Guest Post by Willis Eschenbach
I had an idea a couple days ago about how to estimate cloud feedback from observations, and it appears to have panned out well. You tell me.
Figure 1. Month-to-month change in 5° gridcell actual temperature ∆T, versus gridcell change in net cloud forcing ∆F. Curved green lines are for illustration only, to highlight how many of the datapoints fall outside those lines in each of the four quadrants. Results have been area-weighted, giving a slightly smaller slope (-1.7 W/m2 per degree) than initally reported (- 1.9 W/m2 per degree). Data colors indicate the location of the gridcell, with the Northern hemisphere starting with blue at the far north, slowly changing to yellow and to red at the equator. From there, purple is southern tropic, through pink to green for the farthest south latitudes. Updated.
Cloud feedback is what effect the changing clouds have if the earth warms. Will the clouds act to increase a warming, or to diminish it? The actual value of the cloud feedback is one of the big unknowns in our current understanding of the climate.
The climate models used by the IPCC all say that as the earth warms, the clouds will act to increase that warming. They all have a strong positive cloud feedback. My thunderstorm and cloud thermostat hypothesis, on the other hand, requires that the cloud feedback be strongly negative, that clouds act to decrease the warming.
My idea involved the use of what are called “gridded monthly climatologies”. A monthly climatology is a long-term month-by-month average of some climate variable of interest. “Gridded” means that the values are given for each, say, 5° latitude by 5° longitude gridbox on the surface of the planet.
My thought was to obtain the monthly actual temperature gridded climatology. This is the real temperature “T” as measured, not the anomaly. In addition, I would need the gridded net cloud forcing “F” from the ERBE (Earth Radiation Budget Experiment) data. Net cloud forcing is the balance of how much solar energy the clouds reflect away from the earth on the one hand, and on the other, how much the same clouds increase the “greenhouse” downwelling longwave radiation (DLR). Net cloud forcing varies depending on the type, thickness, altitude, droplet size, and color of a given cloud. Both positive and negative cloud forcing are common. By convention, positive net cloud forcing (e.g. winter night-time cloud) is warming, while a negative net cloud forcing (e.g. thick afternoon cumulus) is cooling.
Remembering that a cloud feedback is a change in net forcing in reference to a change in temperature, I took the month to month differences of each of the two climatologies . I did this in a circular fashion, each month minus the previous month, starting from February minus January, around to January minus December. That gave me the change in temperature (∆T) and the change in forcing (∆F) for each of the twelve months.
The ERBE satellite only covers between the Arctic and Antarctic circles, the poles aren’t covered. So I trimmed the polar regions from the HadCRUT absolute temperature to match. Then, the HadCRUT3 absolute temperature data are on a 5° grid size, while the ERBE satellite data is on a 2.5° grid. Since the grid midpoints coincided, I was able to use simple averaging to “downsample” the satellite cloud forcing data to correspond with the larger temperature gridcell size.
The results of the investigation are shown in Figure 1. The globally averaged cloud feedback is on the order of -1.9 watts per square metre for every one degree of monthly warming.
This result, if confirmed, strongly supports my hypothesis that the clouds act as a very powerful brake on any warming. At typical Earth surface temperatures, the Stefan-Boltzmann equation gives about five watts per square metre (W/m2) of additional radiation per degree. That is to say, to warm the surface by 1°C, the amount of incoming energy has to increase by about 5 W/m2. This, of course, means that if there were no feedbacks, a doubling of CO2 (+3.7 watts per square metre per the IPCC) would only cause about 3.7/5 or about three-quarters of a degree of warming. The models jack this three-quarters of a degree up to three degrees of warming by, among things, their large positive cloud feedback.
But this analysis says that the cloud feedback is strongly negative, not positive at all. As a result, a doubling of CO2 could easily cause less than eight-tenths of a degree of warming. If the cloud negative feedback is actually -1.9 W/m2 per degree as shown above, and it were the only feedback, a doubling of CO2 would only cause half a degree of warming …
If confirmed, I think that this is a significant result, so I put it up here for people to check my math and my logic. I’ve fooled myself with simple mistakes before …
Code for the procedures and data is appended below.
All the best,
w.
