Trenberth’s Claim: What can “easily” get 15 year flat trends?

This is another post discussing Trenberth’s RMets blog post Has Global Warming Stalled?. Some may recall, I addressed his discussion of observed earth trends (see this and with the snark figure only version here.) I deferred addressing the single sentence in his explanation of why we should somehow ‘expect’ 15 year ‘stalls’ in global warming; I’ve highlighted that below:

Coming back to the global temperature record: the past decade is by far the warmest on record. Human induced global warming really kicked in during the 1970s, and warming has been pretty steady since then. But while the overall warming is about 0.16°C per decade, there are 3 10-year periods where there was a hiatus in warming. From 1977 to 1986, from 1987 to 1996, and from 2001-2012. But at each end of these periods there were big jumps. We find exactly the same sort of flat periods in climate model projections, lasting easily up to 15years in length.

Recall that the arguments Trenberth seems to be countering is not “there is no global warming” but the much milder: “impression[.] that the global mean temperature is not increasing at its earlier rate or the long-term rate expected from climate model projections.” That is: his argument at least appears to be rebutting the impression that warming is happening either at less than 0.16C/decade (the previous long term trend) or less than ‘about 0.2C/decade’ (the projection from the AR4.)

If that is what he is rebutting, it would seem that Trenberth is, indeed, suggesting that we could see “flat” periods in the record even if warming is ‘about 0.2C/decade’. Of course we can’t be sure what Trenberth is really rebutting or claiming because his blog post is utterly vague about precisely what he is claiming or what he is rebutting. The level of clarity might be described as “conveying a general notion that people who are not alarmist are wrong”.

Going forward, I will assume that regardless of what Trenberth really is trying to argue, readers, or even non-readers who are merely curious about the probable path of warming will be interseted in knowing what the recent trends suggest about whether the observations of the earth’s trend is consistent with the multimodel mean from the AR4 (i.e. ‘about 0.2C/decade’ for the first 30 years of the 21st century.)

Discussion of Trends in the AR4.
As some of you are aware the projections in the AR4 were based on realization (i.e. runs) from a collection of a number of different models (AOGCMs) with forcings dictated by various ‘scenarios’ (i.e. emissions paths). Examples of emissions paths are “A1B”, “A2” and so on. Examples of models are “GISS ER”, “GISS EH” and so on. Each ‘run’ represents is initiated from a different ‘initial condition’, which would correspond to different “weather” states for earth weather back in the 1800. Owing to the chaotic nature of weather, each run has a different “weather trace”. Because the the actual weather state at every single point on the planet is not know for 1800, none of the realizations would be expected to match earth weather even if models were perfect.

However, for each model the average over many multiple runs driven by identical emission paths would be thought to represent that mean response for that model to the emissions path applied for to those runs. In the limit that the number of runs was very large (i.e. Nmodel,runs->∞) the average over all runs would be considered the “mean response” or “deterministic response”. At any time, variations about that mean response would be explained as due to “weather” in that particular model.

With respect to the current blog post then:

  1. For a given scenario , the deterministic trend in response to a particular scenario will be different for each model. For example: If we averaged the 20 year trends from a bajillion runs for Jan 1993-Dec 2012 from Model GISS ER and compared that to the average of a bajillion 20 year trends for the same period from CCSM3.0 we would expect these two mean trends to differ by some amount. This difference is due to structural uncertainty in our ability to create models that represent the earth’s response to emmissions paths.

    I do not have a bajillion runs from each of these models. But the general idea can be understood by comparing the location of the mean trends for GISS ER and CCSM3.0 below (i.e open circles.) forced using the A1B SRES:
    Trends_1990Trenberth
    The open circles denote the 20 year trends computed over multiple runs from each model during that time period. Note these trends differ. (Discussion of tests to determine whether these difference can be explained by “weather” is deferred, but the result of the test is they can’t be.)

  2. If we then focus on the bajillion 10 year trends from GISS ER, the standard deviation of those trends about the mean for GISS ER is a statistic that describes an aspect of weather in GISS ER. In the figure provided above, the spread for 20 year trends about the mean for GISS ER is indicated by vertical blue lines with horizontal dashes. The inner dash indicates the 2-standard deviations in 20 year trends computed from non-overlaping 20 year periods from 1913-2100. Because that is a sample value, there is some uncertainty in that estimate for the variability of 20 year trends. The outer dash is the 2-standard deviation interval given our uncertainty in estimating the variability of 20 year trends from the finite sample.

About the Multi-Model Mean

It happens that when creating projections from the AR4, the authors chose to highlight the “multi-model mean” in their projection advising that the earth would warm at a rate of “about 0.2C/decade” during the first 30 years of the 21st century. In a sense, this is statement that the deterministic component of earth’s weather trajectory would be “about 0.2C/decade” with “weather” resulting in some variation about this trajectory. Even if there might be deficiencies in using the multi-model mean for projections, it can be useful to test whether the earth’s observed trend is consistent with the multi-model mean with deviations explained by “weather”.

There are, of course a number of ways to estimate the variability of “earth weather”. But if we are to use variability of weather from this batch of models then the variability of “weather” should be estimated based on the variability of weather in each model. We could find the variability of 20 year trends from models by:

  1. Computing the standard of 20 year-trends for each model that provides multiple runs. (Shown for individual models on the left side of the graph above. The graph is limited to models with multiple runs in the A1B forecast.)
  2. Averaging the variance of 20 year trends for each of these models
  3. Taking the square root of the mean variance just computed.

