AGWists are sore losers
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From: Jonathan Kirwan on 3 Aug 2007 21:09 On Fri, 03 Aug 2007 17:35:45 -0700, Bill Ward <bward(a)REMOVETHISix.netcom.com> wrote: >On Fri, 03 Aug 2007 23:31:11 +0000, Jonathan Kirwan wrote: > >> On Fri, 03 Aug 2007 16:34:00 -0700, Bill Ward >> <bward(a)REMOVETHISix.netcom.com> wrote: >> >>>On Fri, 03 Aug 2007 22:20:07 +0000, Jonathan Kirwan wrote: >>> >>>> On Fri, 03 Aug 2007 15:09:01 -0700, Bill Ward >>>> <bward(a)REMOVETHISix.netcom.com> wrote: >>>> >>>>>On Fri, 03 Aug 2007 20:32:40 +0000, Jonathan Kirwan wrote: >>>>> >>>>>> On Fri, 03 Aug 2007 12:57:24 -0700, Bill Ward >>>>>> <bward(a)REMOVETHISix.netcom.com> wrote: >>>>>> >>>>>>>On Fri, 03 Aug 2007 19:36:02 +0000, Jonathan Kirwan wrote: >>>>>>> >>>>>>>> On Fri, 03 Aug 2007 12:43:57 -0700, Bill Ward >>>>>>>> <bward(a)REMOVETHISix.netcom.com> wrote: >>>>>>>> >>>>>>>>>On Fri, 03 Aug 2007 19:13:04 +0000, Jonathan Kirwan wrote: >>>>>>>>> >>>>>>>>>> On Fri, 03 Aug 2007 11:35:19 -0700, Bill Ward >>>>>>>>>> <bward(a)REMOVETHISix.netcom.com> wrote: >>>>>>>>>> >>>>>>>>>>>On Fri, 03 Aug 2007 16:58:03 +0000, Jonathan Kirwan wrote: >>>>>>>>>>> >>>>>>>>>>>> On Fri, 03 Aug 2007 09:28:24 -0700, z <gzuckier(a)snail-mail.net> >>>>>>>>>>>> wrote: >>>>>>>>>>>> >>>>>>>>>>>>>On Jul 27, 11:57 pm, kdth...(a)yahoo.com wrote: >>>>>>>>>>>>> >>>>>>>>>>>>>> So throw down on some none lies and irrelevancy on this >>>>>>>>>>>>>> SIMPLE TOPIC of the changing temperatures and CO2 levels >>>>>>>>>>>>>> according to the ice cores which show the lag of about 900 >>>>>>>>>>>>>> yrs for CO2 to temperature. >>>>>>>>>>>>> >>>>>>>>>>>>>Sure, that's easy enough for you to say. >>>>>>>>>>>> >>>>>>>>>>>> Nowhere in his comment does he show any knowledge about the >>>>>>>>>>>> error bars in the ice core time measurements. I believe they >>>>>>>>>>>> quite often exceed 900 years. Not that it matters, as there >>>>>>>>>>>> wasn't 6 billion people on the planet at the time dumping huge >>>>>>>>>>>> quantities of CO2 into the atmosphere and no one is arguing >>>>>>>>>>>> that CO2 must always __lead__ a temperature rise, back then. >>>>>>>>>>>> CO2 levels can (as can CH4 levels) be driven by Milankovitch >>>>>>>>>>>> cycles, for example. >>>>>>>>>>> >>>>>>>>>>>OK, I'll bite. How can Milankovitch cycles drive CO2 and CH4 >>>>>>>>>>>levels without involving temperature? >>>>>>>>>> >>>>>>>>>> Who said it didn't involve temperature? >>>>>>>>> >>>>>>>>>Then are you implying that rising temperatures from the >>>>>>>>>Milankovitch cycle caused the CO2 and CH4 to increase? >>>>>>>> >>>>>>>> Yes, that consideration should be in the mix. >>>>>>>> >>>>>>>>>It's not clear what you mean. >>>>>>>> >>>>>>>> Sorry about that. >>>>>>> >>>>>>>S'OK, nobody's perfect. What other effects of the Milankovitch cycle >>>>>>>on CO2 and CH4 do you see in your "mix"? >>>>>> >>>>>> My purpose was just as I said, that Kent's comment about a 900 years >>>>>> lag (whether taken from a factual source, or otherwise) isn't >>>>>> determinative. For (1), the error bars in the time measurements are >>>>>> rather wide in some places in the datasets and can easily wipe out >>>>>> something that appears to be a mere 900 yr lag. (In other words, >>>>>> it's possible that it is a lead and not a lag, at all, and that the >>>>>> errors in time measurement account for that difference.) For (2), a >>>>>> lag taken to be the actual case in some circumstances may very well >>>>>> be an effect or response and not a driving force and, due to >>>>>> atmospheric CO2's effect on warming itself, is a positive feedback >>>>>> factor enhancing another natural cause (such as Milankovitch cucles.) >>>>>> >>>>>> For the current state of science on these things, one must be fairly >>>>>> comprehensive and study quite a few reports. I don't hold myself out >>>>>> as an expert in this area. Just an interested consumer of some of >>>>>> it. >>>>> >>>>>OK, fair enough, I'm about the same. The reason for my question was >>>>>your comment, "CO2 levels can (as can CH4 levels) be driven by >>>>>Milankovitch cycles, for example." >>>>> >>>>>I took that to imply the M cycle could directly affect something other >>>>>than temperature, such as CO2 and CH4. Apparently that's not what you >>>>>meant. >>>>> >>>>>On the original point, according to what I've seen, the CO2 vs >>>>>temperature lag was determined by correlation of the two datasets (T >>>>>and CO2) from each of a number of icecores from differing locations. >>>>>The lag is fairly consistent across cores. Error bars were calculated >>>>>normally (3 sigma?), and seem to rule out any lead of CO2 ahead of T. >>>>>Hence the assumption that CO2 cannot drive temperature. >>>> >>>> A couple of comments here from my narrow and non-comprehensive >>>> perspective. >>>> >>>> The lag is larger in portions of the data sets, large enough to exceed >>>> the error bars in time, so that in those places there is a fairly >>>> strong argument that a lag does in fact exist in those periods. That >>>> much I grant, from my own reading. >>>> >>>> But this doesn't mean that every place it is a lag. >>> >>>On the average, though, when the noise is reduced, it's a lag. This is >>>how you find it: >>> >>>http://en.wikipedia.org/wiki/Cross-correlation >>> >>><begin quote> >>>Explanation >>> >>>For example, consider two real valued functions f and g that differ only >>>by a shift along the x-axis. One can calculate the cross-correlation to >>>figure out how much g must be shifted along the x-axis to make it >>>identical to f. The formula essentially slides the g function along the >>>x-axis, calculating the integral for each possible amount of sliding. >>>When the functions match, the value of (f\star g) is maximized. The >>>reason for this is that when lumps (positives areas) are aligned, they >>>contribute to making the integral larger. Also, when the troughs >>>(negative areas) align, they also make a positive contribution to the >>>integral because the product of two negative numbers is positive. >>><end quote> >>> >>>It's a common technique for finding signals lost in noise, or in this >>>case finding the time relation between two noisy signals. >>> >>>> Nor, even if it is >>>> always a lag in the past, does that mean that humans dumping the levels >>>> of CO2 we currently dump cannot present a lead effect. (And, in fact, >>>> we know the mechanisms by how this does work, as well.) >>> >>>That argument would be stronger if CO2 could be shown to actually have a >>>significant effect on temperature. As of now, it's an implicit >>>assumption in the climate models, which are generally stipulated not to >>>handle convective transport well, especially in the tropics. Water vapor >>>at 20000ppm may totally swamp 380ppm of CO2. >>> >>>> It remains that in some places it may still be a lead effect. In other >>>> words, I don't think the data RULES OUT the possibility, for example, >>>> of a CO2 intrusion from unusual volcanic activity having its impact on >>>> the environment. >>>> >>>> In short, various circumstances may lead to similar outcomes. Just as >>>> in the case of "consumption," back a century and more ago, was caused >>>> by a variety of diseases with similar manifestations. >>>> >>>> I completely disagree with your comment "that CO2 cannot drive >>>> temperature." This is NOT SHOWN by either theory or science result. >>> >>>I meant that in the context of the lag in the ice core data. CO2 has not >>>been shown directly to significantly affect climate temperatures. >>> >>>That's an assumption based on the IR absorption spectrum and climate >>>models of dubious value. >>> >>>>>The positive feedback you refer to is, I believe, derived entirely from >>>>>climate models and unconfirmed assumptions about the behavior of water >>>>>vapor in the troposphere. Given your interest in math, you may find >>>>>climate models interesting: >>>>> >>>>>http://www.giss.nasa.gov/tools/modelE/ >>>> >>>> I do find them interesting, though I also find them prodigious to >>>> master. When I find the time to dig in as a hobbyist, I may do so. >>>> Until then, I will have to be