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Comments 26 to 50 out of 308:

26. Patrick 027 at 04:16 AM on 21 September, 2008
    "No more than the normal "wobble" "..."For supporting evidence for actions of oscillations you can check the threads on this site. "..."it's the vulcanism driving the drift" I think we're talking about 3 or 4 distinct phenomena now. By normal wobble, do you mean Milankovitch cycles or the Chandler wobble or...? 1. Milankovitch cycles: ~100,000 yr eccentricity; ~40,000 yr (obliquity) and ~20,000 yr (precession) cycles that involve changing orientation of the Earth's axis. However, the importance to climate being the change in the axial tilt relative to the orbit around the sun; the body of the Earth itself stays aligned with it's axis the same way - the geographic north pole is still in the Arctic ocean the whole time, etc. Causes of the Milankovitch cycles: gravitational effects of other planets, solar and lunar tidal torques on the Earth's equatorial bulge (The precession cycle, a wobble of the direction of the Earth's tilt relative to it's orbit about the sun, is actually due to a combination of changing direction of tilt and a changing orientation of the semimajor axis of the Earth's orbit). (The equatorial bulge is due to the centrifugal force of rotation - the geopotential surfaces of the Earth, such as sea level, are distorted in such a way that the gravity due to mass and centrifugal force from rotation, as vectors, add to produce an effective gravitational vector locally perpendicular to the surface so that there is no local 'sideways gravity'. PS equilibrium tidal bulges can also be computed by setting 'sideways gravity' to zero. Tidal dissipation of the Earth's rotation and transfer of angular momentum to the moon's orbit result in changes in lunar tidal forces and the Earth's equatorial bulge over time (many millions of years), both affecting the obliquity and precession cycles.) 2. Chandler Wobble and True Polar Wander. As vector quantities, a spinning object has a rotation w which is parallel to the axis of rotation, and an angular momentum L. L is parallel to w if the object is symmetrical about the spin axis - specifically if the spin axis is aligned with a principle axis. (Angular momentum is equal to the rotation times the moment of inertia; but the full moment of inertial is actually a tensor quantity (written as a 3 by 3 matrix) - but if the coordinate axes are chosen to align with the principle axes of the body, 6 of the 9 components are reduced to zero, leaving three moments of inertia, each about a principle axis, so that the component of rotion along each such axis can be multiplied by the corresponding component of moment of inertia to get the component of angular momentum along that axis.) So if the rotation w is aligned with a principle axis, the angular momentum L is also aligned with w and the same principle axis. If there are no external torques applied and the body is not being deformed, there is no wobble. If the three moments of inertia are equal (such as for a perfect homogeneous sphere or a sphere with only spherically-symmetric density variations centered on the center of the sphere), L and w are always parallel. But when the body has different moments of inertia (such as due to an equatorial bulge), then L and w can be in different directions. Without external torques, L must be constant in an inertial reference frame (that does not rotate with the body); but w may shift around; in the reference frame of the body itself, I think both can shift around - the changes over time are described by the Euler Equations. In what can be called the "Tennis Racket Theorem", if w is shifted from a principle axis by a small amount, then: A. if L and w are near one of the 'extreme' principle axes - with the larges or smallest of the three moments of inertia, then L and w oscillate about that axis (specifically I think L traces out a circle about the principle axis though I'm not sure offhand), and so rotation about such an axis is stable. B. But if L and w are initially near the intermediate principle axis, L and w move away from that axis and so rotation about that axis is unstable. The Chandler wobble is a shift of Earth's rotation axis about the principle axis of the Earth most nearly parallel to the rotation axis (this is an extreme principle axis - it has the largest moment of inertia due to the equatorial bulge - the other two principle axes are in (or almost in) the equatorial plane). The spin of the Earth is perturbed by small amounts from the principle axis by earthquakes and seasonal mass distributions, but rotation about this axis is stable. (And over time, some kind of viscous dissipation would actually tend to return the rotation axis to alignment with the principle axis - for fixed L in an inertial reference fram, such alignment minimizes the square of |w| and thus minimizes the rotational energy; on Earth, the spin axis is never found more than ~ 10 meters** (much less than climatologically insignificant) from the principle axis at the Earth's surface, and the period of the Chandler wobble is ~ 440 days** - this specific info is found on p. 261 of Classical Mechanics: A Modern Perspective. Second Edition. Vernon Barger and Martin Olsson. 1995. **Caution - most info is fairly correct but I have found a few specific numbers in that book which were wildly off - the mass of Venus on p.396, and I think the rate of tidal damping and the rate of lunar orbital change by tidal damping were also off.) 3. The two moments of inertia about the principle axes in or near the equatorial plane are about equal. However, if a supercontinent persisted in mid-to-high latitudes for a time and heat built up in the mantle beneath (continental crust is of course thicker but also has more radiactive heating per unit volume than oceanic crust, both of which have more than the mantle) so that the supercontinent were elevated, conceivably if this were extreme enough (I'm not sure how far this would have to go or how likely it is it could ever get that far, especially in the distant past when the equatorial bulge would have been larger), the principle axes could be shifted out of alignment from the spin axis enough and maybe the principle axis nearest the spin axis would become an intermediate axis (? or maybe that part's not necessary) and then the rotation becomes unstable ?? - or maybe it doesn't become unstable ?? - but the end result is that the supercontinent ends up at low latitudes so once again the principle axis with the largest moment of inertia is close to the spin axis. This process shifts the whole body of the Earth around; this is true polar wander. PS if this ever happenned - conceivably it might happen (that's the impression I have as of yet) faster than it takes for the equatorial bulge to deform back to equilibrium, which means parts of the equatorial bulge could be shifted into higher latitudes - the ocean would of course respond much faster, so parts of the mid-to-high latitudes could have 'land' made of exposed oceanic crust (which could result in much release of CH4 from hydrates/clathrates) while parts of the equatorial ocean would be extremely deep. But it depends on how fast or slow the different processes occur relative to each other. The only hypothesized instances of true polar wander on Earth that I know of would be in the late Neoproterozoic, and I don't know what the state of the evidence is for it. 4. And of course over time there is continental drift as the plates grow at rifts or ridges and go back into the mantle at subduction zones. Faster plate movements should tend to correspond to greater geothermal heat transport to the surface, wider mid-ocean ridges and thus higher sea levels (although I read something recently...), and faster geologic CO2 emission. At first glance (could be wrong?) it would also make sense to expect faster mountain building and thus an enhanced erosion rate (with some time lag) - which itself would at least partly counteract the tendency for a warmer climate to sustain an equilibrium elevated CO2 level by causing faster geologic sequestration of CO2 to balance the faster CO2 release. At first glance it also would make sense to expect more frequent eruptions of all or many kinds, including those explosive low-latitude eruptions that have a short-term cooling effect - but collectively over time this would have a persistent cooling effect, but CO2 builds up over time and eventually would have the larger effect on long-term climate. The size of the plates would also have an effect - smaller plates would require a longer total length of plate margins, which could correspond in part to a longer length of mid-ocean ridges, etc. Globally the average geothermal heat loss is ~ 0.1 W/m2; even if it could have been doubled ~ 100 million years ago or whenever, that would still only be ~ 0.2 W/m2. It's a small climatological forcing and it doesn't change very fast; in contrast, doubling CO2 is a forcing of about ~4 W/m2; a 1% increase in solar TSI would be a forcing of about 3 W/m2. Have to take a break now...
