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Aerosol effects and climate, Part II: the role of nucleation and cosmic rays

Filed under: — group @ 15 April 2009 - (Italian)

Guest post by Bart Verheggen, Department of Air Quality and Climate Change , Energy research Institute of the Netherlands (ECN)

In Part I, I discussed how aerosols nucleate and grow. In this post I’ll discuss how changes in nucleation and ionization might impact the net effects.

Cosmic rays

Galactic cosmic rays (GCR) are energetic particles originating from space entering Earth’s atmosphere. They are an important source of ionization in the atmosphere, besides terrestrial radioactivity from e.g. radon (naturally emitted by the Earth’s surface). Over the oceans and above 5 km altitude, GCR are the dominant source. Their intensity varies over the 11 year solar cycle, with a maximum near solar minimum. Carslaw et al. give a nice overview of potential relations between cosmic rays, clouds and climate. Over the first half of the 20th century solar irradiance has slightly increased, and cosmic rays have subsequently decreased. RC has had many previous posts on the purported links between GCR and climate, e.g. here, here and here.

The role of ions

The role played by ions relative to neutral (uncharged) molecules in the nucleation process is still very much under discussion. For instance, based on the same dataset, Yu and Turco found a much higher contribution of ion induced nucleation (to the total amount of particles produced) than Laakso et al did. Evidence for a certain nucleation mechanism is often of an indirect nature, and depends on uncertain parameters. Most literature points to a potential importance of ion induced nucleation in the upper troposphere, but the general feeling is that neutral pathways for nucleation (i.e. not involving ions) are likely to be dominant overall. Most field studies, however, have been performed over land, whereas over the open ocean nucleation rates are generally lower due to lower vapor concentrations. In theory at least, this gives more opportunity for ion induced nucleation to make a difference over the ocean (even though the ion production rate is smaller).

The ion production rate (increasing with altitude from ~10 to ~50 ion pairs per cubic centimeter per second over land) sets a limit to what the particle formation rate due to ion induced nucleation can be. Based on his model for ion induced nucleation, Yu found that at low altitude, the number of particles produced is most sensitive to changes in cosmic ray intensity. At first sight, this may be a surprising result in light of the increasing cosmic ray intensity with increasing altitude. The reason is that high aloft, the limiting factor for particle formation is the availability of sulfuric acid rather than ions. Above a certain GCR intensity, increasing ionization further could even lead to a decrease in ion induced nucleation, because the lifetime of ion clusters is reduced (due to increased recombination of positive and negative ions). In contrast, at low altitude particle formation may be limited by the ionization rate (under certain circumstances), and an increase in ionization leads to an increase in nucleation.

How important is nucleation for climate?

Different modeling exercises have been performed to investigate this question. The strong dependency on input data and assumptions used, e.g. relating to primary particle emissions and nucleation parameterizations, and the different sensitivities tested, hampers an overall assessment. However, it is clear that globally, nucleation is significant for the number of cloud condensation nuclei (CCN) e.g. in the absence of boundary layer nucleation, the number of CCN would be 5% lower (Wang and Penner) or 3-20% lower (Spracklen et al.), and in a recent follow up study, they concluded that the number of cloud droplets would be 13-16% lower (in 2000 and 1850, respectively). Pierce and Adams took a different approach and looked at the variation of predicted number of CCN as a result of using different nucleation schemes. The tropospheric number of CCN varied by 17% (and the boundary layer CCN by 12%) amongst model runs using different nucleation rate parameterizations. Note that the globally averaged nucleation rates differed by a factor of a million (!).

It should be noted that the sensitivity of the number of CCN to nucleation depends greatly on the amount of primary emissions and secondary organic aerosol (SOA) formed. These are very uncertain themselves, which further limit our ability to understand the connection between nucleation and CCN. If there are more primary emissions, there will be more competition amongst aerosols to act as CCN. If more organic compounds partition to the aerosol phase (to form SOA), the growth to CCN sizes will be quicker.

Locally, particle formation has been observed to contribute significantly to the number of CCN; the second figure in Part I gives an example of freshly nucleated aerosols which grew large enough to influence cloud formation. Kerminen et al observed a similar event, followed by activation of part of the nucleated aerosols into cloud droplets, thus providing a direct link between aerosol formation and cloud droplet activation.

How important are cosmic rays for climate?

At the recent AGU meeting (Dec 2008), Jeff Pierce presented results on the potential effects of GCR on the number of CCN (their paper at GRL (sub. required)). Two different parameterizations for ion induced nucleation were used (Modgil et al and an ‘ion-limit’ assumption that all ions go on to form a new particle). They ran their model with both high and low cosmic ray flux, simulating conditions during solar maximum and minimum, respectively. This happens to be comparable to the change in cosmic ray flux over the 20th century (mostly confined to the first half), and amounts to a 20% change in tropospheric ion production. With both mechanisms of ion-induced nucleation, this leads to a 20% change in globally averaged particle nucleation, but only to a 0.05% change in globally averaged CCN. The authors concluded that this was “far too small to make noticeable changes in cloud properties based on either the decadal (solar cycle) or climatic time-scale changes in cosmic rays.” To account for some reported changes in cloud cover, a change in CCN on the order of 10% would be needed. More studies of this kind will undoubtedly come up with different numbers, but it’s perhaps less likely that the qualitative conclusion, as quoted above, will change dramatically. Time will tell, of course.

The bottom line

Freshly nucleated particles have to grow by about a factor of 100,000 in mass before they can effectively scatter solar radiation or be activated into a cloud droplet (and thus affect climate). They have about 1-2 weeks to do this (the average residence time in the atmosphere), but a large fraction will be scavenged by bigger particles beforehand. What fraction of nucleated particles survives to then interact with the radiative budget depends on many factors, notably the amount of condensable vapor (leading to growth of the new particles) and the amount of pre-existing particles (acting as a sink for the vapor as well as for the small particles). Model-based estimates of the effect of boundary layer nucleation on the concentration of cloud condensation nuclei (CCN) range between 3 and 20%. However, our knowledge of nucleation rates is still severely limited, which hampers an accurate assessment of its potential climate effects. Likewise, the potential effects of galactic cosmic rays (GCR) can only be very crudely estimated. A recent study found that a change in GCR intensity, as is typically observed over an 11 year solar cycle, could, at maximum, cause a change of 0.1% in the number of CCN. This is likely to be far too small to make noticeable changes in cloud properties.

309 Responses to “Aerosol effects and climate, Part II: the role of nucleation and cosmic rays”

  1. 251
    steve says:

    Going back to the evaporation pan question for a minute. I have found a paper by Hobbins and Ramirez in Geophysical Research Letters Vol 31 2004 which shows the location of the greatest loss in pan evaporation in the U.S. and it occurs to me that the places showing the greatest loss increase are also the places most likely to have had increases in irrigation for farming and residential areas which of course would increase water vapor and decrease pan evaporation. Does this seem logical?

  2. 252
    Brian Dodge says:

    William @ 25 avril 2009 at 9:05 AM, quoting another source, says
    “The proposed ion-mediated nucleation (IMN) theory can physically explain the enhanced growth rate (a factor of ~ 10) of sub-nanometer clusters as observed by Weber et al. [1997],”

    in support of his earlier statement (24 avril 2009 at 6:43 PM)

    “Svensmark’s Sky experimental results showed that the same ion is re-used which multiplies the GCR effect by roughly an order of magnitude. The paper you quote assumes a one to one ion ratio for ion mediated.”

    William, you are confusing growth in size of each individual ion mediated condensation nucleus(which is enhanced by the charge) with growth in numbers of GCR CCN (which would be required to “multiply the GCR effect”).

    You also state “How does one re-use an ion? Ions do not wear out. The same ion moves from molecular cluster to molecular cluster.”

