Climate Science: Roger Pielke Sr. Research Group News

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 (20^oN to 20^oS) 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 (β_PDOPDO + β_SOISOI ) - λT                (2)

where                   β_PDO + β_SOI = 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 β_PDO & β_SOI; 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 (β_PDO = 0.37, β_SOI = 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.

REFERENCES

Aires, F., and W. B. Rossow, 2003: Inferring instantaneous, multivariate and nonlinear sensitivities for analysis of feedbacks in a dynamical system: Lorenz model case study. Quart. J. Roy. Meteor. Soc., 129, 239-275.

Forster, P. M., and J. M. Gregory, 2006: The climate sensitivity and its components diagnosed from Earth Radiation Budget data.  J. Climate, 19, 39-52.

Forster, P.M., and K.E. Taylor, 2006: Climate forcings and climate sensitivities diagnosed from coupled climate model integrations.  J. Climate, 19, 6181-6194.

Intergovernmental Panel On Climate Change, 2007:  Climate Change 2007,  World Meteorological Organization, Geneva, Switzerland.

Kiehl, J.T., and V. Ramanathan, 2006: Frontiers of Climate Modeling, Cambridge University Press, 367 pp.

Kummerow, C., W. Barnes, T. Kozu, J. Shiue, and J. Simpson, 1998: The Tropical Rainfall Measuring Mission (TRMM) sensor package, J. Atmos. Oceanic Technol., 15, 809-817.

Mantua, N. J., S. R. Hare, Y. Zhang, J. M. Wallace, and R. C. Francis, 1997: A Pacific interdecadal climate oscillation with impacts on salmon production. Bull. Amer.  Meteor. Soc., 78, 1069-1079.

Renno, N. O., K. A. Emanuel, and P. H. Stone, 1994: Radiative-convective model with an explicit hydrological cycle 1.  Formulation and sensitivity to model parameters.  J. Geophys. Res., 99, 14429-14441.

Spencer, R.W., W. D. Braswell, J. R. Christy, and J. Hnilo, 2007: Cloud and radiation budget changes associated with tropical intraseasonal oscillations. Geophys. Res. Lett., 34, L15707, doi:10.1029/2007GL029698.

Spencer, R.W., and W.D. Braswell, 2008: Potential biases in cloud feedback diagnosis: A simple model demonstration. J. Climate, in press.

Stephens, G. L., 2005: Clouds feedbacks in the climate system: A critical review. J. Climate, 18, 237-273.

Tsonis. A.A., K. Swanson, and S. Kravtsov, 2007: A new dynamical mechanism for major climate shifts. Geophys. Res. Lett., 34, L13705, doi:10.129/2007GL030288.

Wentz, F., C. Gentemann, and D. Smith, 2000: Satellite measurements of sea surface temperature through clouds.  Science, 288, 847-850.

Wielicki, B. A., B. R. Barkstrom, E. F. Harrison, R. B. Lee III, G. L. Smith, and J. E. Cooper, 1996: Clouds and the Earth’s Radiant Energy System (CERES): an Earth Observing System experiment, Bull. Am. Meteor. Soc., 77, 853-868.

Wielicki, B. A., T. Wong, R. P. Allan, A. Slingo, J. T. Kiehl, B. J. Soden, C. T. Gordon, A. J. Miller, S.-K. Yang, D. A. Randall, F. Robertson, J. Susskind, and H. Jacobowitz, 2002: Evidence for Large Decadal Variability in the Tropical Mean Radiative Energy Budget. Science, 295, 841-844.

As Climate Science offers, we are open to the presentation of announcement of papers and of viewpoints by individuals actively involved in the climate science and climate policy community who want to widely distribute their views and analyses on climate science. Today, Climate Science presents a guest weblog by Christopher Monckton on the issue of radiative feedback.  Christopher Monckton has been an outspoken commentator on climate policy issues, however, his guest weblog on Climate Science concerns a science issue; namely what is the magnitude of the radiative feedback as reported by the IPCC? Climate Science has weblogged on this subject in

Climate Metric Reality Check #1 - The Sum Of Climate Forcings and Feedbacks Is Less Than The 2007 IPCC Best Estimate Of Human Climate Forcing Of Global Warming

Other climate scientists are encouraged to submit guest weblogs which support or seek to refute the analysis presented below. Ultimately, each contribution of this type needs to be submitted to peer reviewed scientific journals which is the most appropriate aribitrator of science.

Guest Weblog Christopher Monckton

In the IPCC’s methodology, climate sensitivity ΔT_λ to radiative forcing is the product of three factors:

1. Tropopausal radiative forcing ΔF

ΔF  ≈  5.35 ln(C/C₀)  ==>   ΔF_2x   ≈  5.35 ln 2         W m^-2,        (1)

where (C/C₀) is a proportionate increase in CO₂ concentration and, specifically, ΔF_2x ≈ 3.708 W m^-2 is the radiative forcing at CO₂ doubling. For simplicity, no significant error will arise here if it is assumed that all other anthropogenic forcings are slightly net-negative, so that ΔF_2x ≈ 5 ln 2 ≈ 3.466 W m^-2.

