IPCC and Solar Correlations

Here’s a post which I wrote last June but didn’t post up at the time because the NAS Panel report came out and I had other pressing matters to comment on. My post as then drafted started:

Last week, through Chefen, Jean S and myself, here here here and here , we showed that MBH98 contained questionable statistical methodology for assessing the relative contribution of solar and greenhouse gases to increased warming and outright false claims about the robustness- the falseness of which was easily determined, making it remarkable that they’ve remained undetected so long.

Now one of the things that we know about the Hockey Team is that most things have a purpose. It may not be obvious and it may not be stated. (I don’t think that one can properly understand the MBH98 reconstruction and its rapid inhaling into policy other than in the context that the IPCC wanted to “get rid of the MWP”‘?.) So what was the purpose of MBH98 Figure 7 in the context of the times? What scores were they trying to settle? What was the pre-MBH98 status of attempts to correlate forcings and temperature?

IPCC reports prior to TAR are usually a good place to start. Here are some notes, which (I think) place MBH98 Figure 7 in context and which, in turn, provide some very interesting leads to follow up on, now that Figure 7 has been overturned.

The rest of my notes follow only slightly modified. I’ll try to post up some notes at some point on the work of Reid 1991 and White et al (JGR 1997) on correlations between solar and tropical SST.


IPCC 1992. (p 65)

IPCC 1992 referred to then recent results from Reid (1991) which they acknowledged as yielding “strong visual correspondence between solar cycle changes and temperature”, but pointed out concerns from Kelly and Wigley related to the reconciliation of solar and greenhouse forcing. Also note the last sentence of the first paragraph, which I’ll comment on below.

These [airborne] show an apparent change of irradiance between the late 1960s and the late 1970s of around 0.4%. There is considerable doubt however about the representativeness of these values (measured over the time-scales of a day) and about the absolute accuracy of the instruments used to obtain them (Lean 1991). Although Reid (1991) argues against these problems, it is clearly difficult to identify a long-term trend using extremely noisy daily data from instruments of uncertain accuracy.

Apart from these measurements, there are no useful direct irradiance measurements prior to 1978 so various authors have tried to deduce irradiance forcing indirectly. For example Reid (1991) has suggested that low-frequency irradiance changes in parallel to the envelope of sunspot activity which shows quasi-cyclic behavior with a roughly 80-year period and Friis-Christensen and Lessen 1991 have hypothesized that low-frequency irradiance changes are related to changes in the length of the solar cycle. In both cases, there is a strong visual correspondence between temperature changes over the past 100 years “€œ see Section C4.2.1. These results are intriguing but they have yet to be fully evaluated in terms of implied changes in solar forcing compared to greenhouse forcing (Kelly and Wigley 1990).

I don’t disagree with the bolded comment in the first paragraph, but do observe that this bit of prudence has not been consistently applied by IPCC e.g. no such comment was later made about MBH.

The bolded comment in the 2nd paragraph refers to the issue that a physical interpretation linking solar changes to temperature changes requires a greater sensitivity of temperature to solar forcing than to greenhouse forcing. As an editorial aside, I don’t like seeing Wigley cited so often as an omnibus authority to support IPCC, ranging from statistic significance to glaciers in the Holocene Optimum to solar forcing. Given this over-exposure, one needs to see an authority other than Wigley to substantiate a claim for reliance in public documents. (2007 – I also note that the Friis-Christensen results have been criticized by Damon and Laut (as noted by Lee on an another thread).

IPCC 1994 p 191-2

IPCC 1994 re-visited the issue of solar correlation devoting an entire subsection devoted to the topic. Again they noted a seemingly compelling statistical relationship, but argued that (1) the relationship was dubious on statistical grounds and, as bolded below, (2) that the relationship was inconsistent with then current ideas of climate sensitivity, which held that climate sensitivity to solar forcing was not greater than climate sensitivity to forcing from additional CO2. Anyway here’s IPCC:

4.5.3 Correlations between Climate and Solar Variability

“Suggestive correlative evidence for an enhanced role of the Sun in forcing climate has been presented by many authors including Labitzke and Van Loon 1993 and references, Reid 1991, Friis-Christensen and Lassen 1991 and Tinsley and Heelis 1993, In these studies the correlations between solar indices such as sunspots and solar cycle length and observed characteristics of the atmosphere (e.g. temperature at particular locations, global average SST etc) are examined. Some authors have questions the usefulness of solar-cycle correlation studies noting that undersampling and/or aliasing of other periodic atmospheric phenomena could lead to spurious results (Teitelbaum and Bauer 1990, Salby and Shea 1991, Dunkerton and Baldwin 1992)”⤮

Labitzke and von Loon 1993 noted remarkably high correlations between stratospheric temperatures and solar indices (such as solar emissions at a wavelength of 10.7 cm) as well as an apparent net propagation of such correlations in the form of planetary scale temperature patterns throughout the troposphere with amplitudes exceeding 1 deg C in some cases. Kodera 1993 showed by examining running correlations that undersampling is not the origin of the Labitzke/van Loon oscillations. However it is clear that large changes in temperature noted by Labitzke and Van Loon 1993 and others are inconsistent with observed changes in the radiative forcing associated with the well-documented total solar irradiance fluctuations of the past decade and very probably the last century”⥔hese wavelengths( UV) are all absorbed well above the tropopause. If this forcing resulted in only local stratospheric temperature changes, then there would be little direct impact on surface climate. .

Friis-Christensen and Lassen 1991 found a high correlation between solar cycle length and NH land temperatures. Hoyt and Schatten used solar cycle length as one of their parameters in deducing a quantitative variation in solar output over recent centuries. Hoyt and Schatten 1993 also found a good correlation between solar output and NH surface temperatures over the past century. However, these results imply that a 0.14% increase in solar output (equivalent to a forcing of 0.34 wm-2) causes a surface warming of 0.5 deg C; this is a high climate sensitivity which, if applied to the 4 wm-2 forcing associated with doubling the concentration of CO2, would result in a warming of about 6 deg C. Thus the hypothesis that variability in solar irradiance explains the observed temperature variations over the past century is inconsistent with our current understanding of climate sensitivity and would require a dramatically different forcing-response relationship for solar forcing than for other forcing mechanisms; there is no known physical mechanism and no modeling evidence to support such a difference, *****

Studies using limited records indicate correlations of winds and temperatures with the solar cycle. However their interpretation remains controversial on statistical grounds. No physical mechanism has been proposed that is quantitatively consistent with the relationships implied by the correlations.

Again, as an editorial point, “efficacy”‘? seems to me like a large and interesting question: it does not seem at all axiomatic that equal wm-2 of high-energy short-wavelength solar forcing at surface should have the same impact on surface temnperature as low-energy long wavelength infrared forcing at high altitudes from additional CO2. The supposed equivalence is relied on but not demonstrated; and continues to be relied on a virtual axoim (See HAnsen et al 2005). In addition, Labitzke, 2006, with the benefit of a nearly douled amount of data, denied that the validity of the above criticism:

Several publications criticized the short data record and suggested that the correlations are due to aliasing caused by dividing the data according to the phase of the QBO (e.g., Teitelbaum and Bauer, 1990; Salby and Shea, 1991). But even when 20 more years of data became available, the correlations remained stable, see Table 1 (Labitzke, 2006).

IPCC TAR, 2001

IPCC TAR’s treatment of solar correlations is reduced from 1994, with Reid 1991 dropping off the radar screen altogether. In their handling of solar correlations, as Jean S observed, IPCC got “punk’d”‘? by MBH98, which included both misrepresentations and incorrect statistical handling of solar correlations. An amusing statement in IPCC TAR, relying on MBH98, was that the use of “multiple correlations avoided the possibility of spuriously high correlations”‘? to solar. It’s hard to believe that something reviewed by entire stadiums of scientists could say something like this, but here it is:

A number of authors have correlated solar forcing and volcanic forcing with hemispheric and global mean temperature time-series from instrumental and palaeo-data (Lean et al., 1995; Briffa et al., 1998; Lean and Rind, 1998; Mann et al., 1998) and found statistically significant correlations. Others have compared the simulated response, rather than the forcing, with observations and found qualitative evidence for the influence of natural forcing on climate (e.g., Crowley and Kim, 1996; Overpeck et al., 1997; Wigley et al., 1997; Bertrand et al., 1999) or significant correlations (e.g., Schàƒ⵮wiese et al., 1997; Free and Robock, 1999; Grieser and Schàƒ⵮wiese, 2001). Such a comparison is preferable as the climate response may differ substantially from the forcing. The results suggest that global scale low-frequency temperature variations are influenced by variations in known natural forcings. However, these results show that the late 20th century surface warming cannot be well represented by natural forcing (solar and volcanic individually or in combination) alone (for example Figures 12.6, 12.7; Lean and Rind, 1998; Free and Robock, 1999; Crowley, 2000; Tett et al., 2000; Thejll and Lassen, 2000).

Mann et al. (1998, 2000) used a multi-correlation technique and found significant correlations with solar and, less so, with the volcanic forcing over parts of the palaeo-record. The authors concluded that natural forcings have been important on decadal-to-century time-scales, but that the dramatic warming of the 20th century correlates best and very significantly with greenhouse gas forcing. The use of multiple correlations avoids the possibility of spuriously high correlations due to the common trend in the solar and temperature time-series (Laut and Gunderman, 1998). Attempts to estimate the contributions of natural and anthropogenic forcing to 20th century temperature evolution simultaneously are discussed in Section 12.4.

