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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Comments On The Testimony Of Senator Dick Lugar On Climate Change and Deforestation On April 22 2008

There was a Hearing on Climate Change and Deforestation in the U.S. Senate yesterday (April 22 2008) [Thanks to Dev Niyogi of Purdue for alerting me to this Hearing].  There will be a presentation of the results so far on the excellent Vulcan project, which Climate Science weblogged on last week (see). 

Senator Lugar starts his testimony with the text

 “I thank the Chairman for holding this important hearing.  A year ago today, I was on my farm in Marion County, Indiana, for a ceremony recognizing the role of agriculture and forestry in mitigating the social, economic, and political threats posed by climate change.  I was joined by Richard Sandor, Chairman and CEO of the Chicago Climate Exchange, and Tom Buis, President of the National Farmers…, to promote how certain no tillage agricultural practices and forestry can sequester carbon dioxide and help offset the environmental threats from excessive carbon emissions.”

Later he writes,

 “Clearly, there are economic opportunities in clean energy sources, solar, wind and biofuels, and carbon sequestration and storage technologies.  But improvements in farming and forestry practices may be among the lowest hanging fruit in the quest to deal with climate change.”

The planting of trees certainly should be encouraged for a variety of reasons. However, Senator Lugar has not adequately communicated the following issues:

  • The conversion of the landscape by deliberate management practices, is itself a climate change forcing (Kabat et al, 2004; NRC, 2005; Feddema et al, 2005; Pielke 2005).
  • The net effect of deliberate landscape change such as afforestation may actually result in a radiative warming effect even though CO2 is extracted from the atmosphere by the plants. This occurs if the resulting surface albedo is less than for the original landscape and due to the added water vapor that is transpired into the atmosphere from the vegetation (i.e. see Pielke Sr., R.A., 2001: Carbon sequestration — The need for an integrated climate system approach. Bull. Amer. Meteor. Soc., 82, 2021.). [Update: Thanks to Barry Hearn for alerting us to two typos in this paragraph!]

Further discussion of these issues is in the papers

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.

Marland, G., R.A. Pielke, Sr., M. Apps, R. Avissar, R.A. Betts, K.J. Davis, P.C. Frumhoff, S.T. Jackson, L. Joyce, P. Kauppi, J. Katzenberger, K.G. MacDicken, R. Neilson, J.O. Niles, D. dutta S. Niyogi, R.J. Norby, N. Pena, N. Sampson, and Y. Xue, 2003: The climatic impacts of land surface change and carbon management, and the implications for climate-change mitigation policy. Climate Policy, 3, 149-157.

 Unless these issues are addressed in the context of developing climate policy that includes rewards for landscape management, the desired goal of reducing the human impact on climate will not be achieved.

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Internal Radiative Forcing And The Illusion Of A Sensitive Climate System By Roy Spencer

Guest Weblog By Roy Spencer of the University of Alabama at Huntsville titled

“Internal Radiative Forcing And The Illusion Of A Sensitive Climate System

 1.  Background

Many of us, especially those who were trained as meteorologists, have long questioned the climate research community’s reliance on computerized climate models for global warming projections.  In contrast to our perception that the real climate system is constantly readjusting to internal fluctuations in ways that stabilize the system, climate models built upon measured climate behavior invariably suggest a climate system that is quite sensitive – sometimes catastrophically sensitive — to perturbations such as those from anthropogenic greenhouse gas emissions.  Unfortunately, it has been difficult to articulate our ‘hand-waving’ concerns in ways that the modelers would appreciate, i.e., through equations.    

After years of pondering this issue, and after working on our two latest papers on feedbacks (Spencer et al., 2007; Spencer and Braswell, 2008, hereafter SB08), I believe that I can now explain the main reason for this dichotomy.   Taking the example of clouds in the climate system, the issue can be introduced in the form of a question:

To what extent are climatic variations in clouds caused by temperature change (feedback), versus temperature change being the result of cloud variations? 

I will demonstrate that the answer to this seemingly innocuous question has a huge impact on whether we view the climate system as either sensitive or insensitive.  And since models, by necessity, are constructed based upon the observed behavior of the climate system, their behavior also depends on our interpretation of what is causing what in the climate system.