PS – please, no claims that the “greenhouse effect” is a myth or that DLR doesn’t exist or that DLR can’t transfer energy to the ocean. I’m beyond that, whether you are or not, and more to the point, there are plenty of other places to have that debate. This is a scientific thread with a specific subject, and if necessary I may snip such claims (and responses) to avoid thread drift. If so, I will indicate such excisions.
NOTE: The slope of the trend line in Figure 1 is now properly area-adjusted, making the following section andFigure 2 superfluous. .[UPDATE] I’ve gone back and forth about whether to area-average. The problem is that the gridcells are not the same size everywhere. The usual way to area-average is to multiply the data by the cosine of the mid latitude, so I have done that.
Figure 2 shows the area-adjusted version. Still a significant negative feedback from clouds, but smaller than in the non-adjusted version.
FIGURE 2 REMOVED
Figure 2. Area adjusted cloud feedback. Note the lower estimate of the cloud feedback, a bit smaller than my initial estimate. Color of the dots indicates latitude, ranging from blue at the furthest north through cyan to the equator, then in the southern hemisphere through yellow to red at the furthest south.
Note that we still see the same form in the four quadrants. It is still rare for a large temperature drop to be associated with anything but a rise in the cloud forcing.
I’m still not completely happy with this method of area-adjusting, because it adjusts the data itself. But I think it’s better than no area-adjusting at all. The best way would be to convert both of the datasets to equal-area cells … but that’s a large undertaking and I think the final result won’t be much different from this one.
[UPDATE] Here’s the two hemispheres:
Figure 3. Northern Hemisphere Cloud Feedback. Color of the dots indicates latitude, ranging from blue at the furthest north through yellow in the subtropics, to red at the equator.
Figure 4. Southern Hemisphere Cloud Feedback. Color of the dots indicates latitude, ranging from green at the furthest south through pink in the subtropics, to purple at the equator.
[UPDATE] To better inform the discussion, I have made up the following maps of the variables of interest, month by month. These are the monthly absolute temperatures T, the monthly net cloud forcings F, and the month by month changes (deltas) of those variables, ∆T and ∆F.
Figure 5. Absolute temperature (T)
Figure 6. Net Cloud Forcing (F)
Figure 7. Change in absolute temperature (∆T)
Figure 8. Change in net cloud forcing (∆F)
APPENDIX: R code to read and process the data (not including the updated charts). I've tried to keep wordpress from munging the code, but it likes to either put in or not put in carriage returns.
===================================
# data is read into a three dimentional array [longitude, latitude, month]
diffannual=function(x){# returns month(t+1) minus month(t)
x[,,c(2:12,1)]-x
}
# rotates the circle of months by n
rotannual=function(x,n){
if (n!=0) {
if (n>=0){
x[,,c((n+1):12,1:n)]
} else {
x[,,c((13+n):12,1:(12+n))]
}
} else
x
}
#_averages_2.5°_gridcells_into_5°_gridcells,_for_[long,lat,mon]_array
downsample=function(x){
dx=dim(x)
if (length(dx)==3){
reply=array(NA,c(dx[1]/2,dx[2]/2,dx[3]))
for (i in 1:dx[3]){
reply[,,i]=downsample2d(x[,,i])
}
} else {
reply=downsample2d(x)
}
reply
}
# averages 2.5° gridcells into 5° gridcells for [long, lat] 2D array
downsample2d=function(x){
width=ncol(x)
height=nrow(x)
smallforcing=matrix(NA,height/2,width/2)
for (i in seq(1,height-1,2)){
for (j in seq(1,width-1,2)){
smallforcing[(i+1)/2,(j+1)/2]=mean(c(x[i,j],x[i+1,j],x[i,j+1],x[i+1,j+1]),na.rm=T)
}
}
as.matrix(smallforcing)
}
# EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE End Functions
# LLLLLLLLLLLLLLLLLLLLLLLLLL LOAD DATA ----- gets the files from the web
# HadCRUT absolute temperature data
absurl="http://www.cru.uea.ac.uk/cru/data/temperature/absolute.nc"
download.file(absurl,"HadCRUT absolute.nc")
absnc=open.ncdf("HadCRUT absolute.nc")
download.file("http://badc.nerc.ac.uk/browse/badc/CDs/erbe/erbedata/erbs/mean5jan/data.txt","albedojan.txt")
download.file("http://badc.nerc.ac.uk/browse/badc/CDs/erbe/erbedata/erbs/mean5feb/data.txt","albedofeb.txt")
download.file("http://badc.nerc.ac.uk/browse/badc/CDs/erbe/erbedata/erbs/mean5mar/data.txt","albedomar.txt")
download.file("http://badc.nerc.ac.uk/browse/badc/CDs/erbe/erbedata/erbs/mean5apr/data.txt","albedoapr.txt")
download.file("http://badc.nerc.ac.uk/browse/badc/CDs/erbe/erbedata/erbs/mean5may/data.txt","albedomay.txt")
download.file("http://badc.nerc.ac.uk/browse/badc/CDs/erbe/erbedata/erbs/mean5jun/data.txt","albedojun.txt")
download.file("http://badc.nerc.ac.uk/browse/badc/CDs/erbe/erbedata/erbs/mean5jul/data.txt","albedojul.txt")
download.file("http://badc.nerc.ac.uk/browse/badc/CDs/erbe/erbedata/erbs/mean5aug/data.txt","albedoaug.txt")
download.file("http://badc.nerc.ac.uk/browse/badc/CDs/erbe/erbedata/erbs/mean5sep/data.txt","albedosep.txt")
download.file("http://badc.nerc.ac.uk/browse/badc/CDs/erbe/erbedata/erbs/mean5oct/data.txt","albedooct.txt")
download.file("http://badc.nerc.ac.uk/browse/badc/CDs/erbe/erbedata/erbs/mean5nov/data.txt","albedonov.txt")
download.file("http://badc.nerc.ac.uk/browse/badc/CDs/erbe/erbedata/erbs/mean5dec/data.txt","albedodec.txt")
albnames=c("albedojan.txt","albedofeb.txt","albedomar.txt","albedoapr.txt","albedomay.txt","albedojun.txt","albedojul.txt","albedoaug.txt","albedosep.txt","albedooct.txt","albedonov.txt","albedodec.txt")
# read data into array
forcingblock=array(NA,c(52,144,12))
for (i in 1:12){
erbelist=read.fwf(albnames[i],skip=19,widths=rep(7,13))
erbelist[erbelist==999.99]=NA
erbeout=erbelist[,13][which((erbelist[,1]>-65) & (erbelist[,1]
length(erbeout)
forcingblock[,,i]=matrix(erbeout,52,144,byrow=T)
}
# DOWNSAMPLE FORCING DATA TO MATCH TEMPERATURE DATA,
# and swap lat and long to match HadCRUT data
smallforcing=aperm(downsample(forcingblock),c(2,1,3))
smallforcing[1:72,,]=smallforcing[c(37:72,1:36),,]# adjust start point
# GET ABSOLUTE DATA, TRIM POLAR REGIONS
absblock= get.var.ncdf(absnc,"tem")
smallabs=absblock[,6:31,]
#dim(absblock)
# GET MONTH-TO-MONTH DIFFERENCES
dabs=diffannual(smallabs)
dforcing=diffannual(smallforcing)
dim(dforcing)
#SAVE DATA
save(forcingblock,smallforcing,smallabs,dabs,dforcing,file="erbe_cloud_forcing.tab")
# make cosine weight array
cosarray=array(NA,c(72,26,12))
cosmatrix=matrix(rep(cos(seq(-62.5,62.5,by=5)*2*3.14159/360),72),72,26,byrow=T)
cosmatrix=cosmatrix/mean(cosmatrix[1,])
cosarray[,,1:12]=cosmatrix
cosarray[,,2]
# GET CORRELATION, SLOPE, AND INTERCEPT
#cor(dabs,dforcing,use="pairwise.complete.obs")
module=lm(dforcing~dabs)
m=module$coefficients[2]
b=module$coefficients[1]
#Plot Results
par(mgp=c(2,1,0))
plot(dforcing~dabs,pch=".",main="Cloud Feedback, 65°N to 65°S", col="deepskyblue3",xlab="∆ Temperature (°C)",ylab="∆ Cloud Forcing (W/m2)")
lines(c(m*(-20:15)+b)~c(-20:15),col="blue",lwd=2)
textcolor="lightgoldenrod4"
text(-20,-60,"N = 18,444",adj=c(0,0),col= textcolor)
text(-20,-70,paste("Slope =",round(m,1),"W/m2 per degree C of warming"),adj=c(0,0),col= textcolor)
text(-20,-80,paste("p = ","2E-16"),adj=c(0,0),col= textcolor)
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“”””” P. Solar says:
October 9, 2011 at 10:54 pm
Interesting and informative post George. However you seem to have misunderstood what ‘positive’ is all about.
