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Climate Insensitivity

Filed under: — group @ 16 September 2007

Guest post by Tamino

In a paper, “Heat Capacity, Time Constant, and Sensitivity of Earth’s Climate System” soon to be published in the Journal of Geophysical Research (and discussed briefly at RealClimate a few weeks back), Stephen Schwartz of Brookhaven National Laboratory estimates climate sensitivity using observed 20th-century data on ocean heat content and global surface temperature. He arrives at the estimate 1.1±0.5 deg C for a doubling of CO2 concentration (0.3 deg C for every 1 W/m^2 of climate forcing), a figure far lower than most estimates, which fall generally in the range 2 to 4.5 deg C for doubling CO2. This paper has been heralded by global-warming denialists as the death-knell for global warming theory (as most such papers are).


Schwartz’s results would imply two important things. First, that the impact of adding greenhouse gases to the atmosphere will be much smaller than most estimates; second, that almost all of the warming due to the greenhouse gases we’ve put in the atmosphere so far has already been felt, so there’s almost no warming “in the pipeline” due to greenhouse gases already in the air. Both ideas contradict the consensus view of climate scientists, and both ideas give global-warming skeptics a warm fuzzy feeling (but not too warm).

Despite the celebratory reaction from the denialist blogosphere (and U.S. Senator James Inhofe), this is not a “denialist” paper. Schwartz is a highly respected researcher (deservedly so) in atmospheric physics, mainly working on aerosols. He doesn’t pretend to smite global-warming theories with a single blow, he simply explores one way to estimate climate sensitivity and reports his results. He seems quite aware of many of the caveats inherent in his method, and invites further study, saying in the “conclusions” section:

Finally, as the present analysis rests on a simple single-compartment energy balance model, the question must inevitably arise whether the rather obdurate climate system might be amenable to determination of its key properties through empirical analysis based on such a simple model. In response to that question it might have to be said that it remains to be seen. In this context it is hoped that the present study might stimulate further work along these lines with more complex models.

What is Schwartz’s method? First, assume that the climate system can be effectively modeled as a zero-dimensional energy balance model. This would mean that there would be a single effective heat capacity for the climate system, and a single effective time constant for the system as well. Climate sensitivity will then be

S=τ/C

where S is the climate sensitivity, τ is the time constant, and C is the heat capacity. Simple!

To estimate those parameters, Schwartz uses observed climate data. He assumes that the time series of global temperature can effectively be modeled as a linear trend, plus a one-dimensional, first-order “autoregressive” or “Markov” or simply “AR(1)” process [an AR(1) process is a random process with some 'memory' of its previous value; subsequent values y_t are statistically dependent on the immediately preceding value y_(t-1) through an equation of the form y_t = ρ y_(t-1) + ε, where ρ is typically required to be between 0 and 1, and ε is a series of random values conforming to a normal distribution. The AR(1) model is a special case of a more general class of linear time series models known as "Autoregressive moving average" models].

In such as case, the autocorrelation of the global temperature time series (its correlation with a time-delayed copy of itself) can be analyzed to determine the time constant τ. He further assumes that ocean heat content represents the bulk of the heat absorbed by the planet due to climate forces, and that its changes are roughly proportional to the observed surface temperature change; the constant of proportionality gives the heat capacity. The conclusion is that the time constant of the planet is 5±1 years and its heat capacity is 16.7±7 W • yr / (dec C • m^2), so climate sensitivity is 5/16.7 = 0.3 deg C/(W/m^2).

One of the biggest problems with this method is that it assumes that the climate system has only one “time scale,” and that time scale determines its long-term, equilibrium response to changes in climate forcing. But the global heat budget has many components, which respond faster or slower to heat input: the atmosphere, land, upper ocean, deep ocean, and cryosphere all act with their own time scales. The atmosphere responds quickly, the land not quite so fast, the deep ocean and cryosphere very slowly. In fact, it’s because it takes so long for heat to penetrate deep into the ocean that most climate scientists believe we have not yet experienced all the warming due from the greenhouse gases we’ve already emitted [Hansen et al. 2005].

Schwartz’s analysis depends on assuming that the global temperature time series has a single time scale, and modelling it as a linear trend plus an AR(1) process. There’s a straightforward way to test at least the possibility that it obeys the stated assumption. If the linearly detrended temperature data really do behave like an AR(1) process, then the autocorrelation at lag Δt which we can call rt), will be related to the time constant τ by the simple formula

rt)= exp{-Δt/τ}.

In that case,

τ = – Δt / ln(r),

for any and all lags Δt. This is the formula used to estimate the time constant τ.

