Guest Post by Willis Eschenbach
The CERES dataset contains three main parts—downwelling solar radiation, upwelling solar radiation, and upwelling longwave radiation. With the exception of leap-year variations, the solar dataset does not change from year to year over a few decades at least. It is fixed by unchanging physical laws.
The upwelling longwave radiation and the reflected solar radiation, on the other hand, are under no such restrictions. This gives us the opportunity to see distinguish between my hypothesis that the system responds in such a way as to counteract changes in forcing, and the consensus view that the system responds to changes in forcing by changing the surface temperature.
In the consensus view, the system works as follows. At equilibrium, what is emitted by the earth has to equal the incoming radiation, 340 watts per metre squared (W/m2). Of this, about 100 W/m2 are reflected solar shortwave radiation (which I’ll call “SW” for “shortwave”), and 240 W/m2 of which are upwelling longwave (thermal infrared) radiation (which I’ll call “LW”).
In the consensus view, the system works as follows. When the GHGs increase, the TOA upwelling longwave (LW) radiation decreases because more LW is absorbed. In response, the entire system warms until the longwave gets back to its previous value, 240 W/m2. That plus the 100 W/m2 of reflected solar shortwave radiation (SR) equals the incoming 340 W/m2, and so the equilibrium is restored.
In my view, on the other hand, the system works as follows. When the GHGs increase, the TOA upwelling longwave radiation decreases because more is absorbed. In response, the albedo increases proportionately, increases the SR. This counteracts the decrease in upwelling LW, and leaves the surface temperature unchanged. This is a great simplification, but sufficient for this discussion. Figure 1 shows the difference between the two views, my view and the consensus view.
Figure 1. What happens as a result of increased absorption of longwave (LW) by greenhouse gases (GHGs), in the consensus view and in my view. “SW” is reflected solar (shortwave) radiation, LW is upwelling longwave radiation, and “surface” is upwelling longwave radiation from the surface.
So what should we expect to find if we look at a map of the correlation (gridcell by gridcell) between SW and LW? Will the correlation be generally negative, as my view suggests, a situation where when the SW goes up the LW goes down?
Or will it be positive, both going either up or down at the same time? Or will the two be somewhat disconnected from each other, with low correlation in either direction, as is suggested by the consensus view? I ask because I was surprised by what I found.
The figure below shows the answer to the question regarding the correlation of the SW and the LW …
Figure 2. Correlation of the month-by-month gridcell values of reflected solar shortwave radiation, and thermal longwave radiation. The dark blue line outlines areas with strong negative correlation (more negative than – 0.5). These are areas where an increase in one kind of upwelling radiation is counteracted by a proportionate decrease in the other kind of upwelling radiation.
How about that? There are only a few tiny areas where the correlation is positive. Everywhere else the correlation is negative, and over much of the tropics and the northern hemisphere the correlation is more negative than – 0.5.
Note that in much of the critical tropical regions, increases in LW are strongly counteracted by decreases in SW, and vice versa.
Let me repeat an earlier comment and graphic in this regard. The amounts of reflected solar (100 W/m2) and upwelling longwave (240 W/m2) are quite different. Despite that, however, the variations in SW and LW are quite similar, both globally and in each hemisphere individually.
Figure 3. Variations in the global monthly area-weighted averages of LW and SW after the removal of the seasonal signal.
This close correspondence in the size of the response supports the idea that the two are reacting to each other.
Anyhow, that’s today’s news from CERES … the longwave and the reflected shortwave is strongly negatively correlated, and averages -0.65 globally. This strongly supports my theory that the earth has a strong active thermoregulation system which functions in part by adjusting the albedo (through the regulation of daily tropical cloud onset time) to maintain the earth within a narrow (± 0.3°C over the 20th century) temperature range.
w.
As with my last post, the code for this post is available as a separate file, which calls on both the associated files (data and functions). The code for this post itself only contains a grand total of seven lines …
Data (in R format, 220 megabytes)
Nick , sorry if you’ve replied and I missed it but I don’t think so. It seems the simplest way to ask the question is: why would the “arithmatic” produce a correlation between (LW+SW-SW) and SW ?
You suggested a neg. corr. was a necessary consequence of the arithmatic and thus had no significance. I don’t see that.