“Water can only lower the solar energy that reaches the earth surface; it can never increase it.”
I’m not aware of anyone saying that is not the case. That part is negative. However, when you look at the similar effect of outgoing IR a similar argument would lead to saying this can only be positive. The big question is the overall, net effect on ERB. “””””
“”””” I’m not aware of anyone saying that is not the case. “””””
Well P, here at WUWT, we are simply inundated with people constantly posting that that IS the case. I can count on the fingers of one hand, the number of times anyone ELSE has ever posted that.
Essentially 100% of the input energy driving the earth climate system comes from one source; the sun. And over 75% of that input solar energy that reaches the surface, ends up getting stored in the deep oceans; as deep as 700 metres. That heat store ultimately drives the weather and the climate. To the extent that the captured solar energy decreases (due to more water in the atmosphere), the earth must cool down.
It may be months for variations in the stored ocean energy to show up in the climate. On the other hand, variations in the escape of LWIR from earth, as a result of GHGs or clouds; or anything else, takes place in time scales many orders of magnitude faster than the transport of stored ocean energy. Those effects cannot stop the escape of that energy; only delay it. The loss of that input solar energy is however permanent; it is NOT recoverable.
The point is that very short term changes in the atmosphere condition as it relates to GHGs or clouds, is completely swamped by the permanent change in the energy captured by the earth from the sun, as a result of those transient events.
The LWIR emission from clouds, is isotropic, and it is trivially obvious that at least for a small isothermal cloud, the result is that 50% of that emission is lost to space, and only 50% of it returns to earth., and most of that (3/4) simply results in prompt evaporation from the ocean surface, which transports huge amounts of latent “heat” of evaporation back into the atmosphere where convection processes quickly move iot to the upper atmospher for loss to space. Yes for larger clouds the tops could be cooler than the bottoms; but even that is not assured, since the cloud tops are also directly heated by the sun. Unless the escape delay of LWIR surface emissions RAISES the amount of incoming solar energy that the earth captures, that CANNOT be considered to be a positive feedback. The input driving signal to this sytem is ONLY the sun.
P. Solar had said:
P. Solar:
October 9, 2011 at 12:03 pm
Well … no, in a word. So I replied:
Now Mr. Solar is back again, vis:
You likely can “point out some errors”, P. Solar, I can learn from anyone. But what happened was you got so bothered you forgot to answer my question, despite quoting it in your post. Perhaps when try to answer it, you’ll know why I asked you to think this one through before uncapping your electronic pen.
So buck up here, P., the opportunity is not lost yet, give us the benefit of your knowledge. Which of the 18,000+ dots are you proposing that I connect up to make a phase space plot? I was kinda thinking of connecting the dot that is my home gridcell in December with the dot that is the Rio De Janeiro gridcell during Mardi Gras, but I’m sure you can join my wife in telling me why that choice is not possible …
w.
P. Solar also complained about my reply, where I had said:
P. Solar, who is upset because I though his comment was inane, says:
In other words, he’s too busy to read the “inane comments” before posting one of his own.
w.
P. Solar says:
October 9, 2011 at 9:08 pm
No, that’s not a result. A result is where you ACTUALLY DO THE HARD WORK with the data I’ve provided, and you tell and show us what ACTUAL RESULTS of your inquiry are. I’m not going to do it, I don’t have time or interest. You claim to be interested, but you’re all lip. So go and actually do the test you are proposing.
Then, as I requested … report back with your results. If you can establish what you say, the same way I do, by doing the math and reporting back that I’m wrong, I’ll be the first to admit it.