While my claim that causation is important might seem rather obvious to some, it has not been an overriding concern to many researchers whose publications suggest that one needs only to measure the co-variability between different variables – not the direction of causation between the variables – in order to diagnose feedbacks.  For instance, Kiehl and Ramanathan (2006) have offered this definition of cloud feedback:

“The change in a cloud process associated with a fluctuation of the climate state represents a cloud-climate feedback.”

While this definition accommodates the fact that causality can — and does — flow in both directions when clouds interact with other processes in the climate system, it unintentionally obscures an important process which can corrupt feedback estimates if not accounted for. 

Here I will show with a simple climate model that those who have been diagnosing feedbacks in the climate system have, either knowingly or unknowingly, been assuming causation in only one direction, and that faulty assumption has biased their interpretation of climate sensitivity.  That this source of bias is independent of time scale will be demonstrated with two examples: 1) daily noise in cloud cover, and 2) multi-decadal cloud cover changes assumed to be associated with low frequency modes of climate variability such as the Pacific Decadal Oscillation and El Nino/La Nina. 

Finally, we will see that by taking the direction of causation into account, some previously published results which have remained puzzling now take on new meaning.

2.  The 800-Pound Gorilla We’ve Missed: Internal Radiative Forcing

Researchers who diagnose feedbacks from observational data tend to view observed fluctuations in the climate system in the context of temperature changes causing other things to change, which can then feed back upon temperature.  Yet we know that, at least in the case of clouds, there are a wide variety of non-feedback processes that can affect cloud formation and dissipation, thus impacting the planetary albedo and Earth’s radiative budget.  The complexity of the processes which affect clouds was one of the central messages in Stephens’ (2005) extensive and critical review of cloud feedback.

Non-feedback radiative changes internal to the climate system would most easily be envisioned when the general circulation of the atmosphere undergoes fluctuations.  Horizontal temperature gradients, inversion location and strength, wind shear, and even land cover changes are potential sources of top-of-atmosphere (TOA) variations in the Earth’s radiative energy budget which do not have to be caused by a change in surface temperature per se.

For instance, it has been shown that daily noise in cloud cover can cause temperature variability that “looks like” positive cloud feedback (SB08).  But it turns out that this was just one example of a more general problem, a problem which amounts to the omission of a heating term in the heat budget equation.   And since “external radiative forcing” has come to mean radiative changes external to the normal operation of the climate system, it makes sense to call the neglected term “internal radiative forcing”, for which I tentatively propose the following definition:

Internal radiative forcing refers to any change in the top-of-atmosphere radiative budget resulting from an internally generated fluctuation in the ocean-atmosphere system that is not the direct result of feedback on temperature.          

That the work of the IPCC has been biased against the existence of internal sources of radiative forcing is clear from reading the IPCC reports.  For instance, even though “radiative forcing” is defined early in the Technical Summary of the Report of Working Group I in such a way that would include both internal and external sources, the report’s subsequent 100 references to radiative forcing are only in the context of external sources.  These typically include anthropogenic greenhouse gas and aerosol emissions, volcanic eruptions, and variations in solar flux.

We will see that the neglect of internal sources of radiative forcing represents more than just a source of error.  It impacts our perception of natural climate variability and what the climate system is telling us about climate sensitivity.

3. A Simple Climate Model

We start with a simple time-dependent model of temperature anomalies (T) around an equilibrium state,

Cp dT/dt = f + S  – λT + I                               (1)

where Cp is the heat capacity of the system; f is any “external” radiative forcing leading to a TOA radiative imbalance such as anthropogenic greenhouse gas emissions, volcanic aerosols, or solar variations;  S represents non-radiative sources of heating (e.g., variations in upwelling from the deep ocean); and λ is the total feedback parameter. This feedback parameter represents the sum of all (assumed linear) radiative feedbacks on temperature, including the Planck response component of thermally emitted longwave (LW) variability (about 3.3 W m-2 K-1, Forster and Taylor, 2006, hereafter FT06).   