satisfied with smaller bites. >>> >>>Good luck. I think the key to the puzzle will be found in assumptions >>>made in the climate models. >> >> I don't have direct responses to your replies except that they don't carry >> much water with me. I am already fairly familiar with some quantum >> mechanics (1-D variety simplified versions usually taught in a course on >> basic QM), understand ideas of photon-electron interactions both in bound >> and unbound states, am aware of illegal state transitions like triplet >> states in lattices, and have a feel for the idea of mean-free path and >> thermalization. There is no doubt at all in my mind about both the >> theoretical as well as experimental results which confirm all aspects of >> these things. > >That's all very good, and quite applicable to CO2 radiative heat transfer. >Overkill, even. > >Now, how about the relative effect of convective heat transport via the >latent heat of water vapor? There's an solar powered elevator under every >cumulus cloud taking latent heat right past the GHG radiative transfer >region to cloud top, where it has a straight shot at radiating to the sky. > >What about the cooling effect of cumulus clouds high albedo, and the >resulting strong negative temperature feedback? And the explicit >admission that climate models don't have enough resolution to >handle tropical moisture? How does CO2, constant at 380ppm, somehow >overwhelm water vapor, variable at 10000-40000ppm? > >How can you have "no doubt in your mind" without also understanding how >these phenomena work? Looking at only the one side you understand is >unlikely to yield accurate results, and is basically yielding to authority. > >> This is NOT a matter of assumption. > >I agree, but you seem to be assuming the AGW view of issues you are >unfamiliar with is correct, because you understand the physics of CO2. >I'm suggesting you question everything until you understand it. Make >people convince you. That's the basis of science. And it's a lot more >interesting than simply believing. > >Thanks for your comments. No, I assume that if scientists get the parts I do happen th fathom well and to get it right where I check on those parts, that they probably are getting the rest correct, as well, where I haven't yet had time. It's a quite reasonable position and it's not a static one. I've lived long enough and have been through enough study of physics and its application in the world to realize that this rule of thumb holds up very well. As I've tackled more than I knew before, and uncovered areas where I assumed scientists got it right before, I've found that they have indeed not only got the parts I was assuming before very close to the mark but have also considered a great many other details in the process, where I failed to even know about them beforehand. Trust isn't given away, it's earned. But in these areas, it has been earned in spades. In the specific case of anthropogenic global warming, I have gone through my own gradual learning process starting a few years before 1990. And the process of my own growth has been almost entirely one of discovering just how well important details were considered and areas of weakness pointed out early on and offered as areas where new research should take place. There are a few cases that remain of concern to me, today, where I think the models are off the mark for longer range projections. But then, I think the scientists generally realize most of these things and are trying to investigate further those they can. Jon
