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I’ve been traveling in North America for a few months now. This has required me not only to relearn how to drive on the right-hand side of the road, but also the Fahrenheit temperature scale. So this XKCD comic describes a day to day occurrence for me. This can be quite important, since when reported in Fahrenheit winter temperatures in the Northern U.S. sound much like winter temperatures in Cape Town, but with very different meanings. In both places someone might say to you “It’s five degrees out, you should wear a sweater.” Translated, however, this means “The temperature is minus fifteen degrees Celsius, you should wear a sweater in addition to the heavy winter coat that I already assume that you wear every day.”

Popular legend is that Danial Gabriel Fahrenheit defined his scale so that zero represented the coldest know temperature experienced in his home town of Gdańsk. He then set the degree intervals so that standard human body temperature would be three times higher than the freezing point of water, set [at the time, this changed soon after] to be 96 and 32, respectively. The point of this was to put 64 ‘units’ between the two values, both to make it easier to mark his instruments with geometrical rigor, and to deliberately space out the range of temperature values that could be used to express typically experienced states.

This is all very convoluted and certainly when being presented with temperatures in Fahrenheit for the first time this information doesn’t do a lot to help someone intuit what the numbers are telling them. However, it is an early example of an attempt to create a human relevant index. This is an often claimed goal of climate scientists; to quantify an experience of the atmospheric state in terms relevant to an individual, admittedly someone that lives under certain circumstances. There have been many different temperature scales invented over the years (Issac Newton had his own personal scale). One interesting example is the Delisle scale, which uses the boiling point of water as the zero point, and then reports the amount which the mercury in the thermometer contracts as the temperature becomes colder. So, in this scale larger numbers mean colder temperatures. This scale was developed in Saint Petersburg as a means to document the severity of Russian winters. So a higher number implies a harsher environment. While this seems counter intuitive when you’ve spent your life referring to the temperature “going up” to indicate that it’s getting hotter, and “going down” for cooling, it describes very directly the topic that Joseph-Nicolas Delise was attempting to communicate.

Most people are more familiar with the Celsius temperature scale. Zero is the temperature where water freezes, and one-hundred is when it boils, which is all and all a much more universal basis than 18th century weather anecdotes from a Baltic seaport. Well, except of course that the temperature that water freezes at depends on what else is in the water, and boiling points will depend on how far above sea level you are. The real universality of the Celsius scale comes from how widely it’s used, making it easy to compare reported temperatures across most regions of the world (as long as you’re not trying to compare what the different environments feel like).

So with some reference points, and a notion of how ‘far apart’ you’d like them to be on the scale, you can create a temperature system. That’s empowering, but maybe not that emotionally satisfying. Well, not to a physicist anyways. Is there something more, definitive? Yes, and it’s called thermodynamics and is an entire branch of physical science. From this we get the Kelvin scale. The zero point of this scale is considered to be a theoretical no-energy-state, well, minimal-energy-state if you consider quantum mechanics. From there you move up in the same increments as used in the Celsius scale, because, well, because that makes it very simple to convert between them, and not everything has to be difficult all of the time. This absolute zero can never actually be reached, although the temperature of deep spaces is considered to be only 2.73 Kelvin. This is often quoted to be the average temperature of the universe, despite that the universe is full of stars, which are essentially giant nuclear reactors burning at surface temperatures between 3,500 and 40,000 Kelvin. Because the universe is huge and vastly empty. For comparison, a comfortable room temperature is about 294 Kelvin. I suppose that when I wake up to find that the temperature is -20 degrees Celsius (not that uncommon an occurrence), saying that the temperature is 250.42 units (Kelvin) warmer than the furthest reaches of deep space, is perhaps putting a more positive spin on the situation than saying that the temperature is 4 units (Fahrenheit) colder than I would probably ever have to experience if I lived in coastal Poland. While putting my experience into the context of the range of states of the known universe is a refreshingly humbling approach, it does make communicating and intuiting the numbers much more challenging.

This is the dilemma that is faced when trying to create numerical representations of our environment. We can try to talk in physical absolutes, but sometimes this requires conceptualizing the purely theoretical state of utter stillness as understood at the quantum level, something typically not addressed until the third year of a physics degree, and a subject of ongoing scientific research and development. Or we try to map the scales as close as possible to our own experience. This can be useful if we’re ‘on the same page’ and clunky and overly subjective otherwise. [Although, the one strength I see in the Fahrenheit, Celsius, and other empirical scales is that they are overtly subjective, it’s pretty clear that either you know the baseline or you don’t, there’s no temptation to guess what a value ‘should’ mean.]  You can try to have both, adjusting the theoretical scale around a few more or less recognizable goalposts and prioritize having a common standard. All fair approaches, depending on your goal. Personally, I find the Celsius scale very serviceable, but I’ve spent most of my life at sea-level, with my two primary activities being making tea (boiling water) and worrying about whether a frost (freezing water) was going to kill the garden plants. So works for me, but I’m just one (apparently pretty dull) guy. I’m sure a lot of people have their own favorite system, and I’m sure many of them think that they have objective reasons why theirs is ‘correct’. Although I’m also sure that these reasons mostly just boil down to either them being familiar with something, or else thinking that their opinion links them with some social group they believe association with to be advantageous, because, well, humans