27. Patrick 027 at 10:44 AM on 21 September, 2008
    ... Actually the climate forcing due to a 1% change in solar TSI would be closer to 2.4 W/m2. And while solar TSI may often go up and down by 0.1% or something like that, a change of 1% would be more likely over ~ 100 million years, associated with the long-term solar brightenning over it's stellar lifespan. (A formula for solar TSI as a fraction of the present day value is 1/(1 - 0.38*t/4.55), where t is the number of billions of years from now, negative for in the past. This is an approximation that may be innaccurate for near the beginning or end of the solar lifespan - I got it from a paper by James Kasting, forgot which paper. From this formula, solar TSI as a percent of present day solar TSI: 75.0 % at 4 Ga (billion years ago) 80.0 % at 3 Ga 82.7 % at 2.5 Ga 85.7 % at 2 Ga 88.9 % at 1.5 Ga 92.3 % at 1 Ga 93.0 % at 900 million years ago (Ma) 93.7 % at 800 Ma 94.5 % at 700 Ma 95.2 % at 600 Ma 96.0 % at 500 Ma 96.8 % at 400 Ma 97.6 % at 300 Ma 98.0 % at 250 Ma (~Paleozoic/Mesozoic boundary) 98.4 % at 200 Ma 99.2 % at 100 Ma 99.6 % at 50 Ma ... and in the future: 104.4 % in 500 million years 109.1 % in 1 billion years 120.1 % in 2 billion years ---------- And 'wobbles' in mantle convection and continental drift - these wobbles are analogous to day-to-day weather changes in the atmosphere; it is mantle weather. The weather reshapes itself in (depending on the weather features in question - I'm thinking of midlatitude synoptic-scale features) days as the winds reshape the pressure variations (depending in part on temperature variations) that shape the winds. In the mantle, momentum (and therefore the coriolis effect) is negligible; pressure gradients (due to density variations) drive motion against friction. The density variations that force the motion cannot change much faster than the motion itself - thermal diffusion being a much slower process. So large rapid changes in mantle convection and continental drift don't happen. But over many millions of years, the mantle and lithospheric weather will change; as cold slabs of material descend down from subduction zones, continents collide, and material is no longer fed to the descending slab, while the remaining slab continues descent; as continents overide midoceanic ridges; as heat builds up within the mantle near the core or perhaps around pieces of recycled crust to produce buoyant plumes, and as heat builds up under supercontinents, and as continents rift apart and sink a bit. Continents individually are warped and tilted, rise, and sink, as the move over density variations in the underlying mantle (a slow process). Over a long time, one might define a mantle climate. One kind of mantle climate change could then be the transition from layered convection to whole mantle convection. Whole mantle convection is simply convection cells with updrafts and downdrafts extending from top to bottom. In layered convection, the mantle would convect in two seperate layers (boundary at about 660 km depth from surface). When there is a boundary to convection (the top of the mantle, the bottom of the mantle, the bottom of the outer core, and possibly at 660 km depth in the mantle), heat must be transported by conduction to the next layer, which requires a higher thermal gradient, so heat can build up in the lower layer relative to the upper layer. Why would there be two layers of convection? As pressure increases with depth, material is compressed; this is associated with an adiabatic lapse rate where temperature rises or falls within a mass without the conduction of heat. But in solids there can also be phase transitions (I've also heard of different liquid phases of the same substance but ...). As with the phase transitions of melting/freezing and evaporation/condensation, a solid phase transition may involve a change in heat as well as density. Obviously as pressure increases, phase transitions to higher-density phases are favored. If a phase transition gives off latent heat (like condensing of water vapor to form clouds), than that transition will occur 'sooner' at lower temperature - more specifically, the Clapeyron slope dp/dT = change in entropy / change in volume, where dp is the change in pressure of an equilibrium phase transformation with a change in temperature dT. There are multiple phase transitions within the mantle from about 410 to about 660 km from the surface. The Clapeyron slope of the 660 km phase transition (which, going down, involves a change of much of the mantle's material to a perovskite crystal structure) 660 km is a nominal position used for identification - the actual position varies) is negative, which means that at higher temperature, the phase transition occurs at lower pressure. Without phase transitions and in the absence of significant coriolis effect, warmer material at a given pressure will generally rise and colder material will sink due to the effect of temperature on density. But as warmer or colder material rises or sinks across the 660 km phase transition, the actual position will rise or fall, respectively, due to the temperature change, and this produces a density variation that is opposite that caused by the temperature variation, and if strong enough, will produce a force that prevents convection across the boundary. From what I have read (not much, really), I've gotten the impression that there is some layered convection and some whole mantle convection at present; earlier in Earth's history, there may have been mainly just two-layered convection, and perhaps changing conditions caused a transition toward some whole mantle convection around the time of the Archean-Proterozoic transition (?)... Why would that happen? - well, material properties change with changing temperature; as the mantle as a whole cools, the 660 km transition should gradually rise upward overall - in the future, if it goes far enough, it would catch up with other phase transitions (which, if they have positive Clapeyron slopes, would be moving downward - where they meet I would expect a new phase transition to occure with an intermediate Clapeyron slope) ... not all of the mantle substance actually goes into the perovskite structure, ... the overall viscosity increases over time with decreasing temperature overall ... layered convection would allow heat buildup in the lower mantle relative to the upper mantle, so perhaps the temperature difference could have become so great that eventually it overcame the impediment to whole-mantle convection ? - if that's how it works, then one would expect episodic whole mantle convection, after each episode of which, the temperature change with depth would be reduced and so one would go back to two-layer convection - but I'm not sure that's how it would have worked - anyway, the advent of whole mantle convection could then have increased the cooling of the core, which would affect inner core growth rate (ps that liberates latent as well as buoyant composition variations, which help drive outer core convection, which of coarse powers the magnetic field), and this could also affect the geochemistry of the layers and the crust (?)... BUT also so far I have been describing phase transformations as being at equilibrium, but particularly in colder material, it isn't so easy for atoms to rearrange themselves, so phase transformations can be delayed beyond equilibrium, and the resulting microstructure that results when the phase transformation finally occurs can affect the viscosity (and/or rigidity?) of the material, and this would apply to the behavior of cold descending slabs coming from subduction zones. The rate of subduction affects the temperature of the slab, which affects the position and result of phase transformation, the effect on rigidity, and that could affect whether or not the descending slab penetrates into the lower mantle or comes to rest on the 660 km boundary ... SEE Karato, "The Dynamic Structure of the Deep Earth" --- 5. "We almost went extinct once already" Would you be refering to the supereruption of Toba about 75,000 years ago? While it did occur as an ice age was starting or setting in or growing stronger, a supereruption's effects would be particularly sudden, and eventually would have subsided into the background as Milankovitch forcing went on - of course there would be some climatic inertia from any buildup of snow/ice during the cooling from the supereruption. A supereruption, as with single eruptions and earthquakes, etc, are episodic events, and takent one at a time, not necessarily indicative of any overall trend in continental drift, mantle convection, or geothermal heat fluxes.
28. Patrick 027 at 11:12 AM on 21 September, 2008
    Back to 4. for a moment: ... "At first glance (could be wrong?) it would also make sense to expect faster mountain building and thus an enhanced erosion rate (with some time lag) -" ... Of course, mountain building is not quite as continuous and ongoing a process as sea-floor spreading. Faster sea floor spreading (or a greater total length of mid-ocean ridges) and continental rifting will tend to raise sea level (assuming the wider mid-ocean ridges result from faster sea-floor spreading), as will erosion of continents with sediment transfered to continental shelves, etc, while continental collisions and associated mountain and plateau building will of course tend to lower sea level, while individual continents may be raised or lowered for other reasons. That can affect global average temperature by changing the albedo - this depends on cloud cover and vegetation, though.
29. Quietman at 04:54 AM on 22 September, 2008
    Patrick Re: 27.5 The extinction I was referring to was during out split in Africa before we were fully human and only numbered in the thousands during a period of severe climate change. But rather than extinction it resulted in increased genetic diversity. But that aside: I have no argument with your explanations. My point is that the reason our planet is so active is gravitational stresses. Tidal stress from the moon plays the largest role. But when compounded by gravitational stress from other solar bodies we see cycles occur. This is where the Fairbridge hypothesis comes into play. His hypothesis predicts sunspot activity (or lack thereof) with apparent accuracy. But sunspots are symtomatic. It is the cause of the sunspots I believe that is also the cause of the current heat imbalance. Your TSI table bears witness to the 5 million year positive slope that I was referring to in other posts on this site. But that is a long gradual process and has not much to do with the current situation. As we as a species are responsible for 2% of the increased CO2 (per NASA) I can not see any way that it can be pertinant to GW. In fact, I don't see GW at all, but I do see northern polar warming and increased equatorial temperatures which only makes sense if ocean driven (tectonic caused) oscillations are at fault.
30. Quietman at 05:00 AM on 22 September, 2008
    PS The wobble I refer to is long term geographic polar wobble and not orbital. As I do not know the cyclic rates of planetary alignments compared to this wobble I don't know if there is a connection or not. I was simply pointing out that there is a cyclic climate shift involved in the wobble.