Alec Rawls: “I think Willis and Greg need to look at this again. The more SW is reflected back into space by clouds the less reaches and warms the planet’s surface, reducing the amount of upwelling LW. Thus clouds should be expected to CAUSE the negative correlation between upwelling and SW and upwelling LW that Willis has found. (In other words, Jan and I have this right: we are talking about upwelling SW and we are talking about its negative correlation with upwelling LW, as documented by willis.)”
As I implied above, I agree with Mr. Rawls. There may well be a good reason to ignore the causal direction to which Mr. Rawls refers, but I have seen no clear explanation on this thread of what it is.
Causal direction. If it’s cloud that causes LW change, it raises the question : what causes the cloud?
1. External eg. Svensmark, oceanic or atmospheric tides …
2. SST => Willis
3. mutually caused oscillation arising from chaotic variability: chicken and egg.
WIllis: I find this analysis very interesting, but have some concerns about working with monthly temperature anomalies rather than absolute temperatures. Outgoing LWR varies with the fourth power of absolute temperature, not temperature anomaly. Temperature anomalies obscure relatively large seasonal changes in temperature. The mean global surface temperature is 3-4 degK higher in July, than in January, a roughly a 20 W/m2 seasonal difference in average surface emission. The roughly +/-1 W/m2 variation in LWR and SWR anomalies in your Figure 3 represents the small differences after correcting for much larger seasonal changes with anomalies.
A number of people have tried to calculate feedbacks using the seasonal change in surface temperature and TOA radiation. The latest effort (and references to earlier work) can be found at the link below. The paper looks at outgoing LWR and SWR from all skies, clear skies and cloudy skies and conclude that cloud radiative feedback is small. Interestingly, reflected SWR from CLEAR skies (and all skies) decreases 4-5 W/m2 as mean global temperature rises 3+ degK every year, probably due to less reflection from snow and ice-covered surfaces during summer in the NH. In contrast, reflected SWR from cloudy skies increases about 1 W/m2 as the global warms 3+ degK. (They don’t tell us how much the cloud fraction changes with the season, but the all-skies result shows that the most important SEASONAL change in SWR comes from clear skies.) None of my comments are meant to imply that your analysis is wrong; just that other interesting methods have been applied to the same data set you are using.
http://www.pnas.org/content/110/19/7568.full
Greg says: January 9, 2014 at 1:41 am
“Nick , sorry if you’ve replied and I missed it but I don’t think so. It seems the simplest way to ask the question is: why would the “arithmatic” produce a correlation between (LW+SW-SW) and SW ?”
Well, I said above that the formula for correlation of A with B-A is
ρ=(σ_B ρ_AB – σ_A)/sqrt(σ_A^2+σ_B^2)
There’s an error in the denominator, which doesn’t affect the sign; it should be
ρ=(σ_B ρ_AB – σ_A)/sqrt(σ_A^2 + σ_B^2 – 2ρ_AB σ_A σ_B)
Setting the sd ratio r=σ_A/σ_B, that gives:
ρ=(ρ_AB – r)/sqrt(r^2 + 1 – 2ρ_AB r)
Now ρ_AB is between -1 and 1. If r>1, ρ must be negative. For any r, the centre case is ρ_AB=0, when ρ=-r/sqrt(r^2 + 1). The -r in the numerator is a consequence of the B-A “arithmetic”, and creates a tendency to negative ρ.
But again, I’m not claiming that ρ is always negative. I’m saying that it happens in so many cases that there’s nothing to be concluded just from a case where it proves to be so.
“the formula for correlation of A with B-A is”
but I don’t see A with B-A , I see A with B+A-A
Greg says: January 9, 2014 at 2:56 am
“but I don’t see A with B-A , I see A with B+A-A’
The original problem had measured Tot and SW. LW is calculated as Tot-SW, and was correlated with SW. That is, Tot-SW with SW. B-A with A.
I say we either use the Ceres data or we get rid of all the people and the funding used in operating the instruments.
Whenever someone (Willis in this case) finds something particularly insightful with climate data or climate monitoring devices/systems, the pro-AGW’ers pile in and say you can’t use that particular system. A long series of mostly incoherent posts continue until that person loses faith in their newfound insight.