2. The no-feedbacks climate sensitivity parameter κ

κ  =  ΔT_κ / ΔF  =  ΔT_λ / (ΔF + bΔT_λ)        °K W^-1 m²,              (2)

where ΔT_κ is the temperature response to forcings only, without feedbacks; ΔT_λ is the temperature change in response to forcings plus feedbacks; and b is the sum in W m^-2 °K^-1 of all unamplified temperature feedbacks. The key parameter κ is not mentioned in IPCC (2007), and no error-bars are given. The value κ ≈ 0.313 °K W^-1 m² implicit in IPCC (2007) is the reciprocal of the “radiative cooling response” -

“Under these simplifying assumptions the amplification [f] of the global warming from a feedback parameter [b] (in W m^-2 °C^-1) with no other feedbacks operating is 1 / (1 + [bκ ^-1]), where [κ ^-1] is the ‘uniform temperature’ radiative cooling response (of value approximately -3.2 W m^-2 °C^-1; Bony et al., 2006). If n independent feedbacks operate, [b] is replaced by (λ₁ + λ ₂+ … λ _n).” (IPCC, 2007: ch.8, footnote)

3. The feedback multiplier f

f = (1 - bκ)^-1.                               (3)

This unitless variable is evaluated in IPCC (2007, ch.8) using the feedback-amplification function given in Bode (1945). First, we note the dependence of f not only upon b but also upon κ -

                           ΔT_λ  =  (ΔF + bΔT_λ)κ                       

 ==>       ΔT_λ (1 - bκ)  =  ΔFκ     

 ==>     ΔT_λ                =  ΔFκ(1 - bκ)^-1               

 ==>        ΔT_λ / ΔF       =  λ  

                                  =  κ(1 - bκ)^-1

                                  =  κf

==>    f                      =  (1 - bκ)^-1

                                  ≈  (1 - b / 3.2)^-1    

==>    κ                      ≈  3.2^-1        

                                   ≈  0.313 °K W^-1 m²,              (4)

Equivalently, expressing the feedback loop as the sum of an infinite series,

                          ΔT_λ   =  ΔFκ + ΔFκ ²b + ΔFκ ²b² + …

                                  =  ΔFκ(1 + κb + κb² + …) 

                                  =  ΔFκ(1 - κb)^-1                                  

                                  =  ΔFκf

==>      λ                    =  ΔT_λ /ΔF                                           

                                  =  κf                                (5)

 

Figure 1

How Climate Feedbacks Feed Back

Upper left panel: a forcing dF is input (by multiplication) to the climate sensitivity parameter λ, yielding dT as the output. Lower left panel: the forcing dF is input to the no-feedbacks climate sensitivity parameter κ, successively amplified by temperature feedbacks summing to b. Right panel: the full diagram illustrates the impact of individual climate feedbacks, together with κ, so that λ = κf. Diagrams follow kind suggestions by Dr. David Evans.

Next, b must be evaluated. IPCC (2007) quantifies the principal temperature feedbacks individually for the first time:

“In AOGCMs, the water vapor feedback constitutes by far the strongest feedback, with a multi-model mean and standard deviation … of 1.80 ± 0.18 W m^-2 K^-1, followed by the negative lapse rate feedback (-0.84 ± 0.26 W m^-2 K^-1) and the surface albedo feedback (0.26 ± 0.08 W m^-2 K^-1). The cloud feedback mean is 0.69 W m^-2 K^-1 with a very large inter-model spread of ±0.38 W m^-2 K^-1.” (Soden & Held, 2006).

To these we add the CO₂ feedback, which IPCC (2007, ch.7) separately expresses not as W m^-2 °K^-1 but as concentration increase per CO₂ doubling: [25, 225] ppmv, central estimate q = 87 ppmv. Where p is concentration at first doubling, the proportionate increase in atmospheric CO₂ concentration from the CO₂ feedback is o = (p + q) / p = (556 + 87) / 556 ≈ 1.16. Then the CO₂ feedback is -

λ_CO2  =  z ln(o) / dT_λ  ≈  5.35 ln(1.16) / 3.2    ≈  0.25 W m^-2 K^-1.     (6)

The CO₂ feedback completes the feedback-sum b:

b  =  1.8 - 0.84 + 0.26 + 0.69 + 0.25           ≈  2.16 W m^-2 ºK^-1.      (7)

From κ = 0.313 and b = 2.16, a central estimate of the value of the feedback factor f is -

  f  =  (1 - bκ)^-1  ≈  (1 - 2.16 x 0.313)^-1          ≈  3.077               (8)

This result is broadly consistent with Hansen et al. (1984), where f = 3-4 is suggested.