The discussion in Section 12.4 include the following mention of Reid (together with Soon) as follows:

An alternative approach which has been used to reconstruct TSI (Reid, 1997; Soon et al., 1996) is to assume that time variations in global surface temperature are due to a combination of the effects of solar variability and enhanced greenhouse gas concentrations and to find that combination of these two forcings which best combine to simulate surface temperature measurements. However, these authors did not take natural climatic variability into account and a TSI series derived by such methods could not be used as an independent measure of radiative forcing of climate….

However, because of the large uncertainty in the absolute value of TSI and the reconstruction methods our assessment of the “level of scientific understanding”‘? is “very low”‘?.

At this point, we know that the MBH98 claims in respect to solar correlations cannot be relied on (for quite distinct reasons than principal components or bristlecones – see links at top of post). The dismissal of Reid 1997 here does not include any peer-reviewed citation, and, to that extent, is merely an editorial opinion of the section authors – and these are the same authors who made the silly comment about multiple regression.

Conclusion:

At this point, I’m far from arguing that anyone has established a connection between solar irradiance changes and temperature changes. However, it is incorrect to say that no statistical correlations between solar irradiance changes and temperature changes (in this case, to tropical SST in particular) have been observed. Whether those correlations are valid is a different issue. IPCC relied to some extent on MBH98 in dismissing these supposed relationships, but, given the defects in this specific area of MBH98 (as well as more general problems), alternative grounds for dismissal have to be sought if one repudiates MBH98. I’m not saying that such alternative grounds are not possible – merely that it is not prudent to rely on MBH98 in respect to taking a position on solar correlations. The other large issue is whether there are physical reasons why the efficacy of solar forcing (high-energy low-entropy at surface) might differ from the efficacy of additional CO2 forcing (low-energy high-entropy at altitude). I am not in a position to make statements one way or the other, but merely observe that I see no reason why this should be an axiom and that establishing differing efficacy would be a necessary aspect of research for anyone seeking to argue an increased role for solar forcing in temperature change.

References:
Labitzke website http://strat-www.met.fu-berlin.de/publications/publications_90s.html
K. Labitzke and H. van Loon 1993Some recent studies of probable connections between solar and atmospheric variability Ann. Geophysicae, 11, 1084-1094, 1993
Reid, George. “Solar variability and climate change on the time scale of decades to centuries,” Eos, 69:18, 567, 1988.
Reid, George. “Solar total irradiance variability and global ocean temperature variations.” Eos, 73:14 supplement, 244, 1992.
Reid, GC 1991. Solar total irradiance variations and the global sea surface temperature record. Journal of Geophysical Research 96: 2835-2844.
Reid, G.C. 1997. Solar forcing of global climate change since the 17th century. Climatic Change 37: 391-405.
Reid, G.C. 1999. Solar variability and its implications for the human environment. Journal of Atmospheric and Solar-Terrestrial Physics 61(1-2): 3-14.
Reid, G.C. 2000. Solar variability and the Earth’s climate: introduction and overview. Space Science Reviews 94(1-2): 1-11.

http://www.agu.org/revgeophys/reid00/node2.html

http://www.agu.org/pubs/crossref/1991/90JD02774.shtml


67 Comments

  1. Posted Jan 16, 2007 at 12:13 PM | Permalink | Reply

    The use of multiple correlations avoids the possibility of spuriously high correlations due to the common trend in the solar and temperature time-series (Laut and Gunderman, 1998)

    LOL! And what about the common trend in CO2 and Solar, no multicollinearity problems?

  2. jae
    Posted Jan 16, 2007 at 12:17 PM | Permalink | Reply

    it is clearly difficult to identify a long-term trend using extremely noisy daily data from instruments of uncertain accuracy.

    LOL. As if tree rings were a more accurate “instrument?”

    Great post!

  3. Francois Ouellette
    Posted Jan 16, 2007 at 12:35 PM | Permalink | Reply

    Steve,

    I’ve noted before, and elsewhere, that, from what I’ve learned about the so-called “feedback” effect to the CO2 forcing, it applies equally well to other types of radiative forcings. I don’t like the word feedback because in my opinion it’s just an amplifying factor (IOW the additional warming does not cause more CO2 in the atmosphere). (As an aside, this is an important distinction for a laser physicist like me, as lasers rely on both feedback AND amplification). The “amplification” comes from the fact that a warm surface generates more water vapor, which in turn warms the atmosphere. The net effect, as I see it, is in the lapse rate. But if, for example, less clouds are formed because of a lack of cosmic rays, the additional warming of the surface will also result in more water vapor and a warmer atmosphere. This is all in the case of a “clear” atmosphere, ie. without clouds. As far as I can tell, the value of any sort of “feedback” or “amplification” when clouds are present is still a major unknown, and depends on a number of factors (ie. low clouds vs high clouds etc.). Since it is presumed by the “cosmic ray” hypothesis that these also affect cloud formation, the net result is…, well, you guess is as good as mine. We don’t know and it could take a while to decipher.

    So, in conclusion, there is nothing to preclude “amplifying” factors to the solar (direct or indirect) forcing. That we know little about them is merely the result of the emphasis placed on GHG’s over the last 20 years. When more research effort is devoted to a better understanding of the sun-climate connection instead of trying to publicly discredit the few researchers who are working in that area, then we might make progress.

  4. Steve McIntyre
    Posted Jan 16, 2007 at 1:17 PM | Permalink | Reply

    #1. UC, I thought that you’d like this quote. Can you imagine what a prof would say in a 2nd-year statistics class to someone saying this in a presentation.

    I hadn’t thought about this before, but I guess that the Laut here is from Damon and Laut. I hadn’t noticed this at the time. So the reference is not to a real statistics text. Typical.

  5. Jean S
    Posted Jan 16, 2007 at 5:42 PM | Permalink | Reply

    Steve:

    I hadn’t thought about this before, but I guess that the Laut here is from Damon and Laut.

    Yes, it is the same (Peter) Laut (he was also a reviewer of IPCC TAR. J. Gundermann is also listed under “Authors and Expert Reviewers” in the Synthesis report Appendix). Friis-Christensen, Lassen, Svensmark, Lomborg etc are all Danish, so it seems like this Dr. Laut has taken the refutation of the work by his fellow countryman almost as a personal obligation.

    It is actually worth reading the Laut and Gundermann paper cited:
    Laut, P. and Gundermann, J.: Does the correlation between solar cycle lengths and northern hemisphere land temperatures rule out any significant global warming from the greenhouse gases?, Journal of Atmospheric and Solar-Terrestrial Physics, Volume 60, Issue 1, January 1998, Pages 1-3.

    It is a rather simple paper, where they basicly show that one gets about the same match with the solar data (as F-C and Lassen) even if one adds or substracts a small component to the tempereture data. Fair enough. But how does the paper support the “multicorrelation statement” of IPCC TAR? I could not find anything to that direction…

    There is actually a nice comment to the Laut and Gundermann paper:
    Sonnemann, G: Comment on “Does the correlation between solar cycle lengths and Northern Hemisphere land temperatures rile out any significant global warming from greenhouse gases?” by Peter Laut and Jesper Gundermann, Journal of Atmospheric and Terrestrial Physics, v. 60, iss. 17, p. 1625-1630.
    The paper is basicly about spurious correlation! So Steve, here is a nice “climate science” paper about spurious correlation, if you need one to cite. But how on earth this paper was not cited in IPCC TAR in the very same subsection as the Laut and Gundermann paper: the title of that subsection is “Studies linking forcing and response through correlation techniques”…

    But this gets even more interesting! Namely, Laut and Gundemann had another paper in the very same journal in the very same year:
    Laut, P. and Gundermann, J.: Solar cycle length hypothesis appears to support the IPCC on global warming, Journal of Atmospheric and Solar-Terrestrial Physics, Volume 60, Issue 18, p. 1719-1728.
    This paper appears to be their main criticism (at the time) about the F-C and Lassen papers. One might wonder why this paper was not cited in the IPCC TAR?! Well, read the paper, it is available here. The reason might, or might not, have something to do with their “best fit” value ;) Well, the paper was cited by Lomborg in his book… what an irony! Read also the associated press release/popular account… I found especially “we have delivered no proof” part rather funny :)

  6. Steve McIntyre
    Posted Jan 16, 2007 at 7:13 PM | Permalink | Reply

    Here’s an amusing quote from Laut and Gunderman:

    We find it interesting and a little bit frightening (!) that so many people – inside as well as outside the scientific community – have been referring to this central Figure for several years, apparently without anybody taking the trouble to check the calculation and to ensure that the graph on display is in agreement with the measured data.

    Sounds like something that I would agree with.

  7. Posted Jan 17, 2007 at 7:16 AM | Permalink | Reply

    # 5, linked

    When replacing the old temperature reconstructions in Figure 6 by a recent, much more sophisticated and probably much more reliable one (e.g. Mann et al. in Nature 1998) it turns out – as our preliminary analyses show – that the variation of temperature does not agree well with the solar cycle lengths.

    I can’t imagine how unsophisticated and unreliable the old temperature reconstruction is :)

    MBH98 attribution section is something very special:

    our empirical approach relies on the faithfulness of the reconstructed forcing series and on the assumption of a linear and contemporaneous response to forcings, …

    ..We estimate the response of the climate to the three forcings based on an evolving multivariate regression method (Fig. 7). This time-dependent correlation approach generalizes on previous studies of (fixed) correlations between long-term Northern Hemisphere temperature records and possible forcing agents.

