*Low ECS doubles the cost:benefit shortfall*

**Guest essay by Barry Brill**

Topher Fields’ excellent documentary video http://topher.com.au/50-to-1-video-project/ explains that the overall costs of any global effort to reduce greenhouse gas emissions will be at least 50 times greater than its overall benefits.

But that was based on the UNIPCC’s 2007 report (AR4). Now that the 2013 summary report (AR5) has been leaked, we can see that Topher was much too generous. At the new revised rate of future warming, the assumed benefits will be sliced in half.

Since January 2012, no less than 19 scientific papers http://tinyurl.com/kjxs4kt have been published on the crucial question of climate sensitivity: ie how much warming would result from doubling the volumes of greenhouse gases in the atmosphere? The latest draft of the AR5 summary tip-toes around this subject, but effectively recognises (in convoluted words and figures) that ‘equilibrium’ sensitivity (ECS) is probably around 2°C – about 33% less than the four previous reports had assumed.

But this doesn’t mean that future warming will reduce by only one-third!

**Let’s make the following over-generous assumptions:**

- The ECS is immediately reflected in global average surface temperatures;
- The IPCC models are valid in all other respects (except ECS);
- The greenhouse effect is arithmetic rather than logarithmic;
- The atmospheric concentration of CO2e will reach 560ppm in 70 years;
- The discount rate for climate issues is way below any other investment rate.

The CMIP5 ensemble of models currently projects temperatures at 3°C above 1850 levels by 2085. According to NOAA (the median of the three surface datasets) we have already experienced 1.024 ±0.128°C over the last 160 years. So the official prediction is that temperatures will increase by a further 1.876°C over the next 70 years.

If those CMIP5 models were re-programmed with the updated ECS, the 2088 projection would reduce by one-third to 2°C. From this we deduct the 1.024°C already in the system, so the projected warming for the next 70 years falls to 0.976°C .

This is LESS THAN HALF the warming the IPCC was previously expecting – a very dramatic reduction.

The updated projection suggests that the warming trend will be almost exactly the same as it has been over the past 100 years. During that period, there was no acceleration at all in the rise of sea levels, the retreat of glaciers or sea ice, the incidence of malaria, or the frequency of hurricanes or droughts.

In fact, it was an ‘optimum‘ temperature period. CO2 contributed to the ‘green revolution’, poverty levels and child mortality were decimated, while indicators like life expectancy and literacy boomed. Death rates from extreme weather have declined by 98% since 1920.

Then there is another reason why 50:1 might be a major over-estimate.

The current 16-year temperature standstill suggests that the climate optimum era may now be over. If so, and the world undertakes a crash programme to reduce greenhouse gases, we will presumably produce a cooling effect through the 21st century. Would that give rise to any benefits at all? Or would we be cutting our own throats?

Perhaps the AR5 report of WG3 (due March 2014) will address this scenario. The IPCC says it considers all possible futures without assigning probabilities to any one.

Now, let’s revert to those heroic assumptions we laid out above:

1. The ECS is the theoretical temperature response which continues long after emissions occur – hundreds of years into the future. The short-term impact of greenhouse doubling (Transient Climate Response) is only about 1.2°C – 40% less than the ECS.

2. The CIMP5 and CIMP3 models have actually been wrong by about 100% over the past 20 years. The ECS is certainly not the only error.

3. The greenhouse effect is logarithmic, so (at 400ppm) we have already experienced more than half of the doubling effects.

4. The IPCC scenarios ignore technology change, the shale gas boom, etc and are long out of date.

5. The 50:1 project is conservatively based on the Stern report which opined that climate mitigation was uniquely different to investments in healthcare, education, disease and poverty eradication, climate adaptation, etc. This credo is based on an obscure moral philosophy which few economists can even follow let alone subscribe to.

Finally, the largest impact factor in all the economic models is the speed of temperature change, not just the amount. The AR4 results suggested a rate of change so fast as to exclude most opportunities for species (including humans) to adapt. With the long standstill and the new low sensitivity, this issue is now comfortably overcome.

So, if we were to apply updated science and normal economics to a cost:benefit study, the 50:1 ratio could easily blow out to 500:1.

Still not high enough. Any number divided by zero is infinity.