And what, you wonder, are the estimated values of the time constant from the temperature time series? Using annual average temperature anomaly from NASA GISS (one of the data sets Schwartz uses), after detrending by removing a linear fit, Schwartz arrives at his Figure 5g:

Using the monthly rather than annual averages gives Schwartz’s Figure 7:

If the temperature follows the assumed model, then the estimated time constant should be the same for all lags, until the lag gets large enough that the probable error invalidates the result. But it’s clear from these figures that this is not the case. Rather, the estimated τ increases with increasing lag. Schwartz himself says:

As seen in Figure 5g, values of τ were found to increase with increasing lag time from about 2 years at lag time Δt = 1 yr, reaching an asymptotic value of about 5 years by about lag time Δt= 8 yr. As similar results were obtained with various subsets of the data (first and second halves of the time series; data for Northern and Southern Hemispheres, Figure 6) and for the de-seasonalized monthly data, Figure 7, this estimate of the time constant would appear to be robust.

If the time series of global temperature really did follow an AR(1) process, what would the graphs look like? We ran 5 simulations of an AR(1) process with a 5-year time scale, generating monthly data for 125 years, then estimated the time scale using Schwartz’s method. We also applied the method to GISTEMP monthly data (the results are slightly different from Schwartz’s because we used data through July 2007). Here’s how they compare:

This makes it abundantly clear that if temperature did follow the stated assumption, it would not give the results reported by Schwartz. The conclusion is inescapable, that global temperature cannot be adequately modeled as a linear trend plus AR(1) process.

You probably also noticed that for the simulated AR(1) process, the estimated time scale is consistently less than the true value (which for the simulations, is known to be exactly 5 years, or 60 months), and that the estimate decreases as lag increases. This is because the usual estimate of autocorrelation coefficients is a biased estimate. The word “bias” is used in its statistical sense, that the expected result of the calculation is not the true value. As the lag gets higher, the impact of the bias increases and the estimated time scale decreases. When the time series is long and the time scale is short, the bias is negligible, but when the time scale is any significant fraction of the length of the time series, the bias can be quite large. In fact, both simulations and theoretical calculations demonstrate that for 125 years of a genuine AR(1) process, if the time scale were 30 years (not an unrealistic value for global climate), we would expect the estimate from autocorrelation values to be less than half the true value.

Earlier in the paper, the AR(1) assumption is justified by regressing each year’s average temperature anomaly against the previous year’s and studying the residuals from that fit:

Satisfaction of the assumption of a first-order Markov process was assessed by examination of the residuals of the lag-1 regression, which were found to exhibit no further significant autocorrelation.

The result for this test is graphed in his Figure 5f:

Alas, it seems this test was applied only to the annual averages. For that data, there are only 125 data points, so the uncertainty in an autocorrelation estimate is as big as ±0.2, much too large to reveal whatever autocorrelation might remain. Applying the test to the monthly data, the larger number of data points would have given this more precise result:

The very first value, at lag 1 month, is way outside the limit of “no further significant autocorrelation,” and in fact most of the low-lag values are outside the 95% confidence limits (indicated by the dashed lines).

In short, the global temperature time series clearly does not follow the model adopted in Schwartz’s analysis. It’s further clear that even if it did, the method is unable to diagnose the right time scale. Add to that the fact that assuming a single time scale for the global climate system contradicts what we know about the response time of the different components of the earth, and it adds up to only one conclusion: Schwartz’s estimate of climate sensitivity is unreliable. We see no evidence from this analysis to indicate that climate sensitivity is any different from the best estimates of sensible research, somewhere within the range of 2 to 4.5 deg C for a doubling of CO2.

A response to the paper, raising these (and other) issues, has already been submitted to the Journal of Geophysical Research, and another response (by a team in Switzerland) is in the works. It’s important to note that this is the way science works. An idea is proposed and explored, the results are reported, the methodology is probed and critiqued by others, and their results are reported; in the process, we hope to learn more about how the world really works.

That Schwartz’s result is heralded as the death-knell of global warming by denialist blogs and Sen. Inhofe, even before it has been officially published (let alone before the scientific community has responded) says more about the denialist movement than about the sensitivity of earth’s climate system. But, that’s how politics works.


370 Responses to “Climate Insensitivity”

  1. 151
    AEBanner says:

    Re #149

    Many thanks

    AEB

  2. 152
    John M says:

    John N-G (#137) Thanks for the reference, I’m just starting to look at GW so I’m not familiar with the literature. The reference seems to confirm my newbie observation of the conflict between the models and observations as presented in AR4.

    I’m struggling with their notion that when observations don’t agree with a theory/model the observations are the likely problem, especially after they have already made adjustments to correct for observation errors. My expectation is the largest observation errors have been corrected now so the remaining differences between observation and theory will require adjustment of the theory.

  3. 153
    Hank Roberts says:

    Sanity check on Antarctic temperature change some time back at Stoat, here:
    http://scienceblogs.com/stoat/2007/02/revenge_of_the_killer_cosmic_r.php#comment-349908

    “… there is only one time period available to “falsify” and that is the last 50y. Within that time the models (averaged) predict warming (over the year) but not all that much of it. Far less than the Arctic, for example -W] [And see-also http://igloo.atmos.uiuc.edu/Antarctic.paper.chapwalsh.2005.pdf figure 8 -W]

  4. 154
    SteveSadlov says:

    RE: #100 – just last week, the NWS issued an air quality alert for the Arctic Shore of Alaska. The reason? The smoke from fires in NE Europe was drifting that far an remaining sufficiently intact to warrant the alert. You can’t make this stuff up!

