Monthly Archives: April 2008

Another Paper On Antarctic Climate Trends By Monoghan et al.

Thanks to Tobias Rothenberger at the University of St. Gallen (where he is studying economics), he has referred us to another important paper on Antarctic climate trends (Tobias has a website also; Climate Review). The article is

Monaghan, A. J., D. H. Bromwich, and D. P. Schneider (2008), Twentieth century Antarctic air temperature and snowfall simulations by IPCC climate models, Geophys. Res. Lett., 35, L07502, doi:10.1029/2007GL032630.

The abstract reads 

“We compare new observationally-based data sets of Antarctic near-surface air temperature and snowfall accumulation with 20th century simulations from global climate models (GCMs) that support the Intergovernmental Panel on Climate Change Fourth Assessment Report. Annual Antarctic snowfall accumulation trends in the GCMs agree with observations during 1960–1999, and the sensitivity of snowfall accumulation to near-surface air temperature fluctuations is approximately the same as observed, about 5% K−1. Thus if Antarctic temperatures rise as projected, snowfall increases may partially offset ice sheet mass loss by mitigating an additional 1 mm y−1of global sea level rise by 2100. However, 20th century (1880–1999) annual Antarctic near-surface air temperature trends in the GCMs are about 2.5-to-5 times larger-than-observed, possibly due to the radiative impact of unrealistic increases in water vapor. Resolving the relative contributions of dynamic and radiative forcing on Antarctic temperature variability in GCMs will lead to more robust 21st century projections.”

The conclusion of the paper states

“The annual snowfall trends in the GCMs agree with the observations during 1960–1999, but annual NSAT trends for 1880–1999 are too large by a factor of 2.5-to-5. Our results suggest that the larger-than-observed GCM NSAT trends may be related to unrealistic increases in atmospheric water vapor over Antarctica which enhances longwave radiative forcing at the surface. When applied to the longwave radiation trend, the regression relationship presented in Figure 2b suggests that the positive contribution of longwave radiation to 1880–1999 Antarctic NSAT trends in the GCMs is about 4 times larger than the (overall) negative contribution of the SAM (and at least 2 times larger during 1960–1999 when SAM trends are largest). The monotonic increase of Antarctic NSAT in the GCMs may thus be related to the steady rise in GHGs since the 19th century, perhaps leading to an amplified GHG-temperature-water-vapor feedback that is contributing to the larger-than-observed NSAT trends. IPCC AR4 GCMs project that the SAM will continue strengthening throughout the 21st century [e.g., Fyfe and Saenko, 2006], therefore it should be a priority to clarify the relative roles of the SAM and radiative forcing on Antarctic temperatures and how they may change. Until these issues are resolved, IPCC projections for 21st century Antarctic temperature should be regarded with caution.”

This paper provides further evidence that the multi-decadal global climate models are significantly overstating the water vapor input into the atmosphere, and thus are not providing quantitatively realistic estimates of how the climate system responds to the increase in atmospheric well mixed greenhouse gases in terms of the water vapor feedback. This water vapor feedback is required in order to achieve the amount of warming from radiative forcing projected in the 2007 IPCC report.

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The Real Butterfly Effect

There has been a renewed discussion of the relevance of the “butterfly effect” to describe the actual effect of the flapping of a butterfly wing on large-scale weather (on Real Climate see and on Climate Science see and see).

There is an important research issue with respect to the size of a perturbation of the atmosphere that must occur before it can have any effect on the larger-scale atmosphere. Ray Pierrehumbert and Gavin Schmidt on Real Climate conclude that there is no minimum spatial scale, while Issac Held states that features must be larger than a few millimeters.

Rich Eykholt and I have agreed to complete a paper on this subject over the coming months, as it clearly is an issue that has been neglected, and, in my view, is a misinterpretation of the conclusions from the seminal work of Ed Lorenz.

The real butterfly is illustrated below  


“The Lorenz attractor is a 3-dimensional structure corresponding to the long-term behavior of a chaotic flow, noted for its butterfly shape. The map shows how the state of a dynamical system (the three variables of a three-dimensional system) evolves over time in a complex, non-repeating pattern.  Picture below is a plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3.”