    ..This parameter ranges from 0.48 in the first window (1610–1809) to 0.77 in the final window (1796–1995) of the moving correlation, the considerably larger recent value associated with the substantial global warming trend of the past century. This latter trend has been shown to be inconsistent with red noise [46] and could thus itself be argued as indicative of externally forced variability.

    [46 = Mann & Lees 96]

    Proper determination of the noise background is essential to detecting anthropogenic signal (see e.g. Wigley and Raper, 1990; Bloomfield and Nychka, 1992). A non-robust analysis of the un-trended series leads to the highly questionable inferences (Figure 8b) that the secular trend is not significant relative to red noise, and that nearly the entire interannual band (all periods of 7 years or shorter) of variability is significant well above the 99 % confidence level.

    I really can’t imagine what a prof would say in a 2nd-year statistics class to someone saying this in a presentation!! To me, it seems that someone took the wrong exit off the highway of science in 1996, and never found back ;) And along the way he has confused others:

    http://www.siam.org/journals/problems/downloadfiles/02-004.pdf

    (..or maybe I just don’t get it..)

  8. Jean S
    Posted Jan 17, 2007 at 7:53 AM | Permalink | Reply

    I can’t imagine how unsophisticated and unreliable the old temperature reconstruction is

    Well, check here ;)

  9. Jean S
    Posted Jan 17, 2007 at 8:28 AM | Permalink | Reply

    UC, what the heck is the last link?!? “This problem is open”?!??!

  10. Dave Dardinger
    Posted Jan 17, 2007 at 9:35 AM | Permalink | Reply

    re: #9 Jean,

    “This problem is open”?!??!

    It means that nobody has provided a solution to the problem. Whether or not there is actually a solution which nobody has bothered to derive or send to them, I don’t know. My guess is that there is no general solution. The fact that the A(t) and B(t) are pretty arbitrary means that you wouldn’t expect there to be, in general, constants which would work in every situation. However, it might be interesting for someone to see what conditions would have to be imposed to make the problem solvable; i.e. what is needed in order for a and b to be constants and not some function of t.

  11. Steve McIntyre
    Posted Jan 17, 2007 at 9:58 AM | Permalink | Reply

    #7. UC, this attribution section is the same MBH section that we studied last year with Chefen and found that it contained flat out misrepresentations about the robustness of the results.

  12. Posted Jan 17, 2007 at 10:03 AM | Permalink | Reply

    About the “efficacy” of solar vs. other forcings…

    I had some discussions about that with Raypierre over at RC. Indeed his (theirs) axioma is that all types of forcings have the same feedback mechanisms, thus the same change in forcing by solar causes the same change in temperature as an identical change in GHG forcing. Be it within some borders (Hansen ea. finds and efficacy of 0.92 for solar and 1.10 for CH4 vs. 1.0 for CO2 as the standard).

    But there are specific differences in forcings which may be of influence on the feedbacks:
    - GHGs and aerosols have their largest influence in the troposphere. GHGs are equally spread over the latitudes, which makes that the influence is spread too. Aerosols have their largest spread and influence downwind of their origin, which is for 90% in the NH (which should warm less than the SH, but we see the opposite…).
    - Solar and volcanic variances have their largest influence in the stratosphere, and solar most in the tropics.
    The solar cycle(s) moves the jet stream position poleward at solar maximum and the opposite at solar minimum. This is reflected in clouds/rain/temperature of the NH:
    http://www.gsfc.nasa.gov/topstory/20010712cloudcover.html (NASA)
    http://www.agu.org/pubs/crossref/2005/2005GL023787. (rainfall in Portugal)
    http://ks.water.usgs.gov/Kansas/pubs/reports/paclim99.html (upper Mississippi river basin)
    As far as I know, GHGs have not such an influence on jet stream position.

    More about the solar/stratosphere-troposphere connection:
    http://www.agu.org/pubs/crossref/2005/2005GL024393.shtml
    http://www.nwra.com/resumes/dunkerton/pubs/jastp.xx.xx.xx.pdf
    Again, an influence of stratospheric changes on the troposphere. No known opposite (if GHGs are involved) influences…

    There is a huge influence of solar on clouds: from maximum to minimum the amount of (low level) clouds increases with about 2%, which reinforces the relative small change in radiant energy. No matter what the cause is (GCR or direct IR absorption of clouds…), there is a good inverse correlation observed between solar and low cloud cover (see Fig. 1):
    http://folk.uio.no/jegill/papers/2002GL015646.pdf
    Cloud cover is quite variable, and only for the past decades some more or less reliable (still with problems for multiple layer clouds) data are available. Climate models have a very bad performance for cloud cover in the tropics and the Arctic. Thus the influence of GHGs on cloud cover still is an open question.

    Climate models underestimate solar. A test by Stott ea. of the HadCM3 model with increased solar and volcanic influences was used to make a better estimate of the different efficacies. Best fit was with about 60% GHGs and aerosols and 2x solar. Note that the test was done with some constraints, like no variation of the influence of aerosols. With a variance of aerosols (towards less influence), the score of solar probably would have been higher.
    See: http://climate.envsci.rutgers.edu/pdf/StottEtAl.pdf

    All together, one may conclude that there is a definite difference in efficacy between tropospheric GHGs and aerosols at one side and the mainly stratospheric induced influences of volcanic and solar forcings at the other side, where the influence of solar is clearly underestimated…

    Last but not least, cloud changes over the tropics have a huge influence. Over a period of only 15 years, the insolation in the (sub)tropics increased with ~2 W/m2, about as much as what is expected from the combined GHGs since the start of the industrial revolution. This is reflected in the papers by Wielicki ea. and Chen ea.. But note that the radiation balance at the top of the atmosphere (TOA) changed from negative to positive, due to corrections of errors in the satellite readings (see Wong ea.). This has not much influence on the insolation figures. The increase in insolation of the subtropics is visible in the ocean heat balance Figure 2 from Levitus ea., while GHG heating would be more evenly distributed. The upward ocean heat trend may be reverted in the past few years, it would be interesting to compare that with cloud cover changes…

  13. Jean S
    Posted Jan 17, 2007 at 11:07 AM | Permalink | Reply

    re #10: Dave, it says in the text that A and B are known. I take it as the realization of the series A and B is known. As such, it is just classic multivariate linear regression model (if noise is uncorrelated) and (multivariate) generalized linear regression model (if one allows noise to be correlated). In either case, this one of the most studied problem in statistic. Or am I (and I suppose UC also) missing something here?

    [As a side note: if one assumes that "knowing" the processes A and B means that one only knows the statistical properties of A and B, the problem is totally ill-posed. The possible(?) solution depends not only on the exact form of A and B but also from the exact form of the noise.]

  14. Dave Dardinger
    Posted Jan 17, 2007 at 11:46 AM | Permalink | Reply

    re: #13,

    As I said, Jean, I don’t know if the problem is easily solved or not. Though re-reading it I don’t think your statement actually addresses the problem. What the author (Peter Thejll) is wondering about is using something called “evolving multivariate regression” technique. And it sounds like something like Mann et. al. have done with the various pieces of the multiproxy puzzle to produce the final results. That is using proxies for one time period and then another period and varying the results depending on how many proxies are available for each period. The author seems to be saying that when tests were done, they found bias depending on how well the series A(t) and B(t) each correlate with T(t). [Or perhaps it's more he's talking simply sliding filters.]

    But again, the fact that the problem is “open” doesn’t depend on whether or not it’s easy (or even well forumlated), but on whether or not someone has presented a properly done solution to the author / journal.

  15. Posted Jan 17, 2007 at 12:04 PM | Permalink | Reply

    #13

    Yes, what are we missing? Or is it just too tough problem for SIAM readers? For reference, http://www.siam.org/pdf/news/388.pdf challenge, 20 independent teams obtained 10 correct digits for all 10 problems. Took me almost a day to solve #6 alone ;)

  16. jae
    Posted Jan 17, 2007 at 12:05 PM | Permalink | Reply

    There’s a recent review of solar/warming studies here, concluding that the solar connection remains unproven (as with the CO2 connection).

  17. Bill F
    Posted Jan 17, 2007 at 12:25 PM | Permalink | Reply

    The question of the climate’s large sensitivity to seemingly small changes in solar output can be easily answered by incorporating the influence of GCRs on low cloud cover. I forget where I saw the concept posted (may have been one of Svensmark’s or Christensen’s papers), but the idea is that increases in solar output during active periods are generally accompanied by increases in solar wind that affect the earth’s magnetic field shape and strength and result in fewer GCRs reaching the lower atmosphere, which results in less low level cloud cover to reflect sunlight back into space. The same mechanism results in more GCRs and more clouds during periods of low solar activity. Thus, the climate affects of changes in the output of the sun are amplified by the GCR penetration changes that occur due to the change in output as well. Since this feedback is “extraterrestrial” in a way, it is not a feedback for terrestrial forcings such as CO2. Therefore, the statement in comments that solar output as a forcing is subject to the same feedbacks as GHGs is incorrect.

  18. Jean S
    Posted Jan 17, 2007 at 12:45 PM | Permalink | Reply

    re#14/#15: It is interesting to google the phrase “evolving multivariate regression”, you get essentially two hits: the above problem and MBH98…

  19. Posted Jan 17, 2007 at 12:55 PM | Permalink | Reply

    #18 That’s what I did to obtain link for #7 :) (don’t read SIAM.org pages very often, I wonder how old that question is)

  20. Bill F
    Posted Jan 17, 2007 at 1:30 PM | Permalink | Reply

    Interesting paper with new and convincing evidence of a GCR-cloud link that is independent of satellite data:

    Empirical evidence for a nonlinear effect of galactic cosmic rays on clouds – Harrison, R.Giles, and David B. Stephenson (2006). “Empirical Evidence for a Nonlinear Effect of Galactic Cosmic Rays on Clouds.” Proceedings of the Royal Society A462: 1221-33 [doi:10.1098/rspa.2005.1628].