    But according to Tinsley and Yu*
    “The growth rate of the ion clusters is controlled by [H2SO4], while nt determines the

    -lifetime of charged clusters-

    as well as the availability of ions. The neutralization by ion-ion recombination will make the growing charged clusters lose their growth advantage and the resulting neutral clusters may dissociate if smaller than the critical size. At typical [H2SO4] where significant nucleation has been observed, for very low Q most of the ion clusters have sufficient time to reach the larger stable sizes prior to recombination and the nucleation rate is limited by Q. As Q (or altitude) increases, ion concentration increases but the

    -lifetime of ions decreases-

    and hence the fraction of ions having sufficient time to grow to the stable sizes decreases. As a result, the total number of particles nucleated first increases rapidly but later on decreases as Q (or altitude) increases.” (emphases mine – BD) Oppositely charged ions do ‘wear each other out’.

    *Geophysical monograph ISSN 0065-8448 2004, vol. 141, pp. 321-339 American Geophysical Union, Washington, DC, ETATS-UNIS

  3. 253
    Patrick 027 says:


    “an honest admission of what is actually fair (the later will be as hard as a diamond formed in a black hole – many many people complain reflexively about anything bad for themselves as being unfair, as if in a fair world they would be King Midas).”

    To clarify: though there is some use for stoicism, I don’t meant to suggest that everybody must constantly keep a stiff upper lip (I certainly don’t). But complaint of misfortune need not be based on arguments of fairness.

    A distinction should be made between what is fair and what is deserved. Presumably they are or tend to be proportional, but a fair distribution is limited by physical reality. I have advantages in life beyond what is fair as I was born in a first-world, peaceful country. But I do not necessarily think that I have gotten more than I deserve; rather, I wish everybody could have what I have. (Others with a fire and brimstone attitude may think that what is deserved is far less than what is fair…)



    So overall,take the sum of export subsidies

    (preferably not linked to emissions intensity, or if so, only in broad categories within which individual products/services with differing emissions intensities compete with each other on that basis via the emissions price signal (Remember, more generally, all emissions from all sectors should be treated equally and not walled-off from each other, and the market reaction should decide which sectors change the most, etc.))

    and import tariffs (preferably linked closely to emissions intensity of individual units of products/services). This sum should be proportional to the difference between the emissions price signals of the two countries, allowing for an adjustment and/or grace period for poorer nations.

    Speaking of that adjustment, my formula:
    1-((1 – GPPC/($7,000/year))^1.7)
    was quite ad hoc, though the number I chose ($7000 per capita annual GDP or GNP) is loosely based on a vague memory of what I read (Fareed Zakaria: “The Future of Freedom”) of the wealth per capita threshold that might allow a stable healthy democracy.


    Deforestation and other land use emissions:

    A solution:

    Have all countries as of a starting year pay ‘backtaxes’ on net deforestation/etc. (and soil losses, etc.) emissions (this might include lifetime-methane emissions associated with hydroelectric reservoirs). From that point on, it will be nearly fair if a nation’s net deforestation/etc. emissions are charged and net reforestion/aforestion/etc. sequestrations are credited/subsidized.

    But to be fair to the present, the ‘backtaxes’ should be discounted as a function of time since the changes occured. This is because present day people live where they live, do what they do, etc, as a result of historical events that cannot be changed – civilizations, etc. have been established and they are where they are. Also to be fair to the present, some recognition is needed that – especially in Europe, some of the benificiaries of past habitat changes may currently be elsewhere, so some of the ‘backtaxes’ might be apportioned by total property value of nations.

    A similar procedure could be used with emissions in general to get developing countries to participate more fully without the full need of the grace period, and it would make the spending category E. in the form of GDP/GNP rebates less unfair; the grace period and poor nation adjustments could be removed and replaced with the spending in C. and D., which includes the CDM spending. In that case the trade issues might be mitigated.

    If each nation contributes to the ‘global climate fund’ as per emissions, as with individual businesses within nations with such domestic policies, the price signals will tend to spread naturally to the benificiaries of emitting activities.

    Spending on A. and B. could apportioned to each country as per R&D and subsidy and adaptation compensation efforts (R&D successes would win prizes) of each country.

    But many people are uncomfortable with the U.N. or ____ handling such large sums of money. So:

    The actual payments made by nations could just be the net owed – the total a nation owes minus the funds owed them.


    A fundable solution to migration issues: Of the total payment for adaptation costs of migration of climate refugees, some portion could be payed to the refugees, and some portion could be payed to recieving nations, to get them to accept refugees with open arms (PS I would have implemented such a policy to get neighbors of Iraq to accept Iraqi refugees). Recieving nations could use funds to boost carrying capacity – e.g. desalination and irrigation investments.


    Earlier I mentioned using osmosis to get energy from where rivers meet the sea.

    1. We would not want to do this to the extent that it damages estuary environments, etc. (It might be a way to make the best of meltwater flowing off Greenland and Antarctica?)

    2. Given the present inefficiencies of osmosis and reverse osmosis, it would not make sense to have both osmotic hydroelectric power and water desalination projects in the same region. The market should prevent this from happening. (One possible exception might be a flow of water from the Red Sea into the Dead Sea to replace water from the Jordan river that has been diverted for irrigation; the combination of the Dead sea’s high salinity and low elevation may make desalination + osmotic power a net energy producer, depending on the technology (the initial desalination is to preserve the Dead Sea’s composition in the process). On the other hand, it might make more sense to let the Jordan river flow and use desalinated water. Etc.)


    Wind turbines:

    There are places for them (especially offshore – could we make use of hurricanes (osmotic raincatcher power plants, too)?). However, there is some concern about scenery, bats, and birds – though I have read the later is not such a big problem compared to other anthropogenic bird issues (?). If wind turbines were replaced with arrays of small turbines, then each turbine might not have enough inertia or force to hurt a bird, and from a distance, the motion would not be so obvious (or it might appear as a sparkling, like a distant flock of gulls in the morning light). Motion is a big scenery issue; immobile objects are much easier to ignore.

    Small turbines don’t have to withstand large centrifugal forces and can make use of turbulence. Using many small turbines that can be connected in a modular fashion might reduce costs (by increasing potential for mass production).

    Conceivably one could design a ‘wind tree’, where generators (or pneumatic pumps that lead to generators) are at the base of flapping leaves. Maybe just for niche markets: edges of skyscrapers, etc.


    Temperature dependent color-changing materials for building exteriors and maybe interiors too!

  4. 254
    Patrick 027 says:

    “(It might be a way to make the best of meltwater flowing off Greenland and Antarctica?)”

    Bearing in mind effects on sea ice and thermohaline currents

  5. 255
    Brian Dodge says:

    Dr Verheggen,

    My statement@74 “I would think that more GCR = more clouds = more rain” was oversimplified, not to mention wrong, as you kindly pointed out. That’s a frequent side effect when i’m thinking out loud.

    Would a step change in GCRs, (absent secondary effect chains like increasing albedo = less surface sunlight = cooler ocean surface = less evaporation = less water available for precipitation) only cause a transient change in rainfall? I can see how smaller GCR mediated cloud droplets might take longer to grow large and fall as rain, but shouldn’t that only delay rainfall, rather than reduce it? Would this delay cause distances between source(net evaporation) and sink(net precipitation) areas to increase, and have any changes like this in patterns of rainfall or concurrent latent heat transport been observed?

    According to “Precipitation Trends in the 20th Century”
    Anthony Del Genio, Aiguo Dai, and Inez Fung
    “We find that in much of the middle and high latitudes, precipitation has systematically increased over the 20th Century.”
    and “We find that the precipitation changes recorded over the 20th Century are well-matched to trends in cloud cover measured over the past few decades.” Are these trends continuing, and can any GCR influence be shown?