Image:Lorenz system r28 s10 b2-6666.png


The interested reader can also evaluate the solution for different input values at


In terms of what Professor Lorenz wrote, following is the text from his book The Essence of Chaos by Ed Lorenz in 1993 (from pages 14 and 15) regarding the expression “The Butterfly Effect”. The Figure 2 that he refers to in the text is of the form of the above two figures, and he labels it as “The butterfly”! Professor Lorenz wrote

“The expression has a somewhat cloudy history. It appears to have arisen following a paper that I presented at a meeting in Washington in 1972 entitled “Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”  I avoided answering the question, but noted that if a single flap could lead to a tornado that would not otherwise have formed, it could equally well prevent a tornado that would otherwise have formed. I noted also that a single flap would have no more effect on the weather than any flap of any other butterfly’s wings, not to mention the activities of other species, including our own.  The paper is reproduced in its original form as Appendix A.

The thing that has made the origin of the phrase a bit uncertain is a peculiarity of the first chaotic system that I studied in detail.  Here an abbreviated graphical representation of a special collection of states known as a “strange attractor” was subsequently found to resemble a butterfly, and soon came to be known as the butterfly.   In Figure 2 we see one butterfly; a representative of a closely related species appears on the inside cover of Gleick’s book.  A number of people with whom I have talked have assumed that the butterfly effect was named after this attractor.  Perhaps it was.

Some correspondents have also called my attention to Ray Bradbury’s intriguing short story, “A Sound of Thunder,” written long before the Washington meeting.  Here the death of a prehistoric butterfly, and its consequent failure to reproduce, change the outcome of a present-day presidential election.

Before the Washington meeting, I had sometimes used a sea gull as a symbol for sensitive dependence.  The switch to a butterfly was made by the session convenor, the meteorologist Philip Merilees, who was unable to check with me when he had to submit the program titles. Phil has recently assured me that he was not familiar with Bradbury’s story. Perhaps the butterfly, with its seeming frailty and lack of power, is a natural choice for a symbol of the small that can produce the great.

Other symbols have preceded the sea gull. In George W. Stewart’s novel Storm, a copy of which my sister gave me for Christmas when she first learned I was to become a meteorology student, a meteorologist recalls his professor’s remark that a man sneezing in China may set people to shoveling snow in New York.  Stewart’s professor was simply echoing what some real-world meteorologists had been saying for many years, sometimes facetiously, sometimes seriously.”

Thus, the butterfly effect, which is described by the solution shape in the above figures, has morphed into a symbol that small perturbations can alter large-scale structure.

However, scientists such as Ray Pierrehumbert and Gavin Schmidt at Real Climate have literally interpreted Professor Lorenz’s seminal as applying to all perturbations of atmospheric flow regardless of their magnitude and spatial scale.  This clearly was not the claim of Professor Lorenz.

In the real world, very small perturbations, such as the flap of a butterfly wing cannot have any impact on the large-scale flow (such as the creation of a tornado). In order to do that, the turbulence generated by the flapping wings must retain some coherant flow structure as the nonlinear interactions create larger scale structure. However, this kinetic energy is dispersed over progressively larger and larger volumes such that it will quickly dissipate into heat as the magnitude of the disturbance to the flow at any single location becomes smaller. The atmosphere has an infinitesimal addition of heat, but the coherent information needed to alter the large-scale flow is lost.

This paragraph should, of course, be viewed as a hypothesis, and we will be evaluating this in our paper. Readers, including those at Real Climate, are invited to also seek to falsify this hypothesis.

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Comments on the NOAA Press Release “NOAA Employing New Tools to Accurately Measure Climate Change”

NCDC has released the following press release [see Watts Up With That for more information on NCDC’s plans and NOAA Employing New Tools to Accurately Measure Climate Change]

NOAA has announced the completion of the new Climate Reference Network which is an excellent program in their press release.

However, with respect to the modernization of existing climate observing sites, they have glossed over their serious inadequacies. 


 In their news release, they perpetuate the myth that they can correct “less-than-ideal” sites.  The news release writes:


“Data gathered by those existing HCN stations that were located in less-than-ideal areas have been statistically corrected in the analysis of climate trends routinely reported by NOAA. Though some individual stations were placed in less-than-ideal areas, these data anomalies did not significantly alter overall climate measurements. The modernization will relocate these stations in areas that are closer to ideal.”


