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Blog - warming slowdown? (part 1)

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1. How Heat Flows and Why It Matters

Is there something missing in the recent climate temperature record?

Heat is most often experienced as energy density, related to temperature. While technically temperature is only meaningful for a body in thermal equilibrium, temperature is the operational definition of heat content, both in daily life and as a scientific measurement, whether at a point or averaged. For the present discussion, it is taken as given that increasing atmospheric concentrations of carbon dioxide trap and re-radiate Earth blackbody radiation to its surface, resulting in a higher mean blackbody equilibration temperature for the planet, via radiative forcing (Ca2014a, Pi2012, Pi2011, Pe2006).

The question is, how does a given joule of energy travel? Once on Earth, does it remain in atmosphere? Warm the surface? Go into the oceans? And, especially,if it does go into the oceans, what is its residence time before released to atmosphere? These are important questions (Le2012a, Le2012b). Because of the miscibility of energy, questions of residence time are very difficult to answer. A joule of energy can’t be tagged with a radioisotope like matter sometimes can. In practice, energy content is estimated as a constant plus the time integral of energy flux across a well-defined boundary using a baseline moment.

Variability is a key aspect of natural systems, whether biological or large scale geophysical systems such as Earth’s climate (Sm2009). Variability is also a feature of statistical models used to describe behavior of natural systems, whether they be straightforward empirical models or models based upon ab initio physical calculations. Some of the variability in models captures the variability of the natural systems which they describe, but some variability is inherent in the mechanism of the models, an artificial variability which is not present in the phenomena they describe. No doubt, there is always some variability in natural phenomena which no model captures. This variability can be partitioned into parts, at the risk of specifying components which are not directly observable. Sometimes they can be inferred.

Models of planetary climate are both surprisingly robust and understood well enough that appreciable simplifications, such as setting aside fluid dynamism, are possible, without damaging their utility (Pi2012). Thus, the general outline of what long term or asymptotic and global consequences arise when atmospheric carbon dioxide concentrations double or triple are known pretty well. More is known from the paleoclimate record.What is less certain are the dissipation and diffusion mechanisms for this excess energy and its behavior in time (Kr2014, Sh2014a, Sh2014b, Sa2011). There is keen interest in these mechanisms because of the implications differing magnitudes have for regional climate forecasts and economies (Em2011, Sm2011, Le2010). Moreover, there is a natural desire to obtain empirical confirmation of physical calculations, as difficult as that might be, and as subjective as judgments regarding quality of predictions might be (Sc2014, Be2013, Mu2013a, Mu2013b, Br2006, Co2013, Fy2013, Ha2013, Ha2014, Ka2013a, Sl2013, Tr2013, Mo2012, Sa2012, Ke2011a, Kh2008a, Kh2008b, Le2005, De1982).

Observed rates of surface temperatures in recent decades have shown a moderating slope compared with both long term statistical trends and climate model projections (En2014, Fy2014, Sc2014, Ta2013, Tr2013, Mu2013b, Fy2013, Fy2013s, Be2013). It’s the purpose of this article to present this evidence, and report the research literature’s consensus on where the heat resulting from radiative forcing is going, as well as sketch some implications of that containment.

2. Tools of the Trade

I’m Jan Galkowski. I’m a statistician and signals engineer, with an undergraduate degree in Physics and a Masters in EE & Computer Science. I work for Akamai Technologies of Cambridge, MA, where I study time series of Internet activity and other data sources, doing data analysis primarily using spectral and Bayesian computational methods. I am not a climate scientist, but am keenly interested in the mechanics of oceans, atmosphere, and climate disruption. I approach these problems from that of a statistician and physical dynamicist. Climate science is an avocation. While I have 32 years experience doing quantitative analysis, primarily in industry, I have found that the statistical and mathematical problems I encounter at Akamai have remarkable parallels to those in some geophysics, such as hydrology and assessments of sea level rise, as well as in some population biology. Thus, it pays to read their literature and understand their techniques. I also like to think that Akamai has something significant to contribute to this problem of mitigating forcings of climate change, such as enabling and supporting the ability of people to attend business and science meetings by high quality video call rather than hopping on CO2-emitting vehicles.

As the great J. W. Tukey said:

The best thing about being a statistician is that you get to play in everyone's backyard.