Final climate sensitivity ΔT_λ, after taking account of feedbacks, is the product of the three factors we have briefly considered -

  ΔT_λ  =  ΔF λ  =  ΔF κ f  =  ΔF κ(1 - κb)^-1    °K,    (9)

where λ = κf  is the with-feedbacks climate sensitivity parameter. Thus, at CO₂ doubling,

ΔT_λ  =  ΔF_2x κ f  ≈  3.466 x 0.313 x 3.077    ≈  3.3 °K            (10)

IPCC (2007) gives dT_λ on [2.0, 4.5] ºK at CO₂ doubling, with a central estimate dT_λ ≈ 3.2 °K, to which the value dT_λ ≈ 3.3 °K in equation (10) is sufficiently close to demonstrate that the IPCC’s method has been reasonably replicated.

The feedback factor reconsidered

The feedback factor f accounts for at least two-thirds of all radiative forcing in IPCC (2007); yet it is not expressly quantified, and no “Level Of Scientific Understanding” is assigned either to f or to the two variables b and κ upon which it is dependent.

Several difficulties are apparent.

Not the least of these difficulties is that, if the upper estimates of each of the climate-relevant feedbacks listed in IPCC (2007) are summed, an instability arises. The maxima are -

Water vapor 1.98, lapse rate -0.58, surface albedo 0.34, cloud albedo 1.07, CO₂ 0.57, total 3.38 W m^-2 K^-1.

The equation f = (1 - bκ)^-1 becomes unstable as b → κ^-1 = 3.2 W m^-2 K^-1. Yet, if each of the individual feedbacks imagined by the IPCC is increased to less than the IPCC’s maximum, an instability or “runaway greenhouse effect” is reached.

Yet it is reliably inferred from palaeoclimatological data that no “runaway greenhouse effect” has occurred in the half billion years since the Cambrian era, when atmospheric CO₂ concentration peaked at almost 20 times today’s value, as Figure 2 shows:

Figure 2

Fluctuating CO₂ But Stable Temperature

Timeline of climate stability: Throughout the past 600 million years, almost one-seventh of the age of the Earth, global mean surface temperatures are thought not to have exceeded a plateau in the region of 22 °C, even when carbon dioxide concentration peaked at 7000 ppmv, almost 20 times today’s near-record-low concentration. If the graph is correct, then the instability inherent in the IPCC’s error-bars for the principal temperature feedbacks has not occurred in reality, suggesting that the IPCC’s estimates may be substantial exaggerations.

Given the stability of the climate over the past half billion years, there is little danger that current anthropogenic perturbation of the climate will cause a “runaway greenhouse effect”. It is likely, therefore, that the IPCC’s current estimates of the magnitude of climate feedbacks have been substantially exaggerated.

To verify the likelihood that the IPCC is according too large a role to climate feedbacks, comparisons were made between the 2007 report and the two previous reports, in 1995 and 2001 respectively.

Table 1

Falling Forcing Coefficient, Rising Temperature Response

Table 1 shows that, although the estimated forcing effect of CO₂ has been reduced by more than one-fifth in 12 years, climate sensitivity has risen by a quarter. The sole reason for this increase is feedback

inflation, as Figure 3 shows:

Figure 3

The growing role of feedbacks: In the IPCC’s 1995 report, the value of the feedback factor f appears to have been ~1.80, rising to 3.08 in 2007. In 1995, feedbacks accounted for less than half of all forcings; by 2007 they accounted for more than two-thirds.

Holding κ constant and taking the IPCC’s changing central estimates ΔT_λ and ΔF_2x, it is possible to calculate that the IPCC has increased its central estimate of the value of the feedback factor f by more than two-thirds in the 12 years since 1995. Yet the IPCC’s reports do not explicitly draw the reader’s attention to, still less justify, the magnitude of this “feedback inflation”.

Indeed, in IPCC (2007) the stated values for the feedbacks that account for more than two-thirds of humankind’s imagined effect on global temperatures are taken from a single paper. The value of the coefficient z in the CO₂ forcing equation likewise depends on only one paper. The implicit value of the crucial parameter κ depends upon only two papers, one of which had been written by a lead author of the chapter in question, and neither of which provides any theoretical or empirical justification for the IPCC’s chosen value. The notion that the IPCC has drawn on thousands of published, peer-reviewed papers to support its central estimates for the variables from which climate sensitivity is calculated is not supported by the evidence.

Now that the IPCC has published its estimates of the forcing effects of individual feedbacks for the first time, numerous papers challenging its chosen values have appeared in the peer-reviewed literature. Notable among these are Wentz et al. (2007), who suggest that the IPCC has failed to allow for two-thirds of the cooling effect of evaporation in its quantification of the water vapor-feedback; and Spencer (2007), who points out that the cloud-albedo feedback, regarded by the IPCC as second in magnitude only to the water-vapor feedback, should in fact be negative rather than strongly positive.