You can’t manage, what you cannot measure. Since we cannot measure the effects of carbon dioxide – any attempt to manage it will be fraught with managerial inefficiencies (on top of those present from having governments and the international community involved). This drag should be accounted for with at a least a 10% penalty, with a 110% penalty being possible.

No, any number divided by zero is indeterminant (or label it “/0”). However, any number (ANY number) divided by infinity is zero.

Think of it this way–zero has no sign; it is neither positive or negative. Let’s just say zero has no value, so division by zero isn’t within the realm of possibility.

“According to NOAA (the median of the three surface datasets) we have already experienced 1.024 ±0.128°C over the last 160 years.”

So how much worse/dangerous/weirded is our climate now than 160 years ago? Is worse/dangerous/weirded a logarithmic, linear or exponential quantity. Or based on the last 160 years is it zero, zilch, nought, nothing, unnoticeable?

Normally, if one had a model of a physical process that was wrong by 200%, one would hardly publicise it. One would go back to one’s desk and start thinking.

No, Beng is correct.

“Any number divided by zero is infinity.”

It’s zero divided by zero that is undeterminated.

I am afraid the first poster is wrong. The actual “benefits” of reduced “greenhouse” gases is less greenhouse–less plants. That means the loss of feed for endangered species, more hungry humans rioting as in the Arab Spring, increased risk of nuclear war, and so on.

Having examined the paleontology proxies of carbon dioxide and temperature, there appears to be zero correlation. Thus all the hullabaloo will not affect temperatures–not via Carbon dioxide anyway. But tolerating the nonsense could lead to other actions that would reduce temperatures. And that is not something to be so flippant about (except as in my fave band Minnesotans 4 Global Warming). Twelve degrees C or 54 degrees Fahrenheit is colder than optimum, not a fever. Further reducing temperature would lead to a loss of human life per the research of Indur Goklani, and would also harm the general biosphere, perhaps severely.

It is time to wake up and get serious about this thing.

“It’s zero divided by zero that is undeterminated.”

So, if say, Zero came down on both sides of an issue… No wonder our foreign policy is so chaotic!

And then I see in The Times that Imperial College is festering Lysenkoism: http://www.thetimes.co.uk/tto/environment/article3871902.ece

Jean Meeus says:

September 18, 2013 at 9:27 am

No, Beng is correct.

“Any number divided by zero is infinity.”

It’s zero divided by zero that is undeterminated.

———————-

My head hurts now.

I’m not a scientist so I don’t know the right answers but I doubt many of the people that call themselves

“scientist”have actually done all of the experiments and reading toeither. They’re just taking another’s word for it.knowthe right answersWhat I don’t like is “the only solution” to end global warming.

I think it is extremely

and we’re being conned.stupidHow does anyone believe making Wall Street investment bankers richer will reduce the earth’s temperature? They want to create hedge funds and securities with carbon credits. How does that help “the cause”?

How can giving the world’s governments a new uncontrollable tax and a blank check to piss away our children’s future finances stop CAGW?

Why stop the poorest among us from having a safe and sanitary home?

The benefits of CO2 are obvious and there are some people who would deny the poor a chance.

Why?

ollowFheToney.Mcn

And here I thought that any number divided by itself is 1.

From RockyRoad on September 18, 2013 at 9:20 am:

Hey, I declared this variable as a signed integer, so I don’t care if its current value is zero,

it has a sign.Isn’t dividing by zero an oxymoron?

To divide by zero is to not divide at all.

Or is dividing by zero equal to one?

When you get done dividing you still have the whole.

Huh?

Math’s hard.

No wonder some people make up their answers.

cn

The expression X/(delta Y) approaches the limit of infinity with the sign of X as delta Y approaches 0. When delta Y is zero, the function becomes a singularity which has no defined magnitude. Infinity is not a destination it is only a process. The process is no matter how large the value, a finite quantity can be added to that value -> repeat without end.

Lady Life Grows says: @ September 18, 2013 at 9:31 am …

AGREED

If you look at the last 450Kyr graph we are near the upper bounds of temperature. On the other hand the temperature could fall quite drastically. Worse it is not necessarily gradual as was originally thought.