  21. Paul Linsay
    Posted Jan 17, 2007 at 2:37 PM | Permalink | Reply

    #12, Ferdinand, as Douglas Hoyt has pointed out there is also a difference which depends on the wavelength of the radiation. CO2 acts through long wave IR, which heats the atmosphere which in turn heats the ocean through conduction. Short wave solar in the visible and the UV heats the ocean directly and at great depth. The net effect of n W/m^2 are very different depending on the wavelength.

  22. Dave Dardinger
    Posted Jan 17, 2007 at 3:01 PM | Permalink | Reply

    re: #21

    CO2 acts through long wave IR, which heats the atmosphere which in turn heats the ocean through conduction.

    You need to reword that a bit. The atmosphere heats the outer surface of the ocean via downwelling long-wave IR and that surface heat can then either increase H20 evaporation, outgoing IR, or can be moved deeper into the ocean via convection. Conduction is just too slow to even think about. And the the ocean convection is pretty rapid, though the depth is variable, being much deeper in cooler waters.

  23. Gerald Machnee
    Posted Jan 17, 2007 at 3:14 PM | Permalink | Reply

    Can someone post the various terms and definitions being used so that some of us who are unfamiliar may get a better understanding.
    Some are: galactic cosmic rays, irradiance, total solar irradiance, solar flux, etc.
    Thanks.

  24. Bob Weber
    Posted Jan 17, 2007 at 6:31 PM | Permalink | Reply

    See comment 60, 61 and 64 at

    Bob

  25. Bob Weber
    Posted Jan 17, 2007 at 6:33 PM | Permalink | Reply

    Couldn’t get the link to post. Trying quote tag.

    http://www.climateaudit.org/?p=1063#comments

    Bob

  26. Steve Reynolds
    Posted Jan 17, 2007 at 7:22 PM | Permalink | Reply

    >About the “efficacy” of solar vs. other forcings…

    Would a simple difference between solar and GHG forcing be in water vapor feedback? Since evaporation is exponential with temperature, a small change in high daytime temperature (due to solar) would cause much more evaporation than GHG forcing on the lower average day/night temperature.

  27. Gerald Machnee
    Posted Jan 18, 2007 at 6:20 AM | Permalink | Reply

    Re #24 – I saw those. All the terms being used are not yet there, but I was hoping for a short explanation of them as well.

  28. Posted Jan 18, 2007 at 7:51 AM | Permalink | Reply

    #11 Steve,

    yes, I’ve read those posts. Just wanted to bring this up again, as I find that the MBH98 Attribution of climate forcings section is very ‘descriptive’. (Sorry for the redundancy, and pl. skip the following if this gets boring:)

    LS estimator for model
    Temp = a*CO2 + b*Solar+c*Volcanic+d+n
    replicates Fig7 correlations almost exactly (see here, you have done the same here earlier ). It is a general linear model, with additive error structure. var(n)*inv(X’*X) is the covariance matrix of the estimator, it tells us how well we know a,b,c, and d given the values of the regressor variables ( CO2, Solar, Volcanic in matrix X, assuming that the model is correct). Shorter window, less accurate estimator. The geometry matters as well; for example, the estimator cannot tell much about CO2 effect during those early days. But the estimator knows this from the matrix inv(X’*X), as shown in http://www.geocities.com/uc_edit/mbh98/sensitivity.html (code), first figure. Another important issue is not shown in those figures: Estimation error of CO2 is strongly negatively correlated with estimation error of Solar. Overestimate of CO2 effect implies underestimate of Solar effect, and vice versa.

    But why all this evolving multivariate regression effort?? I just don’t get it. Google gives no answer, SIAM seems to be silent.. What would be different if they had used all the data at once (green line solutions in my figures) ? Afraid of the fact that full data results show that the model is actually very bad, specially for 1880-1920?

    The other puzzling part: those one-lag correlations again:

    This parameter ranges from 0.48 in the first window (1610–1809) to 0.77 in the final window (1796–1995) of the moving correlation, the considerably larger recent value associated with the substantial global warming trend of the past century.

    0.77 is the for 1796-1980!! 1796-1995 gives 0.87 with my Matlab (pl. others, check it), and Mann himself in 1996 told us that for 1850-1990 instrumental, p is 0.93 (without robust chopping of the peaks using ad-hoc median filter, 0.38 with robust chopping). This is not the first time I see underestimated p..

  29. Jeff Weffer
    Posted Jan 18, 2007 at 7:54 AM | Permalink | Reply

    Does anyone have a link to the paper Lean et al 1995 shown in the Figure 6-5.

    http://www.grida.no/climate/ipcc_tar/wg1/fig6-5.htm

    I know she updated the data in 2000 and backed off the 4 W/M2 change shown below (my guess is to keep her job and keep the peace in the climate change community.)

  30. Steve McIntyre
    Posted Jan 18, 2007 at 8:31 AM | Permalink | Reply

    @28. I agree 100%. I agree with bringing it up again as well in the context of solar proxies.

    In our previous discussion, we were thinking about it purely statistically. Looking at it with the benefit of a little more familiarity with the solar proxies, the statistical methods of MBH98 Figure 7 are even more repugnant.

  31. Jean S
    Posted Jan 18, 2007 at 10:11 AM | Permalink | Reply

    #29: Jeff, is this the one you wanted:
    http://www.geo.umass.edu/faculty/bradley/lean1995.pdf

  32. David Smith
    Posted Jan 18, 2007 at 10:43 AM | Permalink | Reply

    Interesting paper linking sunspots and the upper atmosphere is given here .

    The QBO is a stratospheric oscillation which is thought to affect year-to-year hurricane frequency, among other things.

    The polar vortex is the mid-atmosphere whirlwind in polar regions, which affects Arctic weather patterns.

    Sudden stratospheric warmings are weird events in which polar parts of the stratosphere suddenly warm, which can affect the troposphere.

  33. Posted Jan 20, 2007 at 4:26 AM | Permalink | Reply

    #30, It is good to re-visit MBH98 from time to time, there is always something new ;)

    For new readers, Ferdinand Engelbeen brought these sensitivity issues up at RC (correlation between CO2 and Solar, reconstruction errors, etc..)

    You can read mike’s response:

    http://www.realclimate.org/index.php/archives/2006/10/how-not-to-attribute-climate-change/

    , #71. Here’s a synopsis:

    This is nonsense…. You might learn something from .. It is somewhat ironic that you cite .. ..in your efforts to argue for a greater role of solar forcing in past temperature variations.. perhaps you are advocating a negative sensitivity to solar forcing? .. . But it does serve to underscore how naive your interpretations are.. You might benefit from a more thorough and careful reading of the literature…

  34. Steve McIntyre
    Posted Jan 20, 2007 at 7:53 AM | Permalink | Reply

    UC, that’s an interesting thread at realclimate and worth re-reading.

    It’s exchanges like this that raise doubts about their message more than supposed disinformation from ExxomMobil. Ferdinand’s questions were straightforward and merited a straightforward reply. Ferdinand is someone who’s simply trying to understand things. Who knows – they might have answered his questions and he’d be on their side. Instead, they called him names and tried to score debating points, rather than deal with the question.

  35. Posted Jan 20, 2007 at 12:22 PM | Permalink | Reply

    And it makes me wonder..

    Who’s actually in denial : refusing to admit the truth or reality of something unpleasant (all work since -96 proven wrong)

    ..Don’t be alarmed now (And the forest will echo with laughter)

  36. Howard Wiseman
    Posted Jan 20, 2007 at 11:42 PM | Permalink | Reply

    Given some of the recent research linking cloud formation and cosmic rays (I am personally skeptical. What else is new?), I thought this information on the “Forbush Effect” was quite interesting. An increase in solar w/m2 combined with a reduction of cloud formation may actually add up to some type of climate impact. If nothing else, it supports the basic proposition that the solar forcing issue cannot be viewed as a singular phenomenon. You don’t need a weatherman to know which way the solar wind blows, but you might need a good solar physicist (and statistician and publicist and blog and grant writer).

    http://science.nasa.gov/headlines/y2005/07oct_afraid.htm

    Who’s Afraid of a Solar Flare?

    10.07.2005

    Solar activity can be surprisingly good for astronauts.

    October 7, 2005: Last month, the sun went haywire. Almost every day for two weeks in early September, solar flares issued from a giant sunspot named “active region 798/808.” X-rays ionized Earth’s upper atmosphere. Solar protons peppered the Moon. It was not a good time to be in space.

    Or was it?

    During the storms, something strange happened onboard the International Space Station (ISS): radiation levels dropped.

    “The crew of the ISS absorbed about 30% fewer cosmic rays than usual,” says Frank Cucinotta, NASA’s chief radiation health officer at the Johnson Space Center. “The storms actually improved the radiation environment inside the station.”

    Scientists have long known about this phenomenon. It’s called a “Forbush decrease,” after American physicist Scott E. Forbush, who studied cosmic rays in the 1930s and 40s. When cosmic rays hit Earth’s upper atmosphere, they produce a shower of secondary particles that can reach the ground. By monitoring these showers he noticed, contrary to intuition, that cosmic ray doses dropped when solar activity was high.

