Gravity, the Greenhouse Effect and Surface Temperature

When Eli last left the bunnies, he was pointing out how gravity explains much of the greenhouse effect, well, except for the part that you need some things in the atmosphere that absorb IR radiation from the surface.

The first is the lapse rate, the decline of temperature with altitude in the troposphere.  There are plenty of detailed derivations of the dry lapse rate on the net and a bunny can even throw in some water vapor, but the basic principle is that the atmosphere is for all thermodynamic purposes an ideal gas, and the temperature decreases with pressure, and pressure decreases with altitude because of gravity. 

The second is the decrease in density with altitude, again because pressure decreases with altitude because of gravity.  The higher you go the less stuff 

Both of these effects explain why radiative energy transfer from the ground to space slows, the higher greenhouse gas concentrations are.  

In a shortly following post the Rabett quoted pretty much the same from J.S. Sawyer, written in 1972

The chief effect of increasing carbon dioxide is that the gas which is radiating heat to space is found at a higher level in the atmosphere than before - the radiation from lower down in the atmosphere is absorbed by the extra carbon dioxide above and then reradiated to space.  In the troposphere, at least, temperature decreases with height so the effective radiating temperature of the carbon dioxide becomes lower if the amount of the gas is increased and therefore less heat is radiated to space.  Thus the additional carbon dioxide tends to act as a blanket which keeps the Earth warmer - the Earth has to get rid of the incoming radiation from the Sun, and the same amount can only be removed if the temperature of the atmosphere rises a little.

But, to be honest there was some handwaving there, namely the mechanism for heating the surface when the radiating layer moved up.  Ferren in a comment provided the link.  As shown in the figure, when the radiating level moves up because the CO2 mixing ratio increases, since the lapse rate (the slope) stays constant, the surface temperature increases and, of course, the reason the lapse rate stays constant is that it is fixed by gravity.


Anybunny who wants to deny that the greenhouse effect exists or that increasing greenhouse gas concentrations will not warm the surface is denying the law of gravity, which is pretty basic.  Given that humidity increases with temperature, they are also going to have to deny a fair bit of thermodynamics to claim that the concentration of water vapor in the atmosphere will not occur.

Maybe the Republicans will LGBTQ our health care after all

I thought after the election that Republicans' best political strategy on health care was to do what they planned on LGBTQ issues, which is (with several important exceptions) strongly condemn the Democrats for steps taken for gay rights, and then continue those steps. Examples are gays in the military, jobs protection, and gay marriage. Exceptions are in general being transphobic, and gay rights overseas. The exceptions offer some political rewards, but reversing other gains in LGBTQ rights would come at a political cost.

There was no political victory route for Republicans on healthcare, including either repeal or repeal-and-replace. It all ends in disaster for them. Now they can just grouse about Obamacare but announce we'll just have to live with it, rather than make a serious effort to do something about it over the next four years.

The next question is whether they'll actively sabotage Americans' health care in the belief it will help them politically - maybe they'll do it, but I'm not sure it'll help them.

If for some reason they actually do the right thing and work on bipartisan, incremental health care improvements, maybe they can campaign in 2018 on the basis of governance rather than emotion. Just don't hold your breath for this.

An Oldie But Goodie - J.S. Sawyer on the Greenhouse Effect and CO2

In the continuing quest to find excellent descriptions of the greenhouse effect, Eli has come across J.S. Sawyers Nature article from 1972, Man Made Carbon Dioxide and the Greenhouse Effect, which was commented on by Skeptical Science and warehoused (bunnies can read it there) by the Weasel.  Ray Pierrehumbert and David Archer included it in their climate change reader. Nevelle Nicholls wrote an appreciation of Sawyer's ground breaking work in 2007 under the title of A Warning We Ignored 35 Years Ago, unfortunately just as valid  today 45 years later.

In four pages, Sawyer summarised what was known about the role of carbon dioxide in enhancing the natural greenhouse effect leading to warming at the earth's surface, and made a remarkable 28-year prediction of the warming expected to the end of the 20th century. His prediction can now be compared with what has been observed. 

 Nicholls continues

While the IPCC (2007, ER)  assessment devotes a volume to this subject, Sawyer could only conclude, after conceding that climate variations of only a fraction of a degree can have "considerable economic importance" that "although there may be no immediate cause for alarm about the consequences of carbon dioxide in the atmosphere, there is certainly need for further study".

Perusal of the IPCC volume devoted to the impacts of climate change on natural and human systems leaves one feeling far less sanguine than Sawyer was 35 years ago.