If you want to be a worrywart about climate this is the more logical problem to aim money at especially since the geologists are still fighting over whether or not the Holocene will soon end or go for the length of a double precession. Either way significant warming just isn’t in the cards while long term cooling is.

Infinity is a poorly defined concept, don’t try to invoke it until you can write out what it means in a logical manner. But keep in mind that infinity-infinity=0 and also infinity-infinity=infinity (the set of all numbers minus the set of even numbers would still be an infinite set).

The problem is not that the ratio is 100:1 vs 100:0, the problem is that it is more likely 100:-10. That is not only would there be an enormous cost to reducing CO2 emissions, but there would also be harm in decreased photosynthesis, less vegetative cover, and increased runoff.

I like to think of Al Gore as a “Managerial Ineficiency”! Thanks jean..

Division by zero is

undefined. Here’s why.As you divide any positive real number by smaller and smaller positive real numbers, the result is larger and larger positive real numbers. It looks like if you divided by zero then the result would be positive infinity. Same for negative real numbers divided by negative real numbers.

But as you divide any negative real number by smaller and smaller positive real numbers, the result is larger and larger negative real numbers. It looks like if you divided by zero you’d get negative infinity. Same for positive real numbers divided by negative real numbers.

From the one direction, goes to positive infinity. From the other, goes to negative infinity. So what do you have at the center when you’re dividing by zero?

Our math cannot account for it, there is no explanation, no definition. We don’t know. It is undefined.

“Infinite” is not appropriate as they cannot spend an infinite amount of money on the fake problem – even though it seems like they are.

“And here I thought that any number divided by itself is 1.”

Yes, except when that number is zero.

It is easy to show why zero divided by zero is indeterminate.

Let A/B = C. Then C times B is equal to A.

Now, what is the value of 0/0?

Is it 2? Yes, because 2*0 =0.

Is it 5? Yes, because 5*0 =0.

Is it 239? Yes, because 239*0 = 0.

Therefore 0/0 is indeterminate.

From Jean Meeus on September 18, 2013 at 10:52 am:

Depends. Are you using an Intel CPU?

[“The ECS is the theoretical temperature response which continues long after emissions occur – hundreds of years into the future. The short-term impact of greenhouse doubling (Transient Climate Response) is only about 1.2°C – 40% less than the ECS.”]Is there some subtle humour going on here that I’m missing? Is the author implying that TCS actually exists any more than the ECS exists? The ECS is a theoretical construct (as stated by the author) and, therefore,

so is the TCS. Unless anyone has some evidence that the 1.2C figure is correct! Any such figure assumes that all of the warming since 1850 is due to an increase in radiative gasses. No evidence exists to support this assumption.Any discussion about Climate Sensitivity (of any sort) is purely hypothetical.

kadaka (KD Knoebel) says:

September 18, 2013 at 10:51 am

Now, as to calling division by zero “undefined”, that’s more accurate than my definition of “indeterminate”, so KD is correct. For most mathematicians, 0 divided by 0 is indeterminate. For a list if indeterminate forms involving zero, 1 and infinity in arithmetic operations, please see the following:

http://en.wikipedia.org/wiki/Indeterminate_form

For another example of zero in measuring time, consider the example of noon and midnight:

Is the thing we call “midnight” 12:00 am or 12:00 pm? Conversely, is the thing we call “noon” 12:00 am or 12:00 pm?

The answer: None of the above. Noon is noon and midnight is midnight (there is no “time” measured at either point so the correct definition is to call them noon and midnight, respectively). It is technically inaccurate to attach an “am” or “pm” to the two (but many of us do, unfortunately).

Those of us who are critical thinkers need to put these greens on the run. At present they claim to own the scientific truth and the rest of us are skeptics and deniers. The tables need to be turned.

Infinity:1 would apply if CO2 reduction as a goal in itself had zero net benefit. Causing less of that prime nutrient for plants, though, has substantial net harm. So it is worse than zero net benefit.

If non-combustion power really someday became cheaper than natural gas from fracking, it would succeed in the marketplace, and that is fine. But, for example, underground CO2 sequesterization is the height of folly.