The final value is an estimate of the standard deviation of 20 year trends in models. Note that this is an estimate based purely on variability of “weather” about the mean for a typical model with its own unique response to forcings. This spread of weather around the multi-model mean is indicated in by the vertical spread in 2nd from right below:

AnnotatedSpreadOfModels

Above, further to the right, I have also included the spread of “all weather in all models”. This is the spread we would expect for all model runs in the collection. This spread is due both to weather (shown just to the left) and to the spread in the model means caused by the structural uncertainty in the models (that is: caused by the fact that different models obeys slightly different physics for things like heat uptake in the ocean, cloud models and so forth.)

It is worth noting that papers like Easterling and Wehner only test whether earth’s observations fall inside the sorts of spread shown on furthest right.

At this point one might ask: Other than one set of spreads being different from the others, what question is answered by comparing the observed trend to one of the spreads rather than the other. But roughly (in a way that will make a statistician howl):

  1. When the earth observation falls outside the spread of “all weather in all models” that means that deterministic component for the earth’s trend likely falls outside the spread of deterministic components of the full ensemble of models. That is: the earth’s trend is sufficiently low to fall below and outside the larger uncertainty intervals, the deterministic trends from entire ensemble — including the lower range– likely do not represent the earth variability.
  2. When the earth observations falls outside and below the spread of “weather” around the multi-model mean, that means the multi-model mean appears biased high. That is: it is very unlikely the earth’s determistic trend is as high as the multi-model mean
  3. When the earth’s observations falls outside and below the “weather” spread but inside the “all weather in all models” spread that suggests the ensembles is biased high but the deterministic component of the earth’s trend might match one of the models whose deterministic warming falls in the lower range of the ensemble.
  4. When the earth’s observations falls inside both spreads, then one cannot reject the hypothesis that the ensemble contains a mean trend that matches that of the earth and one cannot reject the hypothesis that the multi-model mean is correct. Note that in the figure above, this situation applies for trends computed based on all observational data sets though just barely for NOAA/NCDC observations . Note also: this would be a test of a hindcast because data from 1990-2000 were certainly available before these models were forced using the A1B SRES under consideration as that SRES was formally decided on until 2001.)

What about recent trends?
We started down this path because Trenberth was discussing recent trends. His post specifically mentions 15 year and 10 year trends, not 20 year trends. With that in mind, I created a graph showing the spread of “weather” and “weather + model mean” around the multi-model mean for 10-20 year trends ending in Dec 2012 and beginning in January of each year. The 20 year data below corresponds to the two right most traces in the previous figure. This (annotated) graph is shown below:

KnappebergerStyleSince1990Illustrated

Above, the solid black trace represents the multi-model mean trend, the dashed grey trace indicates the ±95% boundary for “weather + model”, i.e. the spread of all runs, the solid blue trace indicates the ±95% boundary for deviations from the multi-model mean trend that can be caused by “weather” events if weather is typical of the magnitude in models.

Examining this graph we can see the origin for the claim that we can easily expect “flat” 15-year trends from models. That claim originates from the fact that if we compute the spread of all trends in all models (i.e. the spread due both the weather and structural uncertainty in models) we would expect 2.5% of 15-trends to fall below 0C/dec. Of course this is not quite the same as claiming that if the earth trend is equal to the multi-model mean, then we would expect 2.5% of 15 year trends to fall below 0C/decade and in fact, we should not. Rather, including a liberal estimate for measurement error (indicated by the dashed lines) we should expect 2.5% of 12.5 year trends to fall below 0C/decade.

Depending on the definition of “easy”, one might justify Trenberth’s claim that, “We find exactly the same sort of flat periods in climate model projections, lasting easily up to 15years in length.” as “true”, in the sense that 2.5% of 15 year trends in the ensemble have magnitude of 0C/dec or smaller. But I would suggest that this does not mean that if one believes the deterministic trend for the earth is 0.2C/decade, then the models do not tell us to expect flat periods of up to 15 years. Rather, the model ensemble contains runs with trends that low because some of the models show warming at a rate slower than 0.2C/decade!. So with respect to rebutting the “impression[.] that the global mean temperature is not increasing at […] the long-term rate expected from climate model projections.” the fact that the full model spread contains runs with 15 year long trends as low as 0C/decade is irrelevant. Because that can happen merely because the some models in the ensemble have mean trend that are lower than 0.2C/decade, and the observed trend is consistent with those.

What of the 10 -15 year trends
If we examine the graph above, we see that if we limit examination to data ending in Dec. 2012, and examining the shorter term trends dominated by data collected after the projections were created, we are starting to observe a few cases where trends fall outside the ±95% confidence intervals around the multi-model mean created by estimating the variability of trends based on “weather”. We can for example see that the 11-12 and 15 year trends based on NOAA/NCDC and HadCrut are falling below the blue trace for “weather noise” indicating that we would expect seeing such trend in fewer than 2.5% of cases. However, the trace for GISTemp remains inside the ±95% confidence intervals.

In any case, based on the fact that we do currently see some short term trends outside the ±95% intervals that can be explained based on weather, one can see why recent observations of earth trends might give people the impression that the deterministic component of the earth’s trend is lower than the multi-model mean. Though, own might also note that those who wish to believe models have a perfect right to do so based on this graph showing trends ending in Dec. 2012.