Sawyer's description of the greenhouse effect, as well as the rest of the paper, is masterful

As carbon dioxide is one of the principal gases taking part in radiation exchange in the atmosphere and in the radiation of the Earth's heat content, a change in the content of carbon dioxide within the atmosphere is likely to influence the process.  The chief effect of increasing carbon dioxide is that the gas which is radiating heat to space is found at a higher level in the atmosphere than before - the radiation from lower down in the atmosphere is absorbed by the extra carbon dioxide above and then reradiated to space.  In the troposphere, at least, temperature decreases with height so the effective radiating temperature of the carbon dioxide becomes lower if the amount of the gas is increased and therefore less heat is radiated to space.  Thus the additional carbon dioxide tends to act as a blanket which keeps the Earth warmer - the Earth has to get rid of the incoming radiation from the Sun, and the same amount can only be removed if the temperature of the atmosphere rises a little.

He continues

An atmosphere at a higher temperature can hold more water vapour and the additional water vapour produces a similar blanketing effect to that produced by carbon dioxide.  Manabe and Wetherald calculate that an increase of 100% in the content of carbon dioxide would increase the world temperature by 1.3 C if the water content of the atmosphere remained constant, but by 2.4 C if the water vapour increased to retain the same relative humidity.  The increase of 25% of CO2, expected by the end of the century therefore corresponds to an increase of 0.6 C in world temperature, an amount somewhat greater than the climatic variations of recent centuries 

He did pretty well

The Past is Prologue to the Future - EPA Version

With Trumps, Pruitt and Co. busy dismantling EPA Eli has been showing the young bunnies postcards from the past of places like Los Angeles and their future wheresoever they are

However, this being Friday, a musical interlude is required

What's Your Jacoby Number? - 6, 35, 67, 72, 75, 180

Jeff Jacoby has exposed himself to the Skeptical Science in an article that appeared recently in the Boston Globe.  While it's not even a winner in Climate Change Denial Bingo (Trademark Tim Lambert) Eli prefers to simply call out the numbers at Skeptical Science.

Mostly the article simply repeats old nonsense, but there is one new deceptive argument typical of those like Jacoby who know nothing and whose stock in trade is bluster about everything including climate change.  For the sake of argument Eli would like to dissect that

But for the sake of argument, say there are merely 15 variables involved in predicting global climate change, and assume that climatologists have mastered each one to a near-perfect accuracy of 95 percent. What are the odds that a climate model built on a system that simple would be reliable? Less than 50/50. (Multiplying .95 by itself 15 times yields 46.3 percent.) Is it any surprise that climate-change predictions in the real world — where the complexities are exponentially greater and the exactitude of knowledge much less — have such a poor track record?

Eli will call this the Jacoby birthday argument for it's vague relation to the old proposition of how many people do you have to have in a room to get good odds that they have the same birthday.  As everybunny knows you figure this by taking the probability that two people don't have the same birthday, eg. that the second persons birthday is one of the other 364 days and then continuing so the probability is 364/365 x 363/365 x 362/365 etc. and you find that with 23 people it's even odds that two have the same happy day.

When Ms. Not Mr. Bluster says that she knows the value of a parameter to an accuracy of 95%, what she means is that she has evidence that the actual value lies within some range of her estimate of the most likely value.  The most likely value and the range can be set by theory, by observation, by observation, by experience, aka expertise or some combination of the three.

Since at least for climate models the uncertainty in the parameters is two sided, e.g. each parameter estimate is as likely to be too small and too large.  So if you have 15 parameters that you multiply together odds are some will be a little too large and some a little too small, and in the end the result will average out to be just right (or close).

Best sets of parameters can also be inferred from comparison with observations. Climate modelers can create an ensemble of results by systematically or randomly varying the parameters of their model, observing the variation in their results and comparing with observation.

There is even a way out of the one Earth problem, ie that there is only one set of observations which is discussed in Numerical Recipes pp689  Confidence Limits on Estimated Model Parameters describing how uncertainties in parameters can be deduced as well as the best fit parameters.

Top 5 ENSO climate bet - in progress

I'm working on a new climate bet offer - that for 2017 or for a subsequent year that someone would like to bet with me, that year will be in the record top five years for the type of ENSO year that the particular year ends up being, whether it's El Niño, La Niña, or a moderate year. Quickly perusing the temp record suggests it would be a fairly safe (but not guaranteed) bet although I haven't really analyzed it.

I think it could in some modest way help focus attention on comparing apples to apples rather than stupid finger-pointing at La Niña years being colder than El Niños. Showing almost every year is in the top five is usefully alarming, too.