Any temperature deviations away from equilibrium resulting from the heating terms on the RHS of (1) will then lead to radiative feedback on temperature through the λT term, such as through reflected solar shortwave (SW) or thermally emitted longwave (LW) cloud feedbacks. By convention, a negative component of the feedback parameter represents positive feedback, while a positive component of the feedback parameter represents negative feedback.  If the total feedback parameter λ is negative, the system is inherently unstable. These, then, are the customary terms which are included when discussing global mean climate variability.

But what is typically ignored is any source of internally-generated radiative forcing within the climate system, represented by I in Eq. 1.  We will see that its relationship to temperature is fundamentally different from that of the feedback term.

4.  Daily Stochastic Cloud Variations

A finite difference version of the model represented by (1) was run at daily time resolution with the following parameters:  f = 0; a system heat capacity equivalent to a 50 m deep ‘swamp’ ocean; and a total feedback parameter λ = 3.5 W m-2 K-1 representing a slight negative feedback component (0.2 W m-2 K-1), assumed to represent SW cloud feedback, combined with LW Planck response to temperature (3.3 W m-2 K-1). 

The model was forced with daily random fluctuations in non-radiative changes in surface temperature S and internally-generated radiative changes I of sufficient magnitudes to cause the model variability to match the satellite-observed monthly standard deviations of tropical (20oN to 20oS) oceanic reflected SW variability retrieved from the CERES (Clouds and the Earth’s Radiant Energy System, Wielicki et al., 1996) instrument flying on NASA’s Terra satellite, and sea surface temperatures measured by the Tropical Rain Measuring Mission (TRMM) Microwave Imager (TMI, Kummerow et al., 1998).   The resulting modeled temperature time series in Fig. 1a shows substantial low frequency variability, driven entirely by the daily noise in heating.  A change in the noise generator seed leads to different model realizations. 

If we then plot monthly averages of T versus the total radiative variability for the realization shown in Fig. 1a, we get a linear regression estimate of the feedback parameter λ’ = 2.94 W m-2 K-1 (Fig. 1b).  Note that it departs substantially from the specified value of λ = 3.5 W m-2 K-1, thus producing a positive feedback bias of -0.56 W m-2 K-1

In Monte Carlo simulations using the model represented by Eq. 1 and daily random noise in heating, SB08 found positive feedback errors generally in the range -0.3 to -0.8 W m-2 K-1. The magnitude of the positive bias in diagnosed feedbacks depends upon the relative strengths of internal radiative forcing (I) versus internal non-radiative forcing of the surface (S).  If there is only internal radiative forcing, then any feedback diagnosis will, in general, be strongly biased toward positive feedback.  If, on the other hand, the non-radiative forcing is the only source of temperature variability, then there is a perfect correlation, and there is no error in the diagnosed feedback (not shown).  The strength of the correlation as a possible indicator of a biased feedback parameter will be addressed later.


Fig. 1  a) Thirty years of modeled daily temperature variations of a 50 m deep swamp ocean being driven by daily random fluctuations in heat input; b) plot of 80 years of model output monthly average temperature versus total reflected SW (random forcing plus specified feedback).  The diagnosed feedback parameter λ’ (line slope) does not change substantially with averaging times up to yearly.

5.  Low-Frequency Variability from ENSO and the PDO

While the previous section addressed high-frequency noise in cloud cover as a source of bias in our diagnosis of feedbacks, the fundamental issue of internal radiative forcing is independent of time scale.  For example, it is reasonable to hypothesize that internal modes of climate variability have associated changes in albedo which are not the result of feedback on surface temperature.  But while persistent radiative imbalances on the order of 1 W m-2 are sufficient to cause substantial temperature changes on multi-decadal time scales, our satellite measurements of clouds and radiative fluxes are neither long enough, nor accurate enough, to measure such changes. 

This is not, however, a sufficient reason to assume they do not exist.

For instance, the major features of global mean temperature variations since 1900 (Fig. 2a) have usually been explained as a combination of anthropogenic greenhouse gas and aerosol emissions, possibly combined with a small amount of increased solar forcing (IPCC, 2007).  While this is indeed one possible explanation, it is also possible that some part of the temperature change represents internal variability in the climate system in the form of radiative forcing which is not the result of feedback.  After all, it is well known that ENSO has warm and cool phases which occur irregularly every few years, and that the warm phase (El Nino) has been more frequent during the warming experienced since the 1970′s (see Fig. 2b).  Similarly, the lower-frequency Pacific Decadal Oscillation (PDO, Mantua et al., 1997) was more often in its positive phase during the period of global mean warmth around 1940, as well as during the warming since the 1970s (Fig. 2c).