Until then, it’s just more smoke like your claim about connecting up the dots … but then refusing to tell us which dots.
w.
Septic Matthew says:
October 10, 2011 at 6:37 am
I am estimating the slope of ∆ Forcing with respect to ∆ Temperature.
You blithely say “you cannot estimate the slope you want to estimate”.
While it is possible that you are correct, your claim would be more credible if you explained:
a) what you think I’m trying to estimate.
b) exactly why I cannot, under any circumstances or with any possible mathematical models, estimate that slope.
c) just how, if you are correct that I cannot estimate what I claim to estimate, it is still a “nice analysis”?
d) how this relates to my asking P. Solar to provide backup for his claims.
w.
PS – Generally, when someone says to me “It’s well known” that just means that they can’t find any facts to substantiate their claim. I’d avoid that circumlocution if I were you …
PPS – I would also invite you to tell me about P. Solar’s claim that I should “connect up the dots” in the analysis … which dot’s should I connect? Because he seems at a loss to answer that one.
Willis: b) exactly why I cannot, under any circumstances or with any possible mathematical models, estimate that slope.
You can not estimate that slope using linear regression, as you are attempting. You might try with some vector autoregressive methods, but they have problems as well.
“It’s well known” in this case refers to statistical texts on the non-uniqueness of regression estimates with bivariate (and multivariate) normal distributions.
Septic Matthew says:
October 10, 2011 at 6:44 am
Egads, what are you, the new bitchy Miss Manners of the blogs? If you think his plans are so great, you can explain them to us. He hasn’t done so, he hasn’t said which of the dots to connect to make his magic phase diagram, he didn’t provide citations or explanations for his claims. I pointed it out to him. And? … sure, I might have been nicer, I could have blown in his ear and rubbed his tummy while I told him very nicely what I told him crudely, that he hadn’t thought his claim all the way through. And that would be better how?
In any case, one man’s ceiling is another man’s floor, so here’s your chance to shine, Septic. You can step into the breach and do P.’s work for him, and come back and tell us which dots to connect to make the phase diagram.
Or you could take your act down a notch. Your choice, but bitching about what P. Solar and I have to say doesn’t help. Stand back and let us figure it out, why do you want to fight another man’s battles, particularly when you don’t know the answer about the dots?
w.
Dixon says:
October 10, 2011 at 6:46 am
That’s an interesting way to go about it, Dixon. I’ll have to think about that some, and how to best do it.
I’m also a bit concerned about the idea of “seasonal effects”. If the nature of the seasons is that the clouds tend to warm the earth as the temperature drops with the seasons, and they tend to cool the earth as the temperature warms with the seasons … isn’t that an actual, verifiable effect and as such one that we don’t want to remove? This whole question is a bit of a head-scratcher for me.
w.
Willis,
there will be some climate-related presentations at the Joint Statistical Meetings in San Diego, July 28 – Aug2, 2010. I am working to extend your analyses of the TAO data. There will be about 5,000 statisticians present. TAO/TRITON is in the tltle. The program will be posted online next May or thereabouts. Meet me and we can discuss our work.
Maybe by then you’ll have figured out how to connect the dots.
[SNIP – off topic. If you want to claim that visible sunlight cannot warm things, you’ll have to do it elsewhere. – w.]
[Reply: You are invited to submit an article of your own if you wish. You might be surprised at the comments. ~dbs, mod.]
I refuse to join any club that would have me for a member. :-p
Septic Matthew says:
October 10, 2011 at 12:05 pm
Thanks, Matthew, best of luck with your analysis. I’d love to discuss all of these questions over a beer if you are ever around the San Francisco Bay area.
Regarding connecting the dots, I already know how I connect them. What I haven’t be able to do is to get P. Solar to tell me how he thinks they should be connected, despite his obvious willingness to advise me that I’m doing it wrong …
w.
PS – I think you must mean “2012” above.
Septic Matthew says:
October 10, 2011 at 11:57 am
Last time you said I could not estimate that slope at all. Now you say I can’t do it with linear regression. While you may be right, so far all you have done is change your claim. It seems you are saying that some slopes can be estimated with linear regression, but not this particular one. However, that is just another assertion. WHY is this particular dataset not viable for linear regression, and what mathematical methods did you use to establish that fact?