31. Patrick 027 at 11:44 AM on 22 September, 2008
    We as a species are responsible for ~ 100 ppm of the ~380 ppm of CO2 in the atmosphere and some similar amount (in terms of total amount, not concentration) in the ocean. We could easily get it to 400, 450, 500, 550, 600, 700, 800, 1000, ... ppm if we 'wanted to'. We are also responsible for the CH4 increase from ~ 700 ppb to ~ 1700 or 1800 ppb. "Your TSI table" ... "that is a long gradual process and has not much to do with the current situation." Yes. "The extinction I was referring to was during out split in Africa before we were fully human and only numbered in the thousands during a period of severe climate change. But rather than extinction it resulted in increased genetic diversity. " A bottleneck in the population should always reduce genetic diversity; that's not to say that genetic diversity might not increase faster than otherwise depending on the aftermath... What I have heard about the Toba eruption is that humans would have numbered ~ 10,000 or something like that in the aftermath. However, I think Homo sapiens sapiens were on the scene already, although Neanderthals (technically also Homo sapiens, but not Homo sapiens sapiens - if I have my names right) were still around. "My point is that the reason our planet is so active is gravitational stresses. Tidal stress from the moon plays the largest role. But when compounded by gravitational stress from other solar bodies we see cycles occur." My understanding is that most of the tidal energy dissipation occurs in the ocean and some fraction of that helps (along with wind-driven motions) mix the ocean so that it is less stratified than it otherwise would be. From: Oceanography: tides by Dr J Floor Anthoni 2000 http://www.seafriends.org.nz/oceano/tides.htm Total tidal energy dissipation rate: 3.75 +/- 0.08 TW; Of that, most - 3.5 TW - is dissipated in the ocean. The area of the Earth is about 510 trillion m2, so 3.75 TW is a global average of about 0.0074 W/m2; that's roughly a tenth of the geothermal heat flux from the surface. There will of course be some pulsation in the tidal dissipation, but the average over half a lunar month won't change as much, and the average over a year, over 18 years, etc. will vary considerably less. And less than a tenth of that would be dissipated within the solid Earth, core, and atmosphere. (maybe more on that later*) "What would happen to Earth if the moon was only half as massive? http://www.sciam.com/article.cfm?id=half-mass-moon (this approximately gives the same rate of lunar orbit growth given in the 'seafriends' website.) MORE: __________ Tides and ocean: Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data G. D. Egbert and R. D. Ray (a lot of handy numbers there) "OCEAN SCIENCE: Enhanced: Internal Tides and Ocean Mixing Chris Garrett" http://www.sciencemag.org/cgi/content/summary/301/5641/1858 http://www.aviso.oceanobs.com/en/applications/ocean... ----- http://oceanworld.tamu.edu/resources/ocng_textbook/contents.html http://oceanworld.tamu.edu/resources/ocng_textbook/chapter17/chapter17_04.htm http://oceanworld.tamu.edu/resources/ocng_textbook/chapter17/chapter17_05.htm --- "Tides dissipate 3.75 ± 0.08 TW of power (Kantha, 1998), of which 3.5T W are dissipated in the ocean, and much smaller amounts in the atmosphere and solid Earth. The dissipation increases the length of day by about 2.07 milliseconds per century, it causes the semimajor axis of moon's orbit to increase by 3.86cm/yr, and it mixes water masses in the ocean." --- "The calculations of dissipation from Topex/Poseidon observations of tides are remarkably close to estimates from lunar-laser ranging, astronomical observations, and ancient eclipse records. Our knowledge of the tides is now sufficiently good that we can begin to use the information to study mixing in the ocean. Remember, mixing drives the abyssal circulation in the ocean as discussed in §13.2 (Munk and Wunsch, 1998). Who would have thought that an understanding of the influence of the ocean on climate would require accurate knowledge of tides?" Here's section 13.2: ----- __________ Tides, wind and ocean: 50 Years of Ocean Discovery: National Science Foundation, 1950-2000 ----- For some reason I didn't copy the website for this one, but I must have it saved somewhere in my 'favorites', but anyway: "Modelling global and local tidal dissipation rates E. Schrama": "Oceanic tides are a wave phenomenon set in motion by the gravitational work of Sun and Moon. Traditional geodetic and astronomic techniques allow one to assess the global rate of energy dissipation. Satellite altimetry brings this problem one step further, now making it possible to locally estimate the rate of conversion of barotropic tides into internal tides that initiate deep oceanic mixing." "The global dissipation budget strongly suggests that most of the energy in the tides is lost in the ocean;": 2.4 TW lost in ocean from semidiurnal lunar tide M2 0.1 TW for M2 solid Earth tide 0.2 TW atmospheric dissipation for S2 "Our results confirm that": M2 wave dissipates 2.42 TW, of that: approx 1.7 TW dissipated in coastal seas by friction; 0.7 dissipated in deep oceans "Suggested in literature is internal wave generation and the relevance is that this process is responsible for mixing between lighter surface waters and the deeper ocean. The hypothesis by W. Munk to explain the oceanic density stratification is that about 2 TW is required for maintaining this balance, Egbert and Ray were the first to suggest that about half of this amount could come from tidal mixing, the remaining part could come from wind induced mixing." ----- http://www.agu.org/meetings/wp06/wp06-sessions/wp06_OS15B.html __________ Wind and ocean "The Work Done by the Wind on the Oceanic General Circulation Carl Wunsch" http://ams.allenpress.com/perlserv/?request=get-abstract&issn=1520-0485&volume=28&page=2332 "Improved global maps and 54-year history of wind-work on ocean inertial motions Matthew H. Alford" http://opd.apl.washington.edu/scistaff/bios/alford/assets/Alford2003.pdf http://opd.apl.washington.edu/scistaff/bios/alford/alfordglobalmap.html OTHER undifferentiated: http://www.aviso.oceanobs.com/fileadmin/documents/kiosque/... http://www.jamstec.go.jp/esc/publication/annual/annual2006/... http://www.sciencedirect.com/science?_ob=ArticleURL...
32. Patrick 027 at 13:07 PM on 22 September, 2008
    Another website (actually it's a Google book free preview or something like that): “Numerical Models of Oceans and Oceanic Processes By Lakshmi H. Kantha, Carol Anne Clayson” see p.446,447,451... notes I took from that: Kantha’s global model: TW dissipated by each component: total 3.75 M2 2.57 S2 0.41 N2 0.12 K2 0.03 K1 0.38 O1 0.19 P1 0.04 Q1 0.01 Total energy (PE+KE) of ocean tides about 13 times larger than equilibrium (heavily damped and resonant??) Power input into ocean distributed over area (with some patterns); dissipation concentrated in shallow seas -- (M2 is the lunar semidiurnal (twice-daily) tide. I assume S2 is the solar semidiurnal tide. The tidal response is complicated from the geometry of ocean basins, the coriolis effect, etc, but what I know about the equilibrium tide - the full tide is semidiurnal if it is due to a mass permanently in the equatorial plane; the semidiurnal tide, if it reached equilibrium, would be strongest at the equator and zero at the poles; because the moon and sun are usually somewhat removed from the equatorial plane, they also produce diurnal tides - if they reached equilibrium, they would be strongest at midlatitudes, and zero at the equator and poles, and the high tide in each hemisphere (North and South) would occur at the opposite time of day. (Of course, if the tidal deformation ever actually reached equilibrium, you'd need satellites or some other instrument to ever notice it, because the land and ocean would be rising and falling together.) ------ For a given tide-generating mass at a given distance, the equilibrium tidal bulge height is proportional to the mass of the tide-generator, and to the inverse cube of the distance to that mass, to the fourth power of the radius of the body experiencing the tides divided by the mass of that body (or more generally, the mass contained within that radius). The tidal acceleration is proportional to the mass of the tide generator, the inverse cube of the distance to that mass; it is linearly proportional to the radius of the body experiencing the tides (or more generally, the distance to the center of that body), and is independent of the mass experiencing the tides. Gravitational acceleration g is proportional to M divided by the square of radius r; within the Earth's mantle, g is nearly constant, hence ... to make a long story short, the equilibrium tidal displacement of the mantle/core boundary is about 0.30 times that of the surface. The equilibrium tidal range at the surface due to the moon is ~ 0.54 m (my calculation from math and physics) or 0.56 m according to the physics book mentioned earlier in the Chandler wobble discussion. Some notes from the Karato book mentioned earlier: Total heat flux from the core: estimated from ~ 3 to 10 TW. Energy needed to drive the geodynamo (in terms of thermal energy or mechanical energy? - not sure): roughly 0.1 to 1 TW. Because the outer core is convecting, the total heat flux from the core must be greater than that which would be conducted through material at the adiabatic lapse rate (about 0.7 K/km for the outer core) (remember this is liquid metal alloy, thermal conductivity ~ 40 W/(K m), about 10 times that of surface rocks). The estimated conducted heat from the core ~ 4 TW. (This conducted heat would be unavailable to drive the geodynamo. However, the process of forming the inner core, in addition to giving off latent heat, concentrates some (likely) buoyant impurities, which will then rise - this buoyancy from compositional heterogeneity cannot conduct very fast, and so could drive some convection itself). Cooling of the core by 100 K every billion years would release 5.7 TW of heat (I'm assuming that includes latent heat from solid core growth. The reason for the solid core growing from below is that the melting point rises with pressure, as the solid phase is denser than the liquid phase. The same is true of the mantle - if the mantle were gradually heated up, one of the first parts to melt would be the near the top. In fact it is partial melting upon ascent (even as it cools adiabatically from decompression) that produces the crust and lithosphere (according to Karato, upon some partial melting, dissolved water is lost from what becomes the lithosphere - making the lithosphere more rigid - so the asthenosphere (below the lithosphere) is softer not because it is partially molten but because it has not undergone sufficient partial melting to liberate water (in addition to being warmer, of course). Because the mantle is not a pure substance, it doesn't have a single melting point, and melting and freezing involve chemical differentiation - more generally, this concept helps explain the variations in igneous rocks.) The scale of fluid velocity of the outer core has been estimated at around 0.1 mm per second (thats FAST for a deep geophysical process!). That's about 8.6 m per day! Compare that to the motion required to catch up to tidal deformation. Based on an ideal heat engine, the conversion of the heat driving the outer core convection to mechanical energy is ~ 26.8 % or 28 % efficient, based on top and bottom temperatures of 4100 K and 5500 K, and of 3600 K and 5000 K, respectively - that's based on all the heat going in at the bottom, however, which won't be true, although much of it may be (from latent heating). So of the heat that goes into driving the convection, perhaps between 70 % and 85 % (halving the efficiency to approximate the effect of internal heat sources only) would then go on to the mantle. Of course, some of the mechanical energy goes back into heat anyway, and some goes into electromagnetic energy, but some of that may go back into heat within the core (but I'm thinking it would go back into heat always at lower temperature (higher up within the core) than where it went into mechanical energy, so that entropy increases), ... etc. The mantle and crust have there own heat sources (aside from the heat liberated upon cooling, this is where most radioactivity is - radioactive elements increase in concentration from the core to the mantle, to oceanic crust, to continental crust). I think the total geothermal heat flux at the surface is somewhere around 40 TW. Much of that is conducted through the crust (or for heat generated within the crust, conducted through part of the crust) in the final part of it's journey. If a typical thermal conductivity of crustal material were 2 W/(K m) and the thermal gradient in that material were ~ 30 K/km, that's a heat flux per unit area of ~ 0.06 W/m2 - if that's typical, that's a large fraction of the total heat flux at the surface. Although concentrated in geologically active areas, much of the heat leaving the Earth from below the surface comes through geologically quiet regions of the Earth's crust.
