Matt Rogers Can't Math

Another fake climate skeptic has published a misleading article, disappointingly this time in the Washington Post.  Matt Rogers says that there has been a deceleration in surface warming.  To show this, he gives the first difference graph of both surface temperature data from NASA (GISTEMP) and NOAA (NCDC).

His claim is false.  The standard errors of the trends in the first difference graphs are each greater than their respective trends, meaning you can't say even at 1-sigma that the trends are significantly different than zero (and you most certainly may not make a claim at 2-sigma).  For NOAA's data, the trend and standard error are -0.0043 and 0.0055 respectively; for NASA's data, the trend and standard error are -0.0055 and 0.0068 respectively.

NCDC: -0.0043±0.0110 (units ~˚C/year^2)
GISTEMP: -0.0055±0.0137

It is also unclear what data he is using for the GISTEMP dataset.  The 2001-2000 value should not be as low in his graph as it is; the one above is correct.  It's interesting that even with that correction, the trend is still very insignificant.

Rogers also tries to shield himself from criticism of cherry picking, by saying that he could have picked 1998 as a start year.  1998 was a very warm year, and Rogers thinks that this would have amplified the trend line.  As a fake skeptic, it is par for the course he would try to protect against accusations of cherry picking that dreaded year.

This is also a false claim anyway, and embarrassingly so.  If you start with a warm year like 1998 (contrasted to a cold year like 2000), and then do first differencing, you're going to start with a very low datapoint.  The result is not an amplified negative trend, but in fact a more positive trend.  Anyone that had actually graphed out the data would know that.  Anyone that can do basic math would know that, in fact.

NCDC: 0.0030±0.010
GISTEMP: 0.0023±0.0126

These are also not statistically significant.  In fact no first-difference trend is statistically significant, for at least a couple decades back.

Rogers doesn't know what he is talking about.  And this is a rather funny way of illustrating that fake skeptics in general don't know how to handle 1998.

[Edit: The extra attention this post seems to be getting has encouraged me to quickly add trend lines to these graphs.  Hopefully that helps make things a bit clearer!  I've also added indented "tables."  Thanks to Tom Di Liberto for the plug.]

Adiabatic Lapse Rate (Greenhouse v. Gravity, Part 1)

Take a box of gas*:

and crush it (increase pressure by a lot):

(*ideal) It's not really easy to visually show "pressure", but two things happen to the box of air: it will shrink (it's easy to show this), and its internal temperature will increase.

The first effect may seem obvious, but why the second one?  In the particular action we took of crushing the box, we performed work on the box (so we did something that changed its internal energy) but did not add or remove heat from the contents.  And, if we assume that the box is a thermal insulator, then we know that the gas cannot respond to being compressed by radiating away energy.

Thermodynamically, a change of a box of air's internal energy is related to the amount of heat that is transferred into or out of it, and the work performed on the box to change its volume.

 [1]

Where U is the internal energy of the box, Q is the heat that is added to the box, and W is a work term that is equal to PdV, such that an increase in volume is seen as a loss of internal energy (the box expends energy to push its walls out).  Conversely, pushing on the box to make it smaller is an addition to the internal energy.  Broadly speaking, if you do work on the box (shrink it) without letting it radiate, then its internal energy will increase; and internal energy is a function of the temperature of the gas.  This type of action on the box—this type of transformation—is called an adiabatic transformation.  "Adiabatic" means "without transfer of heat."

Why does this matter?

Consider the atmosphere: due to the weight of the air above you, there is higher atmospheric pressure at the surface of the planet than there is, say, 10 kilometers above us.  If we are very sloppy in our treatment of what we just learned, we might conclude that the very fact that pressure at the surface is higher means that the temperature at the surface is higher.

And believe it or not, this is something that is used (again, sloppily and erroneously) by some to deny that the greenhouse effect causes warming on the surface of our, and frankly any, planet.  Because if gravity can cause pressure change and high pressure is associated with high temperature, then who needs a greenhouse effect, right?