Fig. 2.  Monthly running 5-year means of: a) global mean surface temperature from the HadCRUT3 dataset; b) the Southern Oscillation Index (note the scale is inverted), and c) the Pacific Decadal Oscillation Index.  The data included in the 5-year averaging are from January, 1900 through February, 2008.

It is not unreasonable to hypothesize that the small changes in atmospheric and oceanic circulation associated with these modes of climate variability have caused corresponding non-feedback changes in clouds, which then impact the radiative budget of the Earth.  

It is critical to understand that, even though neither of the climate indices in Fig. 2 ‘looks like’ the corresponding temperature time series, we do not expect them to if they are associated with internal radiative forcing (I in Eq. 1).  This is because I is not proportional to temperature, but to the change in temperature with time.

We will hypothesize that the PDO and ENSO indices have associated with them some amount of internal radiative forcing due to cloud changes.  Again using the basic form of Eq. 1, we now assume that the only heating term is a linear function of the SOI and PDO indices,

Cp dT/dt = α PDOPDO + βSOISOI ) – λT                (2)

where                   βPDO + βSOI = 1.                       (3)

In this case, the heating term is a weighted average of the monthly PDO index value (PDO), and the negative of the monthly SOI index value (SOI); the two β coefficients provide the weights; and α is an empirical scaling factor in W m-2.  The total feedback parameter (l) again represents a combination of the infrared Planck response to temperature (3.3 W m-2 K-1) plus all other radiative feedbacks such as clouds, water vapor, lapse rate, etc.

Physically, Eqs. 2 and 3 simply say that the time rate of change of the system temperature around its equilibrium state is assumed to result from a net heating term made up of a linear combination the SOI and PDO climate indices, modified by feedbacks on that temperature.  Since the model is sensitive to noise in the SOI and PDO indices, here we will use monthly running 5-year means of those indices, rather than their raw monthly values.

If we run a finite difference version of the model represented by Eqs. 2 and 3 at monthly time resolution and modify the adjustable parameters of the model (Cp, which is proportional to the ocean depth; the scaling factor α; the heating term weights βPDO & βSOI; and the feedback parameter λ) we quickly find that a high correlation (0.94) is achieved between the model temperature and observed global temperatures for a model mixed layer depth of 1,000 m, and when the SOI term is weighted somewhat more heavily than the PDO term (βPDO = 0.37, βSOI = 0.63).  The correlation and temperature trend of the model output were found to not be very sensitive to positive or negative feedback parameters within 1 W m-2 K-1  of the nominal Planck response value of λ = 3.3 W m-2 K-1

This specific combination of the adjustable parameters produces the model temperature time series seen in Fig. 3b, where Fig. 3a shows the weighted combination of PDO and SOI, scaled by α = 2.7 W m-2, that forms the total heating term which forces the model.  The model was initialized with a heating value -0.53 W m-2 so that the modeled and observed average temperature anomalies were equal for the first 50 years of record (approximately 1900 to 1950).  Adjustment of this initial value causes only a temperature offset of the model curve, not its shape. 

It can be seen from Fig. 3 that this simple model captures a large portion of the major features of temperature change since 1900: warming until about 1940, slight cooling up to the 1970s, and then resumed warming since the 1970s.  The model warming trend (+0.50 deg. C/century) is 70% of the observed warming trend (+0.69 deg. C/century). 


Fig. 3.  a) Assumed internal radiative forcing proportional to a linear combination of the Pacific Decadal Oscillation index and that Southern Oscillation Index, used to force a simple model of temperature variability for a uniformly mixed ocean of adjustable depth; and b) the observed (HadSST2), and model output, sea surface temperatures for a combination of model adjustable parameters that yielded a high correlation between the model output and observations.  See text for additional details.