  5. 155
    SteveSadlov says:

    RE: #104 – Overall background temps raised by AGW + delayed impact of 1979 – 2006(?) PDO warm water turn over (reaching into the East Siberian and Chukchi Seas) + dark crud on ice + ?????

  6. 156
    SteveSadlov says:

    RE: #134 – Ike, well put. Many thanks!

  7. 157
    SteveSadlov says:

    RE: #155 – Warm water from positive PDO ….. “turn over” is not quite the right term. More like pressure wave, density wave or gravity wave. In any case, the concept being, the PDO flip in the Pacific to negative is resulting in “excess” warm water from the past 27 years of positive PDO to be “expunged” into adjacent basins.

  8. 158
    Aaron Lewis says:

    Re 138
    A shallow pool of melt water lined with black carbon does absorb more radiation than the same depth of water sitting in clean ice.

  9. 159
    Rod B says:

    Timothy (135) says, “…the ozone depletion is partly due to global warming… ”

    Really??!!? What happened to that torturous chemical reaction route? How does it work? (Or did you mean to say vice versa?)

  10. 160
    Dave Rado says:

    Re. post 143, Peter Johns, see post 18.

  11. 161
    Dan says:

    Vernon (140) RE: “129 Dan, nice misdirection but your post was very misleading. Why not post the important part, namely that:

    The median in estimated surface forcing in early summer throughout the Arctic was 0.42 W m–2 before 1850, 1.13 W m–2 during the period from 1850 to 1951, and 0.59 W m–2 after 1951.

    That is a ~41 percent increase in warming due to BC on average.”

    You accuse me of being misleading…

    That 41% increase is equal to an incresed forcing of 0.17Wm^-2

    You chose to blame a regional forcing increase of 0.17Wm^-2 (that has decreased over the last 100 years) for the recently increased rate of arctic ice melting, rather than a global increase of 1.6Wm^-2 (that has increased over the last 100 years)? Yup, that fits the picture alright…

  12. 162
    jacob l says:

    re 105:
    the altitude that the troposphere map is equal to 300 mb, 10km
    so check how real world data compares to that height
    also check
    http://www1.ncdc.noaa.gov/pub/data/ratpac/ratpac-b/RATPAC-B-annual-regions.txt
    and
    http://cdiac.esd.ornl.gov/trends/temp/angell/angell.html
    for tropospheric temptures

  13. 163
    dhogaza says:

    Rod B, it’s quite simple, really

    Ozone depletion gets worse when the stratosphere (where the ozone layer is), becomes colder. Because global warming traps heat in the troposphere, less heat reaches the stratosphere which will make it colder. Greenhouse gases act like a blanket for the troposphere and make the stratosphere colder.

    Taken from here.

  14. 164
    David B. Benson says:

    Rod B — From the abstract of

    J. Hansen et al.,
    Climate change and trace gases,
    Phil. Trans. R. Soc. A (2007) 365, 1925–1954:

    “The most important of the non-CO_2 forcings is methane (CH_4), as it causes the second largest human-made GHG climate forcing and is the principle cause of increased tropospheric ozone (O_3), which is the third largest GHG forcing.”

  15. 165
    ChrisC says:

    Antarctica:

    The antarctic continent is insulated to a large degree by two (semi)permanant circulations. The circumpolar Antarctic current, which is the ocean current that flows around the continent, and the cicumpolar vortex, an upper troposhpere circulation that, as descibed by Scientific American: “bottles up cold air over the pole and restricts warm air to the outer ring”.

    Both these circulations have the effect of insulating Antartica from the environment around it. Not completely, but heat and mass transfer with the rest of the global atomsphere and ocean is slowed significantly. These circulations go some way to explaining why Antartica has not warmed at the same rate as the atmosphere globally.

    See this paper for information on the response of the circumpolar vortex to warming:
    http://adsabs.harvard.edu/abs/2003JGRD.108n.ACL7F

  16. 166
    Timothy Chase says:

    Rod B (#159) wrote:

    Timothy (135) says, “…the ozone depletion is partly due to global warming…”

    Really??!!? What happened to that torturous chemical reaction route? How does it work? (Or did you mean to say vice versa?)

    The CFCs are still important – as they resulted in the destruction of ozone by means of chemical reactions. However, global warming implies greater water vapor content in the atmosphere, which means that there is more water vapor that can be lofted into the stratosphere, and both methane and carbon dioxide appear to actually facilitate the transport of water vapor into the stratosphere (although apparently this is something which was not well-understood), chemical reactions involving methane will result in water vapor in the stratosphere, and the increased temperature differential between the stratosphere and troposphere will result in winds that loft water vapor into the stratosphere. Water vapor results in OH radicals which breakdown ozone.

