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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Does the difference in slopes between the last two graphs show a real world effect? Could this be part of a real description of the planetary climate engine?
*****
Paul Westhaver says:
October 8, 2011 at 6:40 pm
100W/m^2 with NO TEMP change… I’d like to explain that!… How can you have -100 W/m^2 and no temp change?
****
Not unprecedented. In winter here, there can be a day or two of very low clouds, fog & rain. Little solar input to the surface. Afterwards an Arctic high moves in w/crystal-clear skies (lots of solar input), but the temp drops to well-below freezing.
Large or fast airmass movement can overcome the general tendency of more watts-input = higher temps, at least on a local scale & for limited time.
Willis, thanks for adding the latitude and hemisphere data. As expected, it clearly shows the temperature moderating effect of the Southern oceans, relative to the large continental land masses in the North. I find the robustness of the R=-0.27 R2=0.08, regardless of how the data is sliced to be remarkable, and would want to double and triple check it. We know from Dr. Spencer’s post above that cloud feedback, regardless of parameter, can only explain a small fraction of the net radiative forcing, and 8 percent seems within the realm of possibility. We know from Svensmark that cosmic ray modulation of clouds can supply a radiative forcing. If clouds are the thermostat, then cosmic rays, volcanoes, ocean currents, industrial aerosols, etc. all have a finger on the dial.
The paucity of points in the third quadrant, especially near the extremes of latitude, suggests that the straight line is an approximation of a true curve that is concave-down. Put into English, that suggests that negative cloud feedback becomes stronger as the temperature anomaly gets hotter, especially at temperate latitudes.
Willis I like your approach – let the data speak for itself and see how it matches the science.
A few points:
1. My concern is not that largish grids introduce smoothing but that using monthly data does. The effects of cloud cover are, more-or-less, instantaneous and on different days of the month feedback could go either way.
2. There is also implicit smoothing – you assumed the effect is the same for all latitudes for all times of the year which could mask seasonal trends. You have enough data to look at 5 sub-sets: northern hemisphere summer, northern hemisphere winter, tropics, southern hemisphere summer, and southern hemisphere winter. For summer you could take April to September (as close to the period between the equinoxes as is possible with monthly data).
My hunch is that your conclusion is right but the closer you can get to showing the ‘fuzzy’ plot of negative feedback is the balance of more clearly defined positives and negatives the stronger your argument will be.
Gail . . I appreciate your point but the danger is that some readers will wonder if comments are being deleted from ulterior motives . . . it also provides scope for petty smearing – the kind that travels well on the net . . .In an ideal world I’d agree with you . . . this one is far from ideal though as the climate wars have shown all too often. Honesty and fairness have got to go out of their way to be seen or heard, lest they be swamped.
Dave Springer says:
October 9, 2011 at 5:01 am
“the downwelling shortwave radiation that is the ocean’s only source of heating. Downwelling longwave radiation has no effect on ocean temperature.”
———————————————–
Dave, how is it possible that shortwave radiation is the only source of ocean heating?
Dave, how is it possible that longwave radiation from the sun has no effect on ocean temperature?
Thanks.
[UPDATE – See, this is the problem. Dave starts off with his claims, and right away someone (reasonably) says “Hey, that makes no sense at all”, and then we’re off the rails. I’ll leave this here to illustrate the point, but I will snip further responses along the same line. If you want to dispute the DLR/ocean issue with Dave, please do so elsewhere. w.]
Observations? It’s all computers these days. Or ball-bearings. Whatever.
Willis,
I made an error in my earlier post. Of the radiation reaching the earth, only about 1% is longwave (> 4 um). The other 99% is shortwave. Sorry to display my ignorance but that’s how I learn.
———————-
So virtually all incoming solar radiation is shortwave. That explains Dave’s comments.
Which leads me to a new question: Are clouds better at blocking shortwave radiation (negative) or trapping outgoing longwave radiation (positive)?
Nick Stokes says:
October 9, 2011 at 3:31 am
Thanks, Nick. I’m using the monthly differences in the absolute (actual measured) temperatures. GISS, unfortunately, deals only in the data with the monthly average absolute temperatures removed from the data. As a result, even using monthly differences doesn’t get back to what I need, which is the actual difference in temperatures.
w.
it also seems particularly strained to insist on explaining conduction, phase change and convective transport in terms of radiation.
ghg-man got bitten by a radiative spider in this comic series so long ago that now it only appears quaint and superstitious.
Steve from Rockwood,
SW blocking is about 30% stronger than LW trapping.
http://wattsupwiththat.com/2011/09/20/new-peer-reviewed-paper-clouds-have-large-negative-feedback-cooling-effect-on-earths-radiation-budget/
jim hogg says:
October 9, 2011 at 5:46 am
Jim, I’ve had my threads hijacked before by endless specious claims that the DLR can’t heat the ocean. I have discussed these claims AT LENGTH, and even written a whole article about them. So there’s lots of places that are appropriate for discussing those claims. And the SIF folks that believe those ideas are more than happy to monopolize the conversation.
