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)
1sky1 says:
January 8, 2014 at 4:17 pm
Sky, sorry if I misunderstood you. You said:
Since you gave airborne dust as an example of just such a “critical factor”, I was merely saying that no, airborne dust was not in any way critical. As the volcanoes have demonstrated, airborne dust does little to the global temperature.
w.
Konrad says:
January 8, 2014 at 6:02 pm
Phil. says:
January 8, 2014 at 5:39 pm
“CO2 does not emit more IR radiation than it absorbs.”
———————————-
Perhaps you might reconsider that claim.
Certainly not, though you perhaps should consider reading the context in which it was made.
Trick says:
January 8, 2014 at 8:56 pm
“Not glorious. Just the ordinary CERES observations of LWIR data posted and discussed by Willis show your small experiments don’t resolve for the earth system at large. In the past, I’ve responded with links to papers and texts showing you the physical reasons.”
———————————————————————————
You were right about that, not glorious at all. Rather pathetic really.
You were asked a specific question about a specific experiment and you come up with some waffle about “the earth system at large”.
Again I ask if you can give a clear and direct answer to the question. A or B. Will the water in the experiment either –
A. freeze
or
B. rise toward 80C?
Perhaps another reader can help Trick out?
janus says:
January 8, 2014 at 5:31 pm
While there are ignorant people, the only ignorant questions are the ones you don’t ask, they are the questions that keep people ignorant.
First, as to the difference, my value is the top-of-atmosphere (TOA) measurement averaged over the surface of the earth. The earth absorbs radiation based on its cross-section. However, the surface area is four times the cross-sectional area, so the total amount needs to be divided by four to give a global 24/7 average.
At the TOA, the “solar constant” is about 1360 W/m2. But since the surface area is four times the area intercepting the 1360 W/m2, the global average is a quarter of that, 340 W/m2.
As to the Wiki quote, they are not looking at a global 24/7 average value as I was. The are looking at a tropical noon-time instantaneous value. As they point out, that’s about a kilowatt per square metre.
However, things are nowhere near as accurate as Wiki claims. The proportions of UV/Near IR/Visible Light are about right, but the amount of energy received at ground level varies greatly with the transmissivity of the atmosphere. Something on the order of 80 W/m2 are absorbed in the atmosphere on a global 24/7 average, but in the tropics, because the downwelling amount is greater and it is an instantaneous measurement, the absorption is greater. As a result, it’s unusual to see noontime values over a kilowatt, although they definitely do occur. My point is, it’s not “1005 W/m2” as the wiki says.
w.
Phil. says:
January 8, 2014 at 5:39 pm
The GHGs definitely emit more IR radiation than they absorb. This is because the atmosphere is warmed by four different sources—absorbed light (~80 W/m2), sensible heat from the surface (~80W/m2), latent heat from the surface (~100 W/m2), and radiation from the surface (~350 W/m2).
This is a total of 610 W/m2 being absorbed by the atmosphere (global 24/7 averages), of which 350 W/m2 comes from radiation absorbed by the GHG (mostly water vapor and CO2).
Of course, since the gaining 610 W/m2 constantly, the atmosphere has to also lose 610 W/m2 constantly
But all of that energy is lost from the atmosphere by radiation. And all of the radiation is coming from GHGs.
As a result, we can say that atmospheric GHGs including CO2 most assuredly are radiating more energy than they are absorbing, in the ratio of 610 / 350.
w.
Phil. says:
January 8, 2014 at 9:04 pm
————————————–
I see that Willis has added a little more “context” 😉
Phil. says:
January 8, 2014 at 5:33 pm
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”?
w.
Willis Eschenbach says: January 8, 2014 at 8:47 pm
“I see the problem. You’ve assumed that the measurement creates the reality. In your example, you are assuming that the underlying physical relationship is that the independent variables are variable A, AND THE TOTAL B, with the other variable C=B-A dependent on the other two.”
Correlation works on the numbers as measured. That’s A and B, or SW and Tot. The point of the coin example is that you get a negative correlation with B-A which does not tell you about the reality of anything. The coins have no correlation.
Just the same arithmetic is done with SW and Tot. If the coins with no correlation gave a neg correlation for the difference, you can’t infer any useful relation between SW and “LW” from exhiibiting the same behaviour. You don’t know a priori about any underlying reality – you’re trying to infer it from the correlation. Measurement is all you have.
People keep making the claim that if on average the anomalies of LW and SW sum to zero, that A and B must perforce be negatively correlated. Nick even put forth a flawed attempt at a proof. However, it’s not true.