33. Patrick 027 at 14:02 PM on 22 September, 2008
    Just to be clear, then, my point about tidal deformation vs convective deformation of the outer core - not only is the outer core convective fluid velocity greater, the convection is heterogeneous motion with much variation within the core and continual motion, whereas the tidal deformation's motion only varies from one extreme velocity to the opposite extreme velocity over the whole diameter of the core, so the deformation is that much smaller, and it reverses itself cyclically. The outer core's convective motions will expend much more energy than tidal motion within the outer core to distort the magnetic field lines and even to move against viscous dissipation. --- Mantle crystal structure- if I understand Fig. 1-7 on p.21 of Karato correctly: For the 'pyrolite' model of mantle composition: At the top, mantle material would be over half (by volume) olivine ( (Mg,Fe)2SiO4 - the (Mg,Fe) notation indicates that the composition can vary - in the case of olivine, there is complete solid solubility between the two extremes, Mg2SiO4 and Fe2SiO4), with the remainder orthopyroxene, clinopyroxene, and garnet. Going down, some pyroxene is transformed into garnet at a gradually increasing rate. At ~ 400 km depth, all the olivine transforms to 'Beta (Mg,Fe)2SiO4'. Then with increasing depth, eventually all pyroxene goes into the garnet phase, and a small portion of the 'Beta' does as well. Somewhere at or just below 500 km depth, all remaining 'Beta' is transformed to a spinel crystal structure that isn't Beta. Going deeper, Garnet starts going into Ca-perovskite, the amount of Ca-perovskite gradually increasing; meanwhile, near 600 km depth, garnet also starts going into an 'ILM' phase, which increases gradually until a depth of 650 km. At 650 km, all 'ILM' and a majority of the spinel go into Mg-perovskite, and the rest of the spinel phase goes into Magnesio-wustite (double dots above the u in 'wustite'). Below that, the amounts of both Ca-perovskite and Mg-perovskite increase gradually from the garnet until all garnet has been converted, which occurs somewhere below 700 km. From p.19, the 'beta spinel' is also called wadsleyite, or modified spinel, and the spinel below 500 km is called ringwoodite.
34. Patrick 027 at 14:40 PM on 22 September, 2008
    wustite is FeO, so I'm guessing magnesiowustite is (Mg,Fe)O. The pyrolite model of mantle composition can be given, for purposes of chemical accounting, in terms of weight percents of individual metal (or other) oxides - it would be more convenient to also have it in molar percents but I don't have the time right now to do that calculation, so in weight percents (Karato, p.4): SiO2 45.4 MgO 36.6 FeO 8.1 Al2O3 4.6 CaO 3.7 other oxides 1.4 --- Okay, so the overall geothermal heat release tends to stay near constant over short time periods - but there are short-term fluctuations because some heat release is in the form of individual plumes of magma, which gradually move upward in the crust, some fueling eruptions... this overall process still takes quite a bit of time but the overall heat transport by plumes could, I suppose, be a little bumpy in time. While tidal dissipation contributes just a little to heating, and not much at all within the crust or mantle, this doesn't address the potential for a role in affecting the transport of other heat. (It takes a lot of heat to heat up a corner of a pool, much less energy to swirl the water around). I suppose tidal stresses could alter the timing of volcanic eruptions and earthquakes. But (aside from butterfly-effects, which for the solid and deep Earth would take a very long time to materialize as different configurations of mantle or even core convection, and wouldn't affect much the 'climate' of that convection) I really don't see how it would affect any time-averaged rate of such things - the earthquakes and volcanic eruptions (and geysers, etc.) will happen anyway because of the accumulation of forces and materials driven by geological forces - tidal forces just come and reverse and reverse again, there is no accumulation - On the other hand, as airplane mechanics well know, materials that are repetitively cycled through small stresses can fail eventually from a much smaller stress than would have otherwise been necessary - in some materials, the cycled stresses have to pass some minimum amplitude for this to happen - but for aluminum, this is not the case. So over time, one could imagine repetivive tidal distortions, over hundreds of millions to billions of cycles, might 'weaken' the crust - at least the upper part which is more brittle (the lower part might 'heal it's wounds' because of the warmth ...?)... but the seismic shaking from episodic earthquakes would also do that. How big are tidal stresses in the crust, anyway? seismic waves have wavelengths that, I presume, are quite a bit shorter than the radius of the earth, whereas tidal deformation is distributed on that length scale, which reduces the stress it could cause. And you only get two cycles of tidal stress a day, at most - how many thousands or millions of years would it take for this to be a factor in the mechanical properties of the crust, if ever? - (which implies a short term change in tides couldn't have an immediate impact).
35. Quietman at 15:01 PM on 22 September, 2008
    Patrick I was aware of these ocean and mantle conditions. It is not what I am talking about, and although the mantle is currently exposed directly to the south Atlantic it is irrelevant, according to the measurements it's thick and not any warmer than other parts of the seafloor. I am talking about gravitational tides in the magma ie. the Earths heat engine. Heat escapes to the oceans along tectonic plate edges and fissures. And if you study the paleodata there are more plate edges and fissures than recently thought. And then you need to add the extra gravitational forces from jupiter and full alignments. If they can affect the sun they can certainly effect the Earth. Many people don't know that Antarctica as well as North America sits on more than one plate. People talk about a Pacific plate but that should be plural as there are several plates of different sizes, and moving in different directions. Obviously since the plates are irregular this movement changes the amount of thermal energy delivered constantly. But the greatest heat transfer occurs in regular cycles at subduction zones and that is the interesting part. What besides tidal forces can cause these cyclic events? And remember, these forces are not the moon alone although it is the most important because of proximity. PS - I found a couple of references for my earlier statement on extinction: Climate Change Spurred Human Evolution By Andrea Thompson, LiveScience Staff Writer 06 September 2007 Megadrought Put the Squeeze on Our Ancestors By Ann Gibbons ScienceNOW Daily News 10 October 2007 Ancient drought ‘changed history’ By Roland Pease BBC science unit, San Francisco, 12/7/2005 This was from 150,000 to 70,000 years ago. Starting 70,000 years ago, the climate turned wetter.
36. Quietman at 15:13 PM on 22 September, 2008
    Patrick From the article: Sloshing Inside Earth Changes Protective Magnetic Field By Jeremy Hsu, Staff Writer 18 August 2008 "A new model uses satellite data from the past nine years to show how sudden fluid motions within the Earth’s core can alter the magnetic envelope around our planet." Read that slowly ["sudden fluid motions within the Earth’s core"] This is not talking about millions of years, or thousands or even hundreds of years. This word "sudden" is very relavent to my argumant.
37. Quietman at 15:26 PM on 22 September, 2008
    PS - It's NASA that claims CO2 induced AGW is only 2% of GHG warming. I don't know how they arrived at that number.
38. Quietman at 15:46 PM on 22 September, 2008
    Also, the bottleneck actually was a split resulting in two bottlenecks. Two seperate groups were evolving independent of each other in different parts of Africa. The resultant diversity and mixing occured when these groups were reunited 70K years ago and emerged from Africa. Our species emerged 40K years ago (displacing Neandertal) but apparently mixing with earlier departures of H. erectus along the way. This is still contested and unresolved as H. heidelbergensis and H. georgicus are still feeding fuel to this fire.
