This is a rather complex chart, but we can quickly break it down pretty quickly.

The subchart (b) is the probability distribution function for a normal fit to the airborne fraction of CO2 emissions from the ultimate resource recovery (URR) of aggregated fossil fuels plus the preindustrial baseline of 280 PPM CO2 and the non-fossil fuel component of landuse and cement manufacturing at 35 PPM CO2. The currently proven reserves are set at -2 sigma. The ‘most optimistic’ scenario (with an unconfirmed reference to the Oil & Gas Journal) is set at +1 sigma. The fit has a maximum likely emission of 6100 gigatonnes of CO2, with a 1700 Gt standard deviation. After retaining only the airborne fraction and adding in the preindustrial and non-fossil fuel components, we calculate a probable future CO2 concentration of 769 PPM with a s.d. of 109 PPM. The figure below shows only the fossil fuel component – add an additional 315 to account for the preindustrial baseline and non-fossil component.

The subcharts (a) show the probability distribution function for the equilibrium climate sensitivity. The PDF was visually fitted to the Meinshausen 2009 PDF with a gamma distribution. The gamma distribution parameters are α = 12, β = α/3.25. This provides an 85% probability of the ECS lying between 2C and 4.5C with a max at 3C.

Previously, we examined a set of temperature responses to a discrete range of climate sensitivities and CO2 scenarios. The ECS range was set at the [2, 3, 4.5]. The CO2 concentrations with the range [551, 660, 769, 878, 987] PPM. It was noted that with a CO2 concentration in the upper 50% of the range and the ECS with the highest value, that there exists a possibility of warming of 6C, one of my two suggested limits for ‘catastrophe.’ The other limit – 1000 PPM CO2 – also lies within the range of possibilities, but outside the 2-sigma limit.

Instead of relying on discrete scenarios for fossil fuel production and climate sensitivities, we can build a near-continuous range of both the temperature responses and their probabilities by creating a matrix of temperature results as a function of ECS and CO2 and a corresponding product matrix of their probabilities. Chart (c) above is the probability distribution for the product of the PDFs for ECS and CO2 (fossil-fuel + non-fossil-fuel). The solid line is the contour for 50% probability. The dashed line is the contour for 84% probability. And the dotted line is the contour for 95% probability.

The temperature response is Chart (d). The green contours on this chart are the temperature responses (degC, leftmost contour = 1C) for various climate sensitivities (x-axis, degC) CO2 (y-axis) and CO2 emissions. I have retained the probability contours from the left hand side for the 2-variable PDF. Visual inspection indicates that there is a 50% likelihood that burning all the fossil fuels we can produce will have a net warming effect of about 2.5-5.5C.

We can use the two charts, the temperature responses and their probability distribution, along with the information calculated earlier for the CO2 distribution, and calculate the likelihood that we will exceed 6C or 1000 PPM CO2 which was one definition of CAGW that I offered in an earlier post.

b = matrix(CO2_VAL>1000,x,x) + matrix(DT_VAL>6,x,x) > 0
sum(DT_PDF[b])

And the answer is … 8.6% 10%.

Given our current knowledge of fossil fuel resources and climate sensitivity, there is a 8.6% 10% chance that if we burn all the fossil fuels available to us that temperatures will rise above 6C and/or atmospheric CO2 concentrations will exceed 1000 PPM.

Addendum: Moving the Goalposts

My original ‘intuition’ for the 6C and 1000 PPM CO2 limits were my (faulty) understanding of the maximums for the Cenozoic climate. My understanding was faulty. Cenozoic maximums appear to be more like 12C warmer than present with CO2 concentration peaking around 1200+ PPM CO2. There is essentially 0% chance that we will exceed either without additional feedbacks not accounted for in the ECS I have used here.