This ignores the evidence to the contrary that we have published in peer-reviewed papers; e.g., see


Pielke Sr., R.A. J. Nielsen-Gammon, C. Davey, J. Angel, O. Bliss, N. Doesken, M. Cai., S.  Fall, D. Niyogi, K. Gallo, R. Hale, K.G. Hubbard, X. Lin, H. Li, and S. Raman, 2007: Documentation of uncertainties and biases associated with surface temperature measurement sites for climate change assessment. Bull. Amer. Meteor. Soc., 88:6, 913-928.




Pielke Sr., R.A., C. Davey, D. Niyogi, S. Fall, J. Steinweg-Woods, K. Hubbard, X. Lin, M. Cai, Y.-K. Lim, H. Li, J. Nielsen-Gammon, K. Gallo, R. Hale, R. Mahmood, S. Foster, R.T. McNider, and P. Blanken, 2007: Unresolved issues with the assessment of multi-decadal global land surface temperature trends. J. Geophys. Res., 112, D24S08, doi:10.1029/2006JD008229.


NCDC continues to have blinders on in terms of the serious of their errors in assessing long temperature near-surface air temperature trends and anomalies.


There is, for example, a warm bias in their assessments which we have documented in the literature but they have chosen to ignore instead of seeking to refute in the literature or accept [i.e., see


Walters, J.T., R.T. McNider, X. Shi, W.B. Norris, and J.R. Christy, 2007: Positive surface temperature feedback in the stable nocturnal boundary layer. Geophys. Res. Lett., 34, L12709, doi:10.1029/2007GL029505,


Lin, X., R.A. Pielke Sr., K.G. Hubbard, K.C. Crawford, M. A. Shafer, and T. Matsui, 2007: An examination of 1997-2007 surface layer temperature trends at two heights in Oklahoma. Geophys. Res. Letts., 34, L24705, doi:10.1029/2007GL031652.


Moreover, if NCDC can statistically adjust the decadal temperature trends of the poorly sited stations (to an accuracy of tenths of degrees per decade, why do they even need to modernize? That they do see this need is clear evidence of the inadequacies of the poorly sited locations.

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Continued Discussion With Real Climate On The Butterfly Effect

The discussion with Real Climate continues. The updated comments as of Saturday April 26 are at

Comment On Real Climate’s Post On The Relevance Of The Sensitivity Of Initial Conditions In The IPCC Models

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More Evidence of LULCC Impact by Dr. Matt Georgescu Of Rutgers University

Guest Weblog by Dr.  Matt Georgescu Of Rutgers University

More Evidence of LULCC Impact

Assessment of anthropogenic influences on climate has primarily focused on changes in globally-averaged metrics (e.g., temperature, tropospheric radiation balance) resulting from emissions of well-mixed greenhouse gases. However, sub-global-scale forcings and their impacts are also important. Understanding regional climate change is essential in its own right, as this is the scale of many impacts of concern for human and natural systems. In addition to drivers at the global scale, thorough attribution of anthropogenic climate change must take into account an additional number of factors. It is my belief that in addition to increases in the concentration of atmospheric greenhouse gases, landscape change plays a significant role on the evolving climate system. This message, of which Prof. Pielke and have been outspoken proponents of (e.g., Pielke et. al., 2002), in my opinion, deserves further attention.

The Greater Phoenix area (i.e., central Arizona) serves as a strategic study region that may be used to better understand the climatic consequences of landscape change – the area has undergone rapid population increase since the initial permanent settlement was established in 1868.  Throughout the next 50 to 75 years, or so, agriculture became the mainstay of the area’s growing economy.  An increasingly diverse economy, attractive climate, and relatively low-cost housing led to a shift in economic priorities during the latter half of the century and urban/sub-urban expansion began to dominate. The city continued to expand, and by 1995 Phoenix’ (the city itself, rather than the metropolitan area as a whole) population increased to nearly 1.2 million. 

My Ph.D. work at Rutgers University [with Advisor Chris P. Weaver] has focused on assessing the impact of landscape change on the summer climate of one of the nation’s most rapidly expanding metropolitan complexes, the Greater Phoenix, AZ, region. The specific importance for research investigations of this area is two-fold:

1.  The area has been undergoing, and continues to undergo, rapid landscape change as sprawl continues nearly unabated, thereby offering scientists a valuable opportunity to observe and relate modeling results to the actual evolving situation on the ground.

2.  Sprawl and landscape change continue in numerous additional semi-arid locales, all serving as centers of human migration, both within the United States (e.g., Las Vegas) and without (e.g., Riyadh).  Therefore, lessons learned regarding possible negative effects over the Greater Phoenix, AZ, region, may lead to improved mitigation strategies in other areas undergoing similar landscape change. 