Haven't quite worked out the details, especially the best data set. Suggestions are welcome, and credible betting opponents are even more welcome.

Why We Will March for Science in April

We will march for what we love, the thrill of discovery, the joy of understanding, and the benefits for all.

Another One of the Problems with Judith Curry

 Innocently working through the daily twitter load Eli came upon a middle low German trickster pushing a line that had been snipped out of the IPCC AR5, and an answer by a high flyer

.@eulenspigel The Arctic is substantially warmer than in the 1930s, accompanied by substantial reductions in sea ice cover. pic.twitter.com/e5iVEtlXzH

— icarus62 (@icarus62) March 6, 2017

Followed by a subtweet (eg dragging the innocent in without telling them), so Eli dragged the innocent in while telling him.

@eulenspigel @icarus62 Why are you subtweeting @StottPeter

— eli rabett (@EthonRaptor) March 6, 2017

the innocent being Peter Stott.

As it turns out Gavin had been doing his assigned reading and provided part of the answer as to where this came from

@EthonRaptor @StottPeter @icarus62 https://t.co/gMdGS6qo8k

— Gavin Schmidt (@ClimateOfGavin) March 6, 2017

pointing to a recent post by Tamino, a handsome prince lost in a distant land, pursuing a serpent (played by Judith Curry) using time series analysis to save himself, in which the handsome prince speculates about how the serpent found this quote

Here’s what I believe happened: Judith Curry combed through the IPCC AR5 looking for stuff she could use to contradict the stronger statement of confidence in dangerous global warming which the report makes explicit. I further believe that she paid little or no attention to stuff which would support the stronger statement in AR5. The seeming inconsistency between Arctic temperature (just as hot in the 1930s as now) and Arctic sea ice (nowhere near as low in the 1930s as now) is one of those things she was looking for. 

 and engages in analysis of what the data says concluding that

I’ve studied the data. Not only does it fail to support the claim about 1930s Arctic temperatures, it actually contradicts that claim. By a wide margin. It ain’t even close. 

There’s something even more important to think about. Judith Curry combed through the IPCC AR5 looking for stuff that would cast doubt. One of the things she found, which she even included in her written testimony to a U.S. Senate committe, turns out not to cast doubt. If I were being hyperbolic I would say “To find evidence against AGW in the IPCC report, it looks like you have to quote stuff that they got wrong — ’cause the stuff they got right is evidence for AGW.” But that would indeed be hyperbole. 

What’s not hyperbole is how it looks to me: that Judith Curry cannot have studied the available data to draw that conclusion because the available data contradict it, that Judith Curry cannot have studied the supporting references because they don’t support it, and that if she believes it “because the IPCC report says so” then it’s obvious she’ll take the IPCC report’s word for what she wants to believe but not for what she doesn’t want to believe.

Where upon Peter Stott appears on Twitter to lay this one to rest

@ClimateOfGavin @EthonRaptor @icarus62 (1) This was a single sentence in section discussing Arctic sea ice decline which referred to temps without citation not ideal but note also

— Peter Stott (@StottPeter) March 6, 2017

@ClimateOfGavin @EthonRaptor @icarus62 (2) that lower in section contrasts Arctic wide increases of temperature in last decade with episodic regional increases in early 20th c

— Peter Stott (@StottPeter) March 6, 2017

@ClimateOfGavin @EthonRaptor @icarus62 (3) point being that "Arctic temperature anomalies" is referring to temps in some parts of Arctic not necessarily Arctic wide.

— Peter Stott (@StottPeter) March 6, 2017

Showing that it pays to ask even if you are handsome prince lost in a distant land, pursuing serpents and not a fuzzy little bunny

The good politics of the carbon dividend idea

The conservative case for carbon dividends (and tax) has attracted a fair amount of attention, mostly positive. Sarah Duffy has a useful critique that I agree with in part, but I have to call out and disagree with this in particular:

There seems to also be a bit of bait-and-switch going on. This stance allows them to oppose any climate change policy that isn’t a carbon tax, supposedly because that is the most economically efficient solution. At the same time, they don’t need to worry about anyone calling their bluff and actually enacting it because they’ve hitched their horse to a policy antithetical to most Republicans: more taxes. It’s disingenuous to claim to recognize the urgency of climate change and simultaneously hold that the only acceptable solution is a carbon tax given that, as Brad Plumer recently noted, every GOP member of the House voted against such a policy only last June. So, the only climate change policy that could ever be acceptable to conservatives is a carbon tax, but all conservatives in office have already rejected the idea. Convenient, no?