Tomorrow: I’ll show the graph ending with April 2013 (of course I’ve already looked.) Going forward, we will re-examine this graph from time to time and see where we are in Dec 2013. I’ll likely also through in a discussion of “Type II” error to better explain what “fail to reject the null” means and also note the power for the tests show above. (Note: “fail to reject” rarely means ‘the null hypothesis is shown to be correct’.) The discussion of “Type II” error will show why the fact that rejections are not “robust” doesn’t mean very much: we are getting rejections in a period where power to reject would be low. We will see that the difficulty for those who wish to convince dougers that models work is that “fail to rejects” are not robust!

60 thoughts on “Trenberth’s Claim: What can “easily” get 15 year flat trends?”

  1. Presumably, in those model runs that do show a long term trend of 0.2C/decade; The flat 10-15 year periods are often going to be preceeded or followed by similar lengthed periods of rates of warming that are above the underlying trend (ie > 0.2C/decade) Or is this flawed thinking??

  2. Chas–
    If a individual model’s long term trend under a particular emissions scenario is 0.2C/decade, then periods with trends < 0.2C/decade will tend the be preceded or followed by periods of faster warming. Otherwise the long term trend would not be 0.2C/decade. The length of the periods of slow or rapid warming might not be ‘similar’.

  3. Thanks, so if the world is like the models then there is a reasonable chance that the rates of warming seen in the period prior to ~1998 are exagerations of the underlying effects of CO2 ?

  4. Chas,
    It is always the case that warmign during any period might be enhanced or slowed by “weather events”. Given that the current observations are lower than previously, that does suggest that earliers warming rates might have been too high because “weather noise” bumped them up to to a faster than average rate. But there could be other causes.

    For example: Some of the apparent fast warming in the 90s was likely due to the fact that temperatures were depressed by a volcanic eruption during the early portion of that decade. (Pinatubo).

  5. I.e. If a model matches the observed warming rate up to 1998, the chances are that it is wrong (to put it too strongly!) ?

  6. Quick question: is your “all weather in all models” spread just a straight computation from all ensemble members, or do you deal in some way with different models contributing different numbers of runs?

  7. Lucia,

    This is a great contribution to rational analysis of recent T trends and what they imply about climate model validity. I note that Gavin Schmidt has done a much more limited analysis of the AR4 models back in 2008, and calculated how long a period one might expect to go without observing a new record high global T (9 years by his analysis) and how long before observing a new high of at least 0.1 deg C (18 years). http://www.realclimate.org./index/php/archives/2008/05/what-the-ipcc-models-really-say/

    Perhaps you could explain or give references for a few aspects of the climate models which are opaque to me as an outsider:

    1. do you know how many different models were used to produce the numerous AR4 simulations? Gavin’s paper presents spaghetti graphs for 53 simulations, but I don’t know how many different models are involved; you mention GISS EH and GISS ER above. I ask because I wonder if the models differ in any substantial way, and if so whether any model is doing a better job of projecting actual subsequent T.

    2. if I understand correctly, each simulation starts with actually observed values for forcings and T at a particular moment in time, then runs the model forward and backward in time using an assumed rate of change in CO2. The use of a range of real starting values presumably assures a realistic approximation of “weather” i.e. noise. Do you know what dates are used for these initial conditions and how they are chosen? I assume the starting points have to be relatively recent since accurate values for T and forcings are not available very far in the past.

    Thanks for the continuing education.

  8. John N-G:
    I weight each model equally.

    I’ve been planning to explain more should I write a paper. (There are going to be a bunch of elements that need to be in the supplemental material.)

    As our time is more open this year, I’m going to go grab all the A2 runs and those the newer runs too. That will permit a better estimate of the “weather noise” for each model.

  9. 1. do you know how many different models were used to produce the numerous AR4 simulations?

    I think a total of 23 but I only have 22 in the batch I got from KNMI. I’m going to have to count again to verify.

    e. I ask because I wonder if the models differ in any substantial way, and if so whether any model is doing a better job of projecting actual subsequent T.

    I’m not sure what you mean by differing in a substantial way. But the mean of 20 year trends differ in different models. See this:

    ccsm3.0 is consistently too warm but some models mean isn’t outside the range consistent with later observations. Also, the variance of trends is different in different models.

    You can create many statistics based on global surface temperature and apply tests and find that the properties of “weather” are generally different in different models and this result is pretty robust to what statistic one picks. (e.g. rms residuals to linear trend in 10 year fits? Variance of trends around their own mean? Pick one, it probably differs in each model. )

    if I understand correctly, each simulation starts with actually observed values for forcings and T at a particular moment in time, then runs the model forward and backward in time using an assumed rate of change in CO2.

    No. Models are initialized by doing a very, very long spin up with specified level of ghgs and emmissions and solar and such though to apply in the preindustrial period. After that, modeling groups march forward in time with ghs, aerosols and solar thought to apply in the industrial period. Then somewhere near Dec. 2000 or dec 2001 or as late as Dec 2003, each modeling group switched to ‘SRES’ which are hypothetical emission paths.

    If the group creates different runs they pick different initial conditions for the per-industrial from points near the end of the spinup.

    These models are never run backwards. They were never set to have similar initial “weather” conditions to the earth. (There are papers discussing models that tried to match “weather” to get better short term forecasts, but that’s not the case with these. )

  10. I forgot this

    I assume the starting points have to be relatively recent since accurate values for T and forcings are not available very far in the past.

    No. The starting points are in the late 19th or at latest 1900.

  11. Lucia,
    The thing I find odd is, in light of the recent trend, and considering that average temperatures are far more likely to continue to diverge from the models than to converge (negative PDO and other indications), that climate scientists are not trying to “get in front of” this issue by saying straight out that it is looking like the models are simply ‘tuned’ to be too sensitive. Hunkering down and hoping there is a return to 1975 to 1995 warming rates seems to me more likely to make people ignore everything they say than to listening to them. Preserving some credibility with the public would seem important, but there is little evidence of any change in the standard ‘talking points’, and the breathless press releases continue to appear for every it’s-worse-than-we-thought paper. It’s clear that climate scientists will never make successful politicians.