Anyone who doubts the fun of doing so, or how statistics enables such, should read Young.

3. On Surface Temperatures, Land and Ocean

Independently of climate change, monitoring surface temperatures globally is a useful geophysical project. They are accessible, can be measured in a number of ways, permit calibration and cross-checking, are taken at convenient boundaries between land-atmosphere or ocean-atmosphere, and coincide with the living space about which we most care. Nevertheless, like any large observational effort in the field, such measurements need careful assessment and processing before they can be properly interpreted. The Berkeley Earth Surface Temperature (“BEST”) Project represents the most comprehensive such effort, but it was not possible without many predecessors, such as HadCRUT4, and works by Kennedy, et al and Rohde (Ro2013a, Mo2012, Ke2011a, Ke2011b, Ro2013b).

Surface temperature is a manifestation of four interacting processes. First, there is warming of the surface by the atmosphere. Second, there is lateral heating by atmospheric convection and latent heat in water vapor. Third, during daytime, there is warming of the surface by the Sun or insolation which survives reflection. Last, there is warming of the surface from below, either latent heat stored subsurface, or geologic processes. Roughly speaking, these are ordered from most important to least. These are all manifestations of energy flows, a consequence of equalization of different contributions of energy to Earth.

Physically speaking, the total energy of the Earth climate system is a constant plus the time integral of energy of non-reflected insolation less the energy of the long wave radiation or blackbody radiation which passes from Earth out to space, plus geothermal energy ultimately due to radioisotope decay within Earth’s aesthenosphere and mantle, plus thermal energy generated by solid Earth and ocean tides, plus waste heat from anthropogenic combustion and power sources (Decay). The amount of non-reflected insolation depends upon albedo, which itself slowly varies. The amount of long wave radiation leaving Earth for space depends upon the amount of water aloft, by amounts and types of greenhouse gases, and other factors. Our understanding of this has improved rapidly, as can be seen by contrasting Kiehl, et al in 1997 with Trenberth, et al in 2009 and the IPCC’s 2013 WG1 Report (Ki1997, Tr2009, IP2013). Steve Easterbrook has given a nice summary of radiative forcing at his blog, as well as provided a succinct recap of the 2013 IPCC WG1 Report and its take on energy flows elsewhere at the The Azimuth blog. I refer the reader to those references for information about energy budgets, what we know about them, and what we do not.

Some ask whether or not there is a physical science basis for the “moderation” in global surface temperatures and, if there is, how that might work. It is an interesting question, for such a conclusion is predicated upon observed temperature series being calibrated and used correctly, and, further, upon insufficient precision in climate model predictions, whether simply perceived or actual. Hypothetically, it could be that the temperature models are not being used correctly and the models are correct, and which evidence we choose to believe depends upon our short-term goals. Surely, from a scientific perspective, what’s wanted is a reconciliation of both, and that is where many climate scientists invest their efforts. This is also an interesting question because it is, at its root, a statistical one, namely, how do we know which model is better (Ve2012, Sm2009, Sl2013, Ge1998, Co2006, Fe2011b, Bu2002)?

A first graph, Figure 1, depicting evidence of warming is, to me, quite remarkable. (You can click on this or any figure here, to enlarge it.)

Ocean temperatures at depth
Figure 1. Ocean temperatures at depth, from Yale Climate Forum.

A similar graph is shown in the important series by Steve Easterbrook recapping the recent IPCC Report. A great deal of excess heat is going into the oceans. In fact, most of it is, and there is an especially significant amount going deep into the southern oceans, something which may have implications for Antarctica.

This can happen in many ways, but one dramatic way is due to a phase of the El Niño Southern Oscillation} (“ENSO”). Another way is storage by the Atlantic Meridional Overturning Circulation (“AMOC”) (Ko2014).

The trade winds along the Pacific equatorial region vary in strength. When they are weak, the phenomenon called El Niño is seen, affecting weather in the United States and in Asia. Evidence for El Niño includes elevated sea-surface temperatures (“SSTs”) in the eastern Pacific. This short-term climate variation brings increased rainfall to the southern United States and Peru, and drought to east Asia and Australia, often triggering large wildfires there.