    “Climate models show cooler stratospheric temperatures happen when there is more water vapor present, and water vapor also leads to the breakdown of ozone molecules,” Shindell said. According to satellite data, upper atmospheric temperatures around the world (20-35 miles high) have cooled between 5.4-10.8 degrees Fahrenheit over recent decades. The stratosphere is the typically dry layer of the atmosphere above the troposphere, where temperatures increase with height.

    When more water vapor works its way into the stratosphere, the water molecules can be broken down, releasing reactive molecules that can destroy ozone. Shindell noted that his global climate model agrees with satellite observations of the world’s stratospheric ozone levels when the water vapor factor is increased in the stratosphere over time. Shindell said, “If the trend of increasing stratospheric water vapor continues, it could increase future global warming and impede ozone stratospheric recovery.”

    Wetter Upper Atmosphere May Delay Global Ozone Recovery
    Apr. 17, 2001
    http://www.giss.nasa.gov/research/news/20010417/

    As noted in the essay, there tends to be positive feedback between global warming and ozone depletion. But either can get started through separate processes. So its vice versa and versa vice.

    Incidentally, there is another way that global warming can lead to ozone depletion, one which involves a biological component, but probably best to leave that for another time.

  17. 167
    Timothy Chase says:

    ChrisC (#165) wrote:

    Both these circulations have the effect of insulating Antartica from the environment around it. Not completely, but heat and mass transfer with the rest of the global atomsphere and ocean is slowed significantly. These circulations go some way to explaining why Antartica has not warmed at the same rate as the atmosphere globally.

    Antarctica used to be nearly tropical when a land bridge still existed between South America and the West Antarctic Peninsula as the Antarctic was warmed by the circulation of water around South America. Once that bridge was gone, ocean circulation reorganized resulting in the oceanic circumpolar circulation. No doubt the atmosphere followed suite. The circumpolar circulation greatly reduced heat exchange between Antarctica and the rest of the world, plunging it into the deep freeze that exists today.

    But with global warming, nearly all of the Southern Ocean is warming with the rest of the world, as are large parts of the interior continent, with melts even further south than 85 degrees latitude.

  18. 168
    Rod B says:

    dhogaza (163): It probably is just a minor point,… but the GW cause of ozone depletion is seemingly odd if not incredible. The ESS News post sounded like a full bowl of hyperbolic soup with all of the correct 2000 talking points, and so not very credible, at least in scientific detail. Even so, the average global tropospheric temperature went up how much in the last decade or even two (2-3 tenths max maybe), which made the average stratospheric temperature drop how much — to cause such an impact on ozone production?? Seems like quite a stretch to me.

    David (164), your post seems to imply that GHG (and presumably the follow-on GW), like methane tend to increase ozone. Or did I get confused?

  19. 169
    Rod B says:

    Timothy (88), my belated point/question is still mostly out of left field from the main topic here, but, to be brief, my biggest question on the forcing math is not so much the log relationship, but the clever raising of the CO2 concentration ratio to the 5th-6th+ power before taking the ln log.

  20. 170
    John N-G says:

    John M (#152): As a general rule, people who work with observations trust models more than observations, and people who work with models trust observations more than models! I too am not willing to grant that observations are the likely source of the discrepancy.
    But…keep the concepts of “theory” and “model” separate. Only the very simplest models are designed to correspond to a particular theory. Current GCM’s are better thought of as kitchen-sink models, where as many processes and interactions as possible are included (based on physics, measurements, or both) and the model is then run to see what it all does. Any agreement between theory and GCM’s is not by design.

  21. 171
    Eli Rabett says:

    Let us talk about temperature and stratospheric ozone depletion. First, the ozone hole.

    The mechanism for forming an ozone hole starts with the formation of polar stratospheric clouds at very low temperatures. NOx species condense on frozen solid particles in these clouds and are removed from the stratosphere. In the natural stratosphere, ClO is sequestered as NO2ClO and cannot react with ozone (destroy it). If you remove the NO2 the ClO is freed to react with the ozone. The removal of NOx occurs during the polar winter. First light sets off a set of reactions of the ClO which destroys the ozone in the spring.

    The colder the stratosphere, the more likely Polar Stratospheric Clouds will form. The arctic stratosphere is warmer than the Antarctic. Thus pscs are more likely to form in the antarctic and we observe ozone holes more often (every damn year now) in the antarctic than the arctic (only in the spring after VERY COLD winters.

    As to destruction of ozone in the normal stratosphere. A colder stratosphere slows up a number of reactions which means that the Cl and Br freed from photodissociation of CFCs and halons lasts longer so we the problem continues for a longer time due to the cooling of the stratosphere by ghg increases. More detail here

  22. 172
    Hank Roberts says:

    > GW cause of ozone depletion is ….