In these circumstances, it is not unreasonable to readopt the value b = 1.43 which, inferentially, was the central estimate in IPCC (1995). Holding the values of ΔF_2x and κ constant, climate sensitivity falls by more than one-third -

ΔT_λ  =  ΔF_2x κ f  ≈  3.466 x 0.313 x 1.808         ≈ 2.0 °K         (11)

If the value of κ were reduced by as little as one-eighth so as better to reflect the range of values actually stated in the papers cited by the IPCC, climate sensitivity would fall still further -

ΔT_λ  =  ΔF_2x κ f  ≈  3.466 x 0.277 x 1.656          ≈ 1.6 °K         (12)

Finally, if, as Lindzen (2008) has suggested, all terrestrial forcings were cut by two-thirds to take account of the absence of the altitudinal difference in decadal warming rates in the tropics that is predicted in all of the models on which the IPCC relies but has not been observed in half a century of radiosonde observations and 30 years of satellite records (Douglass et al., 2007), climate sensitivity would again decline -

ΔT_λ  =  ΔF_2x κ f  ≈  1.155 x 0.277 x 1.656         ≈ 0.5 °K        (13)

It is not for a non-climatologist such as me to say which climate-sensitivity value is correct. On this brief analysis, however, it is evident that the models on which the IPCC relies are little better than expensive guesswork, and that no great reliance can be placed upon the IPCC’s central estimates, still less on its high-end estimates. As a policymaker, I should be profoundly reluctant, given the current state of the science, to recommend to Ministers that they should take the drastic actions advocated in some circles to mitigate “global warming.”

Set aside the self-evident truth that adaptation as (and if) necessary would be orders of magnitude more cost-effective than mitigation, a conclusion that tends to be overlooked as a result of the IPCC’s bizarre decision to establish separate working groups to consider adaptation and mitigation. The simple calculations in this paper have demonstrated a strong likelihood that the IPCC’s estimates of climate sensitivity are prodigiously exaggerated; that there may be a good reason why, contrary to all the projections of the IPCC’s models, temperatures have not risen for a decade and have been falling since the phase-transition in global temperature trends that occurred in late 2001 (see Figure 4); and that there is no “climate crisis” at all.

Figure 4

“Global Warming?”

The trend that caught the IPCC by surprise: Since late 2001, the trend of global surface temperatures has been downward. “Global warming” stopped in 1998; and, though it may resume in future years, the rate of warming is self-evidently less than that which the IPCC had expected, and is very likely to be harmless.

This weblog is graciously provided by Mike Smith.  Mike Smith is CEO of WeatherData Services, Inc., An AccuWeather Company.  Smith is a Fellow of the American Meteorological Society and a Certified Consulting Meteorologist.   He is a recipient of the American Meteorological Society’s Award for Outstanding Contributions to Applied Meteorology and WeatherData has received the Society’s Award for Outstanding Services to Meteorology by a Corporation.

AccuWeather’s global warming blog can be found at: http://global-warming.accuweather.com/ .

Guest Weblog 

In order to understand the effect of soot, the concept of “albedo” has to be explained. The definition of albedo is “The ratio of the outgoing solar radiation reflected by an object to the incoming solar radiation incident upon it.” Fresh, pure white snow has an albedo of nearly 100% — in other words, just about all of the solar energy striking the snow is reflected back into space. Since the heat is reflected rather than absorbed, the solar energy has relatively little melting effect on pure white surfaces.

However, if the ‘color’ of the snow is darked by soot, the albedo drops dramatically. Since the soot absorbs some of the radiation that otherwise would have been reflected, heat transfers from the soot into the snow resulting in an accelerated rate of melting. It is important to state that this heat transfer can cause melting to increase even if the ambient temperature remains constant.

I conducted a backyard demonstration on Christmas Eve 2007.

Here is a photo of fresh snow cover in my backyard over which I had tossed some eight month-old fireplace ash under a totally blue sky.

Keeping in mind this demonstration is occurring just two days after the winter solstace (meaning the albedo effect is less than it would have been under clear skies in February or March), in just one hour, the greater melting in the ash-covered areas is already apparent:

After four hours, the ash-free area has a depth of 5.5 inches

At the same time, the ash-covered areas have a depth of about 2.5 inches

The areas without soot melt about 0.5 inches of snow during this 4-hour period while the soot-covered areas melt 3.5 inches.

Any discussion pertaining to melting glaciers or icecaps must consider the accelerated melting caused by soot pollution in addition to any contribution from changing ambient temperatures.

Photos: Copyright 2007, Michael R. Smith

Today, we have a guest weblog that has been graciously provided to us by Valerio Lucarini. This weblog adds significantly to the discussion on Climate Science with respect to what can be achieved with dynamic downscaling from multi-decadal global models (e.g. see). 

 Guest Weblog by Valerio Lucarini, Department of Physics, University of Bologna

The evaluation of the accuracy of numerical climate models and the definition of strategies for their improvement are crucial issues in the Earth system scientific community. On one side, climate models of various degrees of complexity constitute tools of fundamental importance for reconstructing and projecting into the future the state of the planet, for testing theories related to the basic dynamical properties of the geophysical fluids, and for analyzing the physical and chemical climatic feedbacks. On the other side, the outputs of climate models, and especially future climate projections, are gaining an ever increasing relevance in several fields, such as ecology, economics, engineering, energy, architecture, spatial planning, as well for the process of policy-making at national and international levels. Regarding influences at societal levels of climate-related findings, the impacts of the 4th Assessment Report of the Intergovernmental Panel on Climate Change (IPCC4AR) are unprecedented.