    Recaptcha says “mar genevese”
    Googling “rainfall trend genoa italy” returns (first hit)
    ” Trends in High Frequency Precipitation Variability in Some Northern Italy Secular Stations” by Michele Brunetti, Letizia Buffoni, Maurizio Maugeri and Teresa Nanni, which “gives evidence that in Northern Italy there is a positive trend in the proportion of total precipitation contributed by heavy precipitation events…”

    Could this be an effect of “fluffier” GCR ion mediated clouds lasting longer, growing larger because of more moisture available due to AGW, and when the threshold in cloud droplet size crosses the precipitation tipping point, larger rain events are occurring?

  6. 256
    Hank Roberts says:

    This, steve?
    Can’t help you with the logic, but I think you need to consider all the variables, not just two, to figure out what’s going on. These papers seem to. I think this is the one you’re talking about:
    GEOPHYSICAL RESEARCH LETTERS, VOL. 32, L15401, doi:10.1029/2005GL023549, 2005

    “Figure 2 contains 192 data pairs from 25 basins across the U.S. [Hobbins et al., 2004] … Figures 2 and 3 correspond to a composite of 192 pans in 25 different basins over the continental U.S.,
    spanning the full climatic range from arid to humid….”

    Look at the “Related Articles” links here, for more review articles:

  7. 257
    Patrick 027 says:

    Re Ike Solem:

    “Carbon Dioxide Levels Controlled By Degassing and Chemical Weathering Over Time”

    Thank you. That was quite interesting. Though I should point out I was already aware of the generally slow nature of the geologic branches of the carbon cycle (as I explained here very briefly: ), and had some awareness of the possibility that repetitive glaciations may enhance the longer-term average chemical weathering rate, though I’m not sure I had considered the role of continental shelf erosion (however, that might have two sides – exhumed sediments may contain organic carbon that may be oxydized upon erosion).

    What I had brought up was the possibility that we could artificially increase the chemical weathering rate by grinding up certain kinds of (relatively abundant) rocks – and if the trade off between lost efficiency in cation use at lower CO2 concentrations and the smaller chemical reaction rate at lower temperatures could be made up by the lack of need for CO2 pipelines or … etc, then this could be done by scattering mineral dust into the ocean (from quarries near coasts) – conceivably there might also be a local aerosol cooling effect if the dust is allowed to blow some distance out to sea. I’m not sure of the ecological consequences, but would guess there is less risk of ecological disruption using this sequestration method than with using ocean fertilization which necessarily requires biotic activity (and may be less predictable and less effective) – and it would actually buffer ocean pH; along those lines, even carbonate minerals could help, though not as thoroughly, in increasing the water’s capacity to hold CO2 and buffer the pH.

  8. 258
    David B. Benson says:

    Patrick 027 (257) — That is an interesting variation on ex situ ultra-mafic mineral weathering. I am concerned that the rate might be quite low but in trade for that the costs are not high, on the order $10 per tonne of CO2 removed.

    Pau-pua New Gui-nea and New Cale-don-ia both offer excellent prospective locations.

  9. 259
    steve says:

    #256 Yes Hank I had seen the 2005 study but there is a actually a 2004 study with a map of where the greatest decrease in pan evaporation rates were taking place. The study also included maps of vapor pressure and TSI and the location of the decreases and the variation on these pressure and TSI maps weren’t overly convincing for either case. But what I noticed was decreased evaporation around the areas of Phoenix, El Paso, Chicago, Atlanta, Dallas-Ft Worth, San Francisco, Salt Lake City. All rapidly growing metropolitan areas which would have seen significant urban sprawl.

  10. 260
    Hank Roberts says:

    > not overly convincing

    That’s a statistical determination I don’t know how to do.
    Maybe photographing the sites would help.

  11. 261
    Mark says:

    steve #251, if you have to ask “is this logical?” then either it isn’t or you aren’t logical.

    And if it were, what conclusions would you draw from it? If it weren’t what would you change about what you know?

  12. 262
    steve says:

    #26o Hank, yes probably photographing the sites would help. Until such time as I can get to that I have to rely on my base knowledge, the resources available to me and some basic logic. For instance I know it is illogical that if water vapor pressure were the primary reason for the decrease in pan evaporation that one would see multiple sites showing slight increases in evaporation and then once reaching metropolitan areas in the same area of water vapor pressure a dramatic decrease such as is seen in the Dallas Ft Worth area. Because my interests lead me to read on many problems I can immediately see a connection between the increased use of irrigation in the Rio Grande Aquifer system and the water problems that is likely to create in the future and how the numerous sites which show pan evaporation decreases within the basin of this system could be related to this increased irrigation. Because I am familiar with geography I understand that urban sprawl in places like Charlston SC, Houston TX, and central FL would involve draining wetlands and thus would have the opposite affect. And because I am familiar with both geography and human nature I would find it very suprising if the cluster of decreasing pan evaporation rates between San Francisco and Reno did not match a cluster of developement. Do I know that the answer lies within land use, certainly not. But I at least know enough to know I don’t know.

  13. 263
    steve says:

    #261 Mark, the reason I asked if it was logical is because I’m not sure that the amount of water involved, particularily that used in residential areas, is sufficient to change the local water pressure enough to have the type of affect I believe may be possible. This I am less then well informed enough to make a sound judgement on. If not then it is a rather worthless road to travel and I would seek a new route.

  14. 264
    Hank Roberts says:

    > probably photographing the sites would help.
    > Until such time as I can get to that I have
    > to rely on my base knowledge

    Steve, it sounds like you’re going down the “surfacestations” road without benefit of statistics.
    If you don’t recognize why that’s a problem, see Tamino’s blog. Don’t waste your time, the questions you raise can be answered scientifically, but not by taking pictures and being logical based on a few facts.

    Sorry for the digression. I’m done on that issue.

  15. 265
    Patrick 027 says:

    Re 241, 258 (David B. Benson) – thank you for those links; I haven’t gotten a chance to look at them but look forward to it.

    ” New Cale-don-ia “

  16. 266
    Patrick 027 says:

    As I recall, a great place to get Ni.

  17. 267
    Patrick 027 says:

    (ult-ra-?)mafic rock composition (?). (I have also heard that exposed peridotite (intrusive ult-rama-fic igneous rock; corresponding extrusive rock is komatiite, which rarely if ever forms in recent geologic times because of the higher temperature required to result in complete melting of upwelling mantle; mafic gabbro/basalt is a result of partial melting and resulting fractionation) tends to form a relatively lifeless surface – true?)

    Which reminds me:

    Obviously highly toxic elements have some relatively low abundances in most common rocks (ores can be a different matter), and the usual rate of erosion is not generally a problem (except ore-forming processes?). However, would anthropogenically-forced erosion rates (for CO2 sequestration/ocean pH buffering) cause a problem with As, Hg, Pd, Cd, etc.?

    On the other hand, what if, after grinding up, physical seperation of grains and further physical, chemical seperation (aided by concentrated CO2, H2O, heat from coal or biofuel power plants/fuel cells?) were done so that the non Ca, Mg silicate portion were used to mine for Si, Al, Fe, Na and K (mainly for glass), Ti, P, Mn – and the residue of that operation were mined for S, Cu, Zn, Ni, Cr, V, Sn, V, Zr, Mo, Nb, Ce, La, Nd, Y, Co, etc., and the residue from that operation were mined for Cd, Ag, Ga, Ge, In, Se, Te, Au, Pt, etc… – perhaps a pipedream, but no harm in putting the idea out there (a number of these elements could be used in solar cells).