Of particular significance to the Greater Phoenix area and it’s relentlessly growing population and metropolitan expansion is the impact on precious natural water resources. This region is stressed to begin with and the climatological scarcity of water, together with increasing expansion, may pose significant impacts on the public sector down the road.

New work, recently published (online) in the Journal of Arid Environments (Georgescu et al., 2008), demonstrates the important dual roles of two specific patterns of land-use over the Greater Phoenix area.  The summary of the paper reads as following:

This work evaluates the first-order effect of land-use/land-cover change (LULCC) on the summer climate of one of the nation’s most rapidly expanding metropolitan complexes, the Greater Phoenix, AZ, region. High-resolution – 2-km grid spacing – Regional Atmospheric Modeling System (RAMS) simulations of three ‘‘wet” and three ‘‘dry” summers were carried out for two different land-cover reconstructions for the region: a circa 1992 representation based on satellite observations, and a hypothetical land-cover scenario where the anthropogenic landscape of irrigated agriculture and urban pixels was replaced with current semi-natural vegetation. Model output is evaluated with respect to observed air temperature, dew point, and precipitation. Our results suggest that development of extensive irrigated agriculture adjacent to the urban area has dampened any regional-mean warming due to urbanization. Consistent with previous observationally based work, LULCC produces a systematic increase in precipitation to the north and east of the city, though only under dry conditions. This is due to a change in background atmospheric stability resulting from the advection of both warmth from the urban core and moisture from the irrigated area.

Analysis of results show a dipole pattern of temperature differences between the pair of landscape reconstructions that is magnified during the “dry” simulations as compared to the “wet” simulations; that is to say, during “dry” runs (each run, using a triply nested grid configuration, with the fine grid containing a 2-km grid spacing, lasted for 1 entire July month), the maximum (urban) temperature increases are enhanced for the 1992 landscape relative to the pre-settlement landscape (urban area differences during the “dry” simulations are in excess of 0.7°C, while urban area temperature differences between the pair of landscapes are closer to 0.5°C for the “wet” simulations). Similarly, the maximum temperature decreases are also enhanced (that is, more cooling over plots of irrigated agriculture) during the “dry” simulations when compared to the “wet” simulations.

In addition, this paper (i.e., Georgescu et al., 2008) is the first to present numerical modeling results, to our knowledge, consistent with prior observational analysis (e.g., Shepherd et al., 2006) showing an enhancement of precipitation due to the presence of the Greater Phoenix area. 

The combined effect of warming (over areas that underwent urbanization) and cooling (over plots of irrigated agriculture) tend to counteract one another. This result is especially critical when considering that during the last three or so decades, coverage of irrigated agriculture has declined sharply at the expense of urbanization (suggesting a significantly greater warming effect due to recent LULCC). Two additional manuscripts detailing the radiative, dynamical, and thermodynamical effect(s), also through a numerical modeling framework, depict the evolution of Greater Phoenix’ regional climate in response to the observed changes in landscape (since the dawn of the satellite era to, roughly, today), are nearing completion.


Georgescu, M., G. Miguez-Macho, L. T. Steyaert, and C.P. Weaver, 2008: Sensitivity of summer climate to anthropogenic land cover change over the Greater Phoenix, AZ, Region, J. Arid Env., doi: 10.1016/j.jaridenv.2008.01.004.

Pielke Sr., R.A., G. Marland, R.A. Betts, T.N. Chase, J.L. Eastman, J.O. Niles, D. Niyogi, and S. Running, 2002: The influence of land-use change and landscape dynamics on the climate system-relevance to climate change policy beyond the radiative effect of greenhouse gases, Phil. Trans. A. Special Theme Issue, 360, 1705-1719.

Shepherd, J. M., 2006: Evidence of urban-induced precipitation variability in arid climate regions, J. Arid. Env., 67, 607-628.

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Teleconnections In The Earth System By Chase, Pielke and Avissar

We have a new article published which has not been reported on Climate Science. It is

Chase, T.N., R.A. Pielke Sr., and R. Avissar, 2007: Teleconnections in the Earth system. Encyclopedia of Hydrological Sciences, M. Anderson, Editor-in-Chief, John Wiley and Sons, United Kingdom, 2849-2862.