39. Patrick 027 at 04:24 AM on 23 September, 2008
    First two clarifications of what I wrote earlier: "So of the heat that goes into driving the convection, perhaps between 70 % and 85 % (halving the efficiency to approximate the effect of internal heat sources only) would then go on to the mantle." With just under 30 % conversion of heat to mechanical energy for the heat coming from the base of the outer core, with nearly linear temperature trend with depth and the temperature range being somewhat small compared to absolute temperature, a first approximation for a distributed source of heat within the outer core would be half that efficiency of conversion - just under 15 %. That heat would come from the overall temperature decline of the outer core. However, the volume per unit depth is not invariant but is proportional to the square of the radius. The mass distribution is a bit different because of increasing density toward the center (Karato p.13), and specific heat is not constant, but the distributed heat source from cooling would still likely be skewed toward the cooler parts of the outer core, so the overall efficiency for the conversion of heat from cooling would be less than half of the that of the latent heat from the base of the outer core from inner core growth. For my own curiosity I might sometime try to estimate the proportion of the two heat sources by comparing the "100 K every billion years would release 5.7 TW of heat" to a figure derived from specific heat - unfortunately a figure not easy to find for molten high pressure iron alloy. The other clarification: "Of course, some of the mechanical energy goes back into heat anyway, and some goes into electromagnetic energy, but some of that may go back into heat within the core (but I'm thinking it would go back into heat always at lower temperature (higher up within the core) than where it went into mechanical energy, so that entropy increases), ... etc." That's on average - that the mechanical and electromagnetic energy produced from heat at one temperature will on average go back into heat at a lower temperature - individual packets of energy may go back into heat at higher temperature, destroying entropy, provided other parts of the system are supplying the work (free energy) to drive such a process, and gaining entropy. In the absence of fluid motions, the magnetic field would decay - about exponentially - due to diffusion of the magnetic field. If the core were superconducting, this could not happen - any change in the magnetic field would produce a voltage that would drive an electric current that would restore the magnetic field. The finite conductivity of the material allows some of the electrical energy to go into heat, so that the magnetic field can diffuse and decay. According to Karato (pp.197-198 in particular), the magnetic field would essentially vanish in ten thousand years without a geodynamo to power it up. I would imagine the decay rate is used to estimate the power that must go into maintaining the field - this is rate of magnetic energy conversion to heat energy in the core itself. Because of uncertain toroidal field components in the core that are hard or impossible to detect directly from the surface (though they can be inferred by comparing the seismographic implications of different geodynamo computer models to seismographic observations, taking into account some inner core properties), the actual magnetic field energy density is uncertain, so that would be a source of uncertainty in the power necessary to maintain it. The magnetic field energy will be concentrated within the core - inferred from Karato p.199, the magnetic flux B in the core may be between ~ 3 and ~ 300 times the surface value (30 microTeslas) (B of a typical refrigerator magnetic is about 100 times the natural B at the surface). I think field energy density is proportional to the square of B, in which case the energy density is between 9 and 90,000 times the surface value, the volume of the core is ~ 16 % the volume of the Earth (more than 1/9) (for future reference, surface area of core ~ 30 % that of the whole Earth (which implies the mass of the core is about ~ 30 % the mass of the Earth, since gravitational acceleration is nearly constant within the mantle (that's somewhat of an accident of the specifics of the Earth's mass distribution, not a general principle)), radius of core ~ 54 % that of the whole Earth); the magnetic field changes wouldn't induce much of a current in the mantle and the mass of the magnetosphere and E-region dynamo are very small, so it makes sense to think that most of the geodynamo energy goes back into the heat energy of the core. Any mechanical and electromagnetic energy going back into heat within the core also includes that coming from composition-generated buoyancy. (But I think some small portion of electromagnetic energy must radiate away into space as the Earth moves and the field changes.) As long as I'm on this, notice that 'stretching' the field lines, contorting them by uneven fluid motions, increases the magnetic energy density by putting a greater length of field lines into a unit volume. An interesting analogy could be made between that and the conversion of potential to kinetic energy in the atmosphere to sustain nearly-geostrophic wind shear as isotherms are elongated (without changing the average temperature gradient), such as by a growing wave pattern. There are big differences but there's a cool geometric similiarity. --- "And then you need to add the extra gravitational forces from jupiter and full alignments. If they can affect the sun they can certainly effect the Earth." The vast majority of tidal forces on Earth is from the moon and sun (solar tides being about half the magnitude of lunar tides, I think (roughly from memory ratio of masses divided by cube of ratio of distances: ~330,000*80 * (0.384/150)^3 =~ 0.44 - just under half). Remember planetary tides on the sun from: http://blogs.abcnews.com/scienceandsociety/2008/07/global-warming.html#comments A more complete comparison: height of equilibrium tidal bulge raised on sun by planet, as fraction of that raised on earth by moon, [ignoring out-of-equilibrium complexities of crust,ocean reaction (no Bay of Fundy on sun?)] expressed as ppt (parts per thousand): Jupiter: 1.33 Venus:.. 1.27 Earth:.. 0.590 Mercury: 0.563 Saturn:. 0.0647 Mars:... 0.0179 Uranus:. 0.00122 Neptune: 0.000375 Pluto:.. 0.0000000191 SUM:.... 3.84 Tidal acclerations at solar surface generated by planets, as ppt of lunar tide on earth, : Jupiter: 0.340 Venus:.. 0.325 Earth:.. 0.151 Mercury: 0.144 Saturn:. 0.0165 Mars:... 0.00458 Uranus:. 0.000311 Neptune: 0.0000957 Pluto:.. 0.00000000488 SUM:.... 0.981 The sums would be approached when Venus and Jupiter and a few others are aligned or close to aligned with the sun. When Jupiter-Sun-Venus forms a right angle, the tides on the sun will be more limited. (PS notice Saturn plays a much larger role in the 'solar jerk' (where the importance of a planet is proportional to it's mass times it's distance) than it does in tides on the sun (mass divided by distance cubed). This would have some implications for Fairbridge's concepts. It would also be instructive to consider the product of the above numbers, which gives the tidal acceleration that acts on the tidal bulge: In ppm of equilbrium lunar tides on Earth: Sum of products:.. 1.04 Product of sums:.. 3.77 Jupiter by itself: 0.454 The distinction between the first two is a nonlinearity. This is the tidal force per unit area of the sun per unit density variation with depth at the sun's surface, relative to a theoretical equilibrium lunar tide on Earth. The density variation within the Earth is distributed with some significant concentration near the surface and near the core/mantle boundary. The mass of an equatorial bulge is produced by the vertical displacment of a density contrast. The density variation within the sun is quite small near the surface; one has to get almost halfway to the center before the density is comparable to the ocean, ~ 60 % of the way to the center to find densities similar to that of the Earth's mantle; the great majority of the Sun's mass is contained within half it's radius from the center. to be continued...
40. Patrick 027 at 10:27 AM on 23 September, 2008
    Specifically, about 89 % of the mass of the sun is within half it's radius from the center. This means that the size of the equilibrium tidal bulge above that point is nearly proportional to the fourth power of the distance from the center; and would only be close to 1/16 of it's surface value - more precisely, 1/(16*0.89) = 1/14.24 = 7.02 % of the surface value. At just 20% of the way to the center, only ~ 1 % of the mass of the sun lies above, so the equilibrium tidal bulge is rather close to 0.8^4 = 0.1^4 * 2^12 = ~ 41 % of the surface value. Keep in mind that the equilibrium lunar tide at the Earth's surface has a range of ~ 54 cm at the surface, or close to 16 cm at the core/mantle boundary (I say close to because while g is nearly constant in the mantle, it is not precisely constant); for what it's worth, at 10 Earth radii from the center of the Earth, it would be 5.4 km. If all the planets were aligned with the sun, the equilibrium tidal range at the sun's surface would be about 2.1 mm (close to how much your hair would grow in 5 in 6 days - and points on the sun would go through this range in a bit over 10 days, I think (half solar rotation period)) - at 20% below the surface, 0.86 mm; for what it's worth, at 10 times the solar radius from the sun's center, it would be 21 m (69 feet). to be continued...
41. Patrick 027 at 11:47 AM on 23 September, 2008
    Tidal motion: If a local tide h = A*sin(wt), where A is half of the range, the maximum rate of change of h would be A*w; w=2*pi*frequency; for the maximum possible semidiurnal lunar tide on Earth (where the moon is in the equatorial plane), the frequency (not adjusting for the moon's orbital motion, which would reduce the following numbers just a little) is roughly 2/(86400 s), so w = 2pi/(43200 s) = 0.000145 / s. Thus at the surface of the Earth, the maximum vertical velocity of an equilibrium tide is 0.039 mm/s; at the core/mantle boundary it would be about 0.012 mm/s (just over a tenth the typical fluid velocity in the outer core, and of even less importance to the geodynamo for other reasons). The corresponding velocity at 10 Earth radii from the Earth's center: 39 cm/s. The corresponding velocity on the surface of the Sun for all planets aligned, not adjusting for planetary motions, using a solar rotation period of 26 days (it's in that neighborhood, although it varies with latitude on the Sun): 5.8 microns per second. For what it's worth, the corresponding velocity at 10 solar radii from the Sun's center: 58 mm/s. But how would that pertain to the solar wind? What are tidal accelerations? Earth's surface g = ~ 9.81 m/s2 = G*massEarth/(radiusEarth^2) -- Moon's mass is about Earth's mass / 81 Moon's (average) distance from Earth is about 60.3 Earth radii. 1/81 * [(1/59.3^2)-(1/60.3^2)] = 0.12 ppm -- So the difference in lunar g from Earth's center to the sublunar point at Earth's surface, as a fraction of Earth surface g: 0.12 ppm. That's 1.1 microns per second squared. to be continued...