    Polar stratospheric clouds (PSCs) — increasing with more water vapor and other changes in the stratosphere — provide surfaces on on which the catalysis of ozone is a faster, favored reaction. Nothing “odd if not incredible” — predicted, and observed during the extra-cold winters. Right now the critical temperature for this to happen isn’t happening every year, but the stratosphere continues to cool and PSCs continue to increase.

    Note the USA is now campaigning with other countries to hasten the phase-out of the remaining ozone-destroying chemicals globally. This isn’t in doubt, it’s already scared every country except China, and China’s gaming the system
    http://scholar.google.com/scholar?q=ozone+depletion+China+gaming+

    This isn’t news, the articles on PSCs and ozone loss go back at least a decade. Look them up, you’ll find many cites. Just one:

    http://www.atmos-chem-phys.net/7/435/2007/acp-7-435-2007.pdf

    Atmos. Chem. Phys., 7, 435–441, 2007
    http://www.atmos-chem-phys.net/7/435/2007

    “Rex et al. (2004) have shown a strong correlation between the vertically integrated ozone losses and the volume of air in which temperatures are below the NAT equilibrium point for the Arctic. Moreover, Knudsen et al. (2004) found a remarkable correlation between the total ozone mass depleted in the vortex and PSC area probability in the Arctic (correlation coefficient = 0.96) which
    can be extended to the Antarctic…..”

  23. 173
    jacob l says:

    RF = 5.35 ln(CO2/CO2_orig)
    dear Rod B
    if this is the formula that you are talking about that is multiplication not raising to a power
    check it out at http://www.grida.no/climate/ipcc_tar/wg1/222.htm
    hope this helps

  24. 174
    Timothy Chase says:

    Rod B (#169) wrote:

    Timothy (88), my belated point/question is still mostly out of left field from the main topic here, but, to be brief, my biggest question on the forcing math is not so much the log relationship, but the clever raising of the CO2 concentration ratio to the 5th-6th+ power before taking the ln log.

    Well, someone more knowledgable than myself could undoubtedly do a better job, but here it goes…

    Leaving out some of the complexity, lets just look at the greenhouse effect due to carbon dioxide with no amplification by water vapor or the albedo effect. We are told that for every doubling of carbon dioxide – prior to amplification by various feedbacks, the temperature will rise by something in the neighborhood of 1.2 degrees Celsius – as opposed to the 3 degrees Celsius we get after all of the amplifications.

    Now if you look it up, what is actually roughly proportional to the logarithm of the concentration of carbon dioxide is the forcing as measured in watts per square meter. This is supposed to be about 4 watts per square meter for every doubling of carbon dioxide. So lets begin with the 4 watts and see if we can’t derive the 1.2 degrees Celsius – or something close to it – since we are given only a single digit after the decimal point.

    *

    The average temperature of the surface of the earth is about 15 degrees Celsius – where freezing would receive a zero. But if we are talking about total radiation being proportional to the fourth power of temperature, we need to be thinking in terms of Kelvin.

    Freezing is 273 degrees Kelvin. So the temperature of the surface is approximately 288 degrees Kelvin. Now prior to the doubling of CO2, the amount of radiation leaving the climate system is equal to the amount of radiation entering the climate system: 235 watts per square meter. Thats at 288 degrees.

    *

    A forcing will mean non-equilibrium in which the rate at which energy leaves the system is lower than the rate at which energy leaves the system. In essence, it is as if the doubling of carbon dioxide adds 4 more watts per square meter.

    So if prior to the doubling, we have 235 watts resulting in a temperature of 288 Kelvin, then with one doubling we are talking about 239 watts. Likewise, two doublings will result in 243 watts and three doublings in 247 watts.

    Since total thermal emissions are proportional to the fourth power of the temperature, if 235 watts results in a temperature of 288 degrees Kelvin, then 239 watts will result in a temperature of 289.22, 243 watts will result in a temperature of 290.42, and 247 watts will result in a temperature of 291.61. The rise in temperature from one doubling to the next is respectively 1.22, 1.20 and 1.19. But we typically just round to 1.2.

    *

    Such a round figure will work just fine – until the sixth doubling – since at that point we would be rounding to 1.1 given the same level of accuracy. But by the fifth doubling we are speaking of a rise in temperature due to simply the direct forcing of carbon dioxide of 5.94 degrees Celsius. Assuming that with all the feedbacks (primarily water vapor and albedo) gives you 3 degrees for every 1.2 degrees, we are looking at 14.85 degrees total.

    But long before that happens you are going to have positive feedback from the carbon cycle kicking in, so I most certainly wouldn’t be worrying about six doublings. In fact, after just two doublings (with the carbon cycle contributing to the second doubling), we are talking about an additional 6 degrees – and at that point I doubt you will have to worry about the world economy generating a lot of carbon emissions for very long.