A conversation about defining climate indices is typically much more complicated than choosing between different temperature scales. It’s possible to directly convert between temperature scales. That’s because they all attempt to measure the same thing, just applying different labels. As long as you’re consistent in your choice, or apply the relevant conversion factors, the basic math doesn’t change. It’s not possible to have an increasing trend in Fahrenheit temperatures and a decreasing one in Kelvin. In many situations though, the question is not how to label measurements, but rather what to measure in order to quantify a larger conceptual notion of some pattern or activity.

Using indices to monitor macro states is quite common in economics. The aggregated levels of various stock exchanges are reported and followed constantly across the world. Share prices, currency rates, etc, aren’t material things, but are looked to as, although not always are, indicative of the state of, or confidence in the commercial activities that they represent. Although, often these indices are to some degree such emergent phenomena that even speculating on their future levels is enough to manipulate the real events they are meant to serve as an indicator of.

For a more climate related example, we can consider El Niño events. There’s a common conceptual notion of what is an El Niño: weak winds off the coast of Peru reduce deep sea upwelling, resulting in anomalously warm sea surface temperatures across the Equatorial Pacific. These events can be identified from satellite data, we ‘know it when we see it‘. But what to measure in order to quantify the amount to which it is happening? The temperature of the entire Pacific surface?  Surface temperature in a select region?  Surface temperature in this different but overlapping region? Since we conceptualize an El Niño less by the ocean dynamics and more the atmospheric conditions it creates, should we rather measure certain contrasting atmospheric properties? There are many options, all of which will highlight different attributes and conditions. None of these are right or wrong, but since these different indices measure different attributes, there is no fixed way to convert between them. There is no way to say, “Well because the MEI was this, the SOI must be this…” Different indices will have different histories and associations, and be of varying relevance to different locals.

The question of what to measure to quantify a process comes up in discussion of global warming as well. Often estimates are given of global mean surface temperature. These statistics are interesting, but this can give an incomplete depiction of the total energy balance of the earth system, by ignoring changes in the upper atmosphere and oceans. As well trends in the total energy balance don’t provide information on how these increases are manifesting themselves in shifting patterns of the distribution and circulation of heat and moisture, which drive the changes we actually experience.

In all these examples the dilemmas are the same. What is an effective way to label the variation we observe (as in the case of choosing a temperature scale), and what attribute(s) do we measure as representative of the state of an entity (choosing a region of the East Pacific as a representative of El Niño activity)? There is no singular concrete way to express the entirety of a thing, and we don’t want to lose the forest for the trees. However, we want a measure of the forest that gives some means to extrapolate the sort of trees it might contain. Often it’s hard to separate the goals of describing the mechanics of a process and selecting a convenient system for categorizing its manifestations. A summary statistic isn’t meant to be the undiluted ‘essential feature‘ of a phenomena, it’s just that, a summary. We’re looking for a shorthand indicator. I don’t want to stand outside for five minutes every morning determining how I feel, I want to look at a number on a thermometer that indicates how I should probably dress for the weather. But that’s the danger, we’re looking for a summary, a time saver, but often unwrapping what a statistic actually tells us requires periods of training and gaining experience. My thermometer doesn’t tell me how comfortable I’ll be at a given temperature, nor whether or not its raining. I mentioned economic indicators before. There’s always a strong temptation for investors or governments to take these as incontrovertible instructions, rather than as suggestions of what might be going on on a micro level. History is full of examples of how that typically works out. The trick seems to be to use different statistics and labels as a way to hold data up to a light, not so much to illuminate its true nature, but as a way to highlight different features by exposing it to different spectrum and at different angles. In doing so being able to articulate what the different signals might mean seems as or more important than the approach its self. Universality and common frameworks go a long way towards creating a communicable message, but so does the flexibility to extract nuanced information that considers multiple facets, and that can be readily adapted to context. Personally I would be hesitant to suggest any meta-criteria for a good index, or empirical temperature scale for that mater. I’m not confident that I would ‘know a good one when I saw it’. Probably like everything else, it’s mostly a matter of exploring and developing what proves useful.

Be sure to attend the CSAG Seminar on this topic on Friday (March 11th)!



The base picture from the cover image is from National Geographic.

2 Responses to “Index 451”

  1. peter

    Good article Tristan. Hot and Cold are very relative and we use them so liberally even when they mean different things to people. SAWS, and other forecast sites have (seemingly) arbitrary scales where 30 might be “pleasantly warm” while I might find this excrutiatingly hot. It seems human thermostats are as variable as our other attributes.
    Personally I like the adage: You can gauge the heat of the day by the length of the cat!