However, I have also seen how the climate ran at a max of about 4C warmer with a CO2 concentration near or below 500 PPM CO2 for the last 30 million years or so. We could use this as a marker of a critical threshold, if there is compelling evidence that the modern biosphere will fair poorly under Paleogene climatic conditions. There is a 45% probability will exceed 4C warming and a near certainty that will exceed 500 PPM CO2. There is a 50% probability will exceed 4C warming and a near certainty that will exceed 500 PPM CO2.

Updates

20120528 I consider this whole BOE (“Back of Envelope”) series a work in progress and will be regenerating the charts now and then. They are date stamped if you want to save one off for some reason.

20120529 The code is now available here

We can use the range of potential fossil fuels CO2 emissions developed previously and plot the resulting temperature responses given the common range [2, 3, 4.5] of equilibrium climate sensitivities. Feedbacks are implicitly included in the ECS and do not need to be dealt with explicitly as long as they have been included in the models from which the ECS has been derived.

Ts = Equilibrium Climate Sensitivity = [2, 3, 4.5]
λ = Ts/3.7
ΔF = 5.35 * ln(CO2_future/CO2_preindustrial) W/m2
ΔT = λ * ΔF

I’ve marked with the heavy solid red line what I believe to be the “catastrophic” temperature response of 6C warming. Such catastrophic warming lies within the range of potential ECS and possible fossil fuel CO2 emissions, although it appears unlikely.

I have also marked what I believe to be the “catastrophic” CO2 concentration of 1000 PPM CO2. This level is where I suspect that ocean acidification has the potential to cause a globally-scaled extinction event.

The possibility of 6C warming or 1000 PPM can be quantified given our two PDFs and I will do so in the next post.

Estimating the probability distribution for equilibrium climate sensitivity with a Gamma distribution visually fitted to Meinshausen 2009 Fig 3a” (top). The gamma distribution for the 2 to 4.5C spread for equilibrium climate sensitivity has a cumulative 85% probability.

The gamma distribution is coded as follows:

#gamma distro
x = seq(0.1,10,by=0.1)
alpha = 12# width of dist, higher is narrower
beta = alpha/3.2 # shift, higher is right shift
ts_pdf = beta^alpha/gamma(alpha) * x^(alpha-1) * exp(-beta*x)
ts_pdf = ts_pdf/sum(ts_pdf)
sum(ts_pdf[x>=2&x<=4.5])/sum(ts_pdf)
#[1] 0.8490118

The Gamma Distribution was not my first attempt at a fit. My first fit was a Poisson distribution, rescaled and shifted to fit the Meinshausen ECD PDF. The Poisson function for the 2 to 4.5 spread for climate sensitivity also integrates to an 85% probability.

The code for the Poisson fit is as follows:

lambda = 3 # ECS mean = 3
xmax = 14 # long enough tail to go to zero
xx = 0:xmax
xx2 = xx/2 # scale the Poisson back down to 0:7
xxtck = 0:7 # labels for the chart
yy = lambda^xx * exp(-lambda) / factorial(xx) # Poisson
Ts = approx(xx2,yy,n=71) # need more points, so interpolate to dx = 0.1
shift = 17 # shift peak back to ECS = 3
yy2 = rep(0,71)
yy2[shift:71] = Ts$y[1:(71-shift+1)]
Ts$y = yy2 / 5 # shift complete
sum(Ts$y[Ts$x>=2 & Ts$x<=4.5])
#[1] 0.8526035

The similarity between the two is even more obvious when plotted together. It can’t be accidental, but I haven’t studied the two yet to derive their relationship.