Consider the result of the following series of paired observations, which are randomly generated pseudo-anomalies of LW and SW.
LW, SW
-2.9, -2.2
-14.2, -13.0
5.3, 7.2
0.5, 0.4
2.9, 1.8
2.6, 1.5
-2.4, -3.0
2.7, 2.7
2.4, 2.2
3.1, 2.3
Here’s the oddity. They sum to zero … but their correlation is 0.98. Why? Because basically they move together, but their overall mean is zero.
In other words, even if the sum of two anomalies is physically constrained to be zero over a sufficiently long period of time, there is no special requirement that the two anomalies be negatively correlated.
The data was generated by the following R code:
# generate ten random numbers
LW = rnorm(10, sd=4)
# generate ten more random #s, with the mean of each random number generation
# equal to the corresponding value of LW
SW = rnorm(10, mean=a)
In other words, all I did was require that SW anomalies be correlated to LW anomalies, and as long as the mean of the LW anomalies is zero, the mean of the sum will be zero.
But wait, as they say on TV, there’s more. Here’s another example:
# generate 100,000 random normal pseudo-longwave
# radiation observations, mean 240, standard deviation = 42
# mean and sd values from CERES LW data
LW = rnorm(100000, mean=240, sd=42)
# 100,000 random pseudo-shortwave radiation observations, mean 100, std. dev. = 72
# mean and sd values from CERES SW data
SW = rnorm(100000, mean=100, sd=72)
mean(LW+SW)
# 339.998
cor(LW,SW)
# -0.0014
You see what I’m getting at? The fact that in the long run the longwave (avg. 240 W/m2) and shortwave (avg, 100 W/m2) are constrained to sum to the solar value (avg. 340 W/m2) does NOT mean that they have to be negatively correlated. They can be positively, negatively, or un-correlated and still sum to the solar value.
w.
@Willis Eschenbach at 8:47 pm reply to Nick Stokes
You’ve assumed that the measurement creates the reality.
It is possible you and Nick are both correct.
CERES data from the TERRA, AQUA, AURA satellites may record the individual components of the flux and the correlations are real and not mathematical artifacts.
But again, let’s remember the provenance of the CERES dataSET. It is mostly GOES-MODIS data that is calibrated (SOMEHOW!!) into a CERES look-alike data format. It is also “Adjusted”
To me it is an open question whether the GOES data recalibration into CERES-like data might create a non-zero, and likely negative correlation coefficient. If the correlation is not generated from the GOES conversion, it might still result from the adjustments they made to close the 5 W/m2 gap in the total.
So, Willis your B = A + C example may be correct if the CERES dataset was pure CERES collected data. But it isn’t. CERES instruments are in solar synchronous orbits, in just two orbital planes. CERES instruments cover no more than 4 out of the 24 hours of the day. The rest of the dataset comes from GOES+mathematical magic.
Nick Stokes may have a point given how much of the CERES dataset comes from some fuzzy GOES recalibration process and fuzzier adjustments to partially close a gap.
Nick Stokes says:
January 8, 2014 at 10:20 pm
Thanks, Nick. You are confusing the reality with the measurements. Let me try it again with your coin example.
I’m flipping two coins. I dub one of them LW and the other SW. I flip both of them at once, and in my notebook I write down a pair of values plus their total. I get something like this:
LW, SW, TOT 1, 0, 1 0, 1, 1 0, 0, 0 1, 1, 2 0, 1, 1 1, 0, 1 1, 1, 2 0, 1, 1 1, 1, 2 0, 0, 0Now, I send the notebook page to you … but unfortunately, it gets caught in a letter-sorting machine and torn in half, and all that you receive is the following:
SW TOT 0, 1 1, 1 0, 0 1, 2 1, 1 0, 1 1, 2 1, 1 1, 2 0, 0You, being Nick Stokes, are not so easily deterred. You know that you can reconstruct the value of the LW observation from the total and the SW observation. So in each case you calculate the value of the LW as the Total minus the value of the SW coin.
Now … does the fact that you are calculating the value of LW as (Total minus SW) imply that the values are negatively correlated?
I say no. I say that the reality is not affected by how you calculate it. If LW and SW are correlated in reality, then the calculation of LW will reflect that. The reality is not driven by the calculation method.
Having read your posts for some years now, however, I strongly suspect that even this clear exposition plus the computer code above plus the post from Dr. Robert Brown from Duke (rgbatduke) will fail to convince you. After all, they don’t call you “Racehorse Stokes” for nothing—as far as I know no one has ever actually witnessed you admitting that you were in error … but that doesn’t matter, I’m writing for the lurkers.
w.