“

If those CMIP5 models were re-programmed with the updated ECS, the 2088 projection would reduce by one-third to 2°C. From this we deduct the 1.024°C already in the system, so the projected warming for the next 70 years falls to 0.976°C.”I realize, of course, that this article in general is showing what would be so even if pretending various activist claims were true, as an argumentative strategy and illustration. With that said, there is no room for 1.024 degrees Celsius warming (or a “TCS” figure 60% of that either) in the past 160 years being the net effect of human emissions, because the post-LIA temperature recovery is already so much explained by natural influences as to leave no high percentage of it allocatable to humans, as http://img176.imagevenue.com/img.php?image=81829_expanded_overview_122_424lo.jpg illustrates. While corresponding to a beneficial future temperature change if not for being imaginary, even the lesser projected warming figure is still too much.

“

The CIMP5 and CIMP3 models have actually been wrong by about 100% over the past 20 years. The ECS is certainly not the only error.”Well said.

Let’s assume: “The greenhouse effect is arithmetic rather than logarithmic;”

That is an unusal “assumption” , where did that come from.

A lot of the reasons that cutting emmisions will not make any difference is because the effect is near saturation and it will take one hell of a change to move it either way.

Cutting emmisions by 10% or even 20% (which would be painful) will make no discernable effect.

Side discussion.

In the “standard model” of the real numbers, there is no such thing as division by 0. Dividing a / b *means* multiplying a by b’s reciprocal, a * b^-1. Since 0 does not have a reciprocal, a / 0 is not defined right out of the gate. In arithmetic, any attempt to divide by 0 is simply wrong.

A separate question concerns limits. For example, what is the limit as x –> 0 of, say, x / x? That limit happens to have the “form” 0/0. But a form is not a value. The value of the forgoing limit happens to be 1; other limits with the form 0 / 0 take other values. Hence, the form (not value) of 0 / 0 is the “indeterminate form.” We don’t know the value of the limit until we appeal to a theorem such as the Alias Theorem or to L’Hopital’s Rule.

And again, we could consider lim x–> 0 1/x^2. That “form” is 1/0, and the limit itself is written as +oo. But +oo is not a value or a real number. It is only a short-hand for this statement:

for any positive number M, we can find a deleted neighborhood of 0 such that f(x) = 1/x^2 > M for all x in that neighborhood.Since we don’t like saying that mouthful frequently, we instead say that the limit is +oo as shorthand language.

The downside of shorthand language is confusion. Some end up believing things like “1 / 0 = +oo”, which is false, or “0 / 0 is indeterminate”, which is again false (confusing form with value). The notion of infinity applies only to limits, not to arithmetic.

Again: these comments apply to the standard model of the reals. Complex analysis takes a different stance, in which the point “oo” has a meaning (but no sign).

Further reading: http://en.wikipedia.org/wiki/Indeterminate_form

Jean Meeus says:

September 18, 2013 at 9:27 am

No, Beng is correct.

“Any number divided by zero is infinity.”

It’s zero divided by zero that is undeterminated.

+++++++++++++++++++++++++++++++++++++++++

any number divided by itself = 1

0 is a number.

There for 0/0 = 1

😛

MattS says:

any number divided by itself = 1

0 is a number.

There for 0/0 = 1

😛

Ah, but 0 is not a number, it’s a conceptual placeholder.

Zero is a politician. From Chicago.

We are already half-way to doubling in terms of CO2 or the full “All Forcing” measure.

The negative impacts of the effects so far have been … well there are no real negatives so far. Only positive impacts have been experienced.

– Plants are growing more efficiently,

– the decline of sea ice has made life more tolerable in the summer in the Arctic and opened it up to whatever we need to do there,

– it is a tiny bit warmer in cold northern latitudes.

Other than that, nothing else has really happened at all. Nothing worth mentioning.

And that is the half-way impact.

kadaka (KD Knoebel) says:September 18, 2013 at 11:06 am

From Jean Meeus on September 18, 2013 at 10:52 am:Now, what is the value of 0/0?

Depends. Are you using an Intel CPU?As a geek, I truly understand that reference!!!! ROFLMAO!! So true.

Don’t get me started on random number generation ……..

Bill Illis;

Indeed.

Attempts to stop or reverse the current warming, such as it is, are either suicidal or murderous. Or both.

RC Saumarez says:

September 18, 2013 at 9:26 am

Normally, if one had a model of a physical process that was wrong by 200%, one would hardly publicise it.