The reverse phenomenon, La Niña, is produced by strong trades, and results in cold SSTs in the eastern Pacific, and plentiful rainfall in east Asia and northern Australia. Strong trades actually pile ocean water up against Asia, and these warmer-than-average waters push surface waters there down, creating a cycle of returning cold waters back to the eastern Pacific. This process is depicted in Figures 2 and 3.

Figure 2. Oblique view of variability of Pacific equatorial region from El Niño to La Niña and back. Vertical height of ocean is exaggerated to show piling up of waters in the Pacific warm pool.


Figure 3. Trade winds vary in strength, having consequences for pooling and flow of Pacific waters and sea surface temperatures.

At its peak, a La Niña causes waters to accumulate in the Pacific warm pool, and this results in surface heat being pushed into the deep ocean. To the degree to which heat goes into the deep ocean, it is not available in atmosphere. To the degree to which the trades do not pile waters into the Pacific warm pool and, ultimately, into the depths, that warm water is in contact with atmosphere (Me2011). There are suggestions warm waters at depth rise to the surface (Me2013).

Strong trade winds cause the warm surface waters of the equatorial Pacific to pile up against Asia
Figure 4. Strong trade winds cause the warm surface waters of the equatorial Pacific to pile up against Asia.

Documentation of land and ocean surface temperatures is done in variety of ways. There are several important sources, including Berkeley Earth, NASA GISS, and the Hadley Centre/Climatic Research Unit (“CRU”) data sets (Ro2013a, Ha2010, Mo2012) The three, referenced here as BEST, GISS, and HadCRUT4, respectively, have been compared by Rohde. They differ in duration and extent of coverage, but allow comparable inferences. For example, a linear regression establishing a trend using July monthly average temperatures from 1880 to 2012 for Moscow from GISS and BEST agree that Moscow’s July 2010 heat was 3.67 standard deviations from the long term trend (GISS-BEST). Nevertheless, there is an important difference between BEST and GISS, on the one hand, and HadCRUT4.

BEST and GISS attempt to capture and convey a single best estimate of temperatures on Earth’s surface, and attach an uncertainty measure to each number. Sometimes, because of absence of measurements or equipment failures, there are no measurements, and these are clearly marked in the series. HadCRUT4 is different. With HadCRUT4 the uncertainty in measurements is described by a hundred member ensemble of values, actually a 2592-by-1967 matrix. Rows correspond to observations from 2592 patches, 36 in latitude, and 72 in longitude, with which it represents the surface of Earth. Columns correspond to each month from January 1850 to November 2013. It is possible for any one of these cells to be coded as “missing”. This detail is important because HadCRUT4 is the basis for a paper suggesting the pause in global warming is structurally inconsistent with climate models. That paper will be discussed later.

4. Rumors of Pause

Figure 5 shows the global mean surface temperature anomalies relative to a standard baseline, 1950-1980. Before going on, consider that figure. Study it. What can you see in it?

Global surface temperature anomalies relative to a 1950-1980 baseline
Figure 5. Global surface temperature anomalies relative to a 1950-1980 baseline.

Figure 6 shows the same graph, but now with two trendlines obtained by applying a smoothing spline, one smoothing more than another. One of the two indicates an uninterrupted uptrend. The other shows a peak and a downtrend, along with wiggles around the other trendline. Note the smoothing algorithm is the same in both cases, differing only in the setting of a smoothing parameter. Which is correct? What is “correct”?

Figure 7 shows a time series of anomalies for Moscow, in Russia. Do these all show the same trends? These are difficult questions, but the changes seen in Figure 6 could be evidence of a warming "hiatus". Note that, given Figure 6, whether or not there is a reduction in the rate of temperature increase depends upon the choice of a smoothing parameter. In a sense, that’s like having a major conclusion depend upon a choice of coordinate system, something we’ve collectively learned to suspect. We’ll have a more careful look at this in Section 5. With that said, people have sought reasons and assessments of how important this phenomenon is. The answers have ranged from the conclusive “Global warming has stopped” to “Perhaps the slowdown is due to ‘natural variability”’, to “Perhaps it’s all due to ”natural variability“ to ”There is no statistically significant change“. Let’s see what some of the perspectives are.