    The reason is simple: When sunspots explode, they often hurl massive clouds of hot gas away from the sun.

    These clouds, called CMEs (coronal mass ejections), contain not only gas but also magnetic force fields, knots of magnetism ripped away from the sun by the explosion. Magnetic fields deflect charged particles, so when a CME sweeps past Earth, it also sweeps away many of the electrically-charged cosmic rays that would otherwise strike our planet. This is the “Forbush decrease.”

    Wherever CMEs go, cosmic rays are deflected. Forbush decreases have been observed on Earth and in Earth orbit onboard Mir and the ISS. The Pioneer 10 and 11 and Voyager 1 and 2 spacecraft have experienced them, too, beyond the orbit of Neptune.

    A single CME can suppress cosmic rays for a few weeks. Sustained solar activity can suppress them for a much longer time: “2005 has been a surprisingly active year on the sun,” notes Cucinotta. Since January, astronomers have counted 14 powerful X-class solar flares and an even greater number of CMEs. As a result, “the crew of the ISS has absorbed fewer cosmic rays all year long.”

  37. Howard Wiseman
    Posted Jan 20, 2007 at 11:53 PM | Permalink | Reply

    I throw this in for good measure. 18 pounds to read.

    http://direct.bl.uk/bld/PlaceOrder.do?UIN=030812440&ETOC=EN&from=searchengine

    Pudovkin, M.I., Veretenenko, S.V., 1995. Cloudiness decreases associated with Forbush-decreases of galactic cosmic rays. J. Geophy. Res. 57, 1349-1355.

  38. maksimovich
    Posted Jan 21, 2007 at 12:26 AM | Permalink | Reply

    re 37 There is a good paper here,that covers the issues you are discussing

    http://www.arm.ac.uk/preprints/433.pdf

  39. Howard Wiseman
    Posted Jan 21, 2007 at 8:53 AM | Permalink | Reply

    Re 38:

    Thanks for the article!

    Latitude dependence desribed there is another interesting feature of the phenomenon, as it could relate to NH polar region temperature increase observations. Could also support (gasp) latitude variations in MWP.

    I don’t claim any high level command of the science here, just putting interesting pieces together. I do think Grandma Curry’s comments on who qualifies as an authoritative skeptic have some validity (although her view risks limiting the broad variety of information added to the collaborative science blog review process–anyone who has been here for a while can distinguish the pros from the sincere armchair amateurs, the contemptuous disdainers or the rabid dog blowhards), so if there is some scientific/mathematic/statistical “gotcha”, there is no need to gloat. Just pass along the knowledge, thanks very much. (Maksi…last comment not directed at you in anyway, just a general disclaimer and rant).

  40. Posted Jan 21, 2007 at 10:06 AM | Permalink | Reply

    #28 cont.

    0.77 is the for 1796-1980!! 1796-1995 gives 0.87 with my Matlab (pl. others, check it), and Mann himself in 1996 told us that for 1850-1990 instrumental, p is 0.93 (without robust chopping of the peaks using ad-hoc median filter, 0.38 with robust chopping). This is not the first time I see underestimated p..

    Just for fun I tried how those significance thresholds change if I use 0.87 instead of 0.77. 99% level for CO2 rises from 0.41 close to 0.6.

    MBH98:

    Nonetheless, all of the important conclusions drawn below are robust to choosing other reasonable (for example, 100- year) window widths.

    :) p=0.87 and 100-year window, 99% threshold rises to 0.97 for CO2 and 0.92 for Solar. Not that those thresholds mean anything important..But is there anything in MBH98 that is computed correctly??

  41. Posted Jan 21, 2007 at 10:51 AM | Permalink | Reply

    BTW, pl. let me know when Mann 2006a with :

    The true value of p can in fact be estimated from the proxy data themselves, and Mann et al. (2006a) have estimated the average value of p for the full network of 112 proxy multiproxy indicators used by MBH98 to be p = 0.29 ± 0.03. The value p = 0.32 therefore constitutes an appropriate upper limit for the actual multiproxy network used by MBH98 in past surface temperature

    is published. You know, there is a sharp limit

    (Mann ME, Rutherford S, Wahl E, Ammann C. 2006a. Robustness of proxy-based climate field reconstruction methods. J. Geophys. Res. In press)

  42. Posted Jan 21, 2007 at 5:50 PM | Permalink | Reply

    Some may have noticed (even on RC) that I am a fan of solar…
    That started some 30 years ago with reading a book about solar-climate connections (don’t remember the author), including temperature, rainfall on different places on earth even clusters of earthquakes and number of wars. Some of those connections might be spurious (number of wars – but one never knows the influence of climate on people’s mood?), but several, especially rainfall, have a high correlation with solar cycle(s). As rainfall and energy input/(re)distribution have much in common, this points to a huge solar influence.

    The RC discussion is of interest, as it gives an idea of what the distribution of weight between the different forcings (solar/volcanic/GHGs/aerosols) might be if one uses the MBH-like reconstructions (with little variation in pre-industrial times) vs. the Moberg-like reconstructions (with much larger variation). In the first case, little influence of solar is to be expected, in the second case, the influence of solar (up to now) is much higher. Further, also the influence of volcanic seems to be overestimated (in current climate models) too. For the past 600 years, the cooling influence of volcanic is in average 0.036 K, based on dendro and non-dendro proxy reconstructions (based on fig. 4 of Robock, and the number of large eruptions), which leaves more room for solar influences…

    There is another pair of antipodes of interest too: GHGs vs. aerosols. The first graph in the aerosol discussion at RC gives an impression of the difference in sensitivity for 2xCO2 for different influences of human made aerosols. In my opinion, the cooling effect of aerosols is highly overestimated (which implies that the effect of 2xCO2 is overestimated too). Interesting is that there is no comment from the RC team (on #14 of the above link), neither from the guest specialists here on my comment #6…

  43. maksimovich
    Posted Jan 21, 2007 at 6:58 PM | Permalink | Reply

    Re 39 The mechanisms for modulation are latitude dependent due to the proton cut off levels for geomagnetic disturbance.ie higher energy levels for proton disassembly further from the poles,and vertical scalar differentials with altitude.

    Particles travelling along the magnetic field lines are least affected, and thus the polar regions, where the field lines penetrate the atmosphere and the Earth’s surface, are easier to access. According to the StàƒÆ’à‚ⷲmer theory, every geomagnetic latitude has a cutoff limit which the rigidity of an incoming particle (defined as momentum per charge) must exceed in order it to reach that particular location.Penetration to lower latitudes requires higher rigidities, and a certain latitude is affected by particles having rigidity equal to, or higher than the corresponding cutoff. The cutoff rigidity varies spatially and also with time, being dependent on the IMF on as well as on the Earth’s internal magnetic field, on timescales from minutes to years. The magnetic storms, for example, tend to compress themagnetosphere and lower the cutoff rigidity for a given latitude.

    As a consequence of geomagnetic cutoff, the particles are able to affect atmosphere above a certain magnetic latitude, covering the polar cap regions in both hemispheres. Typically latitudes above about 60àƒ⣃¢’‚¬”à‚⤠are affected more or less uniformly, although the effects have sometimes been observed near the geomagnetic poles first, and later throughout the polar cap.As particles propagate down into the atmosphere they lose their energy in collisions with atmospheric gases. In such a collision, with the proton energies considered, the atmospheric molecule is ionised, and an ion-electron pair is created.

    In addition to the primary protons, the secondary electrons produced in ionisation may have enough energy to further ionise and dissociate atmospheric gases. Approximately 36 eV of energy is required in the production of one ion pair thus a proton with 10 MeV initial energy is able to ionise about 280,000 molecules along its path before all the energy is lost. The atmospheric penetration depth is dependent on the particle energy, the 1–500 MeV solar protons depositing their energy in the mesosphere and stratosphere. The most energetic protons, with E > 1 GeV, are able to reach the ground level, although at these energies the galactic cosmic rays generally predominate.

    The ionisation caused by solar particle precipitation can far exceed the normal geomagnetically quiet-time sources in the middle atmosphere, As a result the ion concentrations are significantly elevated at altitudes below about 100 km and the ion composition may also change. The ion concentrations are closely tied to the ionisation level, and after a reduction in proton forcing the fast recombination with free electrons results in a quick return to quiet-time levels.

    Orgutsov,.Lindolm,et al provided interesting analysis of the mechanisms and atmospheric photochemical changes in the thermosphere and subsequent precipitation of chemical activators at the Astrobiological workshop on mechanisms in atmospheric chemistry.

    Pudovkin who you cite above showed the photochemical reaction NO + O3 àƒ⣃ ‹’€ ‘> NO2 + O2; O3 + O àƒ⣃ ‹’€ ‘> 2O2
    Hence the input of high-energy particles into the atmosphere leads to ozone destruction and generation of NO2. Such changes are particularly strong during powerful proton events, e.g., on 4 August of 1972 at the altitude 30- 35 km the concentrations of ozone and NO2 were reduced by a factors 10 and 2, correspondingly. Because NO2 absorbs intensively solar radiation in green and blue part of spectrum the irradiance at the Earth’s surface decreases.

    We saw this recently in early December we had a large solar proton event indeed the x-class flare was 15th largest recorded .The flare arrived in 15 minutes in the Antarctic sending graphs up30% and forcing ionization towards the equator.This shut down several satellites and the FAA issued a warning to lower altitudes and several satellites were forced to increase height due to thermosphere temperatures in the radiation belts increasing by 500k.The international space station inhabitants were forced into protective areas and altitude corrections for the space station were required

    IZMARIN and Pushkov Institute of Terrestrial Magnetism, Ionosphere and
    Radiowave Propagation centre monitoring this event,measured extended ozone degradation below 42south and desktop calculations of a differential in RF of around -5w/m2.