    Imagine geothermal storage of solar thermal energy. Concentrated solar radiation might be beamed through a hole in the ground (details yet to be worked out) to heat a 500 m x 500 m x 500 m cube of rock (surrounded by refractory bricks). In an initialization period, there is net storage over cycles of storage and retrieval, until the rock is just partly molten (?) – and/or water and CO2 are provided to percolate through it very very very slowly. After some decades (or millenia?), perhaps the rock will have seperated into ore bodies, which can then be mined, and some of the products used in solar cells (not to say there aren’t enough reserves for solar cells in general, though maybe just Te reserves for a significant but small role for CdTe (but perhaps a role that can be realized sooner – it would only be a small percentage ultimately of all solar energy (although there is potential for future reserve gains (as Cu, Zn ?, etc, demand increases), and their is room for improvement in cell efficiency) – and then there’s CIGS, with an In, Ga and maybe Se availability issues, but anyway, there’s amorphous Si, thin film Si with light-trapping, and possibilities of oxides and/or sulfides and/or phosphides, nitrides, antimonides, iodides, etc, or combinations of those, etc, of combinations of Ti,V,Cr,Mn,Fe,Co,Ni,Cu,Zn,Y,Zr,Nb,Mo,La,Ce,Nd(?),…,Hf(?),W,Si,Sn,Al,etc, with rarer elements (and/or others of the above) as dopants and photosensitizers, very thin electrode interfaces, etc,…. not to mention use of the deluxe solar cells in geometric and/or luminescent concentrators – and then there’s organic solar cells, nanoparticle-polymer mixtures…

    (We should have greater funding for solar cell research so that a larger variety of potential photovoltaic materials, optical layers, electrical contact layers, structures (nanostructures, microstructures), manufacturing techniques, combinations, etc, can be researched and developed at the same time.)


    There a a couple interesting solar thermal concepts involving mimicry of weather: Solar towers, with hot air rising (there is a version (forgot who came up with it) without an actual solid tower – instead, the inflow is made to rotate so that the buoyant column’s tendency to detach from its source is limited by the centrifugal force that resists vortex stretching; I’m not sure how well it would work, but that is the mechanism that allows mesocyclones power-up tornados), and an indirect solar tower wherein salt water is injected and evaporated to produce a cold airmass.

    Along those lines, what about having seawater flow into a coastal canal to an osmotic power plant, interfacing with a high salinity brine that evaporates. Salinity will inevitably build up in the seawater inflow, but a deep canal would allow some outflow of enhanced salinity at the bottom; some of that saline water could be taken to replenish the salts in the brine on the other side as salt is removed and sold. Perhaps this would also use saline outflow from seawater-irrigated mangrove plantations.

  18. 268
    Patrick 027 says:

    Sorry for the broken up posting – I was trying to figure out what was tripping the spa-m detector.

    Clarification of ‘backtaxes’ for deforestation, past fossil C emissions, etc.:

    Obviously it would be impractical to pay this out at once. The idea is that once there is agreement that it will be payed, it should be easier to get the developing countries to participate (as in all fairness it should be) in a truly level playing field. The next question – as the ‘backtaxes’ are discounted as a function of time elapsed, would the payments have some additional interest rate from time since the policy is enacted? Perhaps, but I suggest only at the inflation rate, since it is not a high risk ‘lo-an’ (?)

  19. 269
    Mark says:

    Unfortunately then, steve (#263) you’re going to have a lot of problems, because I don’t understand your post there.

    You don’t understand what your question is aiming for and nobody else can answer you because we can’t understand you.

    Try the post again and fill in the blanks.

    “I’m not sure that the amount of water involved”

    Involved in what. State clearly.

    “particularily that used in residential areas”

    You then need to say in what residential areas. Willacoochie, Georgia is a residential area. Then again, so is Tokyo. I would figure a different amount of water involved in the two places, though.

    “is sufficient to change the local water pressure enough”

    Again, this would change based on what you call residential

    “to have the type of affect I believe may be possible.”

    What effect do you think is possible. You must know SOMETHING else you wouldn’t have an idea over what may be possible. Being clear and concrete means that someone may be able to figure out what you DO know and what answer you will be able to understand (or, indeed if you already know more than the person trying to answer, making their effort redundant).

    Why do you think what change you think may be possible doesn’t work with the changes of pressure from water use in residential areas? You haven’t even defined your scenario completely. Therefore there’s no way to rule out any possibility and no way to answer your question.

    Think about your question FIRST.

    Think about what you DO know. See if that makes your question redundant.

    Then, when you’re done writing the question if it is still relevant, read it again. Did you have to refer to your memory rather than what was on the message? If so, put that in.

    Ask an intelligent and intelligible question and maybe people won’t think you’re wasting their time.


  20. 270
    David B. Benson says:

    Patrick 027 — Another link which may interest you, mine tailings:

  21. 271
    steve says:

    #269 Mark, I think Hank understood what I was saying and mearly disagreed with my method of thinking the problem through.

    #264 Hank, I assumed you brought up pictures as an indirect hint that I was copying the work of Watts and didn’t actually take you seriously. I appreciate your emphysis on statistics. I would comment that in my view statistics don’t replace logic they mearly supplement it. If all it took was statistics then what is the probability that some guy off the street such as myself could look at a map of 33 sites on a map which represent the pan evaporation rate to be lowering at a greater then 90% chance and identify without research 24 sites that are connected either with increased irrigation or increased urban developement over the last 50 years. I have found a possible reason why my logic and Hobbins’ statistics may not be matching up but my limited ability to judge the importance of the amount of water involved again hampers me. The paper by Hobbins takes the HCDN stream-flow gauge numbers and compares to the PRISM precipitation numbers to estimate
    the environmental evaporation rate. This would for all appearances ignore the depletion of ground water being experienced in many heavily irrigated and many urban areas. Dr Marcia Schulmeister states the amount of the ground water loss of the Rio Grande Aquifer System at 55,000 to 70,000 acre-feet. I understand if you are tired of the subject and since I have taken this as far as I reasonably can I am pretty much done. thanks

  22. 272
    Mark says:

    “#269 Mark, I think Hank understood what I was saying and mearly disagreed with my method of thinking the problem through.”

    Well whoopie.

    How do you know he disagreed because he misunderstood your question? What if you want to hear from someone else?

  23. 273
    Mark says:

    Since we’re all here to try and spread the word on bettering our environment, you guys should consider checking out the Tomorrows World site.

    Some students won a video contest and it’s been posted for our viewing pleasure. One of them is about climate change and flooding, the other about water efficiency. Both are pretty undeniably important subjects. It’s important we encourage people to keep trying to get the word out on slowing climate changes and reducing carbon footprints. Check out the vids and send them to your friends!

  24. 274
    Patrick 027 says:

    Re 241, 258, 270

    In between 266 and 267 above:

    …”As I recall, a great place to get Ni.”
    “(ult-ra-?)mafic rock composition (?).”…


    Also where the backgrounds for “Walking With Dinosaurs” were filmed, because of a lack of flowering plants – something to do with the


    on that point: just after this comment (from 241 above):
    (which I believe gives a chemical weathering rate that is a factor of 3 too high – unless maybe it includes some bicarbonate production that later releases CO2 before actual mineral formation? (but in the short term could be of help in mitigating ocean acidity, atmospheric CO2))

    A related comment:
    “G.R.L. Cowan, hydrogen-to-boron convert”

    Which provides a quote about olivine massifs:
    “no vegetation grows on them, but they are not “toxic” as often reported, merely deficient in essential elements.”
    (contrary to what I had speculated/remembered/wondered earlier)

    and provides links:

    the last of which has a rather interesting quote about Ga, off-topic but worth posting anyway:

    “Ga has at times driven me to near despair. It seemed an obvious metal to determine by XRF only there was no gallium standard, so I bought some Ga metal to make artificial standards. Unfortunately it melts at about body heat, so these lumps of what appeared to be aluminum melted whenever touched and ran about like mercury. The obvious solution was to reduce it to some salt that did not melt to we put it in various strengths of HCL (to form GaCl3). It did not dissolve as Al would have done. When boiled it glowed like mercury and slowly diminished in size. After prolonged boiling it vanished. When the acid cooled it reappeared as an immiscible liquid globule quite unchanged. It seemed to be quite indestructible. I finally hurled it out a window and luckily some Ga values appeared for the standard W-1.”