42. Patrick 027 at 14:56 PM on 23 September, 2008
    To be specific, 1.1 um/s (u used in leiu of 'mu'; um = micron) is the vertical tidal acceleration at the Earth's surface at points in line with the center of the Earth and the Moon, and is locally upward. The vertical tidal acceleration halfway in between those two points, in a ring on the surface, is downward and half the magnitude. Let 2*T be the vertical tidal acceleration on the surface of a sphere at the near and far point from a tide generating mass. Then, where N is the angle from near point (so N = pi radians (or 180 degrees) at the far point), The local vertical tidal acceleration is: dv = T * [ 1/2 + 3/2 cos(2N) ] And the local horizontal tidal acceleration (positive toward lower N): dh = T * 3/2 sin(2N) So the total range of each is 3T. T is linearly proportional to the distance to the center of the sphere experiencing the tides, and does not depend on the mass of the body experiencing the tides**. The shape and magnitude of the equilibrium tidal distortion can be determined by finding the surface for which the vector sum of the tide experiencing body's gravity and the tidal acceleration are normal (perpendicular) to that surface - the slope of that surface is thus dh/(g-dv) (or the negative of that, depending on perspective), which is almost equal to dh/g since |dv| << |g| **. **-thus far I have ignored the effect of the gravity of the mass anomaly of the tidal bulge itself. This would tend to make the tides a bit larger. When I tried to calculate the equatorial bulge in the same way I got half the actual value, so maybe the actual tidal bulge is twice what I have said so far - at equilibrium, that is (??). However, actually figuring out how a body is deformed is tricky (without knowing more than I do, anyway). The vertical tidal acceleration is related to increased spacing of (geo)potential surfaces - surfaces of constant potential energy - caused by the shape of the bulge. At equilibrium, density variations are only perpendicular to these surfaces. One could imagine a combination of vertical and lateral movement to shift the body around into this shape. As the potential surfaces are spaced differently, the pressure increase with depth increases at a different rate, so that density changes due to pressure changes should fit. However, one could also imagine a response involving initial decompression at high tide and compression at low tide (in response to the vertical tidal acceleration) - a sharp density discontinuity could shift up and down to match the equilibrium shape, but then the mass distribution below that point would not be at equilibrium The pressure variations at depth would then drive lateral movements toward equilibrium. The equatorial bulge is essentially at equilibrium because it's not be cycled or varied rapidly. Tidal deformation is cycled as objects spin through the tidal acceleration and tidal potential energy fields. The tidal bulge must then travel as a gravity wave (or some other wave) around/through the object. A freely propogating gravity wave travels due to the pressure gradients in the fluid caused by a vertical surface displacement through a fluid at a speed c = square root of (gH), where g is the gravitational acceleration and H is the fluid depth. It is a gravity wave because gravity supplies the restoring force. This formula is only true for a shallow fluid (compared to wavelength) which is below a vacuum or very low density material compared to itself, as is the situation for water waves under air. More generally, I think the speed is also proportional to the difference in densities across the surface divided by the density of the underlying fluid (this is an internal gravity wave). When the wavelength is not much longer, or is shorter, than the fluid depth, the full motion of the wave does not extend all the way down because (*I think - haven't done the math yet for myself*) vertical accelerations cummulatively cancel out the pressure variation due to the surface height displacements, so the wave only 'feels' some fraction of the fluid. When the amplitude of the wave becomes significant compared to fluid depth, there are nonlinearities... I don't think the compressibility of water has much effect on gravity waves, but more generally, gravity and elastic forces may both supply a restoring force. In solids, the elastic forces may include a resistance to shearing motion (as in a seismic S-wave, and also I think a 'Love' wave (kind of surface seismic wave) - (of course gravity is insignificant in S, P (compressional, like sound waves), Love, and Raleigh seismic waves). If and when the coriolis effect comes into play, there are also Kelvin waves, which are waves that move along lateral boundaries (like coastlines) with amplitudes that, in the case of constant fluid depth found immediately off the coast and a straight coastline (compared with the wavelength of the wave, I suppose), decay exponentially away from the coast. Such Kelvin waves travel at the same speed as gravity waves (at least in the case of wavlength >> fluid depth). There can also be inertio-gravity waves. Internal gravity waves also occur in a fluid with continuously varying density (the atmosphere), as opposed to a sharp interface - the math gets more complicated in that case. ... To make a long story short, there are certain natural frequencies of various modes of oscillation for the whole Earth, for ocean basins, etc, which depend on the size and shape and the speed and behavior of different kinds of waves. If a system is forced near it's natural frequency, it can resonate. If it is forced much faster than a natural frequency, there may not be much response. If the forcing is much slower, the system may just follow the forcing in near equilibrium (I think). My impression is that not much per unit volume deformation is required to distort the whole Earth by the tides because the horizontal movement is distributed over large vertical distances; the horizontal displacements would be of the same order of magnitude as the vertical displacements. Rather than coming back to it later, notice that implies a tidal strain (at equilibrium) (compressional, tensile, or shear) on the order of 50 cm / 6000 km, or ~ 0.1 ppm. I don't know what stress that would require within the crust offhand. If the whole Earth responded in the same way, the same would be true for the oceans - the vertical depth changes would be small because most of the surface changes would be supplied by changes in the sea floor (and there would be no noticeable changes at the coasts). But the ocean doesn't respond the same way, so the horizontal displacement in the open ocean may be on the order of a kilometer (which the coriolis force may act on so that water parcels move in loops). The changing water depth would also affect changes in the underlying crust and mantle, so it's complicated. Of the energy that is going into the tidal displacments, some comes back out - the 'elastic' fluid motion of the ocean (and outer core in as far as that's concerned), and the elastic deformation of the solid Earth (includes the mantle - it responds more rigidly to high-frequency cycling; plastic deformation takes time). Energy is lost to viscosity in fluid motions and in plastic deformation, electrical resistance in the core, and to any brittle failure that would occur, as well as microscopic fractures. (PS atomic spacing may vibrate about equilibrium spacing, where equilibrium is at the bottom of an 'energy well'. Over small vibrations the energy well is approximately parabolic, so there is a linear proportion of force to deformation (strain). But when atoms are pulled apart, the energy approaches a modest limit, whereas pushed in close enough and the energy shoots way up. Thus, extreme compression can store so much energy that when released, the atoms could fly apart (vaporization).) Anyway, not much tidal energy is lost outside the oceans on Earth. More energy may go into the solid Earth tides then is dissipated there because the energy can come back out to the extent that the Earth 'springs' back. -------------- At the surface of the sun, with all planets aligned, tidal acceleration is 0.981 ppt of the lunar tide on Earth's surface. That's on the order of 1 nm/s2. At 10 solar radii out from the center, it would be on the order of 10 nm/s2. I'm not sure how the solar wind's velocity varies as it moves away from the sun - it would be decelerated by gravity but it is also affected by the magnetic field (and vice versa). For the sake of having some ballpark figure: at 100 km/s, it takes ~ 7,000 seconds to cross a solar radius. In 70,000 seconds, the time taken to cross 10 solar radii, the tidal acceleration would make a difference in velocity on the order of 0.7 mm/s. Even out 100 solar radii, tidal acceleration might cause a variation on the order of 7 mm/s. It seems rather insignificant compared to a speed of even just 10 km/s, let alone 100 km/s or 500 km/s. Of course, while I've been mentioning tidal accelerations out to 10 Earth radii and 10 solar radii, I should mention that the formulas for tides I've been using are nice linearizations - approximations that will fail when the distance out becomes significant compared to the distance to the tide-generating mass. However, for a tide generating object a distance R from the center of the body experiencing tides, the approximation is not off by more than a factor of 10 within ~ 75 % of R toward the tide-generating mass, or ~5 times R in the opposite direction; it's not off by more than a factor of 2 within 1/3 R toward the tide-generator or just over half of R in the opposite direction.
43. Patrick 027 at 15:09 PM on 23 September, 2008
    "When the amplitude of the wave becomes significant compared to fluid depth, there are nonlinearities" And also when the displacements become significant compared to the wavelenth... --- "PS - It's NASA that claims CO2 induced AGW is only 2% of GHG warming. I don't know how they arrived at that number. " Maybe they're comparing the anthropogenic forcing from the increase in CO2 to the total greenhouse forcing that exists (I think something like 155 W/m2, although that includes feedbacks (water vapor and clouds) that maintain the climate as is in the absence of change)? I'll get back to sudden core motion changes tomorrow.
44. Patrick 027 at 10:20 AM on 24 September, 2008
    A few more comments about tides on Earth: fluid oscillations: another fluid oscillation is the inertial oscillation - the cyclical movement of fluid parcels in the absence of any other force but the coriolis force; if the movement is small enough that the coriolis force does not vary much of the course of the cycle, then inertial oscillation takes the form of anticyclonic circular trajectories. The frequency is proportional to the coriolis effect, which is proportional to the sine of the latitude; the period is 1/2 day at either pole and 1 day at 30 deg latitude N or S. Diurnal cycles might then resonate somewhat with inertial oscillations near 30 deg latitude (give or take - one has to adjust a bit for the solar day be slightly longer than a siderial day, and for the lunar diurnal tide period being a little longer still); one example is land-sea breeze cycles; another would be the diurnal tides (?). But there are other factors... PS there is no diurnal tide forcing at the equator but there could still be diurnal tides at the equator because the tides propogate as waves and so can travel around. This might open up the possibility of some resonant behavior near a pole from semidiurnal tides (?). --- when there is a crack, dent, or weak spot that doesn't support a load, the stress 'field lines' (I haven't heard that term used with stress but it works visually), when in steady state, must bend around and get concentrated around the edges of such 'imperfections' - this is what tends to make cracks grow. (Although with a compressive load, the crack might be squeezed shut in the process.) (When not in steady state - well, short-wavelength sound waves can penetrate through the space in front of a crack or gap, and then reflect off of the boundary, this is space which would be bypassed by more slowly varying forces. Which brings up what happens with longer-wavelength sound waves - there is diffraction around the gap, and some scattering off of it; as the wavelength gets longer relative to the size of the gap, the wave 'pays' less attention to the gap, etc...) So one could imagine that tidal stresses are concentrated slightly under valleys and trenches, and the edges of fault lines. But the same would be true for the more constant stresses from geologic forces. Consider mantle rocks with a density around 4500 kg/m3 (Mantle density ranges from a bit over 3000 kg/m3 to over 5000 kg/m3 with increasing depth (Karato p.13 diagram). ----- PS Karato p.123 - the issue with phase transformations with negative Clapeyron is a bit more complicated: first, the total phase transformation ringwoodite to perovskite + magnesiowustite has a negative Clapeyron slope. It is (not independently of the Clapeyron slope) endothermic, which means their is latent heat release upon ascent and latent heat uptake upon descent. That offsets the effect of density in opposing cross-660 km level convection. The density variation becomes bigger with bigger lateral temperature variation, however, while the latent heating effect does not. Thus, two layer convection is more favorable when there are bigger temperature variations driving updrafts and downdrafts - this also corresponds to higher velocity updrafts and downdrafts as the forces within each layer will be greater. I haven't actually read much of this chapter in Karato but one thing that has occured to me is that higher viscosity and rigidity could make whole mantle convection more likely (actually this was discussed with relevance to descending cold lithospheric slabs). What I'm thinking: If you have a stiff slab and you drive it into a wall with enough force (the buoyant force acting on a piece of warm mantle with a deep root below 660 km but protuding above that level, or the reverse for a piece of cold mantle), you might break through. If the slab deforms too easily, you could use the same amount of force and the slab will just bend against the wall. ... This might not be significant in most of the mantle because it may be warm enough and the deformation slow enough that rigidity or viscosity would not do much against the density variations at 660 km... But it would matter to cold descending lithospheric slabs. p.123 Karato: The Raleigh Number (one of those nondimensional numbers used to characterize fluid motion or lack thereof - others: Rossby number, Froude number, ...) ----- Anyway, Karato p.126 mentions a coefficient of thermal expansion of 20 ppm / K (in the context I think it's a volumetric expansion, which is what 'we' want here). Going with that number: A column of mantle 500 km vertically, 10 K warmer than surrounding mantle, with g ~ 10 m/s2, would be 200 ppm = 0.2 ppt less dense - 0.2 ppt * 4000 kg/m3 = 0.8 kg/m3; over the depth of the column, a difference of 0.8*1000*500 kg/m2 = 400,000 kg/m2. Times gravity: a pressure difference of ~ 4 MPa (about 40 atmospheres, ~ 600 psi). Subducting slabs on average are cooler than the surrounding mantle by several hundred degrees (Karato p. 129); although they don't descend straight down so having a 500 km column would be unlikely, I think. ...