It’s a serious question, Matthew, what math did you use to come up with your conclusion? I’ve shown my work … now it’s your turn. Bring out the math to substantiate your point.
Finally, just replacing “it’s well known” with “it’s in the textbooks” is not moving forward as far as increasing our sum of knowledge …
w.
161.Myrrh says:
October 10, 2011 at 12:14 pm
[SNIP – off topic. If you want to claim that visible sunlight cannot warm things, you’ll have to do it elsewhere. – w.]
I specifically said I didn’t want to argue about it here, I merely gave it as background to where I was coming from, traditional physics, what I was posting was on the figures Steve gave for infrared, 53%, and I was adding to that. Stupidly, I thought you’d be interested.
So, now I know where you’re coming from.
[RESPONSE: I’m coming from my request not to discuss extraneous issues, which you have arrogantly abrogated. Calling your idee du jour “background” does not make it suddenly relevant or on-topic. Am I interested? Perhaps, everyone has something to teach me. BUT NOT ON THIS THREAD. I don’t know if you are really that dumb or just trolling, but what part “not interested in that on this thread, please take it elsewhere” is unclear to you? -w.
Willis: Now you say I can’t do it with linear regression.
Sorry, the claim that you couldn’t estimate the slope with linear regression was stated first. I carried it forward implicitly, without restating it.
WHY is this particular dataset not viable for linear regression, and what mathematical methods did you use to establish that fact?
The X and Y variables are both random variables. Your computation of the statistical significance assumes that they are Normally distributed random variables. That gives you a bivariate normal time series. Regression methods assume that the X variables are fixed; or, that you are conditioning on the observed values of the X variables. Either way, the estimate of the regression coefficient of Y on X is biased. I missed the part where you derived the correctness of the formula for computing the observed significance level. Paraphrasing you, you did not put in the mathematics to establish that fact. How to estimate the slope of the regression of a bivariate normal time series is taken up in, for example, in “New Introduction to Multiple Time Series Analysis”, by Helmut Lutkepohl, Springer, 2006, corrected second printing 2007.
PS – I think you must mean “2012″ above. good catch, thanks
I’ve added monthly maps of the variables of interest (T, F, ∆T, ∆F) to the head post above.
w.
Septic Matthew says:
October 10, 2011 at 3:19 pm
Matthew, thanks, now we’re getting down to the good part, where I learn something. However, I don’t understand your statements above. Seems to me that if X and Y were normally distributed random variables as you say, that there would be absolutely no statistical relationship between them.
But it is obvious from looking at Figure 1 that the arrangement of the dots is far, far from random.
So what am I missing here?
w.
I have never understood how causally a net warming effect from clouds could be proposed. It is becoming well accepted that an unrestrained dynamic system will tend to maximize the rate of entropy creation. Radiation from the sun has relatively low entropy. Its the heat divided by the temperature after all and 5000°K is a much bigger divisor than the 288°K of the Earth’s surface. The heat flow in and out has to be the same or the temperature would be changing quickly.
Consider 5000 units of heat coming in from the sun at 5000°K, being converted to 288°K at the Earth’s surface, and radiating out to deep space at 4°K. The entropy change, sun to earth is 5000/28 – 5000/5000 = 16.4 The entropy change, earth to deep space is 5000/4 – 5000/288 = 1233. Clouds that cause net warming have to interfere more with the high entropy generation of earth to deep space than the low entropy generation from sun to earth. That would be the direct opposite of maximum entropy generation.
Furthermore, it is well known that shorter light wavelengths are more easily scattered than long wavelengths. The sky is blue and the sun at sunset is red after all. The long wave radiation from the earth will more easily penetrate clouds than the short wave radiation from the sun. The clouds have to be cooling. The only way clouds could have a net warming effect if for their to be more clouds at night than during the day. That should be easily measurable. In fact as Willis has described in the Thermostat Hypothesis, the opposite is observed. Cumulus clouds and thunderstorms tend to start to build up at mid day and dissipate in the evenings. I believe stratus clouds have more to do with large weather systems where the time scale is longer than a day and do not seem to respond to the daily cycle as much.