An extensive evaluation of the performance of regional and global climate models in their representation of the hydrological cycle in present and future climate has been recently performed by Lucarini et al. (2007, 2008). Such a study, performed in the framework of the EU INTERREG IIIB project HYDROCARE , has focused on the Danube basin. Apart from its primary relevance for the European history, economics, politics, demographics, cultural and environmental heritage, the Danube basin is very interesting from a climatic point of view because it is well within continental Europe while bearing at least a twofold direct relevance to the Mediterranean region. Firstly, the Danube runoff gives a relevant contribution of freshwater flux into the Mediterranean Sea (on the average, more than twice the Nile’s contribution). Secondly, the Danube depends mostly on precipitated water of Mediterranean origin, because of the geographical position (downwind of the dominant westerlies) and the complex orography of the basin. When considering the very intense precipitative and disastrous floodings events in central Europe inside and near the Danube basin, it is well recognized the relevance of the Alps and of the Mediterranean waters in modifying and enhancing the storms of Atlantic origin.

The hydrological cycle has been evaluated by integrating, using the Voronoi-Thiessen polygons formalism, the precipitation and evaporation fields as well as the runoff fields over the area of interest. When long-term averages are considered, because of the conservation of water and of the small infiltrations into aquifers, the basin-integrated value of precipitation minus evaporation should match that of the runoff, and should agree with the discharge of the river at sea. Therefore, since precipitation and evaporation are complex field (e.g., precipitation variability features multifractal properties in space and time), so that gridding of sparse observations cannot be completely robust when volume integral are considered, we have considered the observed discharge of the Danube as given by the data of the Global Runoff Data Center as verification benchmark.

The first striking result is that NCEP-NCAR and ERA40 reanalyses result to be largely inadequate for representing the hydrology of the Danube river basin, both for the reconstruction of the long-term averages and of the seasonal cycle for the second half of the XX century. The ERA40 long-term water balance reanalysis is one order of magnitude smaller than observations, with several years featuring an unphysical negative balance - the Danube basin resulting to be an exporter of water - and a large amount of water is created in the soil model module. The NCEP-NCAR reanalysis is much better in the representation of the long-term average of the water balance, and its soil model is a little more consistent for water treatment (but far from being perfect). Nevertheless, when looking into monthly climatologies, the NCEP-NCAR dataset performances are much worse: the summer precipitations are greatly exaggerated, and, in spite of the evaporative feedback, the water balance is positive and maximizes in summer time, which is quite unreasonable. The reanalyses cannot in any sense be used as verification.

In the first paper (Lucarini et al. 2007) the analysis focuses on the 1961-1990 outputs of about a dozen of regional climate models (RCMs) nested into the same run of the same Atmospheric Global Circulation Model (AGCM), forced by observed SSTs. The considered simulations had been performed in the context of the project PRUDENCE, belonging to the 5th Framework Programme of the EU, and have been (kindly) made publicly available by the project consortium. Large discrepancies exist among RCMs for the monthly climatology as well as for the mean and variability of the annual balances, and only few datasets are consistent with the observed discharge values of the Danube at its Delta, even if the driving AGCM provides itself an excellent estimate. For a given model, increases in the resolution do not alter the net water balance, while speeding up the hydrological cycle through the enhancement of both precipitation and evaporation by the same amount. Moreover, since for some models the hydrological balance estimates obtained with the runoff fields do not agree with those obtained via precipitation and evaporation, some deficiencies of the land models are also apparent. Therefore, some RCMs seem to degrade the information provided by the large-scale flow, once the local, downscaled information they produce is upscaled to an intermediate range between the minimum resolvable scale and the domain size. This emphasizes the fact that the downscaling and upscaling procedures do not commute and are both problematic, for a combination of reasons ranging from the effect of the model buffer zone, to the representation of the large scale circulation in the RCM, to resolution effects, to the parameterization of unresolved physical processes in the atmosphere and in the soil.

In the second paper (Lucarini et al. 2008), the analysis focuses on about 20 global climate models (GCMs) included in the IPCC4AR for 1961-2000 and for the 2161-2200 SRESA1B scenario runs. For 1961-2000, the span of the simulated mean annual balances is about 50% of the observed discharge values of the Danube at its Delta; the true value is within the range simulated by the models. The existence of deficiencies in some land models is shown by the disagreement between the hydrological balance estimates obtained with the runoff fields with respect to those obtained via precipitation and evaporation. The overall performances and the degree of agreement of the GCMs are comparable to those of the RCMs, in spite of the much coarser resolution and the common nesting of all the RCMs. This suggests that global modeling may be a robust procedure for simulating climate also when relatively small scales are considered. In the 2161-2200 SRESA1B scenario runs, for basically all models, the water balance decreases, whereas its interannual variability increases. As opposed to the common wisdom, the response of the GCMs to climate change is not consistent regarding the strength of the hydrological cycle - models are split evenly between those featuring an increase, a decrease and a zero-response. It is apparent that is hard for models to provide a clear picture of the impact of climate change on the hydrological cycle over land areas.