45. Patrick 027 at 11:40 AM on 24 September, 2008
    Tidal stress from tidal acceleration acting on that same mantle column: 4000 kg/m3 * 500,000 m = 2 billion kg/m2 1.1 um/s^2 * 2 billion kg/m2 = ~ 2200 Pa. Tidal stress from horizontal tidal acceleration acting over 6000 km (this is just to get a sense of the order of magnitude - PS that 10 K warmer bit- just to see what's possible; I don't know what the typical temperature variation is outside of those descending lithospheric slabs.): 60/5 * 2200 Pa = 26400 Pa = ~ 1/4 atmosphere = ~ 4 psi - that would be the kind of stress you'd see in the crust directly from the tidal forcing of the moon. But the oceanic response would exert other stresses in the crust. 0.54 m * 1000 kg/m3 * 10 m/s2 = ~ 5000 Pa ~ 1/20 atmosphere = ~ less than 1 psi. What about shear stresses...
46. Patrick 027 at 14:27 PM on 24 September, 2008
    Actually, the shear stress would be about the same, or at least the same order of magnitude, ~ 26 kPa =~ 1/4 atm =~ 4 psi. Unless the asthenosphere and below didn't hold themselves against it but pushed up or pulled down on the crust above. with constant mass per unit area and constant tidal acceleration with depth, it would increase by a factor of ~ 60 within the crust and lithosphere. BUT tidal acceleration drops to zero at the center, so it would only be a factor of ~ 30 - AND mass is concentrated at depth but area declines... per unit area at the surface, underlying mass is somewhat concentrated higher rather than lower, ... Well, you get the idea. 30 * 4 psi = 120 psi. But plastic deformation takes time; the core wouldn't hold itself against shear but the mantle would somewhat... well I did a visual estimate from a graph and came up with a factor of 2.35/6.37 *63.7 = 23.5; 23.5 * 4 psi = 94 psi =~ 6 atm = ~ 0.6 MPa - that's if the mantle acts like liquid, which I wouldn't expect, so it's likely a bit less than that, and perhaps closer to the original 4 psi. --- Dissipation: cracks: well, 100 psi = ~ 6 atm = ~ 0.6 MPa is the pressure found at 60,000/3000 m = 20 m below the surface - well, between 20 m and 30 m depending on the type of rock - the point is, any tensile stress due to tides is still, except in a very thin layer on top of the crust, just a reduction in the compressive stress due to the pressure. So brittle failure by pulling apart would be odd. I would expect heat and compression to, over time, weld cracks shut, which would limit the ability of many millions of tidal cycles to build up weaknesses in the material. (PS I've really gotten away from things I really know about here, but I suspect both heat and pressure combine to make the lower crust less brittle than the upper crust. This has an interesting effect on the deformation and fracturing patterns one may see in a cross section of mountain ranges (fractures tend to curve to near horizontal at depth - at least in the drawings I'm remembering - is that because of the reduced tendency to brittle failure at depth and/or is it something else?). Also, I think higher pressure increases viscosity, and from what I recall, below the asthenosphere, viscosity increases downward (until the core, of course).) There are, of course, 'pre-existing' cracks - joints and faults - I doubt the tides could ever pull these apart completely anywhere, but it could very slightly reduce compression, which might then reduce the threshold of shear stress necessary to cause sideways slips (which is the motion that would occur along any fault's plane) - so statistically one might look for earthquake (and volcanism) frequencies relative to variations in tides. But I wouldn't expect anything big. The presence of these faults and joints would also reduce the amount of tension that could be realized in the intervening rock. A little bit. Slightly. I'm downplaying it because it's not like the crust is just sitting there in space - it's stuck to the mantle. Even if there were a clean break all the way through the crust and lithosphere (and not just in the sense that the mantle is poking up through it), the mantle underneath would still transfer tensile stress to the crust above by pulling on it sideways (the horizontal shear stress)... Dissipation: heat - atoms have to move around in a phase transition; conceivably, even in a short period, some portion of the atoms near phase transitions in the mantle might be cycled through different arrangements (statistically - I wouldn't imagine the phase transition is knife-edge, or that on that timescale it could get near equilibrium (?), and there are the gradual phase transitions from or to garnet, so I wouldn't expect it's the same atoms each time around) - that might be a location where there is some relative concentration of tidal dissipation into heat energy. Not that it would be a significant source of heat. I would try comparing it to the radioactive heat generation in the mantle per unit volume if I had the time. Back to tidal accelerations of charged particles - in the Earth's magnetosphere, at 10 Earth radii from the center of the Earth, for example, tidal acceleration is on the order of 11 um/s2. How fast do charged particles travel in the magnetosphere of the Earth? I really don't know, so this is just a sample calculation, to be multiplied by whatever corrective factor is necessary later: How about 4 km/s ? At 10 Earth radii, it would then take on the order of 70,000 km path to cross a region of tidal acceleration in one direction. 70,000 km / (4 km/s) = 17,500 s (several hours). 11 um/s2 * 17,500 s =~ 190 mm/s. So the lunar tides could be expected to alter particle velocites in the magnetic field of the Earth at 10 radii out by on the order of 0.2 m/s, 1/20,000 of their velocity - if they are moving at 4 km/s. Of course, that doesn't account for the paths they take, typically a helical path rebounding from polar region to polar region along magnetic field lines, with either an overall eastward or westward drift (it may just be one or the other, or depend on charge, I forgot which). This means their east-west motion is quite a bit slower than their north south motion (overall, averaging over each turn of the helix), so they would pass through the same tidal acceleration field multiple times. However, if they are rotating with the Earth (I'm not clear on that part), that eliminates that concern (unless they are drifting west at high speed)... otherwise, they may come out of high tide drifting outward, drift east/west and then drift back down after passing low tide ... If it took ~ 20 hours (70,000 seconds) to exit a high tide or low tide, they might accumulate an extra velocity of ~ 0.8 m/s, which over 70,000 seconds would mean a displacement of ~ 56 km, which isn't much out of 70,000 km. ____________ Bottom line on tides: Yes they have effects, but outside of oceanic processes, they're really small. Oh, and (you probably realized this but it bears mentioning) tidal dissipation is not fixed by tidal forcing - if the Earth's properties (spin rate, ocean basin shapes and locations, natural frequencies, material properties) were different, tidal dissipation might be much higher or lower. If the tidal deformation were perfectly elastic, their would be no tidal dissipation - the Earth wouldn't be slowed down by the tides - which means there wouldn't be a net torque on the tidal bulges - for simple equilibrium bulge shape, that would imply the tidal bulge is either completely in phase (high tide occurs with moon overhead) or completely out of phase (high tide occurs with moon setting or rising, as seen from equator). On that note: A couple of interesting papers on the topic of tidal changes over geologic time (and one also discusses Milankovitch cycles): http://journals.cambridge.org/download.php?file=%2FIAU%2FIAU2004_IAUC197%2FS174392130400897Xa.pdf... http://www.journalarchive.jst.go.jp/jnlpdf.php?cdjournal=pjab1977&cdvol=69&noissue=9&startpage=233... Which reminds me - if you went back in time far enough, you might reach a point where the tides (on Earth) were quite a bit more influential in things. Also, with solar tides included, that's almost a 50 % increase or decrease in tidal acceleration and tidal displacements from the lunar tides alone. That implies the tidal torque, a product of the two (integrated over the tidal density perturbation, multiplied by ... etc.), ranges from just under 1/4 of lunar tide alone at neap to around 2 times lunar tide alone at spring tides (with a reduced range when the moon is farther from the ecliptic). This is nonlinear. However, the average effects (on the torques) should add up linearly - this is because, over time, the lunar tidal bulge rotates relative to solar tidal forcing, so that the average solar tidal torque on the lunar tidal bulge is zero - and it works the other way around, too - well, almost, there's a correction to be made from the eccentricities of the orbits, although the tides will be smaller during the time of the month when the moon is moving slower, so...