# COAL: TONNES TO TONNES OF OIL EQUIVALENT
# BP Statistical Review 2011
# 7273 tonnes of coal / yr (2010)
# 3731 tonnes of oil equivalent /yr (2010)
# conversion factor of tonnes coal to ‘tonnes of oil equivalent’
coal_toe_conv = 3731/7273 # .513

# NATURAL GAS: BILLION CUBIC METERS TO GIGATONNES OF OIL EQUIVALENT
# BP Statistical Review 2011
# 3193 billion cubic meters / yr (2010)
# 2.88 gigatonnes of oil equivalent / yr (2010)
# conversion factor of tonnes coal to ‘tonnes of oil equivalent’
ng_toe_conv = 2.88 / 3193 # bcm to gigatonnes

# BP Statistical Review 2011
gt_proven_coal = 861 # gigatonnes of coal
gt_proven_oil = 189 # gigatonnes of oil
bcm_proven_ng = 187000 # billion cubic meters NG

# BP Statistical Review
coal_conv_co2 = 3.96 # tonnes CO2 per tonne of oil equivalent
oil_conv_co2 = 3.07 # tonnes CO2 per tonne of oil equivalent
ng_conv_co2 = 2.35 # tonnes CO2 per tonne of oil equivalent

# BP Statistical Review
co2_proven_coal = gt_proven_coal * coal_conv_co2 * coal_toe_conv
co2_proven_coal # 1749
co2_proven_oil = gt_proven_oil * oil_conv_co2
co2_proven_oil # 580
co2_proven_ng = bcm_proven_ng * ng_conv_co2 * ng_toe_conv
co2_proven_ng # 396

co2_proven_ff = co2_proven_coal + co2_proven_oil + co2_proven_ng
co2_proven_ff # 2725

# Wiki / Oil & Gas Journal
years_optimistic_coal = 417
years_optimistic_oil = 43
years_optimistic_ng = 167

# BP Statistical Review 2011
rate_coal = 7.273 # gigatonnes
rate_oil = 3.914 # gigatonnes
rate_ng = 3193 # bcm

gt_optimistic_coal = years_optimistic_coal * rate_coal
gt_optimistic_oil = years_optimistic_oil * rate_oil
bcm_optimistic_ng = years_optimistic_ng * rate_ng

# converstion factors same as above

co2_optimistic_coal = gt_optimistic_coal * coal_conv_co2 * coal_toe_conv
co2_optimistic_coal # 6161
co2_optimistic_oil = gt_optimistic_oil * oil_conv_co2
co2_optimistic_oil # 517
co2_optimistic_ng = bcm_optimistic_ng * ng_conv_co2 * ng_toe_conv
co2_optimistic_ng # 1130

co2_optimistic_ff = co2_optimistic_coal + co2_optimistic_oil + co2_optimistic_ng
co2_optimistic_ff # 7808

UPDATE 20120524: Reworked the estimates for coal, oil, and natural gas under both the proven and ‘optimistic’ scenarios. The original two charts can be found here and here.

In the previous post, I used two estimates of emissions from the burning of coal, oil, and natural gas reserves – proven and ‘optimistic’ – to estimate total fossil fuel CO2 emissions at 2200 2700 gigatonnes and 5200 7800 gigatonnes respectively via conversion factors lifted from BP Statistical Review 2011. The estimate excluded methane/methyl hydrate emissions as either a forcing (fuel consumption) or a feedback (triggered by arctic warming).

The basis for the ‘optimistic’ reserve estimate is unclear. The claim is not well cited. The given reference, Oil & Gas Journal is not freely available for review. I cannot find a well referenced version of the claim (eg one that includes OGJ vol and date). I continue to research the source of the claim.

Proven reserves are those that can be extracted profitably under current economic conditions and current technology. Proven reserves have been continually growing even as reserves are exploited faster than new discoveries are made. This is because higher prices and improvements in extraction techniques make a greater percentage of the discovered resources available for production. Because of this continued reserve growth, it is very likely that the amount fossil fuels ultimately extracted will exceed the amount of fossil fuels currently considered as proven, just based on price and technology growth. In addition, new discoveries will continue to add incrementally to the both the ‘discovered resources’ and ‘proven reserve’ counts.’