  12. Lucia,

    Thanks for setting me straight about the GC models. I had assumed they adopted a semi-empirical approach because starting a calculation of that complexity from first principles seems waaay too ambitious. No wonder they’re wedded to super-computers.

    Do you perhaps know of a discussion of the workings of these models suitable for readers who know some science but don’t intend to turn pro in the climate modelling biz?

    In particular, assuming values of the relevant forcings for the preindustrial era in the necessarily near-total absence of any direct evidence seems to embody an excess of hubris. Not to mention that since “preindustrial” era temperatures varied dramatically, the forcings must have varied just as much. How do the modelers manage to root themselves to reality if the calculations are ab initio and the input values are assumptions rather than measured values?

    Finally, I see in retrospect that the details of the models and the calculations themselves do not attract much attention in the main climate blogs, although the comparison of the model results to the T record is a matter of intense interest. Is there more to see under the tent? Should we be scrutinizing the details of the models and calculations more attentively? What bodies are hidden there?

  13. Hunkering down and hoping there is a return to 1975 to 1995 warming rates seems to me more likely to make people ignore everything they say than to listening to them.

    There is a group who published a paper saying models over responded to CO2– last fall. I’ll find it for you.

  14. In particular, assuming values of the relevant forcings for the preindustrial era in the necessarily near-total absence of any direct evidence seems to embody an excess of hubris. Not to mention that since “preindustrial” era temperatures varied dramatically, the forcings must have varied just as much. How do the modelers manage to root themselves to reality if the calculations are ab initio and the input values are assumptions rather than measured values?

    I think “near total absence of … evidence” for things like CO2 is an overstatement. I’m pretty sure some measurements of CO2 were made quite long ago. Also, there is some evidence for volcanic aerosols. So I don’t think it’s all meaningless. Is there uncertainty? Sure.

  15. Barry E:

    You ask:

    “Should we be scrutinizing the details of the models and calculations more attentively? What bodies are hidden there?”

    A recent paper in Science looked at “the details of the models” with respect to how they treat precipitation and clouds. A wonderful figure showed how two models predicted EXACTLY OPPOSITE trends in the tropics for both variables. The authors concluded that modelers need to go back to basics and actually understand the physics and chemistry inputs. This was written up (showing the figure) in WUWT and more recently (without the figure) in Judith Curry’s blog, with >100 responses.

    http://wattsupwiththat.com/2013/06/09/more-climate-models-fail-a-chink-in-the-armor-at-science/

    http://judithcurry.com/2013/06/16/what-are-climate-models-missing/

  16. I wonder what the odd’s of the models showing three 10 year periods of flat temperature in a 43 year period?

  17. So is this ultimately heading towards an argument that the warming trend is more consistent with the long term trend rather than the recent brief period of more rapid warming?

  18. Lance Wallace (comment 116471) references a publication in Science:
    “A wonderful figure showed how two [GC] models predicted exactly opposite trends in the tropics for both variables [clouds and precipitation].”

    Thanks, Lance; that is a graphic demonstration of the differences among models in dealing with clouds and water vapor. IIRC Spencer has been arguing for years that GCMs fail to deal adequately with cloud formation and water vapor.

    The inherent problem in any a priori model is that it implicitly assumes that every significant process is understood and adequately accounted for. In a system as complex as climate, how can anyone presume that to be true? Moreover, how can you demonstrate that the presumption is correct?

    Now, since we’re here…let’s treat this as a real question and not a rhetorical device. If cloud cover and water vapor treatment are a problem with the models, how could one evaluate the adequacy of the current models? One possibility might be to take a GCM, input current values for forcings etc., and allow it to project climate outputs going forward a few years; in particular you might focus on how its projections for cloud coverage compare to subsequently observed cloud coverage. Over a period of a decade or so you might at least decide that some GCMs are less competent than others.

    Are the climate modelers doing things like this, in particular with prospective projections? The Science paper referenced by Lance Wallace, interesting as it is, calculated differences for a hypothetical 4 deg C increase in T and does not readily allow for prospective evaluation of models against reality. Doesn’t a reductionist prospective evaluation of individual elements of the GCMs seem needed and overdue?

    Again: an a priori model cannot generate accurate answers unless all processes are well understood. And whether all processes are well understood and accounted for in the models is itself an empirical question which can only be answered with prospective data.

  19. Lucia (comment 116470) says:

    “I’m pretty sure some measurements of CO2 were made long ago. Also, there is some evidence for volcanic aerosols.”

    Co2 was measured as far back as the first half of the 19th century using methods with pretty good accuracy. Many of the measured values seem high relative to the presumed preindustrial values; this may reflect the fact that the labs were heated and lighted by burning carbon fuels.

    The dates and relative magnitudes of volcanic eruptions were certainly available, and I would be willing to accept inferred aerosol values, in large part because volcanic effects are transient and don’t seem to change the long-term T trend.

    But how can anyone reliably estimate the cloud cover or ice extent in 1800 or 1850 or 1900? The variations in albedo could be large, but were not directly measured.

  20. DocMartyn (Comment #116472)
    “I wonder what the odd’s of the models showing three 10 year periods of flat temperature in a 43 year period?”