======

Truly, the quality of cliamte science is worse than we thought.

today with much less famine than we did with 3 billion people 50 years ago. we have more people living longer than at any time in history.

the problem is that the super gluttons at the top, the Al Gores of the world, they don’t want to share. they want the rest of us to cut back so they can have more. whatever they say we should use less of, they want to more of.

they want us to only have a sliver of pie, so they can have a huge piece. they want us to have 1 kid so they can have 4. they want us to live in small apartments so they can live in big houses. they want us to move away from the waterfront so they can live there in luxury. they want us to stop burning fossil fuels so they can burn more. they want us to pay taxes so they won’t have to.

mostly, they want the poor to stay poor, because if everyone was rich, they would be just like everyone else.

In AR5, the IPCC lowers the numerical value that it assigns to the equilibrium climate sensitivity (TECS). From the premise that TECS is a meaningful concept, Mr. Brill concludes that the benefit/cost ratio from curbs on CO2 emissions is reduced by a factor of 2. However, TECS is not a meaningful concept.

Supposedly, TECS is the proportionality constant in a functional relation that maps the change in the logarithm of the CO2 concentration (LOTCO2C) to the change in the global surface air temperature at equilibrium (GSATAE). However, the change in the LOTCO2C provides a policy maker with no information about the change in the GSATAE, for “information” is the measure of a relationship between observables but the GSATAE is not an observable.

Terry Oldberg says:

September 18, 2013 at 9:20 pm

——————————————————-

Stoppit Terry, you’re beginning to sound like Mr Logic from Viz:

http://davoe.deviantart.com/art/Viz-Comic-My-top-5-characters-267747647

Isn’t it an easier message that that the climate frauds, liars and charlatans are frauds, liars and charlatans ?? Why bother trying to quantify it.

Bring it on climate frauds, liars and charlatans. I’m here.

philincalifornia:

In adhering to logic, my aim not quantification but rather proof. It can be proved in a court of law that belief in man made global warming is a consequence from a deceptive argument on the part of climatologists. I present this proof in the article at http://wmbriggs.com/blog/?p=7923 . Convictions for fraud would additionally require evidence that this argument was made for the purpose of taking money, e.g. from taxpayers for support of these climatologists.

To paraphrase the article, when a term changes meaning in the midst of an argument, this argument is an example of an “equivocation.” By logical rule, a proper conclusion may not be drawn from an equivocation. To draw an IMPROPER conclusion is the equivocation fallacy. The conclusions of the warmists are examples of equivocation fallacies and are logically invalid.

Many people have been duped by uses of the equivocation fallacy on the part of warmists. Among them are the majority of skeptics. In making their arguments, these skeptics routinely draw improper conclusions from equivocations thus being guilty of the equivocation fallacy. As one of the few people who understand what is going on I have the dreary job of pointing out their error to them.

Greg says:

September 18, 2013 at 12:51 pm

Let’s assume: “The greenhouse effect is arithmetic rather than logarithmic;”

That is an unusal “assumption” , where did that come from.

===

Still no answer on that one from Barry Brill.

I have not worked out what effect this would have on his calculations because it seems to rediculous an assumption that I did not read the rest.

CO2 is logarithmic , that is the whole reason that cutting emissions is so pointless, why “assume” otherwise.

Greg

The object of the assumptions (none of which is true, this being climate science) is to simplify the calculation of ECS warming that has not been experienced already.

As atmospheric concentration of CO2e has increased from a pre-industrial level of 270ppm to 400ppm this year, approximately half of the predicted 2085 doubling has already occurred. But the greenhouse effect being logarithmic, much more than half (more like 75% as I understand it) of the consequent temperature forcing is already “in the can”.

But logarithms, TCR, modeling errors, SRES and discount rates are complicated. So I assumed them all away in the first instance to get directly to the effects of reducing ECS by one-third. Then, the article returns to the assumptions to observe that their combined effect could blow out the ratio by a whole lot more than the ECS change.

Wow, never thought my off-the-cuff reply would elicit responses…

As someone noted, reducing CO2 is actually

bad. In the long-term future when fossil fuels have dwindled, I surmise we may need to do something else to maintain/increase CO2 for the sake of crop-production — like mining and “cooking” limestone.