I have chosen to fit these two scenarios to a Guassian curve to create a probability distribution for CO2 emissions from fossil fuel consumption. That the probable range of fossil fuel consumption fits a normal distribution is my first assumption. To complete the fit, I need to make two additional assumptions. The first is that it is 95% likely that we will consume all the proven reserves. The other is that it is only 16% likely that we will consume as much fossil fuels as in the ‘most optimistic’ reserve estimate. These two fits are graphed as points (a) and (b) on the chart above. It should also be apparent that the two points, as determined by my above assumptions, are three sigma apart, making it trivial to define the peak of the gaussian PDF (point (c)) and giving us a third scenario to play with … the ‘most likely’ scenario with cumulative emissions at 4200 6100 gigatonnes of CO2.

Setting the ‘optimistic’ scenario at +1 sigma allows for consumption of non-conventional fossil fuel sources such as oil sands and oil shales and are assumed to be included in this PDF.

While fossil fuels emit CO2, only about 50% of it remains in the atmosphere. This 50% is known as the airborn fraction. The other 50% or so is absorbed into the oceans or into land-based carbon stores (mostly the biosphere). The IPCC estimates the airborn fraction variously as 60% and 55%. Knorr’s 2009 finds a near constant airborn fraction of 43%. (h/t sks) For this purpose, I am using a constant 50%.

We can estimate the amount of CO2 emitted up to now by working the concentration calculation in reverse. Currently, CO2 concentration is about 100 ppm above preindustrial levels. It is estimated that about 65% of this is from fossil fuel sources and 35% from land use changes and a bit from cement production. Given a 50% airborn fraction and a conversion factor of 7.81 GtCO2 per PPMV, we can estimate that we emitted just over 1000 gigatonnes of CO2 from fossil fuel sources prior to the present. (CDIAC FAQ).

The chart below shows the cumulative CO2 concentration PDF due to fossil fuel production assuming a constant airborne fraction of 0.5 and 1000 GtCO2 of emissions prior to the present. You can roughly estimate future CO2 concentration by adding 280 ppm CO2 for the preindustrial concentration and another 35 for the land use changes and cement production prior to the present.

Just exploring a new theme.

This post is a back of the envelope calculation to answer: “How much would CO2 increase if we burned all the available fossil fuels.” It does not consider feedbacks. It considers two scenarios: Proven and Optimistic

Proven reserve estimates are gleened off wiki. Proven is a subset of discovered and refers to only those reserves which can be developed with current technology and under current economic conditions. My estimate is that there are 2,200 gigatonnes of CO2 in proven reserves which is in the same ballpark as the approx 2,800 gigatonnes estimated in Meinhausen 2009. This will result in an approximate increase of 274 ppm. To which I add the approx 100 ppm already produced in the industrial era for a net increase of 374 ppm.

Given an increase in CO2 (dCO2) sourced from fossil fuels, we can calculate the change in Radiative Forcing: dRF = 5.35 * ln( (280+dCO2)/280 ).

Likewise, we can calculate lambda λ as the Equilibrium Climate Sensitivities (ECS) divided by the radiative forcing of doubled CO2: λ = ECS/3.7

Given those two values, an estimate of the change of Temperature due to fossil fuel CO2 forcing is trivial to calculate: dT = λ * dRF

Using a spread of possible ECS [2,3,4.5,7], we can estimate that previous fossil fuel consumption and the future consumption of all proven reserves of fossil fuels will result in a warming of 2.5-5.5C for ECS of 2-4.5C and a warming of 8.6C for an ECS of 7C.

I include ECS = 7, due to our recent discussion of Sherwood and Hubert 2010 which claims that Meinhausen 2009 estimates that there is a 5% possibility of an ECS exceeding 7.1C. As an aside, I think this claim may be a misunderstanding based on the following Meinhausen quote: We chose a Bayesian approach, but also obtain ‘frequentist’ confidence intervals for climate sensitivity (68% interval, 2.3–4.5C; 90%, 2.1–7.1C), which is in approximate agreement with the recent AR4 estimates.. If the 90% interval had an even split of 5% on either tail, you could claim 5% chance that ECS > 7.1C. But examining Fig 3 indicates that almost the entire remaining 10% lies on the cool side of the 90% range, not evenly split between the two. It is likely that given distribution shows an ECS > 7.1C probability of less than 1%.