Meanwhile clime science goes on wasting millions of dollars per year continuing to operate the systems (that the pro-AGW’ers say we can’t use). And then the pro-AGW’ers continue on writing papers using the same data from the same systems.
This data presented by Willis is particularly insightful. It answers a huge question with respect to the theory. What do clouds do (or total SW reflectance which is more comprehensive than clouds by themselves anyway) when there is warming.
The feedback is negative and the data says it is a large negative. Opposite to the theory.
ρ=(σ_B ρ_AB – σ_A)/sqrt(σ_A^2 + σ_B^2 – 2ρ_AB σ_A σ_B)
I’m not sure how you derived that but by symmetry it looks like a term has been lost in denom:
ρ=(σ_B. ρ_AB – σ_A)/sqrt(σ_A^2 + ρ_AB^2.σ_B^2 – 2ρ_AB σ_A σ_B)
??
“Tot-SW with SW. B-A with A.”
I can see there could be problem with measurement errors and variation not related to SW,LW relation correlating, since both are surely present in large doses. But isn’t that the point of signif estimations?
Can you suggest a formula for 95% confidence value of correlation coeff ?
Willis Eschenbach says:
January 8, 2014 at 9:45 pm
Phil. says:
January 8, 2014 at 5:33 pm
… “For particles much larger than the wavelength of the incident light, the scattering efficiency approaches 2. That is, a large particle removes from the beam twice the amount of light intercepted by its geometric cross-sectional area. What is the explanation for this paradox?”
Ah, I finally see the problem. The meaning of “incident” was unclear. To everyone out here, the “incident light” is all of the light that is affected by the object in question, and “non-incident light” is the light that is unaffected by the object.
To you, “incident light” is the NOT the amount of light intercepted by the actual phenomenon. Instead, it is just a number, it’s the light intensity times the cross-sectional area of the particle. As such, to you the incident light does NOT include all of the light affected by the phenomenon. In your terminology, some “non-incident light” is also affected.
It’s a problem with specialists, they forget that the words that have special meaning within a discipline do not have the same meaning to the general public.
Because to us, if light is getting either scattered or absorbed by a particle, then perforce it is “incident light”, and the light that is not scattered is not incident light.
But to you, the light being scattered by a particle is NOT incident light.
As a result, when you say that a particle can absorb 100% of the incident light and also reflect 100% of the incident light, folks like myself say “huh”?
Since you are the specialist, this misunderstanding is on you. When you use a term in some non-standard way, you owe it to your readers to point that out … because there’s no way that your readership can be expected to understand your non-normal use of the term.
Thanks for persevering, I finally got the answer to my “huh”?
Thank you for persevering too, to me the light incident on a droplet is as you say above the cross-sectional area multiplied by the light intensity. The explanation was included in the article I cited. The light scattered is additional to that so the drops remove more light from the beam than falls on that drop. The same phenomenon is observed in macroscopic objects, e.g. we know how much sunlight falls on the earth, it’s the cross sectional area multiplied by the solar irradiance, you’ve calculated it many times. However, if you were out at Jupiter’s orbit observing the sun and earth transited the sun the amount that the sunlight would reduce by is twice that value.
I disagree that my use of ‘incident’ is non-standard, the dictionary definition is:
“(esp. of light or other radiation) falling on or striking something.
“when an ion beam is incident on a surface””
As a scientist I use the language precisely, people reading what I write should take that into account (no criticism intended).
The original reason for my comment was that ‘clouds absorb all the IR incident on them’, the point of my comment was that this is impossible because half of the light incident on the cloud will be scattered and for drops smaller than the incident light wavelength half of that light will be backscattered out of the cloud. In that situation the maximum which could be absorbed would be 75%, I hope that’s clear?
That phenomenon is in fact how drop size in clouds can be measured by remote sensing of that backscattered light.
By ‘backscatter’ I mean light directed in the 180º back towards the observer.
Willis Eschenbach says:
January 8, 2014 at 3:46 pm
Ok, but the important question to ask is why should the albedo increase, and I cannot find any reason for it to do that.