    Observational data saw a decrease in SST of around 1.5c in the focal area of longtitude of 145-180 west of the ITLRapid energy dissipation saw lower then normal SAT for the localities 42 s in this longitudinal box.

    When comparing mechanisms it is better to describe GCR SCR,ACR CME as high energy particles ,the similarities of observed phenomena can be similar and the signals equal in sign.

    PS With regard to Dr Curry maybe she should read about one of the US most important astronomers of the 20th century a mule driver with no formal education past 14 years old who became secretary of the US observatories.

    http://www.bpccs.com/lcas/Articles/humason.htm

  44. Howard Wiseman
    Posted Jan 21, 2007 at 11:00 PM | Permalink | Reply

    Dear Maksimovich: Thank you for your helpful and well-written tutorial. As I understand your explanation, the latitude level and atmospheric depth of of cosmic ray impacts (ozone and NO2 effects) will be determined by the energy content of the cosmic ray emmissions. Are there corresponding impacts on atmospheric heat budgets, with positive redistributions made in favor of depth levels with high cosmic impacts and vice versa? How does this fit in with Santer/Pielke/Christy on the issue of Troposheric warming/stratospheric cooling? It appears the instrument and satellite record is confused and not likely to provide adequate resolution to answer the question.

  45. Howard Wiseman
    Posted Jan 21, 2007 at 11:15 PM | Permalink | Reply

    This article looks like a step in the direction of calculating the forcing values.

    http://arxiv.org/PS_cache/physics/pdf/0612/0612145.pdf

    The Antarctic climate anomaly and galactic cosmic rays
    Henrik Svensmark

    It has been proposed that galactic cosmic rays may influence the Earth’s climate by affecting cloud formation. If changes in cloudiness play a part in climate change, their effect changes sign in Antarctica. Satellite data from the Earth Radiation Budget Experiment (ERBE) are here used to calculate the changes in surface temperatures at all latitudes, due to small percentage changes in cloudiness. The results match the observed contrasts in temperature changes, globally and in Antarctica. Evidently clouds do not just respond passively to climate changes but take an active part in the forcing, in accordance with changes in the solar magnetic field that vary the cosmic-ray flux.

  46. maksimovich
    Posted Jan 21, 2007 at 11:48 PM | Permalink | Reply

    re 44 Here is the conundrum,coupling is not only below but from above,the mesosphere and thermoshere are outside of climate scientists area of “expertise”here the area of aeronomy is the scientific sphere of astrophysics.

    There is an intersting monologue from Michael Mendillo for the IHY
    Atmospheric scientists tend to divide the gaseous regions above a planet into two broad categories called simply lower and upper atmosphere. For Earth, the study of the lower regions (troposphere and strato-sphere) form the discipline of meteorology. The study of the upper regions (mesosphere, thermosphere, exosphere) and their ionized components (the ionosphere) form the discipline of aeronomy. The negative aspect of such a two-fold division is that it encourages thinking of the various atmospheric-spheres as isolated regions of self-contained physics, chemistry, and (in the case of Earth) biology. In reality, there is consider-able coupling from lower to upper regions, an aspect of aeronomy fully appreciated only in the last decade. Com-plimenting this external influence from below, an upper atmosphere has long been known to experience forcing and coupling to and from regions far above it. Aeronomy thus deals with one of the most highly coupled systems in space science — with neutrals, plasmas, and electromagnetic processes that link the planets, moon, and comets from their surfaces to the solar wind and ultimately to the Sun itself.
    The key questions posed in solar system aeronomy are:
    1. What are the constituents of each atmosphere encountered?
    2. How do they absorb solar radiation?
    3. What are the thermal structures resulting from heating versus cooling processes?
    4. What types of ionospheres are formed?
    5. What are the roles of atmospheric dynamics at each site?
    6. Does a planetary magnetic field shield the ionosphere from solar wind impact?
    7. How do trapped energetic particles and electrodynamics affect the atmospheric system?
    If all planets were the same, the answers to these questions would depend primarily on distance from the Sun. Such “seen-one, seen-them-all” space science would indeed render the solar system a boring cosmic neighborhood. Happily, space exploration has led to precisely the opposite situation. Distance from the Sun matters, but so do local conditions. Consider Figure 1 where the temperatures of each planet’s upper atmosphere are plotted versus distance from the Sun. The temperatures at Venus, Mars, and Saturn fall well below the values that might be estimated via a simple interpolation between neighbors. Composition and local energetics
    matter!

    http://www.bu.edu/csp/uv/cp-aeronomy/monograph02.html#Introduction

    Stratospheric coupling is being studied by SPARC for the World climate research programme.

    Joanne Haigh has some interesting observations,

    Although the largest percentage ozone changes over a solar cycle occur in the upper stratosphere, the corresponding column amounts are too small to explain the observed solar cycle variation of total ozone, which is several per cent, depending on latitude and season (Hood, 2004). Therefore, the observed lower stratospheric positive ozone response is likely to dominate the total ozone solar cycle variation at all latitudes. Solar cycle variation is the largest single form of long-term variability for ozone in the tropics and subtropics.
    http://www.atmosp.physics.utoronto.ca/SPARC/News23/23_Haigh.html

    Here we see variability in the vertical column over the solar cycle,ie higher retention at high cycle in mid to low latitudes with more heat retention,greater degradtion of the entire column during times of high energy events in the polar regions.

    As gcm cannot identify the radiation budget accurately the range is 20-25% due to inability of measurement of near infra red and levels of accurate amplitude of TSI still with error bars of 2w/m2 even over the last two solar cycles,there is still a lot of uncertainty

  47. Francois Ouellette
    Posted Jan 22, 2007 at 8:52 AM | Permalink | Reply

    #46 Maksimovich: Thanks for all the useful info.

    quick questions: do we know how much of the sun’s total energy is absorbed at the various layers of the atmosphere? How does that divide between the various parts of the spectrum, from IR to deep UV? Can we quantify the total amount of energy from cosmic rays, both solar and galactic? I’d appreciate if you could give some references where I could find this!

  48. Posted Jan 22, 2007 at 8:56 AM | Permalink | Reply

    Re:46, maksimovich:

    Great contributions, thanks for participating. Your BU server is having problems finding the Figures.

  49. jae
    Posted Jan 23, 2007 at 11:45 AM | Permalink | Reply

    Maksimovich, I too want to thank you, as well as the others that have posted links. I am fascinated by the link in #45, which could explain why the MWP and LIA may not have been as pronounced in the SH. It also could explain why the NH is warming, while the SH The IPPC is hurting its reputation gravely by “writing off” the Solar influences. I just cannot understand any scientist that does not have serious reservations about the amount of A in AGW, considering the probability that the Sun exerts major effects on the climate.

  50. EW
    Posted Jan 23, 2007 at 12:05 PM | Permalink | Reply

    #37
    We have access to that journal online since 1997, so that the Pudovkin-Veretenenko (1995) isn’t there. However, there’s another article about Forbush effect from the same authors from 1997.

    The influence of galactic cosmic rays on the solar radiation input to the lower atmosphere was investigated in the different latitudinal belts. Increases of the total radiation fluxes associated with Forbush- decreases in the galactic cosmic rays were found at thestations with high frequencies of cirrus clouds situated atlatitudes cpz60°-68″. It is shown that the total radiation input in the winter months at stations in subauroral zone anticorrelates with the galactic cosmic ray intensity in the II yr solar cycle. In the aurora1 zone the solar radiation input seems to be affected by aurora1 phenomena. The variations of the total radiation fluxes associated with different cosmophysical phenomena seem to be of great importance for the radiation budget of the lower atmosphere.

    If someone is interested I can send the .pdf

    About their 1995 paper they say:

    According to our previous results (Pudovkin and Veretenenko 1995) the pronounced changes in the high-level cloud amount associated with Forbush-decreases of the galactic cosmic ray (GCR) flux were found in the geomagnetic latitude region @ 2 55″. The variations of the cloudiness found may be of great importance for the radiation budget of the lower atmosphere. The clouds strongly affect both the input of the short-wave solar radiation and the output of the long-wave radiation of the Earth and atmosphere.

  51. Loki on the run
    Posted Jan 23, 2007 at 1:38 PM | Permalink | Reply

    The Sun is More Active Now than Over the Last 8000 Years

  52. maksimovich
    Posted Jan 24, 2007 at 12:42 AM | Permalink | Reply

    Re 47

    Vertical spectral energy studies are mostly specific to certain phenomena ie it is easier to observe variability during times of higher heliogeophysical activity and related atmosphere anomalies.

    Sorce the EOS radiation experiment is undertaking a comprehensive study on solar connections within the atmosphere, there are limitations due to instrumentation, spectral opacity, focal fields of measurement. The database will provide a valuable tool for future studies as long as limitations are understood.

    http://lasp.colorado.edu/sorce/index.html

    The Cawses group is undertaking a number of studies for coupling process in the stratosphere –mesosphere Lubken et al are measuring temperatures, watervapor ,noctilucentclouds, polar mesospheric clouds, and polar mesospheric summer echoes and budgets using-Lidar, radar, satellite-based, and rocket-borne techniques and the combined ENVISAT + ground-based measurements profile.