Wiki also includes an inflated “Optimistic” resource scenario is not optimistic from an AGW point of view, but “optimistic” from a resource availability point of view. While I found these estimates on wiki, they are attributed to “Oil & Gas Journal, World Oil.” I haven’t found the original source and none of the internet cites seem to include a date.

In general, “proven reserves” in the oil industry refers to resources that will probably (~90%) be developed with known technology under current economic conditions. It is possible that the “optimistic” numbers come from “proven, probable, possible” reserves aka 3P.

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

One issue that arises in forecasting production is that as technology increases and/or prices rises, resources that were previously would have been unprofitable to develop, become potentially profitable and the resource previously “unproven” move to “proven.”

Assuming 1) the ‘optimistic’ numbers are discovered resources but unproven and 2) that rising prices don’t destroy demand and 3) resource extraction technology continues to improve, then it seems quite possible that most of the discovered resources will eventually become proven and produced. In that case, as modeled on the table shown below, atmospheric CO2 will increase by 646 ppm (~5200 Gt), more than double the previous estimate. Cell H5 shows that future production plus 100 ppm for previous production.

Uncertainty in ultimate recoverable resources (URR) is not the only uncertainty even in this rough estimate. Currently, the oceans absorb approximately 50% of our fossil fuel CO2 emissions. This number is expected to decrease over time, but I’m not sure how far or how fast. I’ll guestimate that maybe 30% of our future emissions will be absorbed. On the other hand, I don’t think these reserve estimates include fuels potentially derived from oil sands (bitumen) or oil shales (kerogen). It’s possible that there could be as much potential oil in those sources as there is conventional oil, maybe more. Lets add a potential 30% upside to account for these resources. So to cover the spread, lets map the two scenarios – Optimistic and Proven – with 30% greater and 30% fewer emissions. As charted below:

Last word on the BOE. By design, there are two potentially large sources of GHG not included in this fossil fuel estimate. One is the potential exploitation of methyl hydrates as a fuel source. Another is the potential release of methane from permafrost and ocean sources as the planet warms.

As discussed earlier, my rule of thumb for now is that catastrophe lies somewhere around warming > 6C and/or atm CO2 > 1000ppm. If all available fossil fuels are burned, we might be screwed through acidification. If ECS is indeed > 7.1C, we are screwed due to warming. Even at ECS ~ 4.5C, we have crossed out of my “safe zone” if we burn all the fossil fuels at our disposal. If ECS is 3C or less and we avoid burning everything, we have a better safety margin. The potential existential threat appears to lie closer to the realm of possibility than I realized and am moved toward a more cautionary position.

Below is the IPCC AR4 WG1 Technical Summary Table 5 which shows a range of expected warming for different concentrations of CO2. Add 280 ppm to the figures displayed above to get total CO2 in the two scenarios.

Spreadsheet should be available here

In this presentation, I will demonstrate that the Sun drives climate, and use that demonstrated relationship to predict the Earth’s climate to 2030. It is a prediction that differs from most in the public domain. It is a prediction of imminent cooling.

– Solar Cycle 24: Implications for the United States, Archibald, 2008

I contacted Archibald earlier this year as I attempted to reproduce a couple of the graphs in his 2008 Solar Cooling presentation. He responded promptly but wasn’t able to provide me any help telling me that the computer he used for that presentation had crashed some time before and he had no alternate sources. Nor did he recall the methods used.