Willis,
“there is no special requirement that the two anomalies be negatively correlated.”
Indeed. The formula for correlation of A with B-A is
ρ=(σ_B ρ_AB-σ_A)/sqrt(σ_A^2+σ_B^2)
ρ corr coef, σ sd
So yes, you can get positive correlation with large positive ρ_AB (and negative with negative). But you’re reasoning the other way around. The two quantities don’t have to be negatively correlated. But they can be without it meaning what you want it to mean.
Mosher writes “The irony burns.” in response to Willis’
“Scientists may be wrong, and often are. But when you think you’ve uncovered a “major error”, something really obvious, well, you should check your facts very carefully before uncapping your electronic pen ”
Well I think its a major error to be relying so heavily on GCMs for “science”
Things that make you go hummmm include the following extract from CMIP3 model constant section.
http://map.nasa.gov/ModelE_html/html_code/src/CONST.f.html#CONSTANT
!@param lhe latent heat of evap at 0 C (2.5008d6 J/kg)
real*8,parameter :: lhe = 2.5d6
!@param lhm latent heat of melt at 0 C (334590 J/kg)
real*8,parameter :: lhm = 3.34d5
The Cloud module is FULL of unreferenced constants. Soon, I’ll be able to definitively say its a fit and document it but for now I’ll simply marvel at the sloppiness of the implementation.
Will that count as an “uncovering” ?
Stephen Rasey says:
January 8, 2014 at 10:45 pm
Not sure where you got that idea. 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..
As to your question about how the MODIS and GOES satellite data is integrated in the data processing, there’s a good overview here.
w.
Jan made the same point I did:
Willis answers:
Greg Goodman offers a similar reply:
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.)
Cloudiness could also be an effect of increased GHGs (Willis’ thermostat hypothesis). The extra heat trapping (lower upwelling LW) causes increased evaporation and increased cloudiness that reflects more SW back into space. This direction of causality also produces anti-correlation between upwelling SW and LW. My initial suggestion was that the causality in the first direction (where clouds are a cause rather than an effect) probably dominates, obscuring what causality may be going on in the other direction. As I said before:
Steven Mosher says:
January 8, 2014 at 8:45 pm
Unlike most folks, I have actually uncovered major errors by other scientists. Take the claim of the cancellation of LW and SW in the tropics as one example.
And yes, I’m damn careful when I think I’ve found something like that.
However, unlike you, I actually do make mistakes.
Not only that, unlike you and most scientists, I work in total isolation, with no co-workers or associates or graduate students or anything. As a result, the errors that slip by me don’t get caught privately by discussing it with someone. They get caught publicly, and it’s damn embarrassing to me when they do.
But it’s rarely because I didn’t check my facts.
So yes, Steven, I’ve made some very public errors. That’s how science works. People put their work out in public, and other people try to falsify it. And sometimes they do. And when they do falsify my work, unlike many folks, I admit it freely, and science moves on.
Now, it seems that you want to be a total jerkwagon about that process, and accuse me in one of your ugly one-line drive-by shootings of not checking my facts … bullshit. I put hours and hours into checking my facts, and then I re-check them … and I still make mistakes. So what? Does that mean I shouldn’t advise others to check their facts?
Yes, I make mistakes, unlike you, I assume from your snide comment … you know, Steven, many times on the web I’ve gone out of my way to support you and defend you when you’ve been attacked by others.
But in this case? You’ve gone out of your way to be nasty, spewing pure childish spite, and that’s not doing your reputation a damn bit of good.
w.
Willis: He is right about how Lw is measured, but that is meaningless. Whether it is measured directly or indirectly, so what?
The problem is not that it is “indirect”, but that is it the difference between one measurement and another: a – b = c. The difference will be correlated with the terms of which it is made: a is positively correlated with c, and b is negatively correlated with c. The constraint of which Nick Stokes wrote is non-constant because a and b are random variables.
Willis Eschenbach says:
January 8, 2014 at 10:55 pm
“…After all, they don’t call you “Racehorse Stokes” for nothing..”
———————————————————————————–
Fast, but not fast enough.
Makarieva et al 2010 discussion paper….
“The Moving Finger writes; and, having writ,
Moves on: nor all thy Piety nor Wit,
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it”
There is no escape from the Following Dark.
Willis: Nick Stokes wrote: Willis,
“there is no special requirement that the two anomalies be negatively correlated.”