One could presumably use other climate indices to force the model with, or more complex interactions between the indices.  For instance, Tsonis et al. (2007) addressed the nonlinear interaction of four different internal modes of climate variability in a statistical framework for explaining climate variability since 1900.  But there are only a few degrees of freedom contained in the low frequency temperature variability since 1900, and the intent here is only to demonstrate that a simple physical model, driven by two well known modes of internal climate variability, can explain most of the major features of global mean temperature changes since 1900 without resorting to anthropogenic greenhouse gas and aerosol forcing.  

While it might be argued that the mechanism proposed here is speculative, it is also speculative to assume that the radiative flows of energy in and out of the Earth system are stable to much less than 1% of their mean (of about 235 W m-2) on multi-decadal time scales in the presence of known modes of internally generated climate variability.  The forcing used here (Fig. 3a) has a standard deviation of only 1.2 W m-2, which is 0.5% of the average radiative energy flows in and out of the Earth’s climate system.          

If we then plot the temperature variations in Fig. 3b against the assumed internally-generated radiative forcing from Fig. 3a (plus the radiative feedback using λ = 3.3 W m-2 K-1), we obtain a diagnosed feedback parameter of 1.3  W m-2 K-1  with a correlation of 0.19 (not shown).  This diagnosis of the feedback parameter thus has a large positive feedback bias of 2 W m-2 K-1 when compared to the specified feedback of 3.3 W m-2 K-1.

It should be noted that this large positive bias in the diagnosed feedback is due to the assumption that all of the forcing was radiative, that is, the forcing was assumed to be entirely contained in the I term in Eq. 1, with no contribution from the S term.  Alternatively, we could have assumed that the heating in Fig. 3a was entirely due to the non-radiative heating term, S, in Eq. 1.  In this case, the model output temperature variability would have been regressed against the only source of radiative variability – the feedback term λT – and then the diagnosed feedback parameter, l’, would have equaled the specified one (λ = 3.3 W m-2 K-1).  But in the former case, the corresponding correlation was very low (r = 0.19), while in the latter case a perfect correlation (r = 1.0, not shown) was the result.

So once again, as was the case for the model forced with daily noise in heating, we see that the issue of causation is critical when we examine cloud variability and make assumptions regarding the existence of feedback in the system.  It is helpful to remember that feedback must have some source of temperature variability on which to operate, and for internally generated variability, that source can either be radiative (the I term), or non-radiative (the S term).  If it is entirely from the non-radiative (S) term, there will be no error in the diagnosed feedback.  But to the extent that some of the temperature variability is internally-generated non-feedback radiative forcing (I), the diagnosis of a feedback parameter from the data will be biased in the positive direction. 

And again, a major difference between these two cases as expressed in model output is a low correlation when only internal radiative forcing is involved, and a high correlation when only non-radiative sources of heating are involved.

6.  Cause or Effect?

While atmospheric scientists are usually reluctant to attribute causation when discussing the complex interactions involved in atmospheric circulation systems, we can be sure that cause and effect do indeed exist, for scientific study would be impossible without them.  As we have seen from the examples above, it makes a great deal of difference when we observe climate variability whether we think clouds drive temperature, or temperature drives clouds, or some combination of both.  If we mistakenly assume that all radiative fluctuations resulting from processes internal to the climate system are only the result of feedback on surface temperature (temperature causing cloud changes rather than non-feedback sources of cloud change causing temperature change), then our estimates of feedback will be biased in the direction of positive feedback and the climate system will appear more sensitive than it really is. 

The reason that the bias in diagnosed feedback is only in the direction of positive feedback is because, as an energetic necessity, a specific change in clouds can cause a change in temperature in only one direction.  Phrased somewhat differently, if cloud variations cause a temperature change, the diagnosed feedback parameter (ratio of the cloud-induced radiative forcing to its temperature response) can have only one sign; true feedback, in contrast, can be of either sign. 

This is one reason why internal radiative forcing needs to be considered as a heating term separate from feedback.  Otherwise, we can be faced with the perplexing situation where a feedback appears to change in its magnitude (or even sign) over time, when what is really happening is that the amount of internal radiative forcing mixed in with the feedback is varying.