The table of the contents of the entire book can be accessed from

The abstract reads,

“This section illustrates the large-scale connectivity of the atmosphere-ocean coupled system and generalizes the concept to regional scales and to other components of the earth system. Connections at a distance, or teleconnections, can occur by the direct transfer of mass by changes in regular circulations or by propagating waves initiated by a variety of mechanisms. Questions as to what extent recognized teleconnection patterns can be associated with identifiable forcing mechanisms, to what extent these patterns are interrelated and how they might cause, react to, or interact with changing forcing such as changes in atmospheric composition, landcover, or the distribution of sea ice to produce climate changes are examined. “

We write,

“… appears that evidence is emerging that the climate system is coupled in a variety of complicated ways and that conceiving of variability in terms of a series of isolated teleconnection patterns may give way to a view that each of the patterns is interrelated in some way, each forcing and being forced by the others. Long chains of causality linking some or all modes of variability might improve predictability if the chains of events are regular, though past experience indicates that relationships between the modes vary with time. “

The summary of the paper states,

“This discussion illustrates the large-scale connectivity of the atmosphere-ocean coupled system and generalizes the concept to regional scales and to other components of the earth system. These connections at a distance, referred to as teleconnections, can occur by the direct transfer of mass by changes in regular circulations or by propagating waves initiated by a variety of mechanisms.

We have not discussed in detail several processes, which could rightfully be included in this section such as the regional monsoon systems, local winds, or the oceanic thermohaline circulation which, if changed, could have large climate repercussions all around the globe. We have, however, addressed the basic remaining uncertainties as to the nature of teleconnection patterns with prominent examples. Questions remain as to what extent recognized teleconnection patterns can be associated with an identifiable forcing mechanism, to what extent these patterns are interrelated and how they might cause, react to, or interact with changing forcing such as changes in atmospheric composition, landcover, or the distribution of sea ice to produce climate changes? “

This article provides further substantiation to the Climate Science weblog of July 28 2005 entitled What is the Importance to Climate of Heterogeneous Spatial Trends in Tropospheric Temperatures? where it is written

“…….regional diabatic heating due to human activities represents a major, but under-recognized climate forcing, on long-term global weather patterns. Indeed, this heterogeneous climate forcing may be more important on the weather that we experience than changes in weather patterns associated with the more homogeneous spatial radiative forcing of the well-mixed greenhouse gases.”

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Comment On Real Climate’s Post On The Relevance Of The Sensitivity Of Initial Conditions In The IPCC Models

Follow Up (April 27 2008)

Ray – In searching for what Professor Lorenz has said on this issue, please  see Chaos Avant-Garde: Memories of the Early Days of Chaos Theory

 In this essay he writes,

“Returning now to the question as originally posed, we notice some additional points not yet considered. First of all, the influence of a single butterfly is not only a fine detal – it is confined to a small volume. Some of the numerical methods which seem to be well adapted for examining the intensification of errors are not suitable for studying the dispersion of errors from restricted to unrestricted regions. One hypothesis, unconfirmed, is that the influence of a butterfly’s wings will spread in turbulent air, but not in calm air”

This certainly would rule out the butterfly in the jar! More importantly, he recognized that there remain questions about the “butterfly effect”, one of which is when small pertubations result in altering larger scale atmospheric flow, and when they do not.

Sixth Update (April 27 2008)

A Further Reply By Ray Pierrehumbett

 [Response:Roger, I can’t make sense of what you’re trying to say here. For those picokelvins of temperature to be lost to space, first they have to appear in the atmosphere as an increase of temperature, right? So there you have your change of one digit in the initial conditions, just like in Lorenz’s example. And your statement is just flatly inconsistent with thermodynamics. The butterfly dissipates heat locally, and that heat will be gradually diluted over a larger and large area. So just divide by Cp and there’s your answer. Do you think there’s some way to magically teleport the heat away, leaving the fluid to heal back to exactly the same condition it would have had without the flap? That’s really a stretch. Your remarks about simple models and GCM’s don’t make much sense to me either. The GCM doesn’t resolve butterfly-scale motions, but once you have influenced a dynamic variable (e.g. temperature) at a resolved scale, any number of actual twin experiments in GCM’s confirm the divergence. If you are claiming there’s some fundamental difference between sensitive dependence to large scale changes in a GCM and sensitive dependence in the atmosphere, I’d like to see some evidence to back up that claim. The success of GCM’s in short term weather forecasting would be pretty much impossible to reconcile with such a claim. –raypierre]

 My Reply

You are correct in that you and I probably agree on most issues in chaos and nonlinear dynamics. All NWP and climate models show the sensitivity of large scale circulation features to initial conditions when perturbations are inserted in their initial state or in their parameterizations (these are all much larger effects than the energy that a butterfly places in the system). We also agree that the added heat from a butterflies flapping wings results in a slightly different system than if this flapping did not occur. However, the issue is whether the heat (the “information”) from this effect can translate (teleconnect) to larger scale so as to result in alterations in large scale features. 