Indeed. The formula for correlation of A with B-A is
ρ=(σ_B ρ_AB-σ_A)/sqrt(σ_A^2+σ_B^2)
ρ corr coef, σ sd
So yes, you can get positive correlation with large positive ρ_AB (and negative with negative). But you’re reasoning the other way around. The two quantities don’t have to be negatively correlated. But they can be without it meaning what you want it to mean.
That is something that I think you need to study. Nick has identified what might be called “a rookie mistake”, though you are more than a “rookie”, and it is a mistake that I missed by being less familiar with the measurements. It is not necessarily the case that your conclusion is wrong, but it is unjustified unless you can get truly independent measures of what I have called a, b, and c. As long as one is measured as the difference of the other two, you will obtain correlations that have not any firm theoretical significance.
Willis Eschenbach says:
January 8, 2014 at 9:14 pm
janus says:
January 8, 2014 at 5:31 pm
However, things are nowhere near as accurate as Wiki claims. The proportions of UV/Near IR/Visible Light are about right, but the amount of energy received at ground level varies greatly with the transmissivity of the atmosphere.
========
In the proportions given by wiki it does not say that it is shortwave infrared making up the whole infrared amount…
The AGW meme actually claims it is mostly visible light and insignificant amounts of infrared (around 1%), so the wiki quote contradicts that too.
Here: http://earthguide.ucsd.edu/virtualmuseum/climatechange1/02_3.shtml
“The incoming energy from the Sun to Earth is mainly visible sunlight, called the �visible portion of the spectrum of electromagnetic radiation.� We perceive visible sunlight as colors from violet (short-wave radiation) to red (long-wave radiation). … A relatively minor amount of energy leaves the sun as radiation with shorter wavelength (�ultraviolet�) and as radiation with longer wavelength (�infrared� or �heat radiation�).”
The AGW claim is that we do not get heat radiation, longwave infrared, from the Sun.
The wiki quote says over half as measured at the surface is infrared.
So which is it?
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/grnhse.html
“The greenhouse effect refers to circumstances where the short wavelengths of visible light from the sun pass through a transparent medium and are absorbed, but the longer wavelengths of the infrared re-radiation from the heated objects are unable to pass through that medium.”
The second reason AGW gives of no longwave infrared heat from the Sun reaching us.
Willis, we cannot feel shortwaves from the Sun, that is simply a physical fact. Shortwaves are incapable of raising the temperature of matter, it takes the bigger heat energy of longwave infrared to move molecules of matter into vibration, which is kinetic energy, heat. Heat heats matter.
We cannot feel visible light as heat, because it cannot heat us up. Visible light, shortwaves, affect matter on the electronic transitional level, not the vibrational level of heat.
Your comparisons do not make sense because you are using AGW ‘physics’, now ubiquitous throughout the general education system because the traditional teaching has been systematically removed to promote AGW.
This is traditional teaching now removed from direct NASA pages: http://science.hq.nasa.gov/kids/imagers/ems/infrared.html
“Far infrared waves are thermal. In other words, we experience this type of infrared radiation every day in the form of heat! The heat that we feel from sunlight, a fire, a radiator or a warm sidewalk is infrared. The temperature-sensitive nerve endings in our skin can detect the difference between inside body temperature and outside skin temperature
“Shorter, near infrared waves are not hot at all – in fact you cannot even feel them. These shorter wavelengths are the ones used by your TV’s remote control. ”
Shrug, I’ll stick with traditional teaching which knows the difference between heat and light.
Which if you go back to my first quote you will notice that they say our perception of visible light is as colour…, we do not perceive visible light as heat as they well know.
Matthew R Marler says:
January 9, 2014 at 12:14 am
Oh, good, someone accusing me of rookie mistakes, that’s always fun.
Matthew, neither you nor Nick have dealt with my example. I will repeat it.
I have a scale and I’m weighing married couples. They both get on the scale, and I record the weight. Then the woman steps off the scale, and I weigh the man. I do this for 1000 couples.
Next, I calculate the woman’s weight in each case as the total minus the man’s weight.
Note that this is exactly the method used by CERES. They measure the total radiation, and they measure part of the radiation. They calculate the value for the rest of the radiation by subtracting one measurement from the other.
Does this method of calculation mean that the weight of the man and the woman are negatively correlated, as you and Nick claim?
No. The method of calculation of the woman’s weight, whether direct or indirect, has no effect on whether or not their weights are correlated.
For example, if we were to do the experiment, since larger men tend to marry larger women and 5’2″ guys rarely marry 6’2″ women, their weights will have a positive correlation. That’s the real correlation, and it has nothing to do with how we measure their weights.