I began with Archibald’s chart entitled ‘A US Rural Data Set.’ I note that 1) he used GISTEMP data and 2) listed the five stations he used by name and 3) that he smoothed the annual average

I know that the source of GISTEMP US data is USHCN, so I turned there for the station data. Strangely, all the USHCN data begins in 1895, but the first time tick on the chart is for 1893.

Archibald has chosen five widely distributed, rural stations as representative of the continental United States. It was easy to locate the Station IDs by name in the USHCN station inventory. The stations are mapped below.

093754 31.9881 -81.9522 61.0 GA GLENNVILLE 3NW
094170 33.2842 -83.4681 74.7 GA HAWKINSVILLE
098535 32.6875 -84.5197 195.1 GA TALBOTTON
161411 32.5133 -92.3478 54.9 LA CALHOUN RSCH STN
314055 35.0536 -83.1892 1170.4 NC HIGHLANDS

Archibald mentions that he smoothed annual averages, but does not recall the exact method. Examining several different smooths, the best fit I could find was a 3 year moving average, which fits well in recent decades, but diverges somewhat in middle decades while maintaining a similar variation throughout. I cut the station data at the year 2003, the last year shown on the original chart. This fit is shown below.

Having found a reasonable fit to the station data, I turn next to the “Projected Temperature Profile to 2030.” The pre-2003 rural US data set has been further smoothed and, strangely, cooled by about 0.5C. This may be due to some sort of averaging with the solar smooth shown earlier in the presentation. Nevertheless, I found a lowess smooth (f=0.04) of the 3 year moving average creates a reasonable likeness of the 2030 projection chart. I have added the post-2003 data points and the continued lowess in red.

This is not a perfect reconstruction by any means. The data sets are not the same. The range appears to be different. The visual matching may be impaired by poor scaling in the background images. Nevertheless, it should be adequate for qualitative comparisons of future observations to the original temperature projection.

Combining the rural US data set we saw earlier and the projected temperature response to the length of Solar Cycle 23, this graph shows the expected decline to 2030.

The temperature decline will be as steep as that of the 1970s cooling scare, but will go on for longer.

– Solar Cycle 24: Implications for the United States, Archibald, 2008

code is here

The following is not intended to “prove” that AGW does not lead to CAGW (defined as extinction events and/or collapse of civilization), but rather outlines why I don’t currently believe it. I do not consider myself well-informed regarding palaeobiology or palaeoclimate, so I welcome corrections to what I have outlined.

Extinction level events

Argument 1A: A 2-6C rise in temps will trigger an extinction event.
Reply: There have been many step changes of similar magnitude (6-8C Antarctic, 2-3C global?) over the last million years, and again with the melt of Antartica 10 million years ago (~4C polar ocean), and again with the PETM 56 million years ago (6C global). Such abrupt changes are anomalous, but they are not unprecedented. None of the upward step changes are associated with named extinction events. Although the *cooling* in the midMiocene has been described as a disruption with notable extinctions.

Argument 1B: The rate of change over the next several hundred years is too fast for the biosphere to handle.
Reply: The rate of change during the PETM may be the best natural analogy. It might have occured over a period of 20,000 years or so, about 1.5 orders of magnitude faster than the rise due to the release of CO2 from fossil fuels. (about 500 years). Wiki says of the PETM: The PETM is accompanied by a mass extinction of 35-50% of benthic foraminifera (especially in deeper waters) over the course of ~1,000 years – the group suffering more than during the dinosaur-slaying K-T extinction. Contrarily, planktonic foraminifera diversified, and dinoflagellates bloomed. Success was also enjoyed by the mammals, who radiated profusely around this time. … There is no evidence of any increased extinction rate among the terrestrial biota. So while impactful, the PETM event does not support a theory that AGW induce a widespread biotic collapse.

Counterpoint: Bad analogy. 1.5 orders of magnitude is too great a difference.