Unfortunately, it seems unlikely that we will be able to separate cause and effect per se from observational data, so we will likely have to estimate feedbacks from statistics of the co-variability between temperature and radiation changes.  For instance, Aires and Rossow (2003) provided a methodology for computing such sensitivity relationships.  But it is not obvious which set of these statistical metrics of climate variability, if any, are a unique signature of the underlying forcings and feedbacks.  For instance, the SB08 model results based upon assumed daily random cloud variations in the context of the model represented by Eq. 1 suggested that the temperature and radiative flux co-variability was not uniquely related to a specific feedback.  They instead found that the same satellite measures of monthly variability in T and SW fluxes could be reproduced with feedbacks ranging from strongly positive to strongly negative. 

It is clear that the cloud feedback problem, as a general issue, is far from solved.  But by recognizing the existence of internal radiative forcing as one component of the climate variability that has been mistakenly assumed to be a part of feedback, it is believed that progress can be made in that direction.  And, in the process, we find that some unexplained results from previous investigations take on new meaning.

7.  A Fresh Look at Some Previous Climate Diagnostics

The problem discussed here is of fundamental importance to our interpretation of observed climate variability.  Forster and Gregory (2006, hereafter FG06) showed that all IPCC models produced total radiative (LW+SW) feedbacks more positive than current best estimates from satellite observations.  Rather than questioning the realism of the model feedbacks, the authors instead attributed this discrepancy to errors in the observational estimates of feedback.  

But this discrepancy between models and observations might alternatively be evidence that the models have cloud parameterizations which are based upon observed cloud behavior for which causality in only one direction was assumed, in which case they would be biased toward positive feedback.  Causation is implicit in climate models due to the specific sequence of coded instructions. 

Again, to the extent that non-feedback sources of cloud variability cause temperature change, the misinterpretation of cloud-temperature relationships as only feedback will result in a bias in the direction of positive feedback.  Cloud parameterizations based upon such misinterpretations could then produce model behavior with unrealistically high sensitivity.

Another curious feature of the observational results shown by FG06 is the low correlation (average of the absolute values, 0.37) between temperature changes and SW fluctuations for the diagnosed feedback parameters.  While one might attribute this to just noise in the observational data, there is an alternative explanation.  If only linear feedback is operating upon non-radiative sources of temperature variation (S), and there are no sources internal radiative forcing (I), then the diagnosed feedback parameter has no error, and the corresponding correlation is always 1.0.  But once a source of internal radiative forcing is included, one gets much lower correlations, an example of which is seen in Fig. 1b (where the correlation is, coincidently, also 0.37).  Thus, the existence of low correlations in FG06 could, by itself, be evidence for internal radiative forcing in the SW fluxes.

A related curiosity of the diagnosed SW feedback parameters in FG06 is the wide range of correlations: from -0.51 to +0.57.  As previously addressed, the magnitude of internal radiative forcing mixed in with the feedback signal can determine the magnitude, and even the sign, of the diagnosed feedbacks.  This makes it appear as though different feedbacks are operating at different times, while instead it could be evidence for different amounts of internal radiative forcing versus non-radiative forcing of surface temperature.

Finally, the existence of internal radiative forcing also implies more total radiative variability in the climate system.  In this context, it is interesting that Wielicki et al. (2002) noted that satellite observations revealed tropical variations in SW and LW radiative fluxes which were considerably larger than those exhibited by climate models.  This large variability might be further evidence of non-feedback radiative ‘noise’, either high frequency or low frequency, generated within the climate system which is underrepresented in the models.

8. Summary and Discussion

It is more than a little ironic that the direction of causation involved in manmade global warming (a radiative change causing a temperature change) has been abandoned, and even reversed, when researchers observe natural climate variability – for they claim to see only temperature change causing a radiative change (feedback).  Here, both observational and theoretical evidences have been presented for the view that non-feedback sources of internally-forced non-feedback variations in the radiation budget of the climate system have not been sufficiently accounted for in either 1) the diagnosis of feedbacks in observational data, or 2) in the assigning of causation for observed climate change.  The issue has a large impact on our perception of climate sensitivity, and could be important for the formulation of cloud parameterizations in climate models.