  25. 175
    Phil. Felton says:

    “Timothy (88), my belated point/question is still mostly out of left field from the main topic here, but, to be brief, my biggest question on the forcing math is not so much the log relationship, but the clever raising of the CO2 concentration ratio to the 5th-6th+ power before taking the ln log.”

    Try deriving the expression using Beer’s Law, start with the ratio of light absorbed at two different concentrations and you’ll get a function of that form.

  26. 176
    Van_Trump says:

    Tamino

    Well done! Unfortunately, the damage has already been done. Even if Schwartz were to resind his article, the Anti Global Warming camp will continue to reference it until the water rises up to their mouths.

    Though not trained in Climatology (Chemistry was my major), I try to keep current with the latest climate change research. It is apparent that political maneuvering caused the IPCC to water down its report.

    One thing confuses me though. Is there no provision for a “Phase Change” in Schwartz’s research?

    Several posters have correctly mentioned the earth reaching a “Tipping Point”, essentially the same thing.

    The way I explain the impending phase change in the Arctic to ordinary people is this:

    You are sitting in a hot conference room. There is a large punch bowl in the middle of the room where delegates can get a drink of water. The water is kept cool by a large block of ice. A small propeller keeps the water circulating. A thermometer keeps track of the temperature of the water.

    After two hours the block of ice is down to one-third its original size. From the delegates’ perspective, all is well; the drinking water has been kept cool and refreshing.

    Once the last of the ice has melted, the temperature of the water skyrockets. This is a simple phase change.

    The Arctic Ice Cap is like that block of ice. Once it’s gone, so is its moderating influence during the summertime. The cascading failure that follows is inevitable: Greenland ice cap melts (sea level rise), permafrost melts (releasing methane, inducing further warming), decreased albedo (further warming)…

  27. 177
    Timothy Chase says:

    PS to 174

    Now it is quite possible that I got something wrong in this post. As I said, someone could probably do a better job than me. If so, then I hope that either Eli or one of the climatologists will correct me. However, the important point as far as this post was concerned is that given how far we are from absolute zero, for small changes in forcing, a linear increase in the forcing results in a near linear increase in the temperature as a direct effect of changes in the concentration of carbon dioxide. Thus the rule that for every doubling of the concentration of carbon dioxide there is a near constant increase in the forcing implies that for every doubling of the concentration of carbon dioxide, the direct effect (prior to the feedbacks) is a near constant increase in the temperature – for the first few doublings of carbon dioxide.

  28. 178
    SteveSadlov says:

    RE: #176 – Phase change cuts in multiple ways. Albedo change on land surfaces does not result in the same side effects as albedo change on polar sea surfaces. This is not rocket science, it’s basic stuff. And then, there are the low and mid level clouds, the elephant in the room.

  29. 179
    Hank Roberts says:

    Van_Trump wrote:
    > The Arctic Ice Cap is like that block of ice. Once it’s gone,
    > so is its moderating influence during the summertime.

    Happy Equinox! Now it starts to come back, for six months. Yes, the total will be thinner next summer (areas of one-year instead of multi-year ice). But be aware of the cycle.

    “At the Autumn Equinox, approximately September 21, the sun sinks below the horizon, and the North Pole is in twilight until early October, after which it is in full darkness for the Winter.”
    http://www.arctic.noaa.gov/gallery_np_seasons.html

  30. 180
    Hank Roberts says:

    Note that you can’t rely on the NOAA “North Pole” webcams — the #1 and #2 cameras actually at the Pole haven’t worked for more than a month (I wonder if anyone is there besides that Russian ship and submersible?). The #3 and #4 cameras are on the Polarstern, and that ship got close to the Pole a while ago,but is now
    http://web-apps.awi.de/MET/Polarstern/psobse.pdf
    well south again. Originally they had said they planned to replace those new cameras on solid ice,
    http://www.arctic.noaa.gov/gallery_np.html
    but the pictures from them the last few days show sunlight and open water. No update at NOAA about this yet. Perhaps they never found solid enough ice to leave the cameras behind? Just guessing.

  31. 181
    Hank Roberts says:

    Last tidbit: the Polarstern’s current update isn’t in English yet, but their previous one identified their closest approach to the Pole as sometime in the weekend of August 30-September 2.

    I love finding ‘accidental’ stereo pairs;
    From NOAA #4 webcam images — including the rain near the Pole, and open water and ice there then.

    If you can view stereo pairs, go to the NOAA gallery page, search camera #4 for 8/31 through 9/2

    These are accidental stereo pairs (and there are others as well):

    noaa4: 2007-08-31 08:33:39 and noaa4: 2007-08-31 08:39:38
    noaa4: 2007-08-31 11:33:23 and noaa4: 2007-08-31 11:39:24
    noaa4: 2007-09-02 23:30:19 and noaa4: 2007-09-02 23:36:18

  32. 182
    Timothy Chase says:

    SteveSadlov (#178)

    RE: #176 – Phase change cuts in multiple ways. Albedo change on land surfaces does not result in the same side effects as albedo change on polar sea surfaces. This is not rocket science, it’s basic stuff. And then, there are the low and mid level clouds, the elephant in the room.