If you think that refusing to discuss those ideas here is “censorship” when I have welcomed them elsewhere and even devoted an entire thread to them, then I fear I can’t help you. I will not debate or discuss whether DLR can heat the ocean or not on this thread, been there, done that elsewhere, go there if you want to discuss it.
w.
Ron Manley says:
October 9, 2011 at 9:07 am
Thanks, Ron. While you are right that on different days the clouds will go different ways, the large dataset allows us to see things like that there is little data in the lower left quadrant, etc.
Hey, it’s early days, there’s a whole host of other slicing and dicing of the data that can be done. I wanted to get the basic idea out in the open early, so if there were issues with the analysis I wouldn’t spend time on a blind alley.
w.
Willis this looks very interesting , it’s going to take time to digest but one big problem jumps right out at me. OLS regression on this kind of data will give BADLY wrong estimates of any linear relationship that is there.
Linear regression ASSUMES there is negligible error in the independent variable. If this is not the case the mathematical derivation of OLS simple does not apply. The net result is a REDUCTION in the estimated slope. One may imagine there is a grey area centred around the fitted line but in fact it can be shown to always reduce the estimated slope. This is called regression attenuation.
In short , it works well for nice clean lab experiments where you can control the quantity plotted on x axis. If you have noise or other effects, like correlated or uncorrelated cyclic phenomena it will reduce the ols estimator. Neither is this just a minor error that can be ignored in a rough estimate, it may be a factor or 3 ro 4 with the sort of cloud you are looking at.
This can be corrected for to some extent , but this requires knowledge of that nature and relative magnitude of the noise/error quantities that is often difficult or impossible. It is often better to try to avoid this happening that try to correct it.
Ignoring this problem is ubiquitous in climate science. This is principally why Dessler, Forster & Gregory etc get a positive feedback , their maths is bad and they under estimate the slope, leading to a false conclusion of +ve feedback.
Fitting straight lines to scatter plots basically and fundamentally wrong.
I hope this does not undo all your hard work , but it does need to be accounted for. Now to digest the rest.
best regards.
Steve from Rockwood says:
October 9, 2011 at 10:19 am (Edit)
Your question is the great unknown in climate science, and is what I’m attempting to answer in this thread.
w.
One thing that will need to be looked at in the future is differences between night and day clouds and temperatures.
One other big difficulty with this approach is that both the data sets are time series. The time element and relationship of relative changes in the two varialbes is at the heart of causality as is rate of change. (Radiation causes a rate of change of temperature, not a simple temperature change).
In doing this sort of scatter plot you are throwing away most of the information that relates the two quantities.
For example , if you do a similar phase space plot (which is what this is) but joint the dots you can will see loops and lines that tell you more about how the two quantities relate. Here you lose that.
I don’t mean to discourage you but I think these points are useful and important to realise. I went though exactly this same process some months back , so I’ve made the same mistakes and found the short-comings.
You may find it instructive to look at dT(t)/dt since that is where the response to a radiative forcing is , not in T(t). It may also be the key to separating forcing and feedback, the latter is a T(t) dependency.
I don’t see your objection to the cosine weighting . ERBS data is W/m2 so you must relate it to an area related term.
As a means of reducing the 2.5 gridded data I’d suggest a 1:2:1 binomially weighted average in lat , then the same in longitude. Alternatively interpolate the 5 degree data with a Catmull-romm spline (quite easy actually)
HTH 😉
PS, one way to test what I say about regression attenuation is to invert the axes and redo the ols fit. If the result is good one slope will be the inverse of the other. I think you will get a shock how different they are. Clearly the result should not depend on which way you plot the data … unless I’m right about OLS.
See a similar discussion at Troy’s blog:
http://troyca.wordpress.com/2011/09/21/ceres-and-era-interim-fluxes-in-dessler-2010/
I would like to point you to a musing from the Chiefio. It is about clouds.
Gives Us This Day Our Daily Enthalpy
http://chiefio.wordpress.com/2011/09/27/gives-us-this-day-our-daily-enthalpy/
Here’s an example of what the two ols estimators on a scatter plot like yours:
http://tinypic.com/view.php?pic=2cqcv28&s=7
It’s not a total loss since the correct slope should be somewhere between the two. Though probably not at ‘in the middle’ , the two wrong results could be used to delimit a range where the right answer lies. This may be enough if you just want to show a negative slope.
After that you have to argue about what the “slope” represents physically.
Willis you are a liar and coward and you make me sick to stomach, GO FUCK YOURSELF!
REPLY: I’m allowing this post, which will be your last, to show what kind of person you are in your own words. And this is why you are banned, permanently – Anthony
Looking at the third plot there maybe some mileage in breaking down latitude bands. There you may be able to get a less hazardous data set where OLS may be more applicable.
If you want a sea mask , you could use hadSST which has some kind of NaN value for land or partially land grid boxes.
Willis, could you redo the analysis by latitude band? Splitting by hemisphere showed a fairly large difference. Perhaps the feedback strength varies by the type of clouds most prevalent in tropics v. temperate latitudes.