The problem comes from a fundamental misunderstanding of what the above equation represents.  The above equation (and all of the ones I will include soon derive the "adiabatic lapse rate" in the title) describes changes in variables of a box, or parcel, of air that is undergoing a transformation.  It does not describe a static system; but, the pressure gradient caused by gravity describes a static system (it actually holds in a variety of dynamic systems as well).

The article linked above tries to make an argument that the temperature profile in the atmosphere with height, which we will call the environmental temperature lapse rate (the rate at which temperature lapses, or falls, with height), can be described merely by gravity.  How?  By thinking that because adiabatic lapse rate, the rate at which a parcel of air will cool as it rises adiabatically (i.e. as it goes through a pressure change adiabatically), can be, then the environmental lapse rate can be.  But these are not the same thing!

To derive the adiabatic lapse rate (skip to equation [14] if you wish), consider our above thermodynamic equation, and plug in the work equivalence:

 [2]

Let's define a term that we'll call "enthalpy," H, as:

 [3]

so a small change in enthalpy is:

 [4]

 [5]

 [6]

 [7]

We can also define the heat capacity of our system as being the amount of heat we need to add (remove) to (from) a system in order to increase (decrease) its temperature by a certain amount.  Typically, we would have to restrain certain parameters of our system in order to measure such a heat capacity, for instance the pressure of the system.  If our system is at constant pressure (dP = 0), and we define constant-pressure heat capacity as below:

 [8]

then it follows

 [9]

And so, in an adiabatic lift of a parcel of air, where heat exchange is zero:

 [10]

If we divide by the mass of the system, we can obtain the specific heat capacity and the specific volume, which are, respectively, the amount of heat needed to cause a temperature change per unit of mass, and the amount of volume a unit of mass occupies (inverse of the density).  These variables will be in lowercase from the uppercase above.  And finally, we can use the hydrostatic equation to finish our derivation of the adiabatic lapse rate:

 [11]

 [12]

 [13]

 [14]

Here, g is a negative quantity (which I find exceedingly more appropriate than how it's treated as a positive variable with a negative sign attached to it, as in the Wikipedia link above).  On Earth, this adiabatic lapse rate value is about –9.8˚C per kilometer in height.  In other words, for every kilometer you adiabatically raise a parcel of air, it will cool by 9.8˚C.

Pay close attention to how the equations still describe the parcel of air, and are under the framework of literally moving a "piece" of air through a medium that has reached a pressure equilibrium with gravity.  We do not know anything about the temperature distribution in this medium, I never had to reference it.  We only know (or at least presumed) that it is stable.

It is also completely worth pointing out that if this was indeed the environmental lapse rate here on Earth, then our environmental lapse rate should equal –9.8˚C/km, no?  But it does not, the environmental lapse rate is instead roughly –6.5˚C/km, up until you hit the tropopause.  This is not a simple "well they're close, it's just an error between measurement and theory"—no, theory actually dictates that in our atmosphere the environmental lapse rate cannot be as negative as the adiabatic lapse rate.  While I will not go into that in particular in this part, allow me to show how a "shallow" environmental lapse rate is still completely compatible with a "steep" adiabatic lapse rate.

Stability

Equation [14] describes how the temperature of an air parcel will change when it rises to a particular height.  Consider what will happen to it if it does: once it reaches that height, it will have the same pressure as the pressure of the air around it, and one of three things will happen.

• The air parcel will wind up being colder than the surrounding air, which means it is denser, and thus will sink.  This is a condition where the environmental lapse rate is "shallower" (lower in magnitude) than the adiabatic lapse rate, a condition of stability where vertical motion is hampered.  A stable atmosphere will stay the way it is.

• The air parcel will reach the exact same temperature as the surrounding air, which means its density is equal, and thus it won't experience a force stopping its motion (but also not helping it).  The environmental lapse rate and the adiabatic lapse rate are equal, and this is a condition of neutrality.  Neutral atmospheres are "stable" in that when you move an air parcel adiabatically, you are not convecting heat from one location to another.  So, the environmental lapse rate will not change.

• The air parcel will be warmer than the surrounding air, which means it is less dense and will accelerate upward further.  The environmental lapse rate is "steeper" than the adiabatic lapse rate, and the atmosphere is unstable.  In an unstable atmosphere, these adiabatically rising air parcels are carrying hot air upward—this will lead to warming higher up, which makes the environmental lapse rate more "shallow".  It will work its way to a stable condition.