47. Patrick 027 at 03:20 AM on 25 September, 2008
    Just to be clear: "well, almost, there's a correction to be made from the eccentricities of the orbits, " - applies to both solar and lunar tides. On reaching equilibrium solid + outer core Earth tides: My understanding is the natural frequencies of whole Earth oscillation is fairly high, enough that tidal deformations might be expected to approach equilibrium over the course of the tidal cycles - HOWEVER that is not the equilibrium tidal bulge shape; it is a balance between the tidal stress pulling the Earth toward that shape and the Earth's rigidity (outer core is constrained by mantle, and also by magnetic field although the later is probably weak in comparison, I'd think) which resists that. During the cycle there would be some correction for plastic deformation, which takes time. Where kinetic energy is not a big factor, plastic deformation doesn't have much of a natural frequency. Hence even if the tidal cycles are too slow to resonate with the solid or inner Earth's natural frequencies, the tidal deformation of the solid and inner Earth may be quite limited relative to the equilibrium tidal bulge in absence of rigidity - that is my impression, anyway. Of course, the tidal forcing on the solid and inner Earth includes both the direct forcing by the moon+sun (other astronomical contributions are very very small) as well as the forces on the solid and inner Earth produced by the responses of other parts of the Earth - the ocean and atmosphere - where the ocean is much more important in that matter. An important note - the term solar tide is also used to describe a diurnal cycle in the upper atmosphere (ionosphere in this case) that is driven by the diurnal heating cycle - this has nothing to do with the solar gravitational tidal forces - it is only a tide in the sense that is cyclical over a day. ---- A final (?) note on mantle convection: Besides rigidy or viscosity, another way to break through the 660 km boundary would be to build up kinetic energy before reaching it. But for the mantle, even relatively fast motion is just way too slow for momentum and kinetic energy to be significant factors. Where they are important is the atmosphere, ocean, magnetosphere, and outer core. An example in the atmosphere is the overshooting top of a thunderstorm, where kinetic energy built up in an updraft is converted back to convective available potential energy (CAPE) as it overshoots a static equilibrium level - it then falls back down. But in the mantle, overshooting far enough could overcome the barrier to convection - this could never happen in an overshooting top unless a superadiabatic lapse rate were found somewhere above the tropopause or if some other condensible vapor in the atmosphere were abundant enough to kick in at some higher level with sufficient latent heating - and either will essentially never happen (the later might conceivably happen on another planet). A case where a barrier could be broken through in the atmosphere involves conditional instability, where the air is stable to dry convection but unstable to moist convection; in that case, supplying enough energy to a moist air parcel near the surface to push it up, reach the lifting condensation level (LCL) where latent heating kicks in, and then a bit further to the level of free convection (? I think that's what the term is), then it can take off. A rising column of warm air may entrain moist air from below to continue feeding the process (especially if the updraft is rotating, but that's a whole other ...) (it can also entrain cooler dryer air from the sides and top, which weakens the process). Now it occurs to me that the latent heating at the 660 km boundary would actually increase the phase transition density variation from the phase transition that would impede convection, but perhaps the thermal expansion (from that portion of heat) effect is larger then the density variation that comes from the portion of the phase transition level shift caused by that same portion of heat - based on Karato, I take this as implied. Okay, enough of that, - that the tides are not a big factor doesn't itself demonstrate a lack of solar, volcanic, or geomagnetic changes, so ...
48. Patrick 027 at 10:03 AM on 25 September, 2008
    (PS descending lithospheric slabs - slower slabs warm up too much before reaching 660 km; they deform and may be deflected from the boundary; faster slabs stay cooler for longer and are more rigid - BUT even faster slabs experience out of equilibrium phase transitions in such a way as to reduce their rigidity by changing microstructures - so it is slabs descending at intermediate speeds that would be most likely to break through the 660 km barrier - see Karato for that and more. Also, along with the desceding lithospheric mantle is the (generally) oceanic crust, which is different compositionally - so ... etc...) ---- "Tidal Motion Influences Antarctic Ice Sheet ScienceDaily (Dec. 24, 2006) — New research into the way the Antarctic ice sheet adds ice to the ocean reveals that tidal motion influences the flow of the one of the biggest ice streams draining the West Antarctic Ice Sheet." http://www.sciencedaily.com/releases/2006/12/061221075130.htm "This unexpected result shows that the Rutford Ice stream (larger than Holland) varies its speed by as much as 20% every two weeks. Ice streams -- and the speed at which they flow -- influence global sea level." "So far, Rutford Ice Stream is the only ice stream where this type of temporal variation has been observed, but it is likely that the phenomenon is widespread, and so important to incorporate in computer models predicting the future contribution of the ice sheets to sea level rise." --- Okay, so the tides did have an extra trick up their sleeves. But here's the other aspect of the tides: how much variance is there beyond ~ 20 years? The biggest change beyond the tides themselves: spring-neap. Granted their is nonlinear behavior, particularly near coasts, etc. But I'd still expect most of the variation to be in the semimonthly spring-neap cycle. --- " "well, almost, there's a correction to be made from the eccentricities of the orbits, " - applies to both solar and lunar tides. " And there could be significant interaction beyond linear superposition of tidal bulges when one gets into coastal areas, shallow areas connected to deeper water... etc. (for example, when the beach slopes into the water (typical), one tide raises the water and brings it inland a little; another tide raises it more and brings it in farther - the combination of higher water and water farther inland might make the local volume of water involved proportional to the square of the sums of the tides... etc. - and obviously there is threshold behavior - if you are higher up you'd only get the highest high tides... etc.) -------- Sloshing Inside Earth Changes Protective Magnetic Field By Jeremy Hsu Staff Writer posted: 18 August 2008 http://www.space.com/scienceastronomy/080818-mm-earth-core.html "The Earth's overall magnetic field has weakened at least 10 percent over the past 150 years, which could also point to an upcoming field reversal." - or not. I saw a graph showing this gradual decline as part of a cycle, based on some archeological data, although I don't know how that idea has held up (I think it was in "The Cambridge Encyclopedia of Earth Science(s?)", from 1980, so it's been awhile... Otherwise, nothing in the article really indicates that what is happening is unusual in the past century or two or five or ten or twenty...
49. Patrick 027 at 14:04 PM on 25 September, 2008
    -- " "PS - It's NASA that claims CO2 induced AGW is only 2% of GHG warming. I don't know how they arrived at that number. " Maybe they're comparing the anthropogenic forcing from the increase in CO2 to the total greenhouse forcing that exists (I think something like 155 W/m2, although that includes feedbacks (water vapor and clouds) that maintain the climate as is in the absence of change)? " -- 2 % of 155 W/m2 would of course be ~ 3 W/m2. Anthropogenic CO2 forcing is somewhere around 1.6 W/m2, which is about 1 % of 155 W/m2, of course. But the total anthropogenic greenhouse gas forcing is over 2 W/m2; anthropogenic aerosol cooling may bring total anthropogenic forcing down to ... 1.7 (?) W/m2. If the climate sensitivity without feedbacks is 0.3 K/(W/m2), then the ~ 155 W/m2 preindustrial greenouse 'forcing' would produce a warming of ~ 47 K. But the Earth's temperature would 'only' be ~ 30 (33 may be more accurate) K cooler without any greenhouse effect. Does this mean climate sensitivity without feedbacks is only 0.2 K/(W/m2) ? Probably not; climate sensitivity doesn't have to be independent of temperature, etc. There are other complexities one could point out - that removing all greenhouse effects would cause the Earth to ice over, so the actual temperature difference would be significantly larger than 33 K, that clouds also have an albedo effect and removing cloud greenhouse effect would also cause warming from the reduced albedo (before freezing over), etc, but that doesn't apply to the comparison above because the 155 W/m2 figure is only greenhouse 'forcing' and the 30 or 33 K figure only includes the greenhouse 'forcing' effect with albedo held constant. With feedbacks, a likely value of climate sensitivity is somewhere near 0.7 K/(W/m2). Remember from: http://blogs.abcnews.com/scienceandsociety/2008/07/tropical-storm.html my comment at "Jul 16, 2008 12:34:05 AM" From: http://www.columbia.edu/~jeh1/keeling_talk_and_slides.pdf -------- "Keeling_20051206" "Is There Still Time to Avoid ‘Dangerous Anthropogenic Interference’ with Global Climate?*# A Tribute to Charles David Keeling James E. Hansen NASA Goddard Institute for Space Studies, and Columbia University Earth Institute New York, NY 10025 December 6, 2005" Particularly interesting is the Climate sensitivity section, and in that, the ice age radiative forcings (which include ice albedo as well as greenhouse gas changes and other things), from which a climate sensitivity of 3/4 +/- 1/4 deg C per W/m2 forcing - (in this case the ice albedo, greenhouse gases, etc, are all put in as forcings for the sake of the calculation - Hansen is not implying that they were not feedbacks to other changes on a long time scale; the remaining feedbacks would include water vapor, clouds, etc.) - this is about what is suggested by computer climate models, though the later have some greater uncertainty. ------------- ... Specifically, from above source: ice sheets and vegetation albedo: -3.5 +/- 1 W/m2 greenhouse gases: -2.6 +/- 0.5 W/m2 aerosols: -0.5 +/- 1 W/m2 Total -6.6 +/- 1.5 W/m2 Change in temperature: -5 +/- 1 K Implied climate sensitivity: 3/4 +/- 1/4 K/(W/m2) For more on total radiative budgets (including the 155 W/m2 LW forcing): "Earth's Annual Global Mean Energy Budget" J. T. Kiehl and Kevin E. Trenberth
50. Patrick 027 at 14:07 PM on 25 September, 2008
    That last part between ------ ------ is taken out of my comment from the earlier discussion; the second part of it is not a quote from the website.

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