An alterative explanation for the correlation you have found is as follows:
I think we can take for granted that there is a very strong correlation between incoming SW and reflected SW. If the albedo is constant the correlation = 1.
I think we also safely can take for granted that there is a strong correlation between incoming SW radiation and temperature in both the atmosphere and the surface. More incoming SW gives more heating which gives higher temperature.
Likewise, there is of course a strong correlation between the surface temperature and the LW radiation. There is also a strong correlation between atmosphere temperature and LW radiation from the atmosphere.
Because incoming SW is correlated to reflected SW, and incoming SW is correlated to temperature, which is correlated to LW, we then have that reflected SW is correlated to LW.
/ Jan
“The original reason for my comment was that ‘clouds absorb all the IR incident on them’, the point of my comment was that this is impossible because half of the light incident on the cloud will be scattered”
cf
“Each droplet in the cloud will absorb ~100% of the incident light and also scatter an equal amount of the incident light.”
What you originally wrote was mis-worded. Whatever the complexity of the mechanisms involved it is incorrect to say ” absorb ~100%” and “scatter an equal amount” ie “~100%” of the same thing (whatever it’s called and how it is defined).
If you had originally said “half of the light incident on the cloud will be scattered”, I’m sure it would have been understood perfectly and would have effectively corrected whoever it was that said a cloud absorbed all incident IR.
This is quite a significant point because the downward LWIR from clouds is usually described as being re-emitted which implies assumptions about spectral content.
I would imagine that MODTRAN / HITRAN model this correctly, however, that some false assumptions are being made by climate modellers or in calibration and interpretation of satellite data seems quite possible. Could such an issue contribute to the CERES TOA budget imbalance?
Thanks for highlighting this important distinction.
By arithmetic. If LW=measured Tot – measured SW, and you correlate LW with SW, you’re measuring how changes in SW match changes in LW. But if SW rises by 1 unit, for whatever reason, , that guarantees a drop component of 1 unit in LW, to which is added a statistical change in Tot. That guaranteed component (via -SW) weighs heavily and artificially in the correlation.
No, it doesn’t, that’s only true if the total is a constrained constant. Think of it the other way around. Suppose that one were directly measuring LW and SW and inferring the total, as it makes it easier to review the possibilities and is, of course, the exact same problem. We have four possibilities: LW and SW go up; LW goes up, SW goes down; LW goes down, SW goes up; LW and SW go down. In two cases LW and SW covary and are positively correlated, in two cases LW and SW countervary and are negatively correlated.
The total will, of course, go up and down more strongly with the positively correlated cases and will remain more nearly constant with the negatively correlated cases, but recall, it is not constrained to be constant and in fact it varies, strongly, all of the time everywhere.
I believe that this is Willis’ point. In fact the have a strong tendency to countervary and in fact are fairly decisively negatively correlated. This makes sense in a model that is essentially stable and I don’t find it surprising, but I don’t think it is in any sense “built in” to the numbers themseleves.
The big question is whether or not it is consistent with the positive feedback, high climate sensitivity models. There I am not convinced that the argument is sufficient, or even necessarily relevant. The problem I have comes from several issues — one is that Willis is using SW, if I understand it correctly, primarily as a proxy for the effect of high-albedo daytime clouds, snow, ice, and the lower amplitude modulation of albedo due to deciduous vegetation and cropland utilization. The Sun’s TOA insolation variability is, after all, nearly constant on a daily basis even though it varies substantially (91 W/m^2) over a year.
Suppose albedo varied completely randomly and due only to clouds. Then what would we expect that LW radiation to do? Well, one thing we would expect it to do is vary in any give cell completely in tandem with the seasons and average seasonal temperature. The way seasons work, we’d expect “ground” LW to vary the same way, but with a lag — it takes time to warm or cool any given parcel in response to a change in solar-inclination forcing, and of course a lot of the response comes not from a direct effect but from indirect effects like the delivery of a pre-cooled arctic air mass down to North Carolina that in no way reflects the actual solar-inclination local equilibrium. So there is a lot of energy transport and noise. Still, one major component of LW varies only with the ground temperature, and that co-varies with the seasonal SW. We’d expect a strong positive correlation between the two on the basis of this alone.