This implies an important point: an atmosphere with a very shallow environmental lapse rate is stable and can coexist with a steeper adiabatic lapse rate.  In fact, an atmosphere that has no greenhouse gases, or in other words does not have gases that can react with thermal radiation, will be isothermal with no environmental lapse rate at all.  This is again something in particular I will not explain in this part.

The next statement necessarily follows: the fact that the pressure is higher at the surface does not dictate that the temperature will be higher at the surface.  (You need to have a radiatively-interactive atmosphere, one with greenhouse gases, in order to have temperatures higher at the surface.)

If you're still not convinced, allow me to derive the temperature-dependent pressure profile of the atmosphere.  In other words, the pressure at a given height that has a given temperature.  That given temperature will depend on the environmental lapse rate.

Starting with the hydrostatic equation, and soon using the ideal gas law:

 [15]

 [16]

 [17]

 [18]

 [19]

 [20]

 [21]

[22]

 [23]

In these equations, in particular our final one, tau is our environmental lapse rate (see the substitution from equation [19] to equation [20]), and variables that have zero subscripts denote values at the surface of the planet (or any surface, so long as that surface remains the same in the problem).

The real question: if we give our tau variable a value very very close to zero, does that make our pressure profile very wonky?  In particular, does it imply that our pressure profile won't be "high at surface, low up above?"  The graph below shows that the answer is no.  In fact, the pressure profile corresponding to a near-zero temperature profile (–0.01˚C/km) is very close to the pressure profile corresponding to an environmental lapse rate close to our adiabatic lapse rate (–9.8˚C/km).  For this graph, the temperature and pressure at the surface for each scenario are the same, and are 14˚C and 100,000 Pa respectively.

Wrap-up

So, not only does the adiabatic lapse rate not describe a static system, instead the change that an individual air parcel experiences when you move it up or down, but the suggestion that a pressure gradient must cause a temperature gradient is unfounded as well and has many mathematical counterexamples.  In the next post, I will offer up a couple theoretical examples to direct how we should think about energy transfer in a simple atmosphere, and why radiative interaction (i.e. greenhouse gases) is needed for the convection that drives our actual environmental lapse rate.  I'll also briefly discuss some of the published science on many of these scenarios.

Cook et al 2013

A couple years ago I helped a small part in collecting emails for researchers who had published climate change-related papers, papers that would end up being the object of study in the since-published Cook et al 2013 "consensus project" paper that has gained a fair amount of due popularity.  Since then I have had very little time to devote to the Skeptical Science author team (especially considering how involved I was, merely a freshman in my latest stint), but from time to time I like to dust off my old coat and wear it around for a couple days while I explore some other climate-related subject.

The Cook et al paper's conclusions of a ~97% consensus in the scientific literature on the topic of anthropogenic global warming (AGW; that is, the question of whether humans are causing climate change) is important in its own right (very important, in particular, toward debunking the "there is no consensus" myth).  I'd like to comment on some of the finer details of the data collected, in particular comparisons between the ratings that the "citizen science" community at Skeptical Science gave each paper based on wording within the abstract, and the ratings that the authors of the papers themselves gave.

Do Most Experts Believe in Global Warming?

James Taylor from the Heartland Institute has recently written in Forbes about a new peer-reviewed study that he says demonstrates no:

Don’t look now, but maybe a scientific consensus exists concerning global warming after all. Only 36 percent of geoscientists and engineers believe that humans are creating a global warming crisis, according to a survey reported in the peer-reviewed Organization Studies. By contrast, a strong majority of the 1,077 respondents believe that nature is the primary cause of recent global warming and/or that future global warming will not be a very serious problem.

 I personally find it hilarious that Taylor led in with that idiom: Don't look now.  It's almost as if he didn't want us to go read the paper.  This is from the abstract:

This paper examines the framings and identity work associated with professionals’ discursive construction of climate change science, their legitimation of themselves as experts on ‘the truth’, and their attitudes towards regulatory measures.