  25. 275
    Patrick 027 says:

    Links from 241:

    Very interesting. It sounds like the actual grinding to dust and oceanic dispersal idea may not be quite competitive (except where the purpose is specifically acidity mitigation)(? – depends on energy and rock type, location – My initial calculation was for 80% mass in grains smaller than 25 microns, according to link in 197), as allowing CO2 to react with rocks in place does it’s own mechanical breaking. And it is exothermic so it can boost the reaction rate and be self-sustaining under some conditions. Nice.

    (That reminds me of … I think they’re called the Lost City hydrothermal vents (?) … where oxydation of ferrous Fe to ferric Fe produces heat and – I think methane – from H2O and CO2 – during serpentinization of the rocks. This particular phenomenon is of interest in the study of the origin of life – abiotic methane production with some mineral catalyst(s), as I recall, produces a similar isotopic signature to biotic methane production – something like that – and biological metabolism could have evolved from such geochemical reactions.)

    (The focus on one country (Oman) is interesting – not that this is the case, but an interesting futuristic movie plot could be based on one country’s rise to power via a near monopoly on CO2 sequestration.)

    (Perhaps it is not enough heat (and it doesn’t work if the temperature gets too high), but I wonder if a geothermal power plant could be run off of carbonate formation? (Water pumped downward to get heat could be first preheated by carrying CO2 to feed carbonate mineral production; it could then come back up with the same heat and temperature as otherwise while extracting somewhat less heat from the hottest rocks.))

    (Would there be earthquake risks if done on a large scale using bedrock in place – or would a few well-placed fractures surrounding selected blocks (shaped like inverted pyramids?) mitigate that issue?)

  26. 276
    Patrick 027 says:

    A few links stated olivine was Mg2SiO4, but olivine is actually (Mg,Fe)2SiO4, varying between forsterite (Mg2SiO4) and fayalite (Fe2SiO4). This link:

    did make the distinction. And I suppose for olivine in ul-tramafic rocks, Mg might dominate if the mineral’s Mg/Fe ratio follows the Mg/Fe ratio of the whole rock.

    (PS I haven’t finished that link but it did give the enthalpy of reactions. Since Gibbs free energy of reaction (G)= enthalpy of reaction (H)- temperature (T)* change in entropy (S), though the enthalpy and entropy of reaction can vary with temperature, for a first guesslinear assumption::

    G = H – T*S

    where Tmax is the temperature where the reaction shifts from being product favored to reactant favored:

    0 = H – Tmax * S
    S = H/Tmax
    G = H*(1-T/Tmax)

    So using H and Tmax (adjusted formulas so that only 1 CO2 molecule is sequestered; CO2 is gas, H2O is liquid, all others are solids, reaction at 1 bar CO2):

    1/2 forsterite + CO2 —- MgCO3 + 1/2 SiO2
    H= -45 kJ/mol, Tmax= 515 K,
    -20.5 kJ/mol (280 K),
    -18.8 kJ/mol (300 K)
    -14.4 kJ/mol (350 K)
    -10.0 kJ/mol (400 K)

    1/3 serpentinite + CO2 —- MgCO3 + 2/3 SiO2 + 2/3 H2O
    H= -32 kJ/mol, Tmax= 680 K,
    -18.8 kJ/mol (280 K),
    -17.9 kJ/mol (300 K)
    -15.5 kJ/mol (350 K)
    -13.2 kJ/mol (400 K)

    (That is not much energy compared to the energy produced when CO2 is emitted from fuel combustion.)


    I haven’t finished going through that last link.


    On osmotic power: 2 versions:

    1 fresh water flowing into seawater or brine, or seawater flowing into brine (brine connected to evaporation pond):

    If the water levels are the same, a tube carrying the less saline water goes down into the more saline water – perhaps ~ 200+ m for fresh water/sea water osmotic pressure (could be 2+ km for a saturated brine?); reaching high pressure near the bottom end of the tube, it passes through a turbine (Tesla turbine?) to reach a near sea level pressure, which is sustained by osmosis; it then flows out of the tube through an osmotic membrane.

    Available energy: ~ close to 2500 J/kg for fresh water/seawater; maybe (?) 25 kJ/kg for fresh water/saturated brine (?)

    2. less saline water flows at sea level through an osmotic membrane into a pressurized chamber; it then flows out through a turbine into an evaporation pond. This has the advantage of not needing a long tube and great water depth (which may require a deep saline aquifer or some outer tube to bring brine back to the surface if drilled into rock, or else it could be done in the open ocean using rainwater, etc.). However, the pressurized chamber is not freely ventilated and will freshen with time, so it will require some energy input – salt (from the evaporation pond) injected at high pressure. This shouldn’t prevent the device from working and being a net energy producer, as the volume of outflow should be greater than the volume of salt input.

  27. 277
    Patrick 027 says:

    A last note about ‘backtaxes’:


    For each year in the past, approximate a CO2 emission quantity, and CH4, etc, in CO2 equivalent for a time horizont extending … (even for those emissions not with us to day and not forcing a new equilibrium towards which the actual state is drawn towards, nonetheless they did add some extra heat energy, so…)

    Apply a discount rate for that year (discount increasing back in time).

    Assign it proportional to nations’ estimated emissions at that time.

    Apply a second time-dependent factor that increases from zero to 1 going back in time.

    Redistribute that portion of the responsibility of each nation’s emissions among nations in proportion to the product of current total wealth and emissions at that time.

    Just a suggestion.

  28. 278
    Jim Eaton says:

    Re # 274: Patrick 027 Says:

    “Which provides a quote about olivine massifs: ‘no vegetation grows on them, but they are not “toxic” as often reported, merely deficient in essential elements.’”

    The website you referenced says that “They are mainly formed of a peridotite or dunite named after “Dun Mountain” a member of the same group found in Nelson three hundred miles to the north.”

    Life on earth has managed to fill many amazing places, including ul tramafic rocks. Check out:

    “Dun Mountain was given its name because of the dun color of its vegetation which is itself a reflection of underlying ul tramafic rocks.” (dreaded spam filter)

    So while these areas may appear to be without plant life at first glance, further investigation will show that the vegetation that has managed to colonize these areas.

  29. 279
    Joe K. says:

    Miguelito (205) – As far as I could understand Shaviv’s paper, he doesn’t assume that the ocean is Isothermal down to 400 meters. He uses ocean data to see what is the globally average mixed layer depth, and below that assumes there is diffusion. So, if there is something wrong in his paper, it is something else.

  30. 280
    Patrick 027 says:

    Re 276 – I forgot to actually convert the Tmax values to K from deg C, and thus my G values were also incorrect. The correct values (with linear assumption) are: …

  31. 281

    Miguelito (196),

    Leif Svalgaard engaged in a discussion of Shaviv’s calorimeter paper over at WUWT last week or so, and voiced quite strong criticism.

  32. 282
    David B. Benson says:

    Joe K. (279) — Shaviv assumes (incorrectly) nearly instaneous mixing. That makes the ocean isothermal down to MLD, yes?

    The correct depth to use is the mixing depth appropriate to the time scale, about 5 years.

    My decidedly amateur take on it.

  33. 283
    Patrick 027 says:

    Re 280 (Re 276) never mind, that was a memory lapse. The Tmax and G values were (assuming constant H and S, which is at best an approximation) correct.

  34. 284
    Patrick 027 says:

    Re 278 – thanks for that info.

  35. 285
    Patrick 027 says:

    Re 277:

    “Redistribute that portion of the responsibility of each nation’s emissions among nations in proportion to the product of current total wealth and emissions at that time.”

    Actually, no. Just redistribute that portion in proportion to the wealth.

    After assigning a debt to each nation, take the global sum, find the global average per capita, subtract that from each nation’s per capita, and let that be the actual amount owed, so that it is a smaller amount of money that is payed by some and to others. Payments can be over 30+ years, with an interest rate that only just keeps up with inflation (global average inflation?), so that the debt, adjusted for inflation, is a constant amount when payed up.