Even Issac Held seemed to indicate that there is a lower limit to when this upscale effect can occur (i.e. this ability disappears when the flow becomes laminar); he said in this thread

“the scale of the perturbation has to be larger than what is often referred to as the Kolmogorov microscale, the scale below which the flow is effectively laminar, to avoid being damped out immediately. This scale is typically a few millimeters in the atmosphere….”

I agree with this, but maintain that the smallest turbulent scales also are damped out due to the physics of non-motion transfers (i.e. radiative transfers) of energy. I have been in communication with Professor Ekyholt on this question, and he and I agree that you are misinterpreting the butterfly effect for very small scale perturbations. We will be preparing a paper on this to demonstrate that there is  lower limit to which the “butterfly effect” applies.

On a separate note, I see commenters on this thread are somehow skewing this discussion to be on climate change. It is not. This issue of the scale at which the “butterfly effect” occurs is a pure discussion of the science such as we all used to have as graduate students and need more of!

Also, you questioned as to why Roy Spencer posted a guest weblog. The answer is that he has introduced a novel and important new perspective into how variations in atmospheric/ocean circulations can result in alterations in the global average radiative balance. Disagreements with his results and conclusions should be on his science. I invite others (including any interested Real Climate climate scientist) to post unedited guest weblogs on Climate Science.  

 Additional Response From Ray  Pierrehumbert

 [Response:Regarding the butterfly in the room — even in a jar in the room — sure I think it’s likely that it would ultimately affect the large scale weather. Look at it this way: Temperature has a dynamic influence through buoyancy. The heat dissipated by the butterfly might warm the room by a few tens of microkelvins, say. That increased temperature will change the heat flow between the house and the environment, which will ultimately change the temperature of some parcel of air by a few nanokelvins. Then before you know it, some parcel of air the size of the state of Illinois has a temperature different by maybe a few picokelvins. I guarantee that if you take a GCM and change the temperature of the air over Illinois by a few picokelvins (given sufficient arithmetic precision) that that will lead to divergence of the large scale forecast given infinite time. I have seen no indication either in dynamical systems theorems or in numerical experiment to suggest that anything else would be the case. –raypierre]

My Reply

Ray- We certainly disagree with respect to the butterfly in the room in a jar.  :-). Other readers of Real Climate (and Climate Science) can make up their own minds on this.

You are, however, taking the concept of chaos too narrowly and are focusing on idealizations (simple illustrative models and GCMs) of  how the real atmosphere (and climate system) works. You are ignoring the consequences of the dissipation of kinetic energy into heat within a open system. The “picokelvins” of heat, even if they could cause such a temperature perturbation over the state of Illinois (which it would not), would be lost to space long before an “infinite” time were reached.

Fourth Update (April 26 2008)

 Additional Response From Ray  Pierrehumbert

[Response:Have a look at Isaac’s remark above. I think what you probably have in mind is the possibility that if a perturbation is at a scale where you have primarily downscale energy cascade to the dissipation range, it might never project on the large scale quantities whose behavior determines large scale predictability loss. Given the nature of turbulence, it is hard to absolutely exclude this possibility a priori, but for this to happen, there would have to be ZERO leakage to large scales. Not just small but ZERO. That is exceedingly unlikely, and would be contrary to most of what is know about turbulent cascades. As a practical matter, I do agree that if the initial perturbation is at sufficiently small scales, the projection on large scales would be small enough that it could take an exceedingly long time before it affected the evolution of the large scales. –raypierre]

My Reply [posted on Real Climate]

Ray – Thank you for getting involved in this discussion.  The question of the leakage time scale is, of course needed, in order to determine when the exceedingly long time scale becomes infinite (in terms of where the heat goes).  If we both agree that ALL of the turbulence quickly dissipates into heat when the flapping stops, then what is your estimate of the residence time of this heat within the atmosphere before it is lost to space?