From: Phil. on 3 Aug 2007 22:59 On Aug 3, 8:35 pm, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: > On Fri, 03 Aug 2007 23:31:11 +0000, Jonathan Kirwan wrote: > > On Fri, 03 Aug 2007 16:34:00 -0700, Bill Ward > > <bw...(a)REMOVETHISix.netcom.com> wrote: > > >>On Fri, 03 Aug 2007 22:20:07 +0000, Jonathan Kirwan wrote: > > >>> On Fri, 03 Aug 2007 15:09:01 -0700, Bill Ward > >>> <bw...(a)REMOVETHISix.netcom.com> wrote: > > >>>>On Fri, 03 Aug 2007 20:32:40 +0000, Jonathan Kirwan wrote: > > >>>>> On Fri, 03 Aug 2007 12:57:24 -0700, Bill Ward > >>>>> <bw...(a)REMOVETHISix.netcom.com> wrote: > > >>>>>>On Fri, 03 Aug 2007 19:36:02 +0000, Jonathan Kirwan wrote: > > >>>>>>> On Fri, 03 Aug 2007 12:43:57 -0700, Bill Ward > >>>>>>> <bw...(a)REMOVETHISix.netcom.com> wrote: > > >>>>>>>>On Fri, 03 Aug 2007 19:13:04 +0000, Jonathan Kirwan wrote: > > >>>>>>>>> On Fri, 03 Aug 2007 11:35:19 -0700, Bill Ward > >>>>>>>>> <bw...(a)REMOVETHISix.netcom.com> wrote: > > >>>>>>>>>>On Fri, 03 Aug 2007 16:58:03 +0000, Jonathan Kirwan wrote: > > >>>>>>>>>>> On Fri, 03 Aug 2007 09:28:24 -0700, z <gzuck...(a)snail-mail.net> > >>>>>>>>>>> wrote: > > >>>>>>>>>>>>On Jul 27, 11:57 pm, kdth...(a)yahoo.com wrote: > > >>>>>>>>>>>>> So throw down on some none lies and irrelevancy on this > >>>>>>>>>>>>> SIMPLE TOPIC of the changing temperatures and CO2 levels > >>>>>>>>>>>>> according to the ice cores which show the lag of about 900 > >>>>>>>>>>>>> yrs for CO2 to temperature. > > >>>>>>>>>>>>Sure, that's easy enough for you to say. > > >>>>>>>>>>> Nowhere in his comment does he show any knowledge about the > >>>>>>>>>>> error bars in the ice core time measurements. I believe they > >>>>>>>>>>> quite often exceed 900 years. Not that it matters, as there > >>>>>>>>>>> wasn't 6 billion people on the planet at the time dumping huge > >>>>>>>>>>> quantities of CO2 into the atmosphere and no one is arguing > >>>>>>>>>>> that CO2 must always __lead__ a temperature rise, back then. > >>>>>>>>>>> CO2 levels can (as can CH4 levels) be driven by Milankovitch > >>>>>>>>>>> cycles, for example. > > >>>>>>>>>>OK, I'll bite. How can Milankovitch cycles drive CO2 and CH4 > >>>>>>>>>>levels without involving temperature? > > >>>>>>>>> Who said it didn't involve temperature? > > >>>>>>>>Then are you implying that rising temperatures from the > >>>>>>>>Milankovitch cycle caused the CO2 and CH4 to increase? > > >>>>>>> Yes, that consideration should be in the mix. > > >>>>>>>>It's not clear what you mean. > > >>>>>>> Sorry about that. > > >>>>>>S'OK, nobody's perfect. What other effects of the Milankovitch cycle > >>>>>>on CO2 and CH4 do you see in your "mix"? > > >>>>> My purpose was just as I said, that Kent's comment about a 900 years > >>>>> lag (whether taken from a factual source, or otherwise) isn't > >>>>> determinative. For (1), the error bars in the time measurements are > >>>>> rather wide in some places in the datasets and can easily wipe out > >>>>> something that appears to be a mere 900 yr lag. (In other words, > >>>>> it's possible that it is a lead and not a lag, at all, and that the > >>>>> errors in time measurement account for that difference.) For (2), a > >>>>> lag taken to be the actual case in some circumstances may very well > >>>>> be an effect or response and not a driving force and, due to > >>>>> atmospheric CO2's effect on warming itself, is a positive feedback > >>>>> factor enhancing another natural cause (such as Milankovitch cucles.) > > >>>>> For the current state of science on these things, one must be fairly > >>>>> comprehensive and study quite a few reports. I don't hold myself out > >>>>> as an expert in this area. Just an interested consumer of some of > >>>>> it. > > >>>>OK, fair enough, I'm about the same. The reason for my question was > >>>>your comment, "CO2 levels can (as can CH4 levels) be driven by > >>>>Milankovitch cycles, for example." > > >>>>I took that to imply the M cycle could directly affect something other > >>>>than temperature, such as CO2 and CH4. Apparently that's not what you > >>>>meant. > > >>>>On the original point, according to what I've seen, the CO2 vs > >>>>temperature lag was determined by correlation of the two datasets (T > >>>>and CO2) from each of a number of icecores from differing locations. > >>>>The lag is fairly consistent across cores. Error bars were calculated > >>>>normally (3 sigma?), and seem to rule out any lead of CO2 ahead of T. > >>>>Hence the assumption that CO2 cannot drive temperature. > > >>> A couple of comments here from my narrow and non-comprehensive > >>> perspective. > > >>> The