However, life is never that simple. First, the data is seasonally detrended. Basically, this means that this huge positive correlation is thrown away. Second — and remember, we’re still asserting completely random clouds here — LWIR doesn’t come just from the ground. Let’s assume that there are three components to the LWIR — one is direct ground radiation (clear sky). One is indirect radiation from greenhouse gases at a band of heights approaching the top of the troposphere and is temperature suppressed. The third is from the random clouds, which block the ground radiation and replace it with more weakly temperature suppressed broadband radiation from an intermediate height (but which also represent a substantial amount of latent heat carried aloft).
Let’s consider clear sky as the baseline. Albedo is low, SW emission is seasonally adjusted “normal”. LW is also seasonally adjusted “normal”. A random cloud wanders by. Albedo rises. SW increases. The cloud blocks LW from the ground, replaces it with LW from the cloud in the unblocked bands and alters a bunch of things nonlinearly in the air above the clouds but I would have to say that the net daytime effect is going to be a decrease in LW. Consequently, even if the clouds were 100% randomly generated, utterly decorrelated from any cause, I’d expect a general negative correlation between SW and LW (which could be overridden, one imagines, by nonlinear transport phenomena e.g. the movement of warm wet clouds into an area that would ordinarily be much colder, as will happen in a couple of days in NC when we get a warm air mass pulled up from the Gulf.
Hence my inclination is to say that what Willis is showing isn’t a demonstration of a causal connection, but something one would predict as a natural feature of “the way clouds work”. So I agree that there is some sort of problem here with the conclusion, but it isn’t because statistical differences of unconstrained quantities “have” to countervary — they don’t, and the result isn’t a statistical artifact — it is an expected feature of the radiation dynamics of clouds. Clouds almost always increase SW and decrease LW over their daytime area, so given that nearly all areas have some average cloud coverage, nearly all areas will exhibit a negative correlation once one has subtracted the probably dominant positive correlation between SW and LW due to seasonal variations out.
The test for this is simple enough. In the map Willis shows above, the areas with positive LW/SW correlation are — deserts. There there is no cloudiness, and LW and SW vary weakly together, even after seasonal adjustment. Where is it strongest over land masses? Places where there is lots of ice and/or are very elevated, and rain belts.
So I’m not at all convinced that the negative correlation is meaningful, but not for the reason you describe. It is because I don’t see how it could be otherwise, given the TOA spectrographs for cloud covered regions in e.g. Petty. It’s just the way clouds work.
I think what Willis WANTS to show is going to be more difficult to show than this. In fact, I think it can only be shown by searching for lagged dynamic fluctuation autocorrelation, not static correlation. It is the parcel that heats and then clouds appear to cool it that is what he is trying to show, but merely showing the clouds are correlated with increased SW and decreased LW does not accomplish it. We already know that.
rgb
Thanks, that clarifies a lot. Nice and clearly put.
I think Willis’ original post on this was looking at the hour of onset of cloud in a band across the equatorial Pacific. It is probably in high temporal resolution data that the phase response can be found to prove such an effect.
There’s generally too much detrending , deseasonalising and incorrectly sampled decimation and averaging going on in climatology. This probably fine if you start out prove everything is “stochastic” noise + CO2 , but often impedes a more serious system analysis.
…if the emitted radiation must equal the incoming radiation (so the earf does not experience an increase or decrease in temperature)… Then what energy forms all that corn, wood, grass, algae and other plant matter? Is that so trivial as to be negligible?
Stephen Rasey: “In the CERES dataSET 12 pm, 1 pm, 2pm, 3pm, etc. coverage comes from low resuolution geosynchronous MODIS data from GOES satellites, that are converted (SOMEHOW!!) into CERES data”
Willis Eschenbach: “[E]ach one of the three satellites images about half of the planet every day.”
Pardon me for kibitizing, but I had hoped that someone who’d slogged through the documentation could answer Mr. Rasey’s question question, and it’s not clear to me that Mr. Eschenbach did.
Mr. Rasey says there are only two sun-synchronous low-orbit satellites but that the data purport to give an output value for each hour at each location. Mr. Eschenbach says there are three such satellites. Given a 99-minute orbit and a horizon distance of about 2900 kilometers, it seems that each satellite would view every equatorial location for about a 13-minute stretch each day and about a 13-minute stretch each night, with higher-latitude locations getting more exposure because of path overlap: each satellite would see every location every twenty-four hours.