Finally, it is to be emphasized that, in several cases, qualitatively different behaviours emerge among the models: often, the ensemble mean does not correspond to the output of any sort of average model, as the ensemble mean falls into nowhere’s land, i.e., between the clusters of the outputs given by the various models. This suggests that the usual procedure of merging data coming as outputs of various models is much more problematic than commonly thought.

Papers:

Lucarini V., R. Danihlik, I. Kriegerova, and A. Speranza, 2007: Does the Danube exist? Versions of reality given by various regional climate models and climatological datasets, Journal of Geophysical Research, 112, D13103, doi: 10.1029/2006JD008360

Lucarini V., R. Danihlik, I. Kriegerova, and A. Speranza, 2008: Hydrological Cycle in the Danube basin in present-day and XXII century simulations by IPCCAR4 global climate models, Journal of Geophysical Research, doi:10.1029/2007JD009167 (in press)

Relevant Bibliography:

Betts, A.K., J.H. Ball, P. Viterbo, 1999. Basin-scale surface water and energy budgets for the Mississippi from the ECMWF reanalysis. J. Geophys. Res., 104(D16), 19.293-19.306

Gutowski W. J. Jr., Chen Y., Ötles Z., 1997: Atmospheric Water Vapor Transport in NCEP–NCAR Reanalyses: Comparison with River Discharge in the Central United States, Bull. Amer. Meteor. Soc. 78, 1957–1969

Hagemann, S., Machenhauer, B., Jones, R., Christensen, O.B., Déqué, M., Jacob, D., Vidale, P.L. 2004: Evaluation of water and energy budgets in regional climate models applied over Europe. Climate Dynamics, 23, 547-567

Hirschi, M., Seneviratne, S.I., Schär, CH. 2006: Seasonal Variations in Terrestrial Water Storage for Major Mid-latitude River Basins. J. Hydrometeor., 7, 39-60

Lucarini, V., S. Calmanti, A. Dell’Aquila, P.M. Ruti and A. Speranza, 2007: Intercomparison of the northern hemisphere winter mid-latitude atmospheric variability of the IPCC models, Climate Dynamics, 28, 829-848, doi: 10.1007/s00382-006-0213-x

Speranza A., 2002: The hydrological cycle of the Mediterranean Basin, Proceedings of the Interreg IIC Conference Drought-Monitoring, Mitigation, Effects, Villasimius (Cagliari), 21-23 September 2000, Eds G. Monacelli and E. Giusta., pp. 103-106

I am pleased to be able to post a weblog by Dr. Joanne Simpson who is among the most preeminent scientists of the last 100 years.  Her comments were first distributed on a limited mail group, and are reproduced here with her permission.

 Dr. Joanne Simpson

“Since I am no longer affiliated with any organization nor receive any funding, I can speak quite frankly. For more than a decade now “global warming” and its impacts has become the primary interface between our science and society. A large group of earth scientists, voiced in an IPCC[1] statement, have reached what they claim is a consensus of nearly all atmospheric scientists that man-released greenhouse gases are causing increasing harm to our planet. They predict that most icepacks including those in the Polar Regions, also sea ice, will continue melting with disastrous ecological consequences including coastal flooding. There is no doubt that atmospheric greenhouse gases are rising rapidly and little doubt that some warming and bad ecological events are occurring. However, the main basis of the claim that man’s release of greenhouse gases is the cause of the warming is based almost entirely upon climate models. We all know the frailty of models concerning the air-surface system. We only need to watch the weather forecasts. However, a vocal minority of scientists so mistrusts the models and the complex fragmentary data, that some claim that global warming is a hoax. They have made public statements accusing other scientists of deliberate fraud in aid of their research funding. Both sides are now hurling personal epithets at each other, a very bad development in Earth sciences. The claim that hurricanes are being modified by the impacts of rising greenhouse gases is the most inflammatory frontline of this battle and the aspect that journalists enjoy the most. The situation is so bad that the front page of the Wall Street Journal printed an article in which one distinguished scientist said another distinguished scientist has a fossilized brain. He, in turn, refers to his critics as “the Gang of Five”.

Few of these people seem to have any skeptical self-criticism left, although virtually all of the claims are derived from either flawed data sets or imperfect models or both. The term “global warming” itself is very vague. Where and what scales of response are measurable? One distinguished scientist has shown that many aspects of climate change are regional, some of the most harmful caused by changes in human land use. No one seems to have properly factored in population growth and land use, particularly in tropical and coastal areas.