The fundamental issue can be framed as a question of cause and effect, for instance: To what extent are climatic variations in clouds caused by temperature change (feedback), versus temperature change being the result of cloud variations?  If variability in cloudiness on any time scale is caused by some internal process other than feedback, the resulting relationship between temperature and radiative fluxes will ‘look like’ positive feedback — possibly even obscuring the signature of true negative cloud feedback.

Note that this issue is not restricted to only cloud feedback.  Water vapor feedback is another example.  We know that higher temperatures are, on average, associated with higher water vapor contents in the atmosphere.  This is commonly pointed to as evidence of positive water vapor feedback.  But what we neglect is the possibility of causation in the other direction.  For instance, changes in precipitation efficiency (say due to a change in wind shear) can cause water vapor contents to change, which then can cause temperature change (e.g., Renno et al., 1994).  If this happens, it will always look like positive water vapor feedback, even if no feedback is involved.

Simple models presented here which are driven with two types of assumed internal radiative forcing have also shed light on some features of observed climate variability which have not been adequately explained before.  These include: the large magnitude of satellite-observed radiative variability on interannual time scales compared to climate models; the low and highly variable correlations between global, time-averaged temperature and radiative fluxes; the tendency for model-produced feedbacks to be more positive than those observed in the climate system; and even the potential role of internally generated radiative forcing as a partial explanation for the major low frequency features of the global mean temperature record since 1900.

On this last issue, low frequency, internal radiative forcing amounting to little more than 1 W m-2, assumed to be proportional to a weighted average of the Southern Oscillation and Pacific Decadal Oscillation indices since 1900, produces ocean temperature behavior similar to that observed:  warming from 1900 to 1940, then slight cooling through the 1970s, then resumed warming up to the present, as well as 70% of the observed centennial temperature trend.  While the proposed mechanism is admittedly speculative, it is also speculative to alternatively assume that low frequency changes in the general circulation associated with ENSO and the PDO do not cause non-feedback TOA radiative budget changes on the order 1 W m-2 – an amount that is less than 1% of the mean radiant energy flows of 235 W m-2 in and out of the Earth’s climate system.

Based upon the evidence, it seems likely that the neglect of sources of internal radiative forcing has resulted in diagnosed feedbacks which give the illusion of a climate system that is more sensitive than it really is. This has then led to the development of climate models which produce too much global warming in response to the external radiative forcing caused by anthropogenic greenhouse gas emissions.


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Roger A. Pielke Sr.’s Perspective On Adaptation and Mitigation

There is considerable discussion on the relative roles of adaption and mitigation with respect to the findings in the 2007 IPCC report (e.g., see).  Thus, I have concluded that it is worthwhile to specifically define my views on this subject, as I did on the related subject of the human role within the climate system; see

Roger A. Pielke Sr.’s Perspective On The Role Of Humans In Climate Change

First, it needs to be emphasized that climate and energy policies, while there are overlaps, are distinctly different issues. As reported on Climate Science (e.g. see and see), the 2007 IPCC approach, and other related reports, are actually energy policy proposals cloaked in the guise of climate change.

Following is a short summary of my view on climate and energy policies with respect to adaptation and mitigation:

  • Climate policy in the past has been, with the limited exception of deliberate weather modification (see), focused on adaptation. Dams, zoning so as to limit habitation in flood plains, etc are examples of this adaptation. 
  • For the coming decades, adaptation still needs to be the primary approach. As reported in the 2005 National Research Council report (Radiative forcing of climate change: Expanding the concept and addressing uncertainties) the human influence on the climate system involves a diverse range of forcings. Thus, a focus on controlling the emissions of carbon dioxide by itself (i.e. mitigation) is an inadequate approach for an effective climate policy.
  • Energy policy, however, clearly must emphasize an active management policy since a vibrant economy and society requires energy. However, all energy sources are not the same in terms of how they affect the environment and their availability. For example, the dependence of the United States, Europe and other countries on oil from politically unstable regions of the world needs to be eliminated.
  • The current focus of the IPCC and others on climate change with their emphasis on global warming, as a guise to promote energy policy, therefore, is an erroneous and dishonest approach to communicate energy policy to policymakers and the public. The optimal energy policy requires expertise and assessments that involves a much broader community than the climate science profession.

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