lag is larger in portions of the data sets, large enough to exceed > >>> the error bars in time, so that in those places there is a fairly > >>> strong argument that a lag does in fact exist in those periods. That > >>> much I grant, from my own reading. > > >>> But this doesn't mean that every place it is a lag. > > >>On the average, though, when the noise is reduced, it's a lag. This is > >>how you find it: > > >>http://en.wikipedia.org/wiki/Cross-correlation > > >><begin quote> > >>Explanation > > >>For example, consider two real valued functions f and g that differ only > >>by a shift along the x-axis. One can calculate the cross-correlation to > >>figure out how much g must be shifted along the x-axis to make it > >>identical to f. The formula essentially slides the g function along the > >>x-axis, calculating the integral for each possible amount of sliding. > >>When the functions match, the value of (f\star g) is maximized. The > >>reason for this is that when lumps (positives areas) are aligned, they > >>contribute to making the integral larger. Also, when the troughs > >>(negative areas) align, they also make a positive contribution to the > >>integral because the product of two negative numbers is positive. > >><end quote> > > >>It's a common technique for finding signals lost in noise, or in this > >>case finding the time relation between two noisy signals. > > >>> Nor, even if it is > >>> always a lag in the past, does that mean that humans dumping the levels > >>> of CO2 we currently dump cannot present a lead effect. (And, in fact, > >>> we know the mechanisms by how this does work, as well.) > > >>That argument would be stronger if CO2 could be shown to actually have a > >>significant effect on temperature. As of now, it's an implicit > >>assumption in the climate models, which are generally stipulated not to > >>handle convective transport well, especially in the tropics. Water vapor > >>at 20000ppm may totally swamp 380ppm of CO2. > > >>> It remains that in some places it may still be a lead effect. In other > >>> words, I don't think the data RULES OUT the possibility, for example, > >>> of a CO2 intrusion from unusual volcanic activity having its impact on > >>> the environment. > > >>> In short, various circumstances may lead to similar outcomes. Just as > >>> in the case of "consumption," back a century and more ago, was caused > >>> by a variety of diseases with similar manifestations. > > >>> I completely disagree with your comment "that CO2 cannot drive > >>> temperature." This is NOT SHOWN by either theory or science result. > > >>I meant that in the context of the lag in the ice core data. CO2 has not > >>been shown directly to significantly affect climate temperatures. > > >>That's an assumption based on the IR absorption spectrum and climate > >>models of dubious value. > > >>>>The positive feedback you refer to is, I believe, derived entirely from > >>>>climate models and unconfirmed assumptions about the behavior of water > >>>>vapor in the troposphere. Given your interest in math, you may find > >>>>climate models interesting: > > >>>>http://www.giss.nasa.gov/tools/modelE/ > > >>> I do find them interesting, though I also find them prodigious to > >>> master. When I find the time to dig in as a hobbyist, I may do so. > >>> Until then, I will have to be satisfied with smaller bites. > > >>Good luck. I think the key to the puzzle will be found in assumptions > >>made in the climate models. > > > I don't have direct responses to your replies except that they don't carry > > much water with me. I am already fairly familiar with some quantum > > mechanics (1-D variety simplified versions usually taught in a course on > > basic QM), understand ideas of photon-electron interactions both in bound > > and unbound states, am aware of illegal state transitions like triplet > > states in lattices, and have a feel for the idea of mean-free path and > > thermalization. There is no doubt at all in my mind about both the > > theoretical as well as experimental results which confirm