What should we as a nation do? Decisions have to be made on incomplete information. In this case, we must act on the recommendations of Gore and the IPCC because if we do not reduce emissions of greenhouse gases and the climate models are right, the planet as we know it will in this century become unsustainable. But as a scientist I remain skeptical. I decided to keep quiet in this controversy until I had a positive contribution to make. That point is to be celebrated in the TRMM 10 year anniversary in a Conference in February, 2008. With a 10-year record the TRMM, users of the data can begin to look for and test for trends. With the TRMM sampling limitations, other data sets, from geosynchronous and other sources are being used now in the group led by Bob Adler. Their products can detect trends in global tropical rain on several scales, including regional.

These patterns can be compared over the past ten years with the patterns predicted ten years ago by the climate models. An example is the Walker circulation, normally with descent of air over the eastern Pacific Ocean and ascent of air over the western Pacific. When this cell weakens, perhaps breaking over the middle Pacific, we have an El Niño. The modelers say that higher greenhouse warming produces recognizable changes in the Walker circulation. What better data is there to test such model results than the tropical rain products from TRMM? While the TRMM data set provides no panacea on the volatile hurricane front, useful information for the several ocean basins relating the rainfall to claimed and observed storm structure can be made if dedicated work is committed. I would be most interested to find out how the distribution of hot towers relates to storm intensity and rain production. Examining the data already posted on the TRMM Website shows that such projects are tractable. The major lack for TRMM data use in testing climate theories is latitude limitation. Global warming impacts appear much more severe in polar latitudes than in tropical regions. The best news is that the Global Precipitation Mission (GPM) is on schedule for a 2013 launch. In conclusion I can just pray that GPM scientists and engineers are as smart and as lucky as we TRMM participants have been.”

Lucia Liljegren graciously agreed to permit Climate Science to post her weblog as a guest contribution on Climate Science. Her weblog was motivated by the Climate Science weblog on February 8 2008 titled

An Error In The Construction Of A Single Global Average Surface Temperature

 Lucia Liljegren’s Guest weblog

In my post at ‘The Blackboard’ on February 13, 2008, I discussed a Global Climate Change Blog kerfuffle over the IPCC equation describing the radiative balance for the Earth’s climate system. The kerfuffle involves one of the conclusions Dr. Roger Pielke Sr. reported in a recent peer-reviewed article and two blog posts (see January 24, 2008 and February 8, 2008 at climatesci.org).

Outside of the blog kerfuffle, Dr. Pielke’s fuller point is rather arcane and relates to the ability of scientists to accurately estimate the magnitude of the climate sensitivity, λ, based on Global Mean Surface Temperature anomalies, T’, as measured and reported using a very specific equation in an IPCC document. Dr. Pielke Sr. made several points on his weblog of February 6 regarding the uncertainties associated with determining the λ, all related to issues associated with the anomaly, T’.

One point in particular, discussed in the following paragraph by Pielke Sr., bothered Eli Rabett:

“Indeed, it is easy to show that weighting by (T+T’)**4 significantly emphasizes the lower latitudes, since the relationship is to the 4th power of temperature. I look forward to your analysis as we have recommended.”

Eli’s response was:

“[This] is just wrong, as anyone who learned about series expansions of functions in Cal I would know.”

Turns out Eli is wrong; Dr. Roger Pielke Sr. is exactly right.

The correctness of Dr. Roger Sr.’s claim can be shown either using series expansions of functions or the simpler arithmetical method Dr. Roger Sr. used. Both give the same results for the magnitude of the effect Dr. Roger Sr.’s describes (as they should.)

Now, it is my opinion, that when possible, it is much wiser to rely on simple arithmetic to illustrate the importance of phenomena: One is less likely to go horribly wrong. However, as Eli claims to have dis-proven Dr. Roger Sr.’s arithmetic using series expansions of nonlinear functions, I think it’s become necessary to illustrate how to do this correctly.

Doing so provides an added bonus: The terms describing the phenomenon Dr. Roger Sr. described will be identified and shown to be leading order mathematically.  We’ll also see the magnitude of the effect is important enough to require including the terms in any empirical analysis to estimate the magnitude of  climate sensitivity, λ.

Conclusions

For those who don’t want to read the math, the main conclusions, in term of phenomenology and the blog kerfuffle follow.

Phenomenology

With regard to the question “Do neglecting spatial variations in surface temperature introduce uncertainty when estimating climate sensitivity using the IPCC equation in question?”

1.  Spatial variations in temperature do matter. If I’m not mistaken in my math, we could fix up up the IPCC equation to include their effect, resulting in:

      (1) dH/dt = f -( T’/λ + (3/λ) <δT_oδT’> /<T_o> )

where H is the heat content of the land-ocean-atmosphere system, f is the radiative forcing (i.e.,  the radiative imbalance), λ is called the “climate feedback” parameter, <T_o> is the absolute value of the global means surface temperature in the reference case, δT_o is the difference between a local surface temperature and the GMST in the reference case (denoted with ‘o’ subscripts) , and δT’ is the difference between the local surface temperature and the GMST at the current time (t).