But even if there are three sun-synchronous satellites and they are optimally spaced, wouldn’t each equatorial site be visited only once every four hours?
Brian says:
January 9, 2014 at 8:09 am
Hi Brian
The thing is that energy cannot be destroyed; it can only be converted to another form of energy. That is one of the fundamental physical laws.
So all the energy that forms corn, grass and other biomass will be stored as chemical bound energy until that biomass is eaten, burned, rot or in other way disappears.
Then that chemically stored energy will be released as heat and radiated as longwave radiation back to space.
/ Jan
@Nick Stokes- Actually, them being negatively correlated (and the stronger, closer to negative one the better) means *exactly* what Willis “wants it to mean.”
What you are not grasping is that Willis’s hypothesis is essentially equivalent to dTot/dt = 0. Therefore he has devised exactly the right sort of test to see if that should be so, for the reasons he thinks.
The only real problem is, he should be testing to see if the correlation is significantly different from -1, not significantly different from 0. Because *if* dTot/dt = 0, always and everywhere, the correlation will be exactly -1, and if Willis *doesn’t* find that correlations are signficantly different from -1, he would *fail to reject his hypothesis* that dTot/dt = 0.
Greg says:
January 9, 2014 at 6:59 am
If you had originally said “half of the light incident on the cloud will be scattered”, I’m sure it would have been understood perfectly and would have effectively corrected whoever it was that said a cloud absorbed all incident IR.
And as I pointed out above half of that would be backscattered under certain circumstances and so be downward LWIR. This is independent of any blackbody radiation emitted from the droplets which is another component of LWIR.
This is quite a significant point because the downward LWIR from clouds is usually described as being re-emitted which implies assumptions about spectral content.
These are two components to the LWIR, the backscatter would depend inter alia on the drop size distribution of the cloud, the emission will depend on the drop temperature.
Willis:
Willis Eschenbach Jan 8 11:39 pm
Not sure where you got that idea [that CERES data is mostly GOES]. Actually, the CERES instruments are flying on four different satellites, Aqua, Terra, TRMM, and Suomi NPP. Three of these have polar sun-synchronous orbits, with different equator-crossing times. They are at 750 km altitude and scan limb-to-limb. The fourth one, TRMM, flies at 350 km altitude at a 35° inclination to the poles.
Next, since they image limb-to-limb, that means that the three polar satellites are each sampling a swath ≈ 6,000 km across. And as you pointed out, they are sun-synchronous, one orbit per day. This means that each one of the three satellites images about half of the planet every day.
In other words, most of the input to CERES is from the four CERES satellites, and there is terabytes of it..
Here is where I got my facts:
From Rasey 10/10 8:35 am
10/8 13:33 – Terra:
Period = t = 98.8 min
Distance to Horizon a Perigee = 2767. km
Distance between passes = Ve*t = 2737 km
Grid Cells between passes = 24.7 cells
Grid Cells between 45 deg oblique on each pass = 12.7
Descending pass at 10:30 am
So an equatorial grid cell will see Terra overhead at 10:30 am. Technically, it will see Terra on the horizon (of questionable usefulness), at 8:51 am and at 12:09 pm. Realistically a grid cell gets one overhead pass or two oblique passes per day from Terra.
As you point out, CERES flies on more than Terra. But Aqua, Auro, and Suomi NPP all have 13:30 equatorial passes. Aqua and Aura are in the same train, about 8 minutes apart. Suomi NPP is a few km higher with a period slightly longer, but with still maintains a 13:30 equator pass. So these three satellites are more redundancy than increased in temporal coverage.
TRMM flies below half the height of the others, so covers half the area per pass, so no oblique overlap. It is at an inclination of 35 deg so TRMM doesn’t see beyond 40 deg north and south.
So there you have it. If the CERES dataset has global hourly coverage, then most of it must come from the geostationary imagers. Each grid cell (in the tropics) sees the CERES instrumentation between 3 to 5 times out of 12 daylight hours per day. Likewise for the night hours. The other hours have to be filled from GOES.