all aspects of > > these things. > > That's all very good, and quite applicable to CO2 radiative heat transfer. > Overkill, even. > > Now, how about the relative effect of convective heat transport via the > latent heat of water vapor? There's an solar powered elevator under every > cumulus cloud taking latent heat right past the GHG radiative transfer > region to cloud top, where it has a straight shot at radiating to the sky. And yet measurements show that latent heat isn't as large as you assume, this has been pointed out to you before but you just ignore it. Also even when at the top of the cumulus clouds the outgoing radiation is still not above the radiative transfer region and there CO2 is dominant. > > What about the cooling effect of cumulus clouds high albedo, and the > resulting strong negative temperature feedback? And the explicit > admission that climate models don't have enough resolution to > handle tropical moisture? How does CO2, constant at 380ppm, somehow > overwhelm water vapor, variable at 10000-40000ppm? This statement takes no account of the relative absorption coefficients of CO2 and H2O, also grossly exaggerating the concentration of water vapor doesn't improve your case! (the lowest end of the range is >100ppmv) > > How can you have "no doubt in your mind" without also understanding how > these phenomena work? Looking at only the one side you understand is > unlikely to yield accurate results, and is basically yielding to authority. > > > This is NOT a matter of assumption. > > I agree, but you seem to be assuming the AGW view of issues you are > unfamiliar with is correct, because you understand the physics of CO2. > I'm suggesting you question everything until you understand it. Make > people convince you. That's the basis of science. And it's a lot more > interesting than simply believing. > > Thanks for your comments. I wonder that you don't take your own advice, you make no attempt to understand the science that contradicts your preconceived ideas.
From: Jonathan Kirwan on 3 Aug 2007 23:48 On Fri, 03 Aug 2007 16:52:22 GMT, Jonathan Kirwan <jkirwan(a)easystreet.com> wrote: >The relationship between cartesian and polar co-ordinates is: > > x = r cos(theta) > y = r sin(theta) > >In this, of course, I mean that you can specify a point as either (x, >y) or else (r, theta), with r being the distance from (0,0) and theta >being the angle made between the positive going x-axis and the line >segment r. > >I will take the derivative as the first step: > > dx = cos(theta) d(r) - r sin(theta) d(theta) > dy = sin(theta) d(r) + r cos(theta) d(theta) > >I don't want to go too fast for you, though. So tell me if you agree >with the above, or not. And if you do understand it, I'll let you >take the next step and fill out the following for me: > > d^2x = > d^2y = > >If you can muster enough to do that, and I agree with your results, we >can then proceed to show one of the basic fundamentals in physics, the >arrival of the idea of angular momentum and its conservation in >central-force problems. Okay. So it's pretty obvious for now that some folks, namely Kent and claudiusdenk, are what Heinlein described as, "At best ... a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house." That out of the way, we can proceed. For the following equations, assume: x position x y position y r position radius z position angle v velocity vector v_x velocity along the x axis v_y velocity along the y axis v_r radial velocity v_t transverse velocity (perpendicular to the radial velocity) a acceleration vector a_x acceleration along the x axis a_y acceleration along the y axis a_r radial acceleration a_t transverse acceleration (perpendicular to the radial velocity) A area swept by planet and that prefixing 'd' means derivative and prefixing 'd^2' means the 2nd derivative. I'm also now going to change from 'theta,' as the angle, to 'z' as noted above. Again, to help make the equations a little less filled with text. So, d^2z is the second derivative of z and dz^2 is the first derivative of