accuracy in presentations, it’s more about the messaging, and in that, he’s succeeded in pushing an alarming message. They are also exceedingly stubborn, and don’t like being shown to be wrong.

Even if Hawkins does retract it, it will be impossible to put the genie back in the bottle, since his graph is shared in millions of social media posts and tweets.

But, in the climate skeptic world, this fiasco will live on forevermore known as “Hawkins spiral trick”.