Also, as another thought example, if a butterfly flaps its wings inside a room with the doors shut, would you still maintain that this has an influence on atmospheric circulation at large distances? All of the heat generated would be absorbed by the walls of the room, and subsequent heat conduction is, of course, laminar.  An analogous behavior will occur in a very stable boundary layer (and any region of the atmosphere for such small perturbations), and if we can agree on this “exception” than we have made progress in understanding this issue. My point here is that if there is an part of the process which results in complete loss of the turbulent flow, then it is not communicated over large distances.

Issac’s Held’s answer also actually contains part of the answer on this issue.  If the turbulence dissipates into heat, as  illustrated in the above example,  than its further behavior can be described by non-turbulent behavior. As he explained, he was “was thinking that the scale of the perturbation has to be larger than what is often referred to as the Kolmogorov microscale, the scale below which the flow is effectively laminar, to avoid being damped out immediately. This scale is typically a few millimeters in the atmosphere “.  This is what occurs with the flapping of the wings of a butterfly; all of its energy dissipates into heat and the spatial structure of this heated air is less than a few mm.  To disprove this total transfer downscale, one would have to show that a coherent turbulent structure remains  and becomes progressively larger in scale and/or is monitored propagating away from the location of the flapping wings as a coherent disturbance of the air flow; in both cases,  while still retaining the conservation of total energy.  Since the total energy of the flaps of the butterfly’s wings must be accounted for (as kinetic energy in the turbulence, heat) what is your estimate of the magnitude of this energy that reaches thousands of kilometers away, as well as the path this energy would take to get there?

Third Update (April 25 2008)

Further Response From Gavin Schmidt

 Response: As we said above, this is what you believe. Why you accused us of misrepresenting you is a mystery. However, your claim about Ekykholt’s belief is contradicted by his quote above. He states very specifically that exponential growth saturates at the time the perturbation reaches the size of the attractor. That, for the atmosphere, is very large indeed and is certainly large scale enough to encompass storms thousands of miles away. Isaac can certainly speak for himself, but as far as I know there is no demonstration that there is a minimum scale below which perturbations do not grow. Such a thing may exist, but your certainty on the matter seems a little overconfident. Perhaps you’d care to point out a reference on the subject? – gavin]

 My Reply [posted on Real Climate] Gavin  – I am glad this discussion is continuing. I will be having more to say on this next week in a weblog on Climate Science, however, you are failing to distinguish between an open and closed system, and between the real world and models.  With nonlinear atmospheric models such as analyzed by Professor Lorenz, the results for large scale features are sensitive to the initial conditions regardless of how small they are. This is because the system is closed.  The real world climate system, however, is not closed, such that energy (i.e. in the form of heat) can leak out of the system.  In the case of such a small perturbation as the flap of a butterfly wing, the kinetic energy of the small amount of turbulent air that it generates will quickly dissipate into heat, once the flapping stops. Radiative loss of this heat to space will prevent the flapping to have any effect at large distances.  

This is one of the reasons that you are mistaken in stating that “there is no demonstration that there is a minimum scale below which perturbations do not grow.” If a perturbation in the system (i.e. the atmosphere) dissipates into heat, it can be lost to the system before affecting atmospheric features at large distances. I will have more on this topic on my weblog next week, and will post a comment on Real Climate when it appears.

Second Update (April 24 2008)

 Gavin Schmidt has replied

Response:You misinterpreted this back on the original thread and you are misinterpreting it here again. However, just repeating the same argument is pointless. Since I agree with Dr. Eykholt’s statement, and so do you, let’s just leave it at that. (if other readers are interested in what this is about, please go to the original thread. The clue is that ‘larger scales’ in the Eykholt quote means the attractor itself (i.e. climate), while RP thinks he means the large scale flow (i.e. the specific position on the attractor)). – gavin]


My Response is

 Gavin- I agree readers can go through the thread to see the discussion. However, you are misrepresenting my views. Rich Eykholt and I are in 100% agreement on this subject. The question that was being discussed is whether an atmospheric perturbation as small as a real world butterfly could actually affect large scale weather features thousands of kilometers away. The answer, as given by Professor Eykholt, is NO under any circumstance. The perturbation has to be much larger (Issac Held, as I recall said meters in his NPR interview; I suspect it is a few kilometers or more) for a perturbation to affect an atmospheric feature thousands of kilometers away.