    Well, you could equally ask, what the odds of the Earth showing three 10 year periods of flat temperature in a 43 year period of rising temperatures? Apparently it happens.

  21. Nick: All model output I have seen, going forward, shows a monotonic temperature increase on decadal scales.

    Perhaps you can show some projections that show flat trends?

  22. Nick Stokes (#116483):
    “Well, you could equally ask, what the odds of the Earth showing three 10 year periods of flat temperature in a 43 year period of rising temperatures? Apparently it happens.”
    Well, two of those occurrences seem to owe their existence to large eruptions. Which raises a question, did the models include occasional eruptions in their projections? If they did, such occurrences were not consistently applied to all runs, as the mean/median of sresa1b runs show no co-ordinated drop in temperatures as the 20th century runs do.

  23. lucia (Comment #116455),

    Given that the current observations are lower than previously, that does suggest that earliers warming rates might have been too high because “weather noise” bumped them up to to a faster than average rate.

    Are you saying that if we could remove “weather noise”, then the warming would be at a pure linear rate?

  24. Barry

    But how can anyone reliably estimate the cloud cover or ice extent in 1800 or 1850 or 1900? The variations in albedo could be large, but were not directly measured.

    They don’t. That’s what the “spinup” is for. A spinup goes like this:
    1) You don’t know condition, so you guess something not to insane.
    2) You apply conditions that set forcings (i.e. solar, aerosols etc)
    3)You run with those (i.e. solar, aerosols etc) for many, many, many years until your model is in pseudo-equilibrium.

    When the model is in pseudo-equilbrium, that’s the amount of ice your models says is at the caps for that level of forcings.

    You then call this *end* condition 1850.

    Note that models *don’t* get 1850 right in an absolute sense. In fact they don’t agree with each other. That’s one of the reasons those making projections use anomalies. The notion (which we can argue about) is that even if the model gets things wrong in 1850, they should get roughly the correct temperature rise if you apply roughly the correct (solar, ghg, aerosols) etc.

    Note also: if the correct amount of ice (i.e. what was on the earth) was used as an initial condition) model agreement during the 20th century might be worse because the model is going to see its equilibrium, not those of the earth.

  25. Skeptical

    Are you saying that if we could remove “weather noise”, then the warming would be at a pure linear rate?

    I’m not saying anything about what we would expect for the earth’s real trend.

    The question asked “if X was true, and Y was also true, then what would you say about Z”. “X” happened to be “if the deterministic trend (i.e. weather free) was 0.2C/dec which is linear. So of course, my answer is premised on the notion that the deterministic trend was 0.2C/dec. That’s not the same as saying I believe that is the deterministic trend. Nor is it the same as saying I believe the earth’s deterministic trend is linear. It’s just accepting the hypothetical premise for the purpose of answering a question. This is a pretty common thing to do (but can be confusing to third parties reading at blogs as they might not scroll back.)

  26. HaroldW

    Which raises a question, did the models include occasional eruptions in their projections? If they did, such occurrences were not consistently applied to all runs, as the mean/median of sresa1b runs show no co-ordinated drop in temperatures as the 20th century runs do.

    The SRES do not contain volcanic eruptions.

  27. Lucia,

    Slightly (but not completely) off topic:

    One thing that is not clear to me in your various postings about climate model output vs. real temperature trends is this:

    Are you using the AR4 models with some assumed CO2 emmissions scenario from the original AR4 report or are you using the models updated with real observed CO2 emmissions?

    SteveG

  28. John N-G,
    I looked at the code to refresh my memory on precisely how I computed “weather + models”.

    First: The estimate is based on the 11 models with repeat runs.

    To get weather I did as explained above. (For each model, compute variance in trends for ‘m’ repeat runs for about N non-overlapping periods that fit between 1913-2100. Then take average of variance, then take square root.) Call this sd_weather.

    To get “model” I did this:
    For the same 11 models, compute the variance in the mean trends over the 11 models during period “i”, found the average variance over all periods. Call this “Var_model_means_est”.

    For the graph shown, I then computed the variance for “models + weather by summing the two variances above and taking square root.

    Oddly, when you asked it occurred to me that I had the method I used works fine in the limit where I have an infinite number of runs for each case. But… it has a slight error if I have a finite number of runs. In that case, on average, the variance of “model means based on ‘n’ samples ” is higher than the variance of the “weather noise free model means”. But I can estimate the excess based on the standard deviation of the weather in that model and the number of runs. So, this morning I added a correction to back that out.

    That correction is : For each model the “excess” variance is

    correction_model_i =(sd_weather)^2/N where N is the number of runs in the set.

    (This same number is used to estimate the uncertainty in the estimate of a mean trend during an individual period, it’s the “standard error in the mean” i.e. se_mean_trend .)

    Each model contributes equally, so the overall correction for finite size is the average over all models of “correction_model_i”. Now, the estimate for the standard deviation of “weather+model spread” is

    So, the variance estimate for the “weather +model” spread becomes

    sd_weather^2 =Var_model_means_est-average(correction_model_i)

    I take the square root of that. Yesterday I was missing the ‘average(correction_model_i)’. Adding the ‘average(correction_model_i)’, I the intersection for the ‘weather+noise” and 0C/dec line shifts very slightly to between 14 and 15 years. So little changes in the narrative.

    (BTW: I realized I could do a “version II” that includes models with only 1 realizations in the estimate. In that case, I would need to estimate the ‘weather noise’ for those models and I could just assume it’s equal to the average from the other 11. But I’d rather just compute it separately because I know I can get more by looking at A2 data or just looking at some runs that didn’t get extrapolated into the future. I just havent done that. )

  29. Lucia (comment 116490) says:
    “The notion… is that even if the model gets things wrong in 1850, they should get roughly the correct temperature rise if you apply roughly the correct [forcings].”