There’s an inconsistency between the order of the longitudes in the ERBE file and the HadCRUT file. The longitudes in the ERBE file go from 1.25 degrees to 358.5 degrees. The longitudes in the HadCRUT run from -177.5 degrees to 177.5 degrees. Your program incorrectly assumes that the order for the two files is the same. The simplest fix is the interchange the first 36 longitudes in the HadCRUT file with the last 36. By my calculation doing so increases the slope for the unweighted calculation from -1.9 to -1.4, and for the weighted calculation from -1.7 to -1.2.
Joseph Dunn says:
October 10, 2011 at 6:08 pm
[UPDATE: I’ve updated all of the graphics in the head post. Thanks, Joseph. -w.]
Willis,
I know that “anomalies” are not always popular, but it seems that they might be helpful in addressing the issues Dixon brought up about seasonal affects. (Others may have brought up seasonal affects too — I just haven’t had time to look thru the whole thread).
It is clear that in the fall (for either hemisphere), the ΔT is negative. Over land in the N hemisphere, this is often -4C to -8 C. Why not subtract out the average change to find out how each particular year performs? I think this is one layer deeper yet for your analysis.
I am thinking something like “At 45 N, 95 W, the temperature drops an average of 6C from Oct to Nov. and the average forcing is 35. In 1986 the drop was only 5 C and the forcing was 40. Thus a high forcing led to a small drop in temperature.” (the numbers are simply for purpose of illustration — they do not represent real data) By repeating this for every year, you could start to get a trend thru time. But doing this at various locations, you could start to get a trend around the globe.
And as I think about it, I would suggest comparisons with the month before or after. Something like “At 45 N, 95 W, the temperature was above average in Oct, 1986. The forcing was above average in Sept, suggesting that the high forcing caused the temperature to be high in the next month. Also, the forcing was high in Nov. This suggests that the high temperature caused the forcing to be high in the next month.” This would help establish whether clouds are a forcing or a feedback.
Of course, now you have thousands (millions?) of potential trends to consider
[SNIP – I’m not discussing it, and I’m not listening to you argue about it. I told you I’d snip off topic posts. Stop trying to sneak them in. – w.]
Shrug, this is to you, not trying to “sneak” anything in… I suppose it’s time I accepted that most climate ‘scientists’, I use the word loosely because the general interest of this attracts scientists and others from different disciplines, see a completely different world to that which traditional physics teaches. How then do you account for the phenomenon of ‘the sun burns up the mist and clouds’ as we wait for it do so? Rhetorical. I’ve given up taking these alternate universe view seriously.
Willis, first let me repeat my first comment, that this is good work. A few day ago I referred to you as a gifted amateur, in the tradition of Florence Nightingale. It’s early days to say you’ll have the same impact (hardly anybody has, but she was an ideal), but your fresh looks at extant data sets should be followed up by others, and I always look forward to them.
However, I don’t understand your statements above. Seems to me that if X and Y were normally distributed random variables as you say, that there would be absolutely no statistical relationship between them.
That’s the special case of independence. You can have normally distributed random variables that have a correlation coefficient that is non-zero. That indeed, is what you found for this case. Estimating the regression of Y on X, or of X on Y is problematical. Mathematically each regression is well-defined (that was the case that Sir Francis Galton was working on with heights of British men and their sons when he consulted a mathematician.) However, to estimate the regression of Y on X or of X on Y from data leads to a problem. Look up “Deming Regression” — used in industry to evaluate the comparability of two methods for assaying the same quantity ( say, testosterone in blood), where neither method is a “gold standard”.
Enough for now. Keep up the good work.
The Joint Statistical Meetings are recurrently held in San Francisco, but won’t be for the next 5 years. You’re bracketed between San Diego and Seattle.
“Data colors indicate the location of the gridcell, with the Northern hemisphere starting with red at the far north, slowly changing to yellow and to red at the equator. From there, purple is southern tropic, through pink to green for the farthest south latitudes.”
Red in the north AND red at the equator? And what about blue? I guess it is blue at the equator, and not red?
Besides this: Really cool work! 😉
[REPLY: Thanks, fixed. -w.]