This issue, based on our disagreement, would benefit from further quantitative evaluation with both analytic and numerical models. We do have papers on the use of analytic models to examine chaos and nonlinear dynamics which document that we are quite familiar with the subject of sensitivity of the climate system to initial conditions; e.g. see

Pielke, R.A. and X. Zeng, 1994: Long-term variability of climate. J. Atmos. Sci., 51, 155-159.

Update (April 24 2008)  : Following is my comment, Gavin Schmidt’s reply, and my response on Real Climate

 Roger A. Pielke Sr. Says:
23 April 2008 at 10:15 AM

Please see

[Response:In the linked piece, you very clearly state that you do not believe that the real world is sensitive to initial condition variations like butterflies. That is all we are discussing here. If you now think that it is, feel free to expound on your viewpoint. We were just trying to make sure that a diversity of points was presented. – gavin]

My Reply

Gavin – Thank you for posting my Climate Science link. In terms of actual butterlies, this is clearly explained by an expert in the physics and mathematics of nonlinear dynamics and chaos in geophysical flows, Professor Richard Eykholt (see, where he writes 

Roger: I think that you captured the key features and misconceptions pretty well. The butterfly effect refers to the exponential growth of any small perturbation. However, this exponential growth continues only so long as the disturbance remains very small compared to the size of the attractor. It then folds back onto the attractor. Unfortunately, most people miss this latter part and think that the small perturbation continues to grow until it is huge and has some large effect. The point of the effect is that it prevents us from making very detailed predictions at very small scales, but it does not have a significant effect at larger scales. 

Richard Eykholt”

Original Post

Real Climate has published a well written summary of the seminal accomplishments of Professor Ed Lorenz in the field of deterministic chaos and nonlinear dynamics (see). Professor Lorenz’s contribution to the understanding of the mathematics and physics of geophysical flows (and other dynamic systems) has altered how the science community investigates these processes. I had the opportunity to sit and talk with Professor Lorenz during one of his trips to Colorado State University, and enjoyed and learned from his perspective on the nonlinear aspects of the climate system including its behavior, as with any other nonlinear system with strong feedbacks, as being sensitive to initial conditions.

At the end of the well deserved recognition to Professor Lorenz, Real Climate writes

“So what does this have to do with the IPCC?”

Real Climate then writes

“Even though the model used by Lorenz was very simple (just three variables and three equations), the same sensitivity to initial conditions is seen in all weather and climate models and is a ubiquitous phenomenon in many complex non-linear flows. It is therefore usually assumed that the real atmosphere also has this property. However, as Lorenz himself acknowledged in 1972, this is not directly provable (and indeed, at least one meteorologist doesn’t think it does even though most everyone else does). Its existence in climate models is nonetheless easily demonstratable. “

I am the “one meteorologist”.  Real Climate refers to one of the Climate Science weblogs on this issue that was published (see).

However, Real Climate is wrong in its statement on my research conclusions!  I have written several papers on climate as an initial value problem: e.g. see

Pielke, R.A., 1998: Climate prediction as an initial value problem. Bull. Amer. Meteor. Soc., 79, 2743-2746.

Pielke Sr., R.A., G.E. Liston, J.L. Eastman, L. Lu, and M. Coughenour, 1999: Seasonal weather prediction as an initial value problem. J. Geophys. Res., 104, 19463-19479.

Rial, J., R.A. Pielke Sr., M. Beniston, M. Claussen, J. Canadell, P. Cox, H. Held, N. de Noblet-Ducoudre, R. Prinn, J. Reynolds, and J.D. Salas, 2004: Nonlinearities, feedbacks and critical thresholds within the Earth’s climate system. Climatic Change, 65, 11-38.

Real Climate should report  accurately on the research of others.

What we disagree on is whether the multi-decadal global climate model predictions can be used to accurately quantify the degree of nonlinearity and predictability of the real world climate system (the nonlinearity of the climate system is shown, for example, in the Rial et al paper).

Real Climate, however, reports on the use of a model to investigate this issue. This is a typical mistake they are making; a model is itself a hypothesis and cannot be used to prove anything! The multi-decadal global model simulations only provide insight into processes and interactions, but we must use real world data to test the models. So far, the models have failed, for example,  in their ability to accurately predict the regional weather and climate features we discuss in the Rial et al paper. Lets have more accurate reporting on Real Climate.

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