  36. 286
    Patrick 027 says:

    I forgot to include sugar-eating bacteria-powered fuel cells in the list of biofuel technology in comment 245.

  37. 287
    Ike Solem says:

    Patrick, are you stating that you can make up for carbon emissions with financial payments? Fiduciary offsets for pollution – it’s cheaper to pay the fine and keep on polluting than to rebuild your factory from the ground up using good designs, isn’t that what you are trying to say?

    Take a look at this instead:

  38. 288
    Patrick 027 says:

    Re 287 – Before I take a look at the link, let me just say:

    “Patrick, are you stating that you can make up for carbon emissions with financial payments? Fiduciary offsets for pollution – it’s cheaper to pay the fine and keep on polluting than to rebuild your factory from the ground up using good designs, isn’t that what you are trying to say?”

    Absolutely not. The point is that if you have to pay more for something, you’re more likely to use some alternative or increase the efficiency of your use of that thing… (hence, demand shifts to cleaner/more efficient options, investment pulls away from the dirtier/less efficient options, and the demand pulls the investment toward the cleaner/more efficient options, thus ultimately increasing the supply of cleaner/more efficient options and reducing the supply of dirtier options).

    That’s the stick.

    Any carrots also need funding (Even though there may be room for improvement that is already affordable, just not yet habitual) and it makes perfect sense that the costs of climate change mitigation – as well as the costs of climate change adaptation (there will be some and it is only fair to compensate those who suffer for other’s emissions) – should be payed by the benificiaries of emissions.

  39. 289
    Patrick 027 says:

    Re 287 –

    That is very good news. Solar power in general has been coming closer and closer to being competitive on the existing grid (one matter that may ‘artificially’ inflate solar cost is the time-horizon and the financing structure. Even with climate change, there is some certainty over years that, after accounting for some hail/tornado/etc losses, solar cells are quite reliable – performance will degrade over time but not quickly (from rated power – there is some initial rapid decline in amorphous Si cells but that is factored into the rated power). It may be that over 70 or 80 years, a solar cell will provide the equivalent of 60 years at rated power (divided by a factor depending on solar resource; rated power is at 1000 W/m2 insolation; a more typical value may be 200 W/m2 (although some places and panel orientations (seasonal tracking) might get 300+ W/m2 panel insolation annual averages, etc.).

    Using an equivalent of 60 years at rated efficiency, assuming 200 W/m2 average solar insolation, (and – this is actually covered by “60 years at rated efficiency”, but – assuming a high enough fill factor (maximum power output at a reference insolation divided by the product of open-circuit voltage and short-circuit current) and given that much solar energy will be concentrated in time and perhaps be closer to 1000 W/m2 than 200 W/m2 (so that the conversion efficiency in the first years stays near the rated efficiency at 1000 W/m2)):

    the levelized cost in cents/kWh for energy provided over an equivalent of 60 years at rated efficiency is a little less than the same as the cost per peak W in dollars.


    For calculations based on a sampling of commercially available solar modules (2005 info): median values: module mass per area: 12.7 kg/m2, energy density of modules 3.5 GJ/kg (267* times coal (*using a high end value for coal), 202 times oil, 156 times methane, for 40% efficient power plants (actual efficiencies closer to 33%)), Energy density (GJ/kg) for just the photovoltaic layer is around 12 times that for conventional crystalline Si; could be 100 or more times the module value for thin crystalline Si, amorphous Si, other thin films, etc.)
    (median price: $5.26/peak W, 5.0 cents/kWh levelized cost).

    For The Sharp 185 W module (single crystal Si) and Sharp 165 W module (polycrystalline Si):

    module masses are both 13.1 kg/m2, costs per area nad mass were $712/m2 ($54.3/kg) and $634/m2 ($48.4/kg), respectively, efficiencies were 14.2 % and 12.7 %, respectively (PS this could be lower than cell efficiency simply due to cell and module borders in module design),

    and the prices per peak W were both $5.00, translating into a levelized electricity price of 4.75 cents/kWh.

    (Module energy densities are 4.11 GJ/kg and 3.67 GJ/kg, 316 and 282 times coal for electricity (using 32.5 MJ/kg coal, a high-end value) , 239 and 213 times oil for electricity, and 185 and 165 times methane for electricity – each assuming a 40% efficient fossil fuel to electricity conversion, which is actually higher than the actual (which is closer to 33%).)

    Average module price in 2006 was $3.50/peak W. (p.295 of the Energy Information Administration’s “Annual Energy Review 2007” and the solar cell/module shipments have been skyrocketing.

    See also:


    source of module information:

    254: optics:




    While the 4.75 and implied

  40. 290
    Patrick 027 says:

    While the 4.75 and implied less than 3.5 cents/kWh do not include balance of system costs, it would seem that solar power is close to cost-competitive with fossil fuel and nuclear electricity – especially oil and gas (fuel costs along may be around 5 cents/kWh electricity, give or take, as I recall, depending on year). And solar pv is headed into the 1 to 2 $/peak W range (CdTe is already there, I think).

    But an interest rate greater than inflation generally must be payed on lo-ans. (On the other hand, maybe solar cells would make a great retirement package.)

    But even with all this success, it still makes sense to have a cost imposed on emissions. Otherwise, fossil fuel power production will not plateau and decline as fast as is logically justified by climate-change costs. (As fossil fuels are increasingly displaced by other power sources and efficiency improvements, they will decline in price (except maybe oil?), thus holding on longer to remaining market share.)

  41. 291
    William says:

    In reply to Brian Dodge 252:

    Ion lifetime. The ion lifetime is proportional to the number of ions. When I stated ions do not wear out, that means the same ion can participate in a number of ion mediate nucleation events in regions that are ion poor.

    It necessary to understand the basic mechanisms to sensibly discuss the GCR modulation of low level cloud cover.

    The GCR modulation of clouds is stronger over the oceans as compared to the atmosphere above the continents. The atmosphere over the oceans is ion poor as compared to the atmosphere over the continents, as the continental crust is slightly radioactive which increase the number of ions over the continents as compared to the oceans.

    As I noted, solar wind bursts remove ions via the process electroscavening. As solar wind bursts increased at the end of the 20th century, GCR vs Cloud cover studies at that time will show there is no correlation low level cloud cover with GCR strength which is not correct.

    The papers quoted above that purport to disprove low level cloud modulation by GCR are flawed as they did not take into account the solar wind bursts caused by an abnormal high number of solar coronal holes that appeared at the end of the solar cycles, at a time when the solar heliosphere was weak and hence high.

    In addition to solar wind changes, changes in the geomagnetic strength also modulate GCR. For some unknown reason the geomagnetic field increases in strength by a factor of about 4 to 5 during the interglacial period as compared to the glacial period. As geomagnetic field intensity changes are long term, GCR modulation of cloud cover has the potential for long term modulation of the planet’s climate.

    When the planet’s geomagnetic field strength is weaker the GCR intensity changes modulate cloud cover at lower latitudes which increase the mechanisms ability to affect planetary temperature.

    Geomagnetic modulation of clouds effects in the Southern Hemisphere Magnetic Anomaly through lower atmosphere cosmic ray effects

    “The study of the physical processes that drive the variability of the Earth’s climate system is one of the most fascinating and challenging topics of research today. Perhaps the largest uncertainties in our ability to predict climate change are the cloud formation process and the interaction of clouds with radiation. Here we show that in the southern Pacific Ocean cloud effects on the net radiative flux in the atmosphere are related to the intensity of the Earth’s magnetic field through lower atmosphere cosmic ray effects. In the inner region of the Southern Hemisphere Magnetic Anomaly (SHMA) it is observed a cooling effect of approximately 18 W/m2 while in the outer region it is observed a heating effect of approximately 20 W/m2. The variability in the inner region of the SHMA of the net radiative flux is correlated to galactic cosmic rays (GCRs) flux observed in Huancayo, Peru (r = 0.73). It is also observed in the correlation map that the correlation increases in the inner region of the SHMA. The geomagnetic modulation of cloud effects in the net radiative flux in the atmosphere in the SHMA is, therefore, unambiguously due to GCRs and/or highly energetic solar proton particles effects.”