Global surface temperature anomalies relative to a 1950-1980 baseline
Figure 6. Global surface temperature anomalies relative to a 1950-1980 baseline, with two smoothing splines printed atop.
Global surface temperature anomalies relative to a 1950-1980 baseline
Figure 7. Temperature anomalies for Moscow, Russia.

It is hard to find a scientific paper which advances the proposal that climate might be or might have been cooling in recent history. The earliest I can find are repeated presentations by a single geologist in the proceedings of the Geological Society of America, a conference which, like many, gives papers limited peer review (Ea2000, Ea2000, Ea2001, Ea2005, Ea2006a, Ea2006b, Ea2007, Ea2008). It is difficult to comment on this work since their full methods are not available for review. The content of the abstracts appear to ignore the possibility of lagged response in any physical system.

These claims were summarized by Easterling and Wehner in 2009, attributing claims of a “pause” to cherry-picking of sections of the temperature time series, such as 1998-2008, and what might be called media amplification. Further, technical inconsistencies within the scientific enterprise, perfectly normal in its deployment and management of new methods and devices for measurement, have been highlighted and abused to parlay claims of global cooling (Wi2007, Ra2006, Pi2006). Based upon subsequent papers, climate science seemed to not only need to explain such variability, but also to provide a specific explanation for what could be seen as a recent moderation in the abrupt warming of the mid-late 1990s. When such explanations were provided, appealing to oceanic capture, as described in Section 3, the explanation seemed to be taken as an acknowledge of a need and problem, when often they were provided in good faith, as explanation and teaching (Me2011, Tr2013, En2014).

Other factors besides the overwhelming one of oceanic capture contribute as well. If there is a great deal of melting in the polar regions, this process captures heat from the oceans. Evaporation captures heat in water. No doubt these return, due to the water cycle and latent heat of water, but the point is there is much opportunity for transfer of radiative forcing and carrying it appreciable distances.

Note that, given the overall temperature anomaly series, such as Figure 6, and specific series, such as the one for Moscow in Figure 7, moderation in warming is not definitive. It is a statistical question, and, pretending for the moment we know nothing of geophysics, a difficult one. But there certainly is no any problem with accounting for the Earth’s energy budget overall, even if the distribution of energy over its surface cannot be specifically explained (Ki1997, Tr2009, Pi2012). This is not a surprise, since the equipartition theorem of physics fails to apply to a system which has not achieved thermal equilibrium.

An interesting discrepancy is presented in a pair of papers in 2013 and 2014. The first, by Fyfe, Gillet, and Zwiers, has the (somewhat provocative) title “Overestimated global warming over the past 20 years”. (Supplemental material is also available and is important to understand their argument.) It has been followed by additional correspondence from Fyfe and Gillet (“Recent observed and simulated warming”) applying the same methods to argue that even with the Pacific surface temperature anomalies and explicitly accommodating the coverage bias in the HadCRUT4 dataset, as emphasized by Kosaka and Xie there remain discrepancies between the surface temperature record and climate model ensemble runs. In addition, Fyfe and Gillet dismiss the problems of coverage cited by Cowtan and Way, arguing they were making “like for life” comparisons which are robust given the dataset and the region examined with CMIP5 models.

How these scientific discussions present that challenge and its possible significance is a story of trends, of variability, and hopefully of what all these investigations are saying in common, including the important contribution of climate models.

Next Time

Next time I’ll talk about ways of estimating trends, what these have to say about global warming, and the work of Fyfe, Gillet, and Zwiers (Fy2013) comparing climate models to HadCRUT4 temperature data.


  1. Credentials. I have taken courses in geology from Binghamton University, but the rest of my knowledge of climate science is from reading the technical literature, principally publications from the American Geophysical Union and the American Meteorological Society, and self-teaching, from textbooks like Pierrehumbert. I seek to find ways where my different perspective on things canhelp advance and explain the climate science enterprise. I also apply my skills to working local environmental problems, ranging from inferring people's use of energy in local municipalities, as well as studying things like trends in solid waste production at the same scales using Bayesian inversions. I am fortunate that techniques used in my professional work and those in these problems overlap so much. I am a member of the American Statistical Association, the American Geophysical Union, the American Meteorological Association, the International Society for Bayesian Analysis, as well as the IEEE and its signal processing society.
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