    As has been pointed out numerous times before, that so-called white elephant of albedo (which results in positive as well as negative feedback) did not stand in the way of a climate sensitivity of roughly 3 degrees Celsius over nearly the last half-million years. I doubt the laws of physics have changed all that much since the introduction of anthropogenic carbon dioxide emissions – and the positions of the continents would still appear to be roughly the same. So its time to get off of that white elephant, Steve. You really aren’t supposed to be riding them in the first place.

  33. 183
    A.C. says:

    #174 – i’m in no position to question whether one doubling does 1.2 degrees of warming or 3 degrees with feedbacks or if the climate might be more or less sensative than that, but i do have one question left over after reading your post: what is the best estimated time for one doubling of the concentration of co2 at current emmissions rates?

    The extent of my math knowledge is the quadratic equation and the extent of my climate knowledge is a handful of bad graphs on Wikipedia. But I’ll take a stab at answering my own question anyway, because the doubling of atmospheric co2 concentration hints at the excesses in our way of life regardless of how much of a temperature change it makes and also because of the off-chance that I might learn something from doing it. I’m sure someone will tell me all the places I screw this up.

    eyeballing the mauna loa emissions graph in the wikipedia article about carbon dioxide, i get the sense of a linear 60 ppmv / 50 years = 1.2 units per year rate of change. If I look only at the top of the graph, I see a 1.5 units per year rate. Starting at 380 units with an increase of 1.2 units/year, the doubling time I figure is in the neighborhood of 320 years. At 1.5 units per year, it’s more like 250 years. This is why if emissions plateau at current rates, rather than continuing to increase, the AGW problem seems relatively small to me (at least when I compare my opinion to Alastair’s assessment of our present situation).

    But if change in co2 concentration is accelerating by 0.2 units / 25 years (another eyeball estimate from the graph) doubling time is roughly 173 years (my best guess for what happens if our world-wide collective way of life doesn’t change). If change in co2 concentration ends up accelerating by 1 unit / 25 years, doubling time is ~81 years (my guess for what happens when two-thirds of the developing world–mostly living in india and china–catches up to our standard of living by 2030). Even though i strongly doubt these numbers reflect true doubling times, they’re the reason why AGW seems destined to become the biggest problem my generation (I’m 25) will have to deal with in our lifetime.

    Side note: sadly, the easiest way out of our global warming problem seems to be the maintainance rather than alleviation of poverty in the third world. Hence my opinion that our governments’ utter lack of interest in Africa’s plight is actually a policy geared around national security concerns rather than simple dispassion. So here’s hoping (and praying) that someone finds a carbon-neutral cure for poverty–not to mention a carbon-neutral cure for opulence–and soon.

    (left over bunny trail questions: does anyone happen to know whether or not manufacturing solar panels is a carbon-neutral enterprise? can someone point me to where i can find the records from the temperature station nearest to the mauna loa co2 station?)

  34. 184
    Jeffrey Davis says:

    And then, there are the low and mid level clouds, the elephant in the room.

    What are you feeding that elephant?

  35. 185
    steven mosher says:

    When I look at the temperatures I see this. Ray Ladbury
    Prove me wrong. Call me a know nothing. Here is what I say.

    We see that in fact, all decades are in accord with the modern-era rate; every one of them gives an error range for the rate that includes the modern-era value. From this I conclude that there is no statistically significant evidence that temperature from 1975 to the present deviates from a linear trend plus red noise.

    I have in the past given the impression that global warming has recently accelerated. Under certain circumstances it has, but those are limited to consideration of special time intervals. For the modern global warming era (1975-present) I see no hard evidence of acceleration. Therefore I will retract the impression, if not the actual statement, that global warming is accelerating; to me it looks like steady warming at 0.018 +/- 0.004 deg.C/yr, plus red noise.

    This was before I could spell AR(1)

  36. 186
    David B. Benson says:

    Rod B (168) — Yes, my reading of the abstract is that more makes more. You may be able to find a lengther treatment in the AIP Discovery of Global Warming website, linked in the Science Links section of the sidebar.

  37. 187
    dhogaza says:

    Mosher seems to have poached his post from Tamino, without attribution …

  38. 188
    Rod B says:

    Jacob (173): 5.35 ln(CO2/CO2_orig) = ln[(CO2/CO2_orig)]^5.35 or the ln of the concentration ratio raised to the 5.35th power.

  39. 189
    Timothy Chase says:

    steven mosher (#185) wrote:

    I have in the past given the impression that global warming has recently accelerated. Under certain circumstances it has, but those are limited to consideration of special time intervals. For the modern global warming era (1975-present) I see no hard evidence of acceleration. Therefore I will retract the impression, if not the actual statement, that global warming is accelerating; to me it looks like steady warming at 0.018 +/- 0.004 deg.C/yr, plus red noise.