z, squared. Hopefully, that's clear. Recall the equivalences in mapping between a Cartesian (x,y) position and a polar (r,z) position. Namely: x = r cos(z) y = r sin(z) The first derivative of these is then: dx = cos(z) dr - r sin(z) dz dy = sin(z) dr + r cos(z) dz The second derivative is also then: d^2x = cos(z) d^2r - 2 sin(z) dr dz - r sin(z) d^2z - r cos(z) dz^2 d^2y = sin(z) d^2r + 2 cos(z) dr dz + r cos(z) d^2z - r sin(z) dz^2 These two can be simplified to: d^2x= [d^2r - r dz^2] cos(z) - [2 dr dz + r d^2z] sin(z) d^2y= [d^2r - r dz^2] sin(z) + [2 dr dz + r d^2z] cos(z) If you don't recognize this right off, let me tell you that this is also what a 2-D rotation looks like, though an angle of 'z'. But that will show up, shortly, as important. We can wait before jumping there. Now, acceleration is the second derivative with respect to time. a_x = d^2x / dt^2 a_y = d^2y / dt^2 I can easily introduce time into the above two earlier equations by simply dividing through by dt^2: a_x= [d^2r/dt^2 - r (dz/dt)^2] cos(z) - [2 dr/dt dz/dt + r d^2z/dt^2] sin(z) a_y= [d^2r/dt^2 - r (dz/dt)^2] sin(z) + [2 dr/dt dz/dt + r d^2z/dt^2] cos(z) Very simple and this is a very general statement about the relationship of polar and cartesian coordinate system accelerations. It can be arrived at through basis vectors, etc. But let's leave this here for now. Now, let's examine swept areas (which are equal to the concept of angular momentum.) We will discover an obvious relationship to the above. Imagine that we now impose an arbitrary acceleration vector upon our planet at point P at position (x,y), which is the same as (r,z). I am going to stop short of trying to draw a diagram here, in text, and will refer you to this drawing I just made: http://users.easystreet.com/jkirwan/new/images/acceler_orbits.gif You can easily see the a_x and a_y portions that make up the arbitrary acceleration, related to the fixed coordinate system. (Now, this acceleration we may think we know points back to the star at [0,0], but for now let's not make that assumption and just take this generally.) This forms a right triangle with the acceleration vector itself as the hypotenuse. Now impose another right triangle that also uses the same acceleration vector as its hypotenuse, but this time with the two sides being along the radial and the transverse directions. Different triangle, same resulting hypotenuse. To figure one from the other is just essentially a rotation of coordinate systems through some angle. In fact, this angle (if you look) is just the same angle as 'z' indicated above. This is: a_x = a_r cos(z) - a_t sin(z) a_y = a_r sin(z) + a_t cos(z) Note the similarity to these? a_x= [d^2r/dt^2 - r (dz/dt)^2] cos(z) - [2 dr/dt dz/dt + r d^2z/dt^2] sin(z) a_y= [d^2r/dt^2 - r (dz/dt)^2] sin(z) + [2 dr/dt dz/dt + r d^2z/dt^2] cos(z) By examination (I could derive these directly without inspection, but for these purposes I think inspection is good enough), you can see that: a_r = d^2r/dt^2 - r (dz/dt)^2 a_t = 2 dr/dt dz/dt + r d^2z/dt^2 Now let's look at the areas swept by a planet. If the angle is small, call it dz, then the path swept by the planet is r dz and the area swept is 1/2 r^2 dz. In other words, dA = (1/2) [r dz] [r] = (1/2) r^2 dz Let's hold off making that a rate by dividing through by dt, just yet, and go straight to the second derivative: d^2A = (1/2) [2 r dr dz + r^2 d^2z] = (1/2) r [2 dr dz + r d^2z] Dividing that now by dt^2, we get: d^2A/dt^2 = (1/2) r [2 dr/dt dz/dt + r d^2z/dt^2] Now, from Kepler's 2nd we also know that the rate of area swept is a constant. Thus, we know that: d^2A/dt^2 = 0 So, this means: (1/2) r [2 dr/dt dz/dt + r d^2z/dt^2] = 0 r [2 dr/dt dz/dt + r d^2z/dt^2] = 0 and since r may be non-zero, 2 dr/dt dz/dt + r d^2z/dt^2 = 0 Note that we have previously realized that: a_r = d^2r/dt^2 - r (dz/dt)^2 a_t = 2 dr/dt dz/dt + r d^2z/dt^2 So we know that a_t must be zero. In other words, the transverse acceleration must always be zero. Thus, any acceleration that is present must be entirely due to a_r, the radial acceleration