Well that doesn't sound like an opinion survey. Why would you want to know about professionals' legitimation of themselves as experts if you just want their opinion? Why are you surveying people who might not be experts on climate science anyway? I don't go to my dentist to get his opinion on my house's electrical wiring.

The abstract concludes:

By linking notions of the science or science fiction of climate change to the assessment of the adequacy of global and local policies and of potential organizational responses, we contribute to the understanding of ‘defensive institutional work’ by professionals within petroleum companies, related industries, government regulators, and their professional association.

This isn't an opinion poll.  The authors clearly state that they're trying to elaborate on defensive institutional work by professionals in various industries or agencies; if I may phrase it this way, it's a psychological analysis, not a polling.

Need some convincing still that this is not a poll? From their methodology section (my italics):

Since 1999, climate change had been debated among professionals in APEGA in over 150 articles and letters to the editor that had appeared in the association’s monthly publication The PEGG. [...] Given this debate, APEGA initiated a broad survey of its 40,000 members (as of 2007) concerning their beliefs about climate change, sources of knowledge, and opinions about the appropriate roles for individuals, industry, APEGA, and government. The first author was engaged by APEGA to develop the survey and analyze the results. The survey questionnaire contained closed- and open-ended questions and was published in The PEGG and on the website in October 2007. A total of 1077 completed surveys were received and 12 respondents emailed or mailed in additional comments.

There are two reasons in this paragraph why there's no need to go further:

1) Taylor's claims can be dismissed just on the very basis that the results from this survey were not random; there is absolutely no way to account for non-response bias.  This is a huge failing from an opinion polling POV – you cannot be certain that you have a representative sample if you have a fully open survey, because it may very well be that those who have one viewpoint are much more vocal about it than those that have a different viewpoint.  Perceived threat to status quo, perceived importance, perceived self-interest, etc.: each of these can influence whether a person will respond to a survey, and can all be influenced by ideology.

In defense of the study, the survey methodology may not be very relevant for their purposes.  If they want to do a psychological analysis of sorts on each of the subpopulations, then so long as they have enough from each group to generalize to the subgroups as well (not quite guaranteed by the open survey format, still), they can probably do their analysis.  It's like me wanting to find out how the Westboro Baptist Church members frame religious questions; they're a very small minority, but I don't need to interview them as a proportional subset of a much larger group of people.

2) This survey was conducted only on a very narrow sub-population of professionals, members of the Association of Professional Engineers and Geoscientists of Alberta. This group very likely has a negligible number of climate scientists in its membership, and is very disproportionately populated by scientists that work with one of the most active anti-climate-science industries on the planet, the fossil fuel industry.

We can see from the responses from all of the sub-groups too that these people are not experts in matters of climate science:

"Absolutely! 1000%. [The Kyoto Protocol] is the only effective way to curb pollutions[...]"

"If you think about it, global warming is what brought us out of the Ice Age."

"It is a mistake to think that human activity can change this… It would be like an ant in a bowling ball who thinks it can have a significant influence the roll of the ball."

Quoting the paper: "They are most likely to speak against climate science as being science fiction, ‘manipulated and fraudulent’. They are least likely to believe that the scientific debate is settled, that IPCC modeling is accurate, and oppose all regulation ‘based on the incorrect assumption that greenhouse gases cause climate change’."

"This present hysteria on 'global warming' is purely political and has little to do with real science."

"Kyoto is simply designed to transfer large sums of money from the wallets of citizens of mostly Caucasian countries to the Swiss bank accounts of third world dictators."

"This is obviously a left wing/liberal survey… You folks were probably calling out the sky is falling when Ozone was the latest left wing craze [this was a real issue BTW]… The earth ‘weather’ has always been changing. Now you want to blame me and my gas furnace, big house, two cars, etc. Well get over it."

"It is only reasonable to assume that we are changing our environment and climate, all you have to do is look out your window to see it."

 These aren't statements from people who are climate experts. These are the statements of non-experts, or ideologues, or both.