    Lucia, thanks for demolishing my assumptions about how the models work. (Judy Collins sings softly in the background, “… I really don’t know models at all”).

    Nevertheless…I’ll guess that if the models don’t accurately reproduce the earth climate of 1850 (and don’t need to) then they probably don’t accurately reproduce the climate of 2013 either (and perhaps don’t need to since the projections are derived from anomalies). But this makes me wonder how far the models differ from the actual present climate; and wonder how far they can stray before the magnitude of that difference interferes with calculating the anomalies correctly.

  30. Les Johnson

    All model output I have seen, going forward, shows a monotonic temperature increase on decadal scales.
    .
    Perhaps you can show some projections that show flat trends?

    I don’t know about models but observations saw decadal trends peak around 1992-2001 at 0.3ºC per decade, just about every decade since (allowing for ENSO) there has been a decline in decadal rate of warming until that rate goes negative (cooling) in 2001-2010 where it has remained.
    .
    The relationship with the increase in decadal rate of CO2 rise is stark, if not exactly supporting consensus CO2 as a control knob theory

  31. Lucia: Are the models vetted in any way to conform to the sort of one to 15 years cyclical patterns visible in the measured data?

    Do they produce such patterns or are they just ‘noise’ at that level?

  32. RichardLH,
    What do you mean by “vetted”? By patterns do you mean do they produce things sort of like ENSO? Kinda sorta yes. Depends on the model. Some produce wild oscillations. Some less so.

  33. can you make a betting book on the count-down to the “inevitable” tamino take-down? He has to do it regardless of whether he has any scientific instincts.

  34. Diogenes–
    I have no idea what we would be betting on. Tamino writing a post that links to this Trenberth article? Bets need to be on a concrete specific event that every one can agree has happened or not.

  35. sorry..but i guess it is a badge of honour to have tamino devote a post to showing how ill-educated you are. While his pet chimps chirp along in the background. dhogaza, etc…the poor simpletons

  36. Diogenese–
    I’m not going to run a bet on the next date when Tamino write a post referring to something discussed at The Blackboard.

  37. Lucia, I have just read quickly through your introductory post for this thread, and only a few of the subsequent posts so bear with me if I have misunderstood some of the content. I am most interested in the model variability that can cause 10 and 15 year trends with 0 slope and to what that variability should be attributed. I have done some analyses of the recent CMIP5 models using the KNMI data with the RCP26, RCP45, RCP60 and RCP85 scenarios. I may link some these analyses which could be relevant to your discussion on this thread.

    I know you have referred to some of the model variability contributing to flat decadal length trends as “weather”. The quotes on that term lead me to believe that you are not convinced that weather is the most appropriate terminology. I have been looking initially at 10 year flat or negative trends in the CMIP5 models in the period from 2000-2100. Interestingly I have found some models with replicate runs can have very different numbers of 10 year flat/negative trends, e.g. CCM runs 1 through 4 with the RCP60 scenario where CCM2 has 4 non overlapping 10 year flat/negative trends while CCM1, CCM3 and CCM4 all have just 1 10 year flat/negative trend. All 4 runs have nearly the same overall trend from 2000-2100.

    I point to this example because when Trenberth points to models in general having multiple decadal length flat or negative trends it becomes difficult to see where he is attributing that to “weather” – or weather, since he has a paper that is attempting to explain the recent pause in warming as transport of heat to lower ocean depths than “ordinarily” occurs. If the pause in warming were from “weather” would not that be merely part of a chaotic weather system – or can his attempt to explain the warming pause be considered weather related? How does one explain the very different step pattern in run CCM2 versus the other 3 runs from that model. The inputs and the model are the same and thus the output would appear to be chaotic like weather. Or is something else causing this difference?

  38. Actually I misspoke above as CCM has 6 runs with CCM5 and CCM6 having 3 and 2 non overlapping flat/negative 10 year trends. My point remains the same – what causes the differences between runs?

  39. Kenneth–
    I’m not sure what you are asking me. Different models have somewhat different closures, approximations and so on. This will lead to different sorts of variability. This is true irrespective of what word you use to describe that variability (chaos, weather, what have yoyou.)

    How does one explain the very different step pattern in run CCM2 versus the other 3 runs from that model.

    I don’t try. I don’t know how you could unless you were intimately familiar with the approximations in different models. I think this question is also somewhat orthogonal to the simipler issue discussed in this post which is merely: “Given all the models, what is the variability of ‘N’ year trends in the models”?

    We can know the answer to that question by looking at the trends. We don’t need any more sophisticated analysis. The cause doesn’t matter: it simply matters that those are the variabilities.

    I’m using “weather” for lack of any particular general word. But on the earth, the variations the temperature trends, precipitation etc. all are actually called “weather”. This isn’t an attribution statement. It’s just what we call these variations.

  40. lucia (Comment #116494)

    (but can be confusing to third parties reading at blogs as they might not scroll back.)

    Okay, I’m guilty of that.

  41. lucia (Comment #116533)
    June 19th, 2013 at 12:24 pm

    “RichardLH,
    What do you mean by “vetted”? By patterns do you mean do they produce things sort of like ENSO? Kinda sorta yes. Depends on the model. Some produce wild oscillations. Some less so.”

    I suppose qualified rather than vetted would have been a better choice of words.