Argument 1C: The equilibrium temperature post fossil fuels will be too high for the biosphere to handle.
Reply: The middle Miocene Climatic Optimum, ~17 to 15 Ma, is representative of climate under x2 preindustrial CO2 and about 3-6C warmer in mid-latitudes. While I haven’t seen actual NPP studies for the Miocene, most descriptions are ‘warmer and wetter’, suggesting higher NPP. I am intrigued by the apparent lack of arid deserts in the few Miocene papers I have read.

Counterpoint: http://www.pnas.org/content/107/21/9552.full.pdf Sherwood, Huber (2010)

2. Collapse of civilization

Argument 2A: Climate change will severely impact agricultural production leading to collapse.
Reply: Climate models show a strong increase in “Net Primary Production”, much of which is directly attributable to the increase in CO2. Models are much less certain if the changes in “climate” sans CO2 will have a net positive or negative effect, although they lean towards the negative. It does seem likely that there will be shift in C3/C4 plant ratios and distribution. In addition, barring collapse for other reasons, it seems likely that technological innovation in both modified crops and improved farming technologies will occur faster than climate stress will decrease production. Caveat: the net effect of climate change with other environmental degradations and economic stresses may outstrip our innovation speed. Which is not to say that some regions won’t be net losers in the shifting climate. I believe that the US South West and most of Mexico, North West China, the Mediterranian, and South African(?) regions will be counted among the losers.

See also:
Fig 5 in Terrestrial plant production and climate change Friend (2010)

Fig 3b from Climate–Carbon Cycle Feedback Analysis: Results from the C4MIP Model Intercomparison Friedlingstein et al (2006)
(models cover wide range of results for T-driven NPP; but all model large increase in net NPP)

Fig 3 in Evolution of carbon sinks in a changing climate Fung 2005
(NPP drops south of ~30N, increases north)

Counterpoint:
Modeling the Recent Evolution of Global Drought and Projections for the Twenty-First Century with the Hadley Centre Climate Model Bourke (2006)

Dustbowlifaction Romm (2011)

Argument 2B: Coastal flooding will lead to collapse.
Reply: While sea level rise is inevitable in AGW world, total melting of the Antarctic is unlikely. The Pliocene world at 2-3C warmer, sea levels were about 6 meters higher. Even if we had a rise of tens of meters, this is likley to occur over a period of centuries. Port infrastructure is likely to be replaced several times over that time scale, so it is hard to see how this would lead to collapse of civilization, although the loss of coastal lands is not insignificant.

Counterpoint:

3. Ocean Acidification

Argument 3a. Ocean acidification will trigger an extinction event
See the following for both the point and the counterpoint …

The most salient paleo-analog to the current atmospheric CO2 increase is the strong ocean
acidification event at the Paleocene-Eocene thermal maximum (PETM) 55 Mya. The PETM is
marked by the sudden and massive carbon input to the ocean/atmosphere system, a shoaling of
the deep ocean’s calcite saturation horizon by at least 2 km in less than 2000 years that did not
recover for tens of thousands of years, global warming of at least 5?C in less than 10,000 years,
and major shifts in marine planktonic communities (Kennett & Stott 1991; Zachos et al. 1993,
2003, 2005). The only major extinctions occurred within the benthic foraminifera, though it is
unclear whether ocean acidification was the main factor or whether changes in ocean circulation
led to anoxia in bottom waters (Zachos et al. 2008).

However, the similarity of the PETM and several comparable, but smaller, Eocene events to
modern conditions is incomplete. First, whether the carbon excursion at the PETM was as rapid
as the present-day excursion remains unclear. Second, the PETM and smaller events occurred
within a background of already high CO2 and global temperature. Third, the Mg:Ca ratio, an
important factor that affects the carbonate mineralogy of many organisms, was also significantly
different from that of today (Stanley & Hardie 2001). Finally, the marine biota during the PETM
were also different. Corals and coral reefs had not yet re-established following the Cretaceous-
Tertiary extinction (Wood 2001); modern coccolithophores are very different from those of the
early Tertiary (Young 1994); and modern thecosomatous pteropod families appeared after the
PETM, in the Eocene and Miocene (Lalli & Gilmer 1989).