If James Taylor wants to tout around the views of non-experts as evidence that global warming is not real, then by all means he may dig his grave (maybe he can join Rush Limbaugh, who also recently saw it fit to reward a 13-year-old caller for his library "research" demonstrating that global warming is a scam; the kid, of course, did not give any of this evidence he supposedly found while he was on the line).  We'll still hold on to actual peer-reviewed opinion polling of actual experts, such as Doran et al 2009 and Anderegg et al 2010, or maybe even take in mind analysis done on papers from the Web of Science by James Powell.  For those that are not so fecklessly reckless as Taylor is though, be sure to learn from his mistakes. I would personally recommend, for starters, reading the sources you cite.

Pat Michaels Misleads his Readers on IPCC Draft

As a skeptic, one of the more important goals to me in our society is to make sure that pseudoscience and scientific falsehoods are adequately responded to and shut down.  Evolution and cosmogeny are the more commonly known ones in the atheist/free-thought community, because of the very strong creationist push against them, the very strong push to legislate intelligent design into our schools.  For me, even more important, and I lament less popularly told, is accurate science on climate change.

Forbes has taken upon itself to do just the opposite of educating its readers.  The outlet published about a "story" (written by Pat Michaels) regarding the leaked IPCC AR5 second draft, a story started at WattsUpWithThat? (I will not link to that website) claiming that Figure 1.4 of the draft (below) shows that the models from the IPCC have overestimated the warming that we have actually observed.

(Figure 1.4 from IPCC AR5, second draft)

The different colored bars are the IPCC's First Assessment Report (FAR, 1990), Second Assessment Report (SAR, 1995), Third Assessment Report (TAR, 2001), and Fourth Assessment Report (AR4, 2007).  Each report used climate models of different complexity (generally increasing in time, as computing power is wont to do) and a given input scenario to predict temperature increase based on the current physical understanding of the Earth's climate.  AR4, at least, 'hindcasted' the first decade or so using real greenhouse gas/solar/volcanic data (etc.), and the true 'projection' starts in 2000.

In this graph, each projection was shifted to have the same value in 1990.  We can see that the observations since 1990 (more specifically, since mid-2000s) appear to have gone below the projections from each scenario collection - indeed, why?

The uncritical, like Pat Michaels, say that it's because the models are wrong.  Michaels also thinks that the IPCC will remove this Figure, because apparently there was some change made during AR4 to a draft report Figure that he didn't like.

What happened in the drafting of AR4, we probably won't know.  Michaels probably won't either, since he didn't appear to really do much research into the matter.  This pattern also continues into AR5.  We have already been shown, for instance, that the models do match the observations (such as here, here, and here).  We already do know, for instance, that ocean heat content (a much BIGGER number than atmospheric heat content) continues to rise unabated.

(Ocean heat content data from Levitus et al. (2012))

So, that should leave us wondering, what is up with Figure 1.4 from AR5?  Well, maybe we should actually look at the Figure in context.  The leaked draft is available online and to maintain at least a bit of dignity I won't link to it, but if you want to find it you probably can.  For starters, the caption reads:

"Figure 1.4: [PLACEHOLDER FOR FINAL DRAFT: Observational datasets will be updated as soon as they become  available] Estimated changes in the observed globally and annually averaged surface temperature (in °C) since 1990 compared with the range of projections from the previous IPCC assessments. Values are aligned to match the average observed value at 1990. Observed global annual temperature change, relative to 1961–1990, is shown as black squares  (NASA (updated from Hansen et al., 2010; data available at http://data.giss.nasa.gov/gistemp/); NOAA (updated from Smith et al., 2008; data available at http://www.ncdc.noaa.gov/cmb-faq/anomalies.html#grid); and the UK Hadley Centre (Morice et al., 2012; data available at http://www.metoffice.gov.uk/hadobs/hadcrut4/) reanalyses). Whiskers indicate the 90% uncertainty range of the Morice et al. (2012) dataset from measurement and sampling, bias and coverage (see Appendix for methods). The coloured shading shows the projected range of global annual mean near surface temperature change from 1990 to 2015 for models used in FAR (Scenario D and business-as-usual), SAR (IS92c/1.5 and IS92e/4.5), TAR (full range of TAR Figure 9.13(b) based on the GFDL_R15_a and DOE PCM parameter settings), and AR4 (A1B and A1T). The 90% uncertainty estimate due to observational uncertainty and internal variability based on the HadCRUT4 temperature data for 1951-1980 is depicted by the grey shading. Moreover, the publication years of the assessment reports and the scenario design are shown."