    Is it possible to rank the models so that those that produce natural patterns (in the 1 to 15 years range) are selected as opposed to all of them.

    Those patterns must exist as stepping stones to any overall change or change in rates surely? They are the gap between weather and climate.

    Random/noise output at these sort of ranges must make the models more suspect.

  42. RichardLH,

    Is it possible to rank the models so that those that produce natural patterns (in the 1 to 15 years range) are selected as opposed to all of them.

    If someone defined a particular “natural pattern” and identified a quantitative feature that characterized that “pattern” based on some observation of the earth, someone could get all the gridded data from the model, do a comparison and rank. I suspect something has been done with ENSO, but I have no idea what test have been done or the result.

    These sorts of tests are done for many different features. You can read a little here:
    http://blog.chron.com/climateabyss/2013/06/looking-under-the-hood-of-a-climate-model/

  43. I should add: Those tests seem to be for annual cycles. It strikes me that of any cycle, the annual cycle temporal feature is easiest to mimic. (That’s not to say that the test isn’t good. Only that unless the correlation accounts for the fact that the 12 month cycle is sort of a given, I’m not sure how one can interpret that.)

  44. The natural patterns that I believe should act as constraining factors on the models (so that we know they are at least likely to be modelling this world – not another one with 50m higher sill heights on the ocean basins or such) are that the models should exhibit similar behaviour in the 1-15 year timespan to the patterns that we have already measured in the satellite record.

    Seems to be reasonable conclusion and requirement.

  45. http://blog.chron.com/climateabyss/2013/06/looking-under-the-hood-of-a-climate-model/

    “Testing a climate model by comparing it to 20th Century trends is fun, but not very useful for model development, because the 20th Century temperature record is just a single realization of the climate, and random variations in the atmosphere and ocean would easily make even a perfect model diverge from the observed temperature trace for years or decades. Plus we don’t know for sure what the forcing was. There’s no real ground truth.

    Much better is to test the model against things that can be observed again and again. That way, you know how well it can capture average observed conditions. Even better, if the events happen frequently, you might even be able to compare the random variability of the model against the random variability shown in observations.”

    I suspect that my point is made above. We only have a single temperature record (whole area, measured series anyway). That record will be one of many that will fall within a ‘normal’ range of temperatures distributed around some underlying natural periodic structure.

    The satellite record is 34 years long now and Nyquist tells us that in that record there will be captured all natural cyclic values that have occured up to ~15 years long.

    Those cycles are the ones I am trying to get at. Hopefully to help validate the intermediate output from the models. At least to better understand climate.

  46. Lucia, I know what you are attempting to do in this post with the “weather” variability. I was hoping to get some feedback on Trenberth’s reference to something akin to chaotic model behavior and the resulting decadal flat/negative trends and at the same time attempting to explain the current flat period by reference to heat transport to lower ocean depths.

  47. Kenneth

    I was hoping to get some feedback on Trenberth’s reference to something akin to chaotic model behavior and the resulting decadal flat/negative trends and at the same time attempting to explain the current flat period by reference to heat transport to lower ocean depths.

    I don’t know how to give you that feedback. In anycase, I don’t think the answer can be obtained by looking at surface temperatures alone. You would need to get data on ocean heat content in models and in observations. I don’t have that and while it’s interesting, I don’t plan to obtain ocean heat content data from models nor do I plan to process it. So, I don’t think I’m ever going to be able to give you that sort of feeback.

    That said: I just posted on Watanabe’s paper and that discussion is possibly suited to answering the sorts of questions you have. See
    http://rankexploits.com/musings/2013/watanabe-strengthening-of-ocean-heat-uptake-efficiency-associated-with-the-recent-climate-hiatus/
    The link to the Watanabe paper is in the first paragraph.

  48. I’ll put it more plainly, I think Trenberth’s reference to the models and what appears to me to be a chaotic “weather” phenomena resulting in 10 to 15 year flat/negative trends and his attempt to explain the current warming pause as one related to more heat going to lower ocean depths is a seeming contradiction – at least to me.

  49. Kenneth–
    Why would it be a contradiction? If “weather” is a chaotic phenomenon and then mixing in the ocean will also be a chaotic phenomenon. The periods when mixing into the ocean is more rapid could coincide with the periods when the surface cools.

    We could do a similar illustration with Lorenz’s Butterfly, which is merely 2-d convection between isothermal plates at specific values of Prandlt number, Rayleigh number of (I don’t remember the third parameter!) Anyway, in that problem, if we put a thermocouple somewhat above the lower warm plate (say about 1/4 of the way, but anyway outside a sort of ‘boundary layer’ near the lower plate), cooler periods would be correlated with faster spinning (i.e. convection) while warmer periods would be correlated with slower spinning. I actually have an R code ginned up because I was going to try to explain something about d=1 with that, but I never got to the point where I could work out how to organize what I was going to say, partly because I was trying to think about too many issues simultanenously and there are too many things one can talk about with that problem! (FWIW: the time series for temperature in that problem is manifestly not d=1. It looked d=0!!)

  50. Meanwhile the models have been sold by the IPCC & Co as “the science is settled” gospel to the body politic, and as a consequence we continue to spend billions/trillions of $$ on policies “addressing”/”combating” CAGW/CACC.

    When it should in fact be abundantly clear to anyone not suffering from cognitive dissonance that we have -to put it mildly- only a very limited and incomplete understanding of the actual drivers of climate [see Judy Curry’s thought on this].