    This was before I could spell AR(1)

    Steven,

    This is an easy one: I goofed.

    There is no statistically significant acceleration in the rate of temperature increase for the United States.

    There is a statistically signficant acceleration in the rate of temperature increase for the world if one is looking at the monthly level. I believe, however, that it helps to include the data points for each month – rather than just doing the individual years. More data points, greater statistical significance. Tamino pointed all of this out earlier.

    When it comes to statistics, I would take anything I have to say with at least a grain of salt. I would recommend you do the same. When it comes to statistics, you can probably put a great deal more trust in Tamino. He knows his art.

  40. 190
    Hank Roberts says:

    steven mosher Says:
    21 September 2007 at 2:38 PM

    > “…. Here is what I say.”

    Every word after that is plagiarized.

    The hosts can see if this is from the same IP used previously for posts under the name “steven mosher” — I trust they’ll check.

  41. 191
    Rod B says:

    Timothy (174), I appreciate your efforts. Some questions/challenges (and bear with me — I’m questioning as I go, and have a few beers under my belt): The 235 watts leaving will always be the same whether CO2 doubles, halves, or stays the same. If it jumps to 239 watts, the earth’s climate system will cool, because the 235 watts incoming will stay the same I think this affects the rest of your calculations, though there may be some semblance of accuracy or insight in them. In any event, I haven’t got to the forcing going to temperature yet; I’m still pursuing concentration going to forcing.

  42. 192
    Rod B says:

    Van_Trump (176) , you say, “…It is apparent that political maneuvering caused the IPCC to water down its report….”

    Shirley your paranoia causes you to jest. Goodness! The IPCC kowtowing to the anti-AGW lobby?? Fact is historically it’s been just the opposite, though the latest reports seem to be more straight down the line.

  43. 193
    Rod B says:

    Timothy (177), this would imply (actually you state) a linear relationship between CO2 concentration and temperature. Are you sure this is correct??

  44. 194
    Timothy Chase says:

    dhogaza (#187) wrote:

    Mosher (#185) seems to have poached his post from Tamino, without attribution …

    Huh.

    I am still not sure how one determines the degree of redness (are we talking only 15% or is this a cherry red?), but it makes more sense that the trend would be linear. That is what you would expect from an exponential growth rate I would presume, and up until the last few years the rate of anthropogenic CO2 growth has been fairly constant rate (as a percentage of the total – which means exponential growth). It was only recently that it started going up – the effects of which over the short-term will be negligible, but over the long-term will be cummulative.

    Anyway, something I am happy to be wrong about – if only that it means that the world makes more sense.

  45. 195
    Vernon says:

    I saw this and had to ask, which Tamino is right?

    Tamino, 16 September 2007 (http://www.realclimate.org/index.php/archives/2007/09/climate-insensitivity/)

    The conclusion is inescapable, that global temperature cannot be adequately modeled as a linear trend plus AR(1) process.

    Tamino, 21 September 2007 (http://tamino.wordpress.com/2007/09/21/cheaper-by-the-decade/)

    From this I conclude that there is no statistically significant evidence that temperature from 1975 to the present deviates from a linear trend plus red noise.

    So which is it?

  46. 196
    tamino says:

    Re: #195 (Vernon)

    You give a fine example of quoting out of context. I think you got this from climateaudit.

    Speaking of global temperature from 1880 to 2007:

    The conclusion is inescapable, that global temperature cannot be adequately modeled as a linear trend plus AR(1) process

    Speaking of global temperature from 1975 to 2007:

    From this I conclude that there is no statistically significant evidence that temperature from 1975 to the present deviates from a linear trend plus red noise.

    I stand by both statements. The first quote denies the applicability of an AR(1) model. The second confirms the applicability of a red-noise model. They are not the same. The noise in temperature time series is red, but not AR(1). The temperature since 1975 conforms to a linear increase plus red (not AR(1)) noise; temperature since 1880 does not.

  47. 197
    ray ladbury says:

    Rod B., Let’s make it clear:
    5.35*ln(C/Co)=ln[(C/Co)^5.35]. That is it is the ratio of the concentrations that is raised to the power, not the log thereof.

  48. 198
    ray ladbury says:

    Re 185. Steven Mosher, no offense, but why should I care what you think. You have no expertise in the field of climate change or data analysis. That much is clear in your implication that data in which there is noise cannot exhibit a trend. While I would certainly prefer that you educate yourself, if you refuse, there is nothing I can do about it. So, believe what you want

  49. 199
    Hank Roberts says:

    Just read what he wrote, follow the math, that’s how opinions change.

  50. 200
    spilgard says:

    Re #195

    Your first quote from Tamino states that the data are not well-represented as a linear trend + white noise (an AR(1) process).

    Your second quote from Tamino is from an entry noting that the data are best represented by a linear process + red noise, rather than as a linear trend + white noise (an AR(1) process).

    Given that the second quote provides additional detail to the first quote, what is the question?


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