    “A continuous record of the inclination and intensity of Earth’s magnetic field, during the past 2.25 million years, was obtained from a marine sediment core of 42 meters in length. This record reveals the presence of 100,000-year periodicity in inclination and intensity, which suggests that the magnetic field is modulated by orbital eccentricity. The correlation between inclination and intensity shifted from antiphase to in-phase, corresponding to a magnetic polarity change from reversed to normal. To explain the observation, we propose a model in which the strength of the geocentric axial dipole field varies with 100,000-year periodicity, whereas persistent nondipole components do not.”

  42. 292
    Patrick 027 says:

    “Energy density (GJ/kg) for just the photovoltaic layer is around 12 times that for conventional crystalline Si; could be 100 or more times the module value for thin crystalline Si, amorphous Si, other thin films, etc.)”

    Example: (PS is there an instruction manual for formatting one’s comments – indented quotes, bold, etc.?)


    $500 per kg of CdTe adds $0.107 per peak W, and 0.102 cents/kWh over the equivalent of 60 years at rated [efficiency, with 200 W/m2 insolation.]

    An increase in the cost of Te of $10,000 / kg would add $1.14/peak W, and 1.08 cents/kWh.

    20,000 metric tons of Te is enough for 37,619 metric tons of CdTe and about 176 GW rated power, or at 200 W/m2 average incident solar power on the panels, about 35.1 GW average power output.

    The effective energy density (for 60 years at rated [efficiency]equivalent [at 200 W/m2 insolation]) relative to the CdTe layer is about 1,770,000 MJ/kg, which is about 136,000 times coal electricity [!!] (coal at 32.5 MJ/kg, [a high end value] it can vary – conversion to electricity assumed 40% efficient [actual efficiency closer to 33%]).

    (Of course, given the energy density of a single component based on total energy production may seem a bit meaningless. The numbers can be used this way – the energy per unit mass used to produce that layer can be divided by the above energy density to give a contribution of energy payback time as a fraction of effective life of 60 years at rated power (a bit fuzzy given a gradual decay – could actually be more like 70 or 80 years to produce that amount of energy).

  43. 293

    Richard Kerr wrote a nice review in Science about Pierce and Adam’s cosmic ray modeling study (see, subsc. required).

    “The reason cosmic-ray variations don’t make themselves felt up the chain, at least in the model, seems to be the daunting matter of millionfold growth. Once a tiny amount of, say, sulfuric acid vapor condenses onto a cosmic-ray–induced ion to form a 1-nanometer particle, a million times more vapor must condense on it within its lifetime of less
    than a week before it grows large enough to trigger cloud drop formation. All the while, other growing particles are competing for the scarce vapor and gobbling up smaller particles that they collide with. Make only a few ion-nucleated particles, and they are not enough to matter; make a lot, and there’s too little vapor to go around, so few particles grow large enough. Other modelers have just started to run global simulations of atmospheric particle formation, provoking a range of reactions. “We see a very similar thing” in our model, says Jan Kazil of the University of Colorado, Boulder. “Cosmic-ray variations have only a small effect on the clouds in our model.” But Fangqun Yu of the University at Albany in New York says he disagrees with the Carnegie Mellon researchers “because of problems in their simulations.” Among other problems, Yu suspects that in simulating only two rates of new particle formation via ionization—very high and much lower—Pierce and Adams may have missed a “sweet spot” production rate in between, at which just enough but not too many particles are produced. Testing the Goldilocks hypothesis will take more modeling and observations.”

  44. 294
    Patrick 027 says:

    I decided to go through my policy posts above and edit it to repost with a more clear organization of thoughts. This is taking awhile… Since it will be long, I won’t post it under one of the more active threads – if this one is closed to comments by the time I’m done, then I might post it under

    “1 May 2009
    Welcome to the fray”

    or, depending on activity level:

    “29 April 2009
    Hit the brakes hard”


    “7 May 2009
    The tragedy of climate commons”

    IN THE MEAN TIME, I worked on some financial formulas for solar panels …

  45. 295
    Patrick 027 says:

    IN THE MEAN TIME, I worked on some financial formulas for solar panels – finding the price per unit energy produced that pays for debt on a lo-an that payed for panels, or for paying for new panels. This analysis does not include additional costs that will make the price a little higher.


    For a fractional change x per unit time t:

    exp[t/U] = exp[t*V] = 1 + x

    t/U = t*V = ln(1+x)

    1/U = V = ln(1+x) / t

    U = 1/V = t / ln(1+x)


    Let a = 1 year

    r = annual interest
    f = annual inflation (of energy price and solar collector price; they are assumed to follow the same inflation rate for simplicity (obviously this analysis does not apply to the present situation with its rate of progress and potential future rate of progress.)

    h = annual fractional gain of solar collector performance, including those modules that are damaged or fail too severely to continue producing energy.

    hs = annual fractional loss of solar collector performance only due to those modules that are damaged or fail to the point that they are removed from operation.

    h and hs are both negative numbers.

    PS: approximation:

    h1 = – annual cell efficiency decay from gradual processes
    h2 = – fractional collector losses (storm damage beyond repair, etc.)
    1+h ~= (1+h1)(1+h2)

    U = age of retirement: Solar collectors that last this long are removed from service because their performance no longer justifies the area they use and the area/collector-proportional maintenance costs, etc. (this analysis uses a simplifying assumption that such retired collectors are not sold to different owners with different conditions, etc, but that they are recycled; obviously different uses in different conditions may allow for solar collectors to retire to different operational life stages, in which case, U is an ultimate retirement age.)

    inverse time constants:

    R = ln(1+r)/a
    F = ln(1+f)/a
    H = ln(1+h)/a

    Hs = ln(1+hs)/a

    G = F + H


    m = price of energy

    m0 = inflation adjusted price of energy, treated as constant unless specified otherwise.

    L0 = inflation adjusted price of collectors per unit installed average power (installed average power will tend to be near the rated power * average solar insolation on the collector per unit collector area / (1000 W/m2)).

    P0 = installed average power (the total amount of solar collectors in terms of their installed average power)

    P = average power

    p = P/P0 in the context of a single installation time.


    SOLUTIONS for m0/L0 (units: [$/(W*yr)] / [$/installed average W] ;

    multiply the number of $/(W*yr) by 100/8.766 to find cents/kWh (averaged over leap years).



    A single batch of collectors is bought with a lo-an. U = infinity.

    m0/L0 required to pay off debt at time t:

    m0/L0 = (R-G) / [ 1 – exp[-t*(R-G)] ]


    m0/L0 = ln[A]/a / [ 1 – A^(-t/a) ]

    where A = (1+r)/[(1+f)(1+h)]

    For t = infinity:

    m0/L0 = (R-G) = ln[A]/a



    P/P0 = p = exp(t*H)

    CUMMULATIVE ENERGY per unit installed P0 produced by time t:

    E = 1/H * [exp(t*H) – 1]

    from integrating:

    dE = p dt = exp(t*H) dt



    At constant rate N = d(P0)/dt, starting at t = 0.

    Date at which remaining solar collectors age out (retirment age of surviving devices): t – t_installed = U

    Start accumulating debt at time t = 0:

    SOLVE FOR m0/L0 where debt = 0 at time t:

    If t is before U:



    – H /

    (R-F)/(R-G) * [ exp[t*G] – exp[t*R] ] / [ exp[t*R] – exp[t*F] ]

    if t is after U



    H * ( exp[t*(F-R)] – 1 )


    [ 1 – exp[U*H] ] * exp[t*(F-R)]
    [ 1 – (R-F)/(R-G) ] * [ exp[U*(G-R)] – 1 ]




    P = N * (-1/H) * [ 1 – exp[t*H] ]

    replace t with U in this formula once t exceeds U.