    Manson part of the Cawese group is using sectional studies 31n to 78 n 01 hpa to 10 hpa measuring airglow and stratospheric warming.There are some interesting links and newsletters.
    http://www.bu.edu/cawses/

    Russia has a substantial number of projects ongoing and in publication. IZMARIN has a substantial database of ionosphere and mesosphere profiles by radio astronomy measurements this has a substantial benefit as the focal area of observation is around 10000 times greater then satellite and covers greater spectral ranges.

    There are a number of Tomes to be published this year as it is International geophysical year, the study groups are as numerous as the IPCC input organizations so we may have an interesting year for debate.

    There are a number of heuristic realities in the sun-climate connection, that the sun modulates climate by a number of simplistic mechanisms.

    As a simplistic caricature by way of metaphor the sun has three states on/off/both

    The “heat engine” of the Sun is closely related to convective and radiation transfer of free energy in the solar interior, which proceeds basically at low Mach– Alfven numbers,i.e., at a relatively small involvement of the magnetic field. The solar “dynamo” in this sense is a product rather than prime cause of solar activity. The latter in this broader meaning is understood as a fundamental property of a star with relatively small variability of energy release and transfer in its interiors against the background of much greater steady energy flux supported by nuclear fusion processes in gravitationally confined core of the Sun. From this point of view the phenomena considered on the Sun are an example of a complex self-organization in a non-equilibrium open physical system with the fluxes of free energy and mass. The “magnetic degree of freedom” from this standpoint is subordinate and controlled by other, more powerful global processes. However, locally in some areas and at some time intervals this degree of freedom can be predominant over others, which is the case during flares. Here, we deal with all manifestations of well-known general laws of physics, characteristic for nonlinear processes with dissipation.

    These processes regulate the energy dissipation of the terrestrial climate by modulation of the terrestrial bi-pole dynamo and atmospheric phenomena.

    The simplicity of nature is not to be measured by that of our conceptions. Infinitely varied in its effects, nature is simple only in its causes, and its economy consists in producing a great number of phenomena, often very complicated, by means of a small number of general laws.

    Pierre Laplace

  53. Posted Jan 24, 2007 at 10:25 AM | Permalink | Reply

    Everyone interested in solar theories of climate should look here:

    http://motls.blogspot.com/2007/01/solar-resonant-diffusion-waves.html

  54. Gerald Browning
    Posted Jan 24, 2007 at 4:44 PM | Permalink | Reply

    maksimovich (#52),

    Clearly the faculae on the sun are very small compared with sunspots and any attempt to numerically model the sun in its entirety is unlikely to be successful. (In the early days at NCAR such an attempt was made and the solar rotation ended up going in the wrong direction.)

    Is the exact reason the solar corona is so hot completely understood (no numerical models, but analytical physics)? Is the reference cited in one of the solar posts the one I should read, or are there others?

    The helmet streamers were thought to be closed magnetic features containing the plasma, but in fact with reduced viscosity in a fine resolution numerical model developed for Tom Holzer, they were shown to leak bubbles near the tip. Are they still thought to leak?

    Have any new continuous equations been developed for ionized plasmas in the earths ionosphere since the manuscript by Holzer and me? If so can you cite recent manuscripts to bring me up to date?

    Thank you.

  55. maksimovich
    Posted Jan 27, 2007 at 2:29 AM | Permalink | Reply

    Re Gerard
    I left my book of abstracts at another location and there are some prohibitions on preprint publication of the articles for the Tomes described above. Some links are only in Russian at present so I have not provided. Fully updated papers are part of the IHY project and will be published from April onwards.

    Clearly the faculae on the sun are very small compared with sunspots and any attempt to numerically model the sun in its entirety is unlikely to be successful. (In the early days at NCAR such an attempt was made and the solar rotation ended up going in the wrong direction.)
    Any adequate description of physics of the processes involved is possible only taking into account the transport of energy, momentum, and mass in considered open systems with their complex space-time structure of corresponding flows. In this case the conceptions of equilibrium and stability of isolated system can serve as useful idealization only in the simplest cases, as well as models of replenishment from above, below, or from side of the considered segment. In general, the main difficulty is that there are no sufficient observational data in order to separate such isolated systems and thus to localize the consideration of causes and effects.

    The type of spectra produced would be important eg with the exception of àƒÅ½à‚Ɑrays from flares, this entire complex of heliospheric sources of energetic ions is virtually invisible via photons. For most of the particle populations, ion acceleration takes place in low-density regions where interactions are rare and measurable intensities of photons are simply not produced.

    Is the exact reason the solar corona is so hot completely understood (no numerical models, but analytical physics)? Is the reference cited in one of the solar posts the one I should read, or are there others?
    High energy particle acceleration as a toroidal mechanism by the gravitational mass of the sun. An analogue would be a tokamak or torus thermonuclear reactor such as ITER.
    The Russian –Ukrainian Coronas f satellite with the Spirit experiment conducted intense analysis of the Corona and interaction in intense events with 20mk measurements during the Halloween storms. This sidetracked the intended analysis, however the observation of high energy particle acceleration is documented in addition Veselovsky has postulated the concept of the turbopause around the Sun based on the dimensionless scaling approach to the analysis of physically distinct radiation MHD and plasma kinetic regimes in the solar wind formation region. New dimensionless parameters like Faraday F, velocity-emission Ve and Trieste T numbers are introduced to evaluate the relative role of potential and inductive electric fields (F), radiation and plasma losses of the solar corona (Ve) and the openness degree of different morphological elements on the Sun (T).

    Veselovsky I., Turbulence and waves in the solar wind formation region and the heliosphere. Astrophys. and Space Sci., 277, 219-224, 2001.
    Veselovsky, I. S. et al. Solar cycles in the energy and mass outputs of the heliospheric plasma. Astronomy Reports, 1999, v. 43, pp.485-486.
    Veselovsky I.S. Scaling approach in the solar and heliospheric plasma. Lecture Notes SMR 1161/10 Autumn College on Plasma Physics, 25 October-15 November 1999, The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, 21 pp.

    The life of the solar corona is mostly governed by the magnetic field. In fact,the global and large-scale magnetic fields control and order the distribution of the whole matter in the corona. The strength and organization of those fields clearly foreordain the presence of different coronal structures (coronal streamers, holes plumes, condensations, etc.), the global form of the eclipse corona, and the position and shape of the heliospheric current sheet. In fact, no direct measurements of the coronal magnetic field exist nowadays,so the magnetic field between the photosphere and the source surface is difficult to study.
    CONNECTIONS BETWEEN THEWHITE-LIGHT ECLIPSE CORONA
    AND MAGNETIC FIELDS OVER THE SOLAR CYCLE
    J. SàƒÆ’àKORA1, O.G. BADALYAN2 and V. N. OBRIDKO2
    http://helios.izmiran.troitsk.ru/hellab/Obridko/17474496.pdf

    The helmet streamers were thought to be closed magnetic features containing the plasma, but in fact with reduced viscosity in a fine resolution numerical model developed for Tom Holzer, they were shown to leak bubbles near the tip. Are they still thought to leak?
    WHITE LIGHT CORONAL STRUCTURES AS TRACERS OF ELECTRON VELOCITY FIELD IN THE SOLAR CORONA
    I.S. Kim Sternberg Astronomical Institute of Moscow University, Universitetsky pr. 13,
    Importance of the white-light corona structures researches is discussed. There are no doubts now that the observed white light structures manifest specific configuration of solar magnetic fields in the corona. Pioneer ground-based multi-station eclipse experiments (S.K. Vsekhsvyatsky et al.) evidently indicate opportunity for coronal rotation investigations. Moreover, polar plumes, helmet coronal streamers, rays, regions with significantly reduced intensity named coronal voids by S.K. Vsekhsvyatsky (they are known now as coronal holes) evidently trace streams of slow and fast solar wind in the picture plane.

    Have any new continuous equations been developed for ionized plasmas in the earths ionosphere since the manuscript by Holzer and me? If so can you cite recent manuscripts to bring me up to date?

    A new theoretical model of the Earth’s low and middle latitude ionosphere and plasmasphere has been developed [Pavlov, 2003]. The new model uses a new method in ionospheric and plasmaspheric simulations. It takes advantage of a combination of the Eulerian (an Eulerian computational grid is fixed in space co-ordinates) and Lagrangian (it is needed to solve only one dimensional time dependent ion and electron continuity and energy equations along a magnetic field B in the moving Lagrangian frame of reference) approaches. New equations which determine the trajectory of the ionospheric plasma perpendicular to B and an electric field E and take into account that magnetic field lines are “frozen” in the ionospheric plasma are derived and included in the new model. Different new strategies for solving the continuity and energy equations and a new direction splitting technique are developed and employed at the same time with the use of low and middle latitude boundary conditions. The model takes into account the role of vibrationally excited N2 and O2 and electronically excited O+ ions in the ionosphere and calculates altitude profiles of electron and ion densities Ne and Ni and temperatures Te and Ti above 130 km. We have presented a comparison between the modelled NmF2 and hmF2 and NmF2 and hmF2 which were observed at the anomaly crest and close to the geomagnetic equator simultaneously by the Huancayo, Chiclayo, Talara, Bogota, Panama, and Puerto Rico ionospheric sounders during the 7 October 1957 geomagnetically quiet time period at solar maximum. The revision of the empirical model local time dependence of the equatorial upward ExB drift velocity is found from the model calculations. It is found that Te at F2-region altitudes become almost independent of electron heat flows along B above the Huancayo, Chiclayo, and Talara ionosonde stations because of the near-horizontal B inhibits the heat flow of electrons. The morning Te peaks which are found above the ionosonde stations at hmF2 altitudes are explained by the sunrise physical processes.
    There were very serious problems with explanations of existence of high plasmaspheric electron temperatures Te (~7200-10700 K) measured by the instruments on board of the EXOS-D satellite and low Te measured by the Millstone Hill radar in the topside ionosphere within the same magnetic field line tube. The additional heating of electrons found brings the measured and modelled Te into agreement in the plasmasphere and into very large disagreement in the topside ionosphere (up to 1000-2000 K) if the classical Spitzer-Harm electron heat flux is used. The discovery of the phenomena of the reduced and nonlocal electron temperature conductivity of the plasmasphere and the topside ionosphere [Pavlov et al., 2000] solves this problem. The new approach are derived leads to a heat flux which is much less (up to a factor of 2-3) than that given by the classical Spitzer-Harm theory. As a result, the high plasmaspheric Te and low ionospheric Te can exist at the same time.