All this is in support of the main question. “Is the CERES dataset what you think it is?” There has been a lot of processing, some infill to “minimize temporal sampling errors”, and that “smoking gun” adjustment to reduce a 5 W/m2 systemic error to Hansen’s 0.75 W/m2 hypothesized error. In all those passes through the black box, are some of the correlation mathematical artifacts? I BELIEVE the negative correlations are REAL; it makes sense. But I also believe the dataset is dirtier than it appears at first blush.
Willis: I have a scale and I’m weighing married couples.
A thousand people enter a weight loss program, and we measure before and after weights and their difference: d = a – b (difference = after – before.) We discover that d is negatively correlated with b and infer, voila, that the weight loss is negatively correlated with initial weight, and positively correlated with final weight. Did the initially heavier people lose less weight, on average? or did the finally heavier people lose more weight? Maybe, maybe not. You have an equivalent example showing the maybe, which in my comment I admitted might be true in your energy flow analysis. But maybe not, and your energy flow analysis does not rule out the equivalent maybe not..
Do you want me to provide an example, or would you like to work one out on your own, as a challenge to yourself? I’ll let you think about it a while. The key is to think of a case in which the measurement error in a and b is large relative to the change d.
Willis Eschenbach says:
January 8, 2014 at 2:17 pm
Bulsit says:
January 8, 2014 at 12:15 pm
In atmosphere temperatures gases dosen’t practically emit or absorb any heat radiation (emission/absorbing factor 0,002 aprox), only in higher temperatures over 600C you can measure something like 0,05, in 1500C something like 0,2.
Dear heavens, the fog is thick out there today.
Yes, Bulsit, there is an emissivity for gases … but no, it’s not 0.002. For any particular gas, he emissivity depends on the frequency of the radiation, and varies from 0 to about 1. See the flux emissivity tables and discussion here.
And don’t try to impress us with your wisdom until you have some. Your claim is patent nonsense that any serious researcher would just laugh at.
w.
Pretty strange that atmosphere behaves under different Physical laws than those coal fired power plant boilers. There is absolute nothing radiative heat transfer which we can use under 500 C fluegas temperatures. CO2 is approx 12%. And when we design those boilers we can do pretty good measurements how the heat transfers from fluegases to pipes and how we have managed to calculate heat transfer surfaces. i don’t know who laughs, boilers and how they work aren’t for sure nonsense.
@Willis Eschenbach at 1:55 pm
RE: PLOT: Seasonal Cycles removed Negative or weakly positive correlations worldwide.
PLOT: Seasonal Cycles Not Removed Strongly positive correlation above 35 deg latitude, strongly negative in tropics.
My apologies for missing that plot last night. Yes it is curious. I guess I can understand positive correlation poleward of the circles (Higher SW and Higher LW during polar daylight). I am surprised to see it that strong at 50 N and even a far south as offshore Baja California.
I’m not sure removal of the seasonal signal should be taken for granted. The story in the polar and high temperate regions might change.
But I gather these are still a full year’s data all lumped together. Is it easy to show this plot only for one or two months, such as Jun-July, Dec-Jan (polar extremes) or Mar-Apr (equinox)?
Greg says: January 9, 2014 at 4:36 am
“I’m not sure how you derived that but by symmetry it looks like a term has been lost in denom:”
I just took cov(A,B-A)=cov(A,B)-cov(A,A)
and juggled sd’s to convert to correlation coefs. The denominator is sd(B-A). I think it’s right (it’s like cos rule); your version is the sqrt of a perfect square.
rgbatduke says: January 9, 2014 at 7:02 am
‘That guaranteed component (via -SW) weighs heavily and artificially in the correlation.’
No, it doesn’t, that’s only true if the total is a constrained constant.
I think it does, and the formula I gave for corr(A,B-A) shows it:
ρ=(ρ_AB – r)/sqrt(r^2 + 1 – 2ρ_AB r), r=σ_A/σ_B
You’re saying it’s only true if σ_B=0 (r very large). Well, that certainly ensures ρ negative, but for that it’s enough that r>1, so certainly r>ρ_AB. The point is that having a -A in there by construction puts the -r in the numerator, which weighs heavily toward negative values.