    It will be of interest to know the average efficiency of all collectors in use relative to installed efficiency values:

    installed power in operation (proportional to area of solar collectors in operation):

    P0 = N * (-1/Hs) * [ 1 – exp[t*Hs] ]

    replace t with U in this formula once t exceeds U.


    = P/P0

    = -Hs/H * (1-exp[t*H])/(1-exp[t*Hs])

    replace t with U in this formula once t exceeds U.




    SOME MAINTENANCE COSTS, etc, will be proportional to P, while some will be proportional to P0 (as would any costs related to occupying space).



    SOLVE FOR m0/L0 sufficient to maintain constant N:

    In the case where t is after U, so that P has reached a constant value; constant N will maintain constant P:

    rate of buying new collectors = L0*exp(t*F) * N
    rate of selling energy: = m0*exp(t*F) * P

    income = expenditures


    m0/L0 = -H / [ 1 – exp[U*H] ]

    H = ln(1+h)/a

    m0/L0 = -ln(1+h)/a / [ 1 – (1+h)^(U/a) ]


    If debt is paid off before time t=U, the m0/L0 needed to pay for constant N will start out larger because P will not have reached its steady value; m0/L0 will decline and reach the value given above when t=U.

    Before t=U, m0/L0 is inversely proportional to P:

    m0/L0 =

    -H / [ 1 – exp[U*H] ]
    [ 1 – exp[U*H] ] / [ 1 – exp[t*H] ]


    m0/L0 = -H / [ 1 – exp[t*H] ]

    until t=U.



    income = m0 * exp(t*F) * P * dt

    expenditure = L0 * exp(t*F) * N * dt

    LET income = expenditure (to find the m0 before profit, maintenance costs, etc.)

    m0 * P = L0 * N

    N = P * m0/L0

    P at time t from power P0 installed at time t2:

    dP = exp[(t-t2)*H] * N(t2) * d(t2) – [ 1 – exp[(t+U-t2)*H] ] * N(t2-U) * d(t2)

    The second term accounts for retirement of collectors when they reach an age t-t2 = U.

    Replacement of H with Hs will give a formula for P0 instead of P.

    SIMPLE SCENARIO: continual exponential growth (inverse time scale S) with infinite past:

    N = exp(t*S) * N1

    therefore, from income = expenditure:

    P = exp(t*S) * N1 / (m0/L0)

    where N1 = N(t=0)


    After finding P(t),

    SOLVE FOR m0/L0

    m0/L0 = 1/ [ ( 1 + exp[U*(H-S)] ) * 1/(S-H) – exp[-U*S] * 1/S ]



    P = N * [ ( 1 + exp[U*(H-S)] ) * 1/(S-H) – exp[-U*S] * 1/S ]

    (note that to find P0, replace H with Hs in the above equation)

    P/P0 =

    [ ( 1 + exp[U*(H-S)] ) * 1/(S-H) – exp[-U*S] * 1/S ]


    [ ( 1 + exp[U*(Hs-S)] ) * 1/(S-Hs) – exp[-U*S] * 1/S ]


    Of course, there will not be an infinite past. That was a simplification so that the issue of a transition from all collectors younger than U to some collectors aging out of the system could be set aside and a constant m0/L0 value could be found. However the initial buildup of N and P is shaped, the trajectory of growth will settle toward an exponential growth (with P and N proportional to exp[t*S] ) with constant m0/L0, provided that m0/L0 is greater than that required to maintain constant P or N.

    If the initial buildup is faster than exponential – for example, if dN/dt is constant up to time t=B and then increases exponentially without a discontinuous jump in either dN/dt or N, then there will not be a spike in collector retirements when retirements begin. Thus, after time t=B, m0/L0 can be lower than the solution found above, and will not ever have to go above that value because the retirement rate will only increase from 0 and eventually reach a steady proportion with N, and not exceed it (alternatively, S could initially be higher with a constant m0/L0).


  46. 296
    Patrick 027 says:

    Hold off on using equations from PART III – I think I goofed something up.

  47. 297
    Patrick 027 says:


    SIMPLE SCENARIO: continual exponential growth (inverse time scale S) with indefinite past:

    N = exp(t*S) * N1

    P = exp(t*S) * N1 / (m0/L0)


    dP = exp[(t-t2)*H] * N(t2) * d(t2) – [ 1 – exp[(t+U-t2)*H] ] * N(t2-U) * d(t2)


    P at time t from power P0 installed at time t2:
    without retirement:

    dP1 = exp[(t-t2)*H] * N(t2) * d(t2)

    P at time t from power P0 retired at time t2 (which was installed at time t2-U):

    dP2 = – [ 1 – exp[(t2-(U-t2))*H] ] * N(t2-U) * d(t2)

    dP2 = – [ 1 – exp[U*H] ] * N(t2-U) * d(t2)


    integral(b to t)[ exp[(t-t2)*H] * N(t2) * d(t2) ]

    exp[t*H] * N1 *
    integral(b to t)[ exp[-t2*H] * exp[t2*S] * d(t2) ]

    exp[t*H] * N1 * integral(b to t)[ exp[t2*(S-H)] * d(t2) ]

    = exp[t*H] * 1/(S-H) * N1 * [ exp[t*(S-H)] – exp[b*(S-H)] ]

    = exp[t*H] * 1/(S-H) * N * [ exp[-t*H] – exp[b*(S-H)-t*S] ]

    = 1/(S-H) * N * [ 1 – exp[(b-t)*(S-H)] ]

    when b goes to negative infinity,

    P1 = 1/(S-H) * N



    dP2 = – [ 1 – exp[U*H] ] * N(t2-U) * d(t2)

    – [ 1 – exp[U*H] ] * integral(b to t)[ N(t2-U) * d(t2) ]

    – [ 1 – exp[U*H] ] * N1 * integral(b to t)[ exp[(t2-U)*S] * d(t2) ]


    – [ 1 – exp[U*H] ] * exp[-U*S] * N1 * integral(b to t)[ exp[t2*S] * d(t2) ]


    – [ 1 – exp[U*H] ] * exp[-U*S] * N1 * 1/S * [ exp[t*S] – exp[b*S] ]


    – [ 1 – exp[U*H] ] * exp[-U*S] * 1/S * N * [ 1 – exp[(b-t)*S] ]


    when b goes to negative infinity,

    P2 = – [ 1 – exp[U*H] ] * exp[-U*S] * 1/S * N


    P = P1 + P2

    m0 * P = L0 * N

    SOLVE FOR m0/L0

    m0/L0 = N/P

    m0/L0 = 1 / [ 1/(S-H) – [ 1 – exp[U*H] ] * exp[-U*S] * 1/S ]


    P = N * [ 1/(S-H) – [ 1 – exp[U*H] ] * exp[-U*S] * 1/S ]

    P/P0 =

    [ 1/(S-H) – [ 1 – exp[U*H] ] * exp[-U*S] * 1/S ]
    [ 1/(S-Hs) – [ 1 – exp[U*Hs] ] * exp[-U*S] * 1/S ]


    m0/L0 = S-H


    P = N /(S-H)

    P/P0 =



  48. 298

    Here’s another estimate of the potential upper limit to the effect of GCR: Kazil et al calculate the effect of GCR based on predicted aerosol concentrations from ion induced nucleation over the oceans. Even neglecting the fact that many of these tiny particles don’t make it to large enough sizes to influence cloud properties, and neglecting the competition with particles from other sources, they find that changes in aerosol concentration due to changes in GCR with the solar cycle can not explain the apparent correlations with cloud cover. The radiative forcing due to the GCR-aerosol-cloud link is at most still smaller than that from the change in total solar irradiance by itself.

  49. 299
    David B. Benson says:

    “Biological Particles Trigger Ice Formation In High-altitude Clouds”:

  50. 300
    Patrick 027 says:

    will post some m0 values tomorrow