    1. Pavlov, A.V., New method in computer simulations of electron and ion densities and temperatures in the plasmasphere and low-latitude ionosphere, Annales Geophysicae, Vol. 21, No. 8, 2003
    http://www.copernicus.org/EGU/annales/ag_pt.htm

    2. Pavlov, A.V., Abe, T., and Oyama, K.-I., Comparison of the measured and modelled electron densities and temperatures in the ionosphere and plasmasphere during 20-30 January 1993, Annales Geophysicae, Vol. 18, No. 10, P. 1257-1272, 2000.

  56. Gerald Browning
    Posted Jan 28, 2007 at 12:59 AM | Permalink | Reply

    Maksimovich (#55),

    I appreciate your candid responses, but believe them to be a bit too technical for readers that are not experts in this area. Therefore, let me try to simplify your answers to my series of questions for a general audience. If my simplifications are incorrect, please let me know.

    Question 1:

    The sun is a very complicated object and although observations of faculae, sunspots, differential solar rotation, helmet streamers, coronal mass ejections, solar cycles, etc. have been made for many years, it is extremely difficult for us to understand these features because we do not have sufficient information (e.g. local lateral boundary conditions) to analytically describe or numerically model the individual objects such as a sunspot. This was the problem with the numerical model of a helmet streamer developed for Tom Holzer, i.e. what boundary conditions does one use at the lower part of the helmet streamer for the inflow from below.

    Question 2:

    Scientists have postulated a number of mechanisms, but there is no definitive analytical explanation for why the solar corona is so hot, at least not at this point in time.

    Question 3:

    The problem with attempting to analytically or numerically model individual phenomenon on the sun already has been discussed in #1.

    Question #4:

    Are the continuum equations for the ionosphere any different from those developed by Holzer and me, and if so, how are they different. I ask that this point be clarified in order to help me understand how the physics has changed from when Tom and I published our manuscript that I thought included all ionospheric plasma particles of interest.

  57. John Creighton
    Posted Jan 28, 2007 at 2:26 AM | Permalink | Reply

    As far as solar forcing goes there is clearly a large spectral component in the temperature signal which accounts for about 25% of the variances and is near the frequency of the 12 year sunspot cycle. As for the 50 year solar cycle I don’t think that signal is particularly strong in the temperature signal. The next big spectral peak in the temperature signal seems to be around 400 years and corresponds nicely with the changes in the length of day. It could also be correlated with the carbon dioxide in the atmosphere. However, a carbon dioxide correlation can’t explain the drop in temperature between 1750 and 1820 while the length of day better reflects the U shape low frequency signal in the temperature records of the last 300 years.

  58. John Creighton
    Posted Jan 28, 2007 at 2:52 AM | Permalink | Reply

    #1 UC, I agree with you in that Laut and Gunderman’s are wrong in their conclusion that using multiple correlations avoids high spurious correlations. However, I do though question your assumption that CO2 and Solar are collinear. It is true that in MBH98 man’s data for solar activity is quite collinear with the carbon dioxide.

    If you look however, at the sunspot data and Man’s solar activity data you will see that Man’s solar activity data just looks like the sunspot data put though a low pas filter. If that is how Man’s solar activity data was obtained one should notice that the filter is nonlinear because the mean was not subtracted before the filtering took place. This opens up the question about how the sunspot data could be nonlinearly related to the temperature on earth. Since Man’s data is just a filter of the sunspot data it is much better to work with the sunspot data since it is richer and is not collinear with carbon dioxide.

    I think that carbon dioxide is far more independent of temperature then most people have been assuming. If you take temperature as a state and carbon dioxide as a state and you try to find a transfer function to predict the future state based on the current state you will find that in the transfer function the CO2 in the next time interval depends very little on the temperature of the previous time interval.

  59. Posted Jan 28, 2007 at 3:14 AM | Permalink | Reply

    John,

    yes, I was referring to Mann’s data,

    corrcoef(solar(:,2),co2(:,2))

    ans =

    1.0000 0.7325
    0.7325 1.0000

  60. Posted Jan 28, 2007 at 3:37 AM | Permalink | Reply

    Inspired by this thread I made a short Solar reconstruction using Mann’s proxies. Here.

  61. Willis Eschenbach
    Posted Jan 28, 2007 at 5:12 AM | Permalink | Reply

    UC, that’s hilarious. Now you need to fit them to the US Dow Jones stock market index or somesuch, and you’ll have your trifecta complete.

    w.

  62. John Creighton
    Posted Jan 28, 2007 at 12:11 PM | Permalink | Reply

    #60 US. I am curious in the version of MBH98 data I have the solar signal is smoother. I am tried to download the data you used but the nature website was down.

  63. Posted Jan 28, 2007 at 12:34 PM | Permalink | Reply

    Nature website works for me.

    #61

    You can flip solar data upside down, or use NH rec data from another period, almost anything goes to get ‘significant’ correlation ;)

  64. Steve McIntyre
    Posted Jan 28, 2007 at 12:55 PM | Permalink | Reply

    #61, http://www.climateaudit.org/?p=370 has a reconstruction using Tech Stock Prices plus white noise; which out-performs MBH. I think it shows rather nicely that MBH multivariate method produces virtually identical results given one trending series and a network of white noise.

  65. John Creighton
    Posted Jan 28, 2007 at 12:58 PM | Permalink | Reply

    #63 Oh my bad. I see the smoother line is the original signal. Usually I think of smoother lines as the fit.

  66. maksimovich
    Posted Jan 30, 2007 at 1:10 AM | Permalink | Reply

    Re 56 Gerard.

    I apologize for non simplification of the problematic questions that arise for the understanding of the manifest phenomena that are observed and our understanding of the stellar systems.This commentary is mostly for the general readership,and I apologize if it is “coals to Newcastle.”for yourself or other readers.

    First we divide the component parts of the earth –sun dynamic complex, into three inter-related sections.

    i)The sun as a thermonuclear reactor.

    ii)The heliospheric coupling, which is the magnetic field connection,the solar wind, transport mechanisms,and particle acceleration.

    iii)The earths upper atmosphere ,radiation belts, magnetosphere,and plasmasphere.

    Here the level of understanding is relatively high for the sun, as both the physics, mathematics, models, and physical replications exist for the macrocosmic mechanisms. The microcosmic mechanisms provide a degree of complexity that as you comment are difficult to understand or even observe or measure adequately.

    As opposed to say climate modelers high energy physicists have both scalable and working experimental models of the thermonuclear mechanism by way of apparatus

    The tokamak fusion reactor. Here we have over 50 years of both theory and physical observation in the areas of high energy plasma ,and the difficulties of magnetohydrodynamics physics which is nearly as hard to spell as explain.

    Background here http://en.wikipedia.org/wiki/Tokamak which provides a good historical perspective.

    The 20 billion dollar international collaboration project is here. http://www.iter.org/.

    The serendipity here with the solar mechanisms and the tokamak reactor enhances the scientific understanding for the astrophysicist.

    The sun of course is poorly designed ,and it is difficult to adequately explain the parameters of the asymmetrical oscillations ,or the unexpected mega phenomena by way of prediction.

    The level of understanding to calculate the solar output by cyclical oscillation is high.

    With regard to the Corona and the temperature differential ,the main understanding is magnetic connection and reconnection with the photosphere.The high energy particle acceleration is consistent with the 5 minute oscillation in the photosphere and emission of high energy particles this sees the changes in the corona to an electric field regime

    A comparative analogy is here with some other studies.
    III. INFLUENCE OF OHMIC HEATING ON ADVECTION-DOMINATED ACCRETION FLOWS

    http://astrosun.tn.cornell.edu/us-rus/adaf.htm

    I apologise for the brevity but work deadlines appear.I will comment on the other components over the next week.

  67. Gerald Browning
    Posted Jan 31, 2007 at 12:43 AM | Permalink | Reply

    maksimovich (#66):

    Reduce the flowery language and lets get to the main points.

    1: You have stated that the individual features on the sun cannot be understood for the reasons I discussed. This we both agree on.

    If the individual features are not understood and important to the understanding of the magnetohydrodynamics of the sun, then how can the variability of the sun be understood?

    2: You claim that because there is a tokamak, you have a good understanding of the sun. I did not know that there was a working fusion reactor. If so, it will solve the world’s energy problems. The sun uses gravity to contain the thermonuclear reaction and that is very different than attempting to contain the reaction with magnetic fields. The amount of money spent on a project is not necessarily an indication of the quality of the project.

    3: I am a numerical analyst and PDE mathematician well aware of the shortcomings of numerical models and the magnetohydrodynamic equations.

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