    Dogmatically arguing -like Trenberth- that in spite of a rapidly growing increasing dissociation between CO concentrations and key temperature metrics, CO2 is the overarching, determinant driver of global climate -and that the warming is “hiding” somewhere [below 700m, no less], is delusional. That is so far removed from Popperian science as to be alchemy and should be called out as such. A travesty, to paraphrase Trenberth.

  51. “If “weather” is a chaotic phenomenon and then mixing in the ocean will also be a chaotic phenomenon. The periods when mixing into the ocean is more rapid could coincide with the periods when the surface cools.”

    I want to avoid semantics here, but I am not so sure that the Trenberth and Watanabe papers are talking about the decadal length pauses that Trenberth notes can occur in the model runs. The Watanabe paper indicates that the models – in the ensemble mean sense – have missed the warming pause because the models do not transport sufficient heat to the deeper oceans. His reasoning appears in agreement with what your conclusion/view of the matter. While Watanabe also notes that the CMIP5 models mean rises monotonically in the 2000-2100 period and without some of the observed period structure, certainly individual model runs have shown lengthy pauses and those models evidently did not put heat into the deep oceans as is required to explain the recent warming pause. The models, in other words, did not know about the deeper ocean heat transport phenomena and yet show lengthy pauses.

    I have linked below the results of my analysis of the CMIP5 RCP60 scenario for the number of non overlapping 10, 12 and 15 year flat/negative trends for the period 2000-2100. All data was taken from the KNMI web site. I have included the overall trend in degrees C per decade for the model runs and the model name. I included the code names I used in my table with the corresponding official model names from KNMI in a separate table to the left.

    http://imageshack.us/a/img46/3538/9g7.png

  52. Ken–

    The Watanabe paper indicates that the models – in the ensemble mean sense – have missed the warming pause because the models do not transport sufficient heat to the deeper oceans

    Maybe. He both notes that the ‘k’ (heat transport to the deep) is too low in the models during the early part of the 21st century and notes that given the low temperatures over the sst, that this might just be an event due to the PDO. At least I think he discusses both. (Though I guess that might be what you mean: After all,the occurance of the PDO is not an “ensemble mean” event.)

    I don’t think variability of trends through to 2100 is relevant either to Trenberth’s discussion or the Watanabe. It’s clealry not relevant to Watanabe, and I suspect Trenberth was alluding to Easterling and Wehner when discussing what models show. They only went through 2030.

    The models, in other words, did not know about the deeper ocean heat transport phenomena and yet show lengthy pauses.

    By running your list out to 2100 you are picking up trends during “stabilization” parts of runs. Those aren’t relevant to the Trenberth or Watanabe discussion. Of course trends can be flat if forcings have been permitted to level off.

  53. Oh– my mistake. I didn’t pay attention to what you said that data corresponded to. If you are going to show that, can you show a graph of the temperature v. time?

  54. The models, in other words, did not know about the deeper ocean heat transport phenomena and yet show lengthy pauses.

    hmmm.. that seems right. Or at least, those models Watanabe discussed did show pauses. If their ‘k’ declined while they showed pauses then at least for those the pause was not caused by an increase in k.

  55. Lucia, I actually started my flat/negative trends in the decade 2010-2019 and obviously ended before 2091 since the I needed at least 10 years for a 10 year trend.

    Most of the model series I graphed show little or no bending at the end for the RCP60 scenario. Anyway here are the number of 10 year flat/negative trends by decade (in which trend started):

    2010-2019 had 18; 2020-2029 had 13; 2030-2039 had 10; 2040-2049 had 18; 2050-2059 had 6; 2060-2069 had 1; 2070-2079 had 4; 2080-2089 had 14

  56. Kenneth– Yes. I haven’t looked at the new models. But Trenberth’s 15 years probably comes out of Easterling and Wehner which is based on AR4 models– so not the set you are looking at. So while that model data is interesting and I’m going to look at it tomorrow, I’m pretty sure that data has nothing to do with what Trenberth was claiming. Though, of course, I might be wrong. (Trenberth did not cite– but his paper does.)

    I also don’t think Watanabe was discussing that list of trend– certianly in his figures he doesn’t discuss trends out to 2100– he gave a figure and it doesn’t go out that far.

    Here’s the figure

  57. Lucia, the trends in CMIP5 for RCP60 and RCP85 do not really have much of a century ending bend. Also why are not all these people talking about and using CMIP5. It has been available for some time now and it is the latest and greatest in climate modeling. Here is a link to the mean of all the model runs for CMIP5 RCP26,45,60, and 85 scenarios as extracted from KNMI.

    http://imageshack.us/a/img580/9615/oqcs.png

  58. Kenneth

    It has been available for some time now and it is the latest and greatest in climate modeling.

    I don’t dispute that. But are you suggesting this has something to do with Trenberth’s RMETs blog post? I don’t think it does. But if you do tell me what you think it has to do with Trenberth’s RMETs blog post.

  59. Trenberth seems to specialize in after-the-fact excuses.

  60. Lucia, for completeness I have linked to a table for RCP85 as I did previously for RCP60. I used the 2010 through 2090 data for RCP85 as I did for RCP60. Unlike RCP26 and RCP45 these 2 scenarios show much less bending at the end of the series. RCP85 has a steeper slope than RCP60 and has less 10 and 12 year flat/negative trends. Notice also that the overall trends are much the same for all the replicate runs of a given model for both the RCP60 and 85 series.

    I found on graphing model run CEC_3 (because it had three 10 year flat/negative trends) that it was either not transferred properly to KNMI or it truly was a screwed up run. I intend to connect the owner of KNMI about this run.

    http://imageshack.us/a/img703/5269/zur.png

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