part. Kepler's 2nd tells you that the acceleration MUST be radial and cannot be anything else. Furthermore, the reverse is also true. If there is no transverse acceleration present, if all acceleration happens to be radial, then the second derivative of area swept with respect to time must be zero and therefore the area swept must remain constant, regardless of what the radial acceleration (in the presence of zero transverse accererations.) In other words, the area swept is conserved in those cases. A little more discussion can point out that the only important part needed to figure out the rate of area swept (or the angular momentum, if you prefer) is to look at the transverse velocity. With that in hand, you know what you need to know. And this leads immediately to the realization that there is an important concept called angular momentum which is just another phrase for the same thing. Jon
From: Jonathan Kirwan on 4 Aug 2007 03:27 On Sat, 04 Aug 2007 03:48:22 GMT, Jonathan Kirwan <jkirwan(a)easystreet.com> wrote: >http://users.easystreet.com/jkirwan/new/images/acceler_orbits.gif Sorry, that should have been this one: http://users.easystreet.com/jkirwan/new/images/acceler_orbits_1.gif (I had unfortunately used 'w' in the earlier version instead of 'z'. Other than that, they are both the same.) Jon
From: Bill Ward on 4 Aug 2007 04:20
On Fri, 03 Aug 2007 19:59:31 -0700, Phil. wrote: > On Aug 3, 8:35 pm, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: <snip dead text> >> >> Now, how about the relative effect of convective heat transport via the >> latent heat of water vapor? There's an solar powered elevator under >> every cumulus cloud taking latent heat right past the GHG radiative >> transfer region to cloud top, where it has a straight shot at radiating >> to the sky. > > And yet measurements show that latent heat isn't as large as you assume, > this has been pointed out to you before but you just ignore it. Also even > when at the top of the cumulus clouds the outgoing radiation is still not > above the radiative transfer region and there CO2 is dominant. Do you have a link to those "measurements" of latent heat transport? I'd appreciate it if you can post one. The best estimate I've seen so far was the paper that assumed the total latent heat was equal to that in the total global precipitation, and IIRC, came up with ~78Wm-2 latent heat transfer, which is the absolute minimum bound. Any time water vapor goes up and precipitate comes down, the convection elevator is working, whether the ppt reaches the surface or not. Virga is one example, and the tremendous up and down drafts in thunderstorms is another. The "forcing" from CO2 doubling is supposed to be just a couple of Wm-2, which is far less than the uncertainty in the latent heat estimate. The CO2 may be "dominant" in the stratosphere because the water is frozen out, but still insignificant compared to water near the surface, because both the concentration and density are lower for CO2. >> What about the cooling effect of cumulus clouds high albedo, and the >> resulting strong negative temperature feedback? And the explicit >> admission that climate models don't have enough resolution to handle >> tropical moisture? How does CO2, constant at 380ppm, somehow overwhelm >> water vapor, variable at 10000-40000ppm? > > This statement takes no account of the relative absorption coefficients > of CO2 and H2O, also grossly exaggerating the concentration of water > vapor doesn't improve your case! (the lowest end of the range is > >100ppmv) I am being (excuse the expression) "conservative". One percent to 4 percent is IIRC, a reasonable range for surface water, while 100ppm would be quite rare. The stabilizing negative feedback effect of water likely swamps the effect of CO2, regardless of absorption coefficient differences. If you have links to any GC models that simulate microscale convective transport without parameterization, and that you understand well enough to discuss, please post them and we'll talk about it. I haven't seen any yet. |