The final term on the righthand side of (1), shown in bold, describes the effect of variations in the spatial distribution of temperature that exist, and may change as the planet warms (or cools.) Mathematically, the term is leading order in temperature differences, noted with primes ′.

2.  A back of the envelope estimate indicates the magnitude of the effect of spatial variation is sufficiently large to retain in (1). Using current measured values of the anomaly T’ and the spatial variations in temperature suggest the new term is roughly 15%-25% the size of the original linear term. Neglecting this physical effect could account for a roughly 1/3 to 1/2 the uncertainty in the estimate for the climate sensitivity to doubled CO₂ in the IPCC estimate of climate range. (Note to those who read my February 13 post on ‘The Blackboard’: This uncertainty in the radiative balance equation (1) is comparable to that obtained using Atmoz’s estimate of the error in using measurements of T’ based on linear averaging and those based on T’ due to power 4 averaging. )

3.  If someone wishes to obtain an empirical estimate of λ_2xCO2 with uncertainties less than ±0.7K, it is important to account for the effect of spatial surface temperature variations in some way. Since the current uncertainty range is thought to be ±1.5K, this means any sensible researcher should consider these variations.

The Blog Kerfuffle:

The main results, with regard to the blog kerfuffle, are:

   1. both Roger Sr.’s arithmetic and identification of a physical phenomenon correct.

   2. Eli’s series expansion was inadequate.

The Boring Proof

The blog kerfuffle is related to this IPCC equation, which is supposed to be an approximation for the energy balance of the earth, expressed in terms of the “Global Mean Surface Temperature Anomaly”, T’, which I will define more precisely later. The equation in question is:

(2)  dH/dt = f -T’/λ

where H is the heat content of the land-ocean-atmosphere system, f is the radiative forcing (i.e., the radiative imbalance), and λ is called the “climate feedback” parameter.

The “Series Expansion Kerfuffle” relates only to one term, which I will call Q_rad. It’s supposed to describe the excess radiation losses from the earth that occur as its surface temperature responds to forcing due to greenhouse gases (or anything for that matter.) In (2) this term is approximated as: Q_rad ~ T’/λ.

That approximation for Q_radaccounts for extra heat lost by radiation when the average surface temperature of the planet warms. In so far as it describes that effect, the term is linearized. As far as I can tell, no one is worried about that linearization.

So, what’s the problem? Roger Sr. is concerned that we can’t use historical records for T’ to estimate λ for a number of reasons. The one important to this kerfuffle is this: Equation (2) is missing terms that arise as a result of the spatial variations in the Earth’s surface, and Dr. Roger Pielke Sr. believes these terms matter.

Fuller Representation of Radiative Losses

How does Dr. Roger Pielke Sr. describe the issue?

As an example, assume a region of the Earth with a base temperature of 270K and another region with a base temperature of 300K. The difference in the outgoing longwave radiation (assuming blackbody behavior where the emission is proportional to T**4) results in a 34% greater emission from the warmer location. Adding a temperature increase of 1K to each location results in a 38% greater change when this increase is applied to the warmer temperature (i.e., comparing the difference between the incremental change in outgoing longwave radiation at the cold and warm locations).

Dr. Roger Sr. is correct. Full expression for the radiative flux should include a T⁴ dependence where T is an absolute temperature, not the temperature anomaly and T should also account for the spatial variations.

So, let’s fix up equation (2) to account for both features.

Because temperature varies over the surface of the Earth, a more detailed representation of the total radiative heat losses should be replaced by a surface integral of the form;

~ σ ∫∫ εT⁴ dA

where σ is the Stefan-Boltzmann constant constant, ε and T are respectively the spatially varying emissivity and integration is performed over the surface area of the Earth, A.

However, equation (2) was obtained by taking a difference with a reference case which means that f is a forcing relative to some absolute value of forcing, F, that causes the temperature on the surface of the Earth to achieve some reference value To. So, any instantaneous local anomaly T’ is defined relative to this temperature. That is T’= T-T_o.

Recognizing this, the more finicky blogger might wish to replace the simple linear T’/λ term with the more complicated integral:

(3)  dH/dt = f - εσ∫∫T⁴- T_o⁴dA

where A is surface area.

This results in an equation sufficiently to repel the average blog reader. Luckily, we aren’t interested in the full equation, but only the portion that describes what might be called the “radiative anomaly”, Q_rad, which I’ll define as:

(4)  Q_rad~ εσA < T⁴- T_o⁴>

Here, the angle brackets are used <> to indicate the surface area average of any quantity “Y” that may vary over the Earth’s surface; which can be written more formally as <Y> =A ^-1∫∫ Y dA

We now have an equation that not only accounts for the full T⁴ dependence for radiation but also permits us to consider the effect of spatial variations in surface temperature.

However, everyone would prefer a simpler, approximate equation, that does not contain a surface integral. We seek something more like (2) but we also wish to do the analysis in sufficient detail to see if the extra terms in (1) appear.