This actually isn't that interesting for the discussion, but we get some more details on how the Figure was made and some basic context behind it.  This description is available with the Figure, but the Figure was added to the end of the draft: the draft does not place each Figure where it goes in the report, but has them collected at the end of the PDF.  We need to go a level deeper, straight to the source of the discussion on this Figure, Chapter 1.3.1.  The section has this to say about the Figure (my emphasis):

"Even though the projections from the models were never intended to be predictions over such a short time scale, the observations through 2010 generally fall well within the projections made in all of the past assessments. Note that before TAR the climate models did not include natural forcing, and even in AR4 some models did not have volcanic and solar forcing, and some also did not have aerosols. The projections are all scaled to give the same value for 1990. The scenarios considered for the projections from the earlier reports (FAR, SAR) had a much simpler basis than the SRES scenarios used in the later assessments. In addition, the scenarios were designed to span a broad range of plausible futures, but are not aimed at predicting the most likely outcome. There are several additional points to consider about Figure 1.4: (1) the model projections account for different emissions scenarios but do not fully account for natural variability; (2) the AR4 results for 1990–2000 account for the Mt. Pinatubo volcanic eruption, while the earlier assessments do not; (3) the TAR and AR4 results are based on MAGICC, a simple climate model that attempts to represent the results from more complex models, rather than the actual results from the full three-dimensional climate models; and (4) the bars on the side represent the range of results for the scenarios at the end of the time period and are not error bars. The AR4 model results that include effects of the 1991 Mt. Pinatubo eruption agree better with the observed temperatures than the previous assessments that did not include those effects. Analyses by Rahmstorf et al.(2012; submitted) show that accounting for ENSO events and solar cycle changes would enhance the comparison with the AR4 and earlier projections. In summary, the globally-averaged surface temperatures are well within the uncertainty range of all previous IPCC projections, and generally are in the middle of the scenario ranges. However, natural variability is likely the dominating effect in evaluating these early times in the scenario evaluations as noted by Hawkins and Sutton (2009)."

We see no discussion in Michaels' article about this section, and the reason is clear: it undermines his message.

The scenarios for each model are predictions of what CO2 will be, what aerosols will be (though only some models could handle that as it said), what other greenhouse gases will be, what sun activity may be, so on.  They have nothing to do with the models.  If the input is incorrect, then the output will be incorrect too.  It does not tell you if the model is wrong, it tells you that your scenario is wrong.  The hindcast for the AR4 models matches observations quite nicely, and that should indicate to us at least that the models do a pretty good job of taking accurate input and giving you the Earth's temperature, because they're based on our physical understanding of the Earth's climate.

What the section tells us is that the scenarios did not properly account for natural variability, such as ENSO (El Nino - Southern Oscillation), solar activity, and aerosol radiative forcing.  We do know that these played a large role in the last decade:

• 1998 was a very strong El Nino year, while 2011 and 2012 were La Nina years (El Nino causes surface warming, La Nina causes surface cooling);
• there was a prolonged solar minimum during 2008/2009, so again there is a cooling bias on the end of the time series;
• aerosol pollution (aerosols reflect and scatter incoming sunlight, so they cool the planet) somewhat increased over the past couple years, likely due to China's booming economy, which thrives off of dirty burning of coal.

Kauffman et al. (2011) helps to explain this in more detail.

The scenarios don't include natural variation much, so when we actually do take natural variability into account and remove it from the observations, as Rahmstorf et al. (2012) do, how do the observations look compared to the climate model runs?  Well:

(Figure 1 from Rahmstorf et al. (2012))

Would you imagine that.

Now one thing that Michaels might be right about is that the IPCC could indeed change this graphic before the final draft is released, and it's clear why: people like Michaels are adamant on taking it out of context and lying about it.  But it wouldn't be because Michaels was ever right about, well, anything.

This blog post will herald in my time as an author for the blog, and foreshadow the topic of many of my posts, which will be bringing into the spotlight the pseudoscience surrounding climate change "skepticism."