Ocean Acidification: The Other CO2 Problem Doney et al (2009)
http://www.psp.wa.gov/downloads/SP2009/0509/12b_doney_ann_rev_proof.pdf

There are many serious consequences aside from extinction events and collapse of civilizations.

Argument 4A: You are neglecting severe consequences by concentrating on extreme crisis.
Reply: I am not neglecting severe consequences. I am trying to define catastrophic consequences and (informally) assess their likeliehood. I am totally open to the possibility that my assessment could be off and welcome references that could be inform it.

–

Edits for typos. I am also likely to edit at will to include additional cites or details.

Figure 6. Isomorphism between resistance-capacitance circuit and two-compartment energy balance climate model. Differential equations on right can be solved to give time dependence for arbitrary applied time-dependent forcing (current). Dashed boxes enclose corresponding one-compartment systems. The figure is modified from the Reply to Comments on my 2007 paper and an in-press paper (Spring, 2012) that interprets the observed increase in GMST over the latter part of the twentieth century in terms of the two-compartment model.

Stephen E. Schwartz Home Page
http://www.ecd.bnl.gov/steve/schwartz.html

I was intrigued by a paper linked from Skeptical Science, J. H. van Hatern’s A fractal climate response function can simulate global average temperature trends of the modern era and the past millennium (2012). The paper can be downloaded here or viewed online.

van Hateren has extended Schwartz’ analysis of a schematic 2-box, 1-tau (e-folding time constant) ebm climate model to use multiple forcings over multiple e-folding times. This particular electronic circuit analog was brought forth in Schwartz’ 2008 reply to comments on his 2007 paper, Heat capacity, time constant, and sensitivity of Earth’s climate system. There were three comments: one by Knutti et al, one by Scaffeti, and one co-authored by Foster, Annan, Schmidt, and Mann.

It should be noted that Schwartz references an earlier version of this (1-box/2007 or 2-box/2008 ?) model on his web page, that of Gregory 2000. I have not been able to obtain a copy to read, confirm, cite, and link. The hazards of residing behind a paywall.

Schwartz’ website also references a work by Held 2010 Probing the Fast and Slow Components of Global Warming by Returning Abruptly to Preindustrial Forcing, a 1-box model, 2-tau model, although the long time scale doesn’t seem to be defined. The short tau is < 5 years.

Whew! But we aren't done yet!

Tamino discussed his response to Schwartz 2007 at Real Climate: Climate Insensitivity (2007).

Lucia discussed it as well at The Blackboard: Time Constant for Climate: Greater than Schwartz Suggests! (2007). And again: Schwartz & Scafetta Estimate Climate Time Scale

The 2007 1-box, 1 time constant model came up again during a WUWT Eschenbach thread via a comment by Paul_K. (2011). Eschenbach followed up that suggestion with his own take Life is Like a Black Box of Chocolates. (2011). And both were commented on by Tamino Fake Forcing (2011).

In addition, this topic holds Isaac Held’s interest who has blogged several times on related topics. Such as …
3. The simplicity of the forced climate response (2011)
4. Transient vs equilibrium climate responses (2011)

A comment from Tamino’s Fake Forcing post …

What kind of physical theory — even rudimentary — might make just as good a fit? There are two major flaws with Schwarz’s model. One is that his method of diagnosing the time constant is flawed. Seriously flawed — even if his model were correct his method would give the wrong result. The other major flaw is that the real climate system has more than one “time constant.”

Tamino presented a 2-box, 2-time factor model (tau = 2 and 45 years). van Hateren enters the field with model fitted to 6 time periods, each set of six scaled uniquely to three different forcings: solar, ghg, and so2/volcanic/aerosols/others.