Are you seriously arguing that because of the way that we’ve calculated the woman’s weight, as the total weight minus the husband’s weight (just as CERES does it), that the real-world positive correlation of the couples’ weights will suddenly become negative? Because that is what you and Nick are claiming …
There is a rookie mistake here … but it ain’t mine …
w.
The NickStokes “arithmetic correlation hypothesis” for Dummies:
(a definitive experiment?)
A) create a blank spreadsheet of , eg, 100 rows
B) fill column LW with randomly-generated numbers between ,eg, [200 .. 300]
C) fill column SW with randomly-generated numbers between ,eg, [50 .. 150]
D) define column TOT as (LW + SW)
E) define column LWx as (TOT – SW) [ie: (LW+SW) – SW ]
F) define column SWx as (TOT – LWx) [ie, (TOT- (TOT-SW))]
G) calculate correlation coefs for this pair of series: (LW, SW)
(( i predict near-zero correlations betwixt random series))
H) calculate correlation coefs for each of these pairs: (TOT, LW) and (TOT, SW)
(( i predict non-zero correlations for these DEPENDENT arithmetically-related pairs ))
I) calculate correlation coefs for this pair: (LWx, SWx)
(( I predict the SAME near-zero result as for (LW, SW) —
despite the arithmetic derivations, the quantities remain INDEPENDENT ))
X) deduction: if LW and SW were generated with some non-zero correlation ,
[to simulate the Willis Hypothesis] ,
the (LWx , SWx) series pair would retain that same correlation.
Willis: “I’m just saying that if you don’t know something, ASK. You didn’t have a clue what the “roundto” variable did, but despite that you accused me of using “crude rounding” … and all the while, my legend numbers were accurate to 100 decimal places.”
In the code you provided in the link you had a different range for the colour legend and when I increased the number of sig figs in the legend 0.2 become 0.25 . While it is turns out that the range you used in fig 2 here the legend falls on exact 0.1 intervals and is accurate, that is what lead me to question whether 0.6 was not a truncated 0.67.
I don’t know why you always any critical comments as a personal affront. I was not “accusing” you, I was trying to discuss what you were presenting. That is what this blog is about. It’s not like you have a peer reviewed paper published and I’m rebutting it. It’s a discussion.
The main point, which I was trying to point out was the impression that the map itself was banding the values into intervals. These are the interval that I have been asking about but you have not understood what I was referring to. However, I have done a screen cap of the R plot and zoom it to 800% in Gimp and the visual impression I had about bands is not the case. There are colour nuances. The fact that this is not very clear is probably a function of the colour mapping in R . The help on that says it is sub-optimal and may not be very good in RGB space. So I guess we’re stuck with it.
This all comes back to what I originally suggested would be visually better and more informative would be a finer colour scale. I have not found out how to get more colours into the colour scale and you have not replied to my request for help on that.
You have your reasons to always use the same colour scheme but it is not the clearest scheme for this data. that is why I reworked the colour scheme to highlight the areas with significant correlation.
http://i39.tinypic.com/2crqzhu.png
One omission in the article is a value of what CC may be considered significant and without that it is difficult to know how to interpret the graph. I find a value of 0.48 which is fairly high due to short data and the smoothing and puts the coastal regions that stood out into ‘no significant correlation’.
I don’t know whether you have a different idea of what the significance level should be, stats is not my speciality. Maybe someone else could comment on that.
Best regards.
Willis,
“Does this method of calculation mean that the weight of the man and the woman are negatively correlated, as you and Nick claim?”
No, but I don’t claim it does. Incidentally, I don’t object to this as a way of getting the weight estimate. Your 7=(4+7)-4 is OK as far as the actual estimate (expected value) is concerned. The issue is trying to make inferences from the covariance, where independence etc matters.
Again, you’re turning the argument around. Yes, in the weighing you may not have negative correlation; in fact maybe none at all. But you are trying to infer something from an observed negative correlation of A and B-A. And my point is that the negative correlation is consistent with various possibilities, including, in the coins example, nothing meaningful at all. So you can’t deduce anything from it.
Alac Rawls: “I think Willis and Greg need to look at this again.”
Yes, Alec, that last comment was posted well past my bedtime 😉 . Your comment made sence when I first read it as you see in my initial reply. I got a bit confused by Jan’s comment and forgot the SW was reflected, not incoming.
As I said originally, it’s a bit of chicken and egg situation. Direction of causation may need more digging.