Well, no, especially because this argument would've worked so well under previous political conditions and falls apart today. Let's run the tape backwards and look at prior times that a call for a carbon tax in lieu of regulations got prominence. Most recent was the runup to Clean Power Plan regulations that use complicated steps to ratchet down emissions, where some people opposed that plan as it reached fulfillment and argued for taxes instead. Prior to that was cap-and-trade legislation in Congress in 2010, another regulatory approach. Prior to that was the Supreme Court consideration in 2007 whether carbon dioxide should be considered a pollutant and regulated under the Clean Air Act.

In all those cases, arguing for a tax was (by some anyway) a disingenuous effort to stop momentum towards a regulatory solution. Duffy's argument then would've been fine, and I made a similar critique at the time.

In the current political situation, the momentum is towards a repeal of Obama's Clean Power Plan and American participation in the Paris Agreement, to be replaced with nothing. These conservatives are saying at least regarding the Clean Power Plan that you've got to replace it with something that gets the job done. The political effect is to make it more difficult to repeal CPP without replacement, the opposite of what Duffy says (and from what I've heard, the proponents are saying carbon dividend > carbon regulation > doing nothing, also contrary to her statement).

Duffy and everyone else is right that these conservative elder statesmen have limited political power today - but to the extent they're getting attention, they're doing something positive.

I agree with her other points on the limits of a carbon tax unless it's really high, but the carbon tax doesn't have to repeal all other government efforts. In particular, government subsidy of new energy research and early implementation could occur, tax subsidies could be left in place, and state regulation could continue.

Units

Before getting into the microscopic basis of temperature, a short digression on units which maybe won't be so short

The product of pressure times temperature volume has units of energy. Pressure is force per unit area and work, which has units of energy is defined as force times distance. It is easy to show that if, for example, pressure is held constant then the amount of work that is done in an expansion is P_ext (V_final - V_intiial)where the volume changes from V_initial to  V_final

  

Libre Texts has more detail if anybunny is interested

The ideal gas law states that PV = n R T where n is the number of moles R is the gas constant and T the temperature.  We have already discussed how at zero pressure (or volume) the temperature of the ideal gas would be zero, and how, since negative pressure and volume are not,  (That's not possible), the zero is absolute.  We have also mentioned how the International Temperature Scale is defined by absolute zero and the triple point of water and a bit about how a triple point uniquely defines a single temperature and pressure.  This, by the way is an answer to the problem of how to define units for those on other planets.

n is a measure of the number of molecules in the gas.  It is the number of molecules divided by Avogado's number.  What is Avogadro's number, NA, somebunny in the last row asks.  Well it's a number, 6.02 x 10²³ but more importantly it's the chemist's bridge between the lab  and the molecular scale.  Chemical reactions occur between individual molecules.  It's pretty hard to count molecules, especially if they are moving about in a gas or a liquid.

If we know the atomic mass of a molecule, then Avogadro's number of them 6.02 x 10²³, weighs the numerical value in grams.  Why grams, because when the idea first came up, everybunny was using the cgs (centimeter/gram/second) system of units, not mks (meter/kilogram/second) and not SI which is based in mks.  Also, because lab balances tend not to weigh more than a few hundred grams.

Slipped one by you there.  How do we get atomic mass.  Well, we define the mass of  carbon-12, (a carbon atom with 6 protons and 6 neutrons and 6 electrons) as 12 atomic mass units, known today as Dalton (Da).  This is a definition.  It is then possible to find the relative masses of all the other atoms relative to ¹² C.  There is something of a history of how carbon-12 was chosen as the basis of the atomic mass scale.  Wasn't always so and it was a bit of cats and dogs or chemists and physicists.

Avogadro's number of ¹² C atoms then weighs precisely 12.000000 grams.  The uncertainty is the uncertainty in Avogadro's number, which is the fundamental constant of most uncertainty.  The hunt for the next decimal places is exciting, even if scientists are easily excited if for no other reason that it will turn the kilogram into something other than a lump of platinum iridium sitting in vault in Paris enabling better communication to other planets.

Which brings us back to the ideal gas law and in particular RT.  Since PV/n has units of energy, then the units of RT must be energy per mole.  If the units of energy are Joules and the units of temperature are Kelvin, then the gas constant has units of J/K.  (added: the inportance of this is to establish a connection between temperature and energy.  The exact relationship awaits)

What remains is to establish the connection on the molecular level.  That's dangerous, because it requires statistical mechanics a well known deadly science