I recently wrote three posts (first, second, and third), regarding climate sensitivity. I wanted to compare my results to another dataset. Continued digging has led me to the CERES monthly global albedo dataset from the Terra satellite. It’s an outstanding set, in that it contains downwelling solar (shortwave) radiation (DSR), upwelling solar radiation (USR), and most importantly for my purposes, upwelling longwave radiation (ULR). Upwelling solar radiation (USR) is the solar energy that is reflected by the earth rather than entering the climate system. It is in 1°x1° gridded format, so that each month’s data has almost 200,000 individual measurements, or over 64,000 measurements for each of those three separate phenomena. Unfortunately, it’s only just under five years of data, but there is lots of it and it is internally consistent. As climate datasets go, it is remarkable.
Now, my initial interest in the CERES dataset is in the response of the longwave radiation to the surface heating. I wanted to see what happens to the longwave coming up from the earth when the incoming energy is changing.
To do this, rather than look at the raw data, I need to look at the month-to-month change in the data. This is called the “first difference” of the data. It is the monthly change in the item of interest, with the “change” indicated by the Greek letter delta ( ∆ ).
When I look at a new dataset like this one, I want to see the big picture first. I’m a graphic artist, and I grasp the data graphically. So my first step was to graph the change in upwelling longwave radiation (∆ULR) against the change in net solar radiation (∆NSR). The net solar radiation (NSR) is downwelling solar minus upwelling solar (DSR – USR). It is the amount of solar energy that is actually entering the climate system.
Figure 1 shows the changes in longwave that accompany changes in net solar radiation.
Figure 1. Scatterplot of the change in upwelling longwave radiation (∆ ULR, vertical scale) with regards to the change in net solar radiation entering the system. Dotted line shows the linear trend. Colors indicate latitude, with red being the South Pole, yellow is the Equator, and blue is the North Pole. Data covers 90° N/S.
This illustrates why I use color in my graphs. I first did this scatterplot without the color, in black and white. I could see there was underlying structure, and I guessed it had to do with latitude, but I couldn’t tell if my guess were true. With the added color, it is easy to see that in the tropics the increase in upwelling longwave for a given change in solar energy is greater than at the poles. So my next move was to calculate the trend for each 1° band of latitude. Figure 2 shows that result, with colors indicating latitude to match with Figure 1.
Figure 2. Linear trend by latitude of the change in upwelling longwave with respect to a 1 W/m2 change in net solar radiation. “Net downwelling” is downwelling solar radiation DSR minus upwelling solar radiation USR. Colors are by latitude to match Figure 1. Values are area-adjusted, with the Equatorial values having an adjustment factor of 1.0.
Now, this is a very interesting result. Bear in mind that the sun is what is driving these changes. The way that I read this is that near the Equator, whenever the sun is stronger there is an increase in thunderstorms. The deep upwelling caused by the thunderstorms is moving huge amounts of energy through the core of the thunderstorms, slipping it past the majority of the CO2, to the upper atmosphere where it is much freer to radiate to space. This is one of the mechanisms that I discussed in my post “The Thermostat Hypothesis“. Note in Figure 2 that at the peak, which occurs in the Intertropical Convergence Zone (ITCZ) just north of the Equator, this upwelling radiation counteracts a full 60% of the incoming solar energy, and this is on average. This means that the peak response must be even larger.
Finally, I took a look at what I’d started out to investigate, which was the relationship between incoming energy and the surface temperature. I may be mistaken, but I think that this is the first observational analysis of the relationship between the actual top-of-atmosphere (TOA) imbalance (downwelling minus upwelling radiation, or DLR – USR -ULR) and the corresponding change in temperature.
As before, I have used a lagged calculation, to emulate the slow thermal response of the planet. This model has two variables, the climate sensitivity “lambda” and the time constant “tau”. The climate sensitivity is how much the temperature changes for a given change in TOA forcing. The time constant “tau” is a measure of how long it takes the system to adjust to a certain level.
Figure 3 shows the new results in graphic form:
Figure 3. Upper panel shows the Northern Hemisphere (NH) and Southern Hemisphere (SH) temperatures, and the calculation of those temperatures using the top of atmosphere (TOA) imbalance (downwelling – upwelling). Bottom panel shows the residuals from that calculation for the two hemispheres.
In my previous analysis, I calculated that climate sensitivity and the time constant for the Northern Hemisphere and the Southern Hemisphere were slightly different. Here are my previous results:
SH NH lambda 0.05 0.10°C per W/m2 tau 2.4 1.9 months RMS residual error 0.17 0.26 °C
Using this entirely new dataset, and including the upwelling longwave to give the full TOA imbalance, I now get the following results:
SH NH lambda 0.05 0.13°C per W/m2 tau 2.5 2.2 months RMS residual error 0.18 0.17 °C
(Due to the short length of the data, there is no statistically significant trend in either the actual or calculated datasets.)
These are very encouraging results, because they are very close to my prior calculations, despite using an entirely different albedo dataset. This indicates that we are looking at a real phenomenon, rather than the first result being specific to a certain dataset.
Now, is it possible that there is a second much longer time constant at work in the system? In theory, yes, but a couple of things militate against it. First, I have found no way to add a longer time constant to make it a “two-box” model without the sensitivity being only about a tenth of that shown above, and believe me, I’ve tried a host of possible ways. If someone can do it, more power to you, please show me how.
Second, I looked at what is happening when we remove the monthly average values (climatology) from both the TOA variations and the temperatures. Once I remove the monthly average values from both datasets, there is no relationship between the two remaining datasets, lagged or not.
However, absence of evidence is not evidence of absence, meaning that there may well be a second, longer time constant with a larger sensitivity going on in the system. However, before you claim that such a constant exists, please do the work to come up with a way to calculate such a constant (and associated sensitivity), and show us the actual results. It’s easy to say “There must be a longer time delay”, but I haven’t found any way to include one that works mathematically. I can put in a longer time constant, but it ends up with a sensitivity for the second time lag of only about a tenth of what I calculate for a single-box model … which doesn’t help.
All the best, and if you disagree with something I’ve written, please QUOTE MY WORDS that you disagree with. That way we can avoid misunderstandings.
w.
DATA: The Excel worksheet containing the hemispheric monthly averages and my calculations is here. The 1° x 1° gridded data is here as an R “save” file. WARNING: 70 Mbyte file!. The R data is contained in four 180 row x 360 column by 58 layer arrays. They start at 89.5N and -179.5W, with the first month being January 2001. There is an array for the albedo, for the upwelling and downwelling solar, and for the upwelling longwave. In addition, there are four corresponding 180 row x 360 column by 57 layer arrays, which contain the first differences of the actual data.
When I went to the site http://www-cave.larc.nasa.gov/cgi-bin/cave/dnldavg.cgi you have a link to at the top of your post, and I was scolded for using a free market system produced web browser Microsoft Internet Explore ) and it said I really should be using a Marxists / Leninist * open source browser. What’s up with that?
* I’m paraphrasing a little. I’m using my Windows Phone and it doesn’t support these open source browsers.
This was very distracting and is not helpful on the part of NASA. Shows their left leaning bias.
Jim Cripwell — I don’t know if it answers your question about lapse rate feedbacks, but Isaac Held’s blogpost #24, http://www.gfdl.noaa.gov/blog/isaac-held/2012/03/01/25-relative-humidity-feedback/#more-4528 , titled “Relative Humidity Feedback” may be informative. It looks at some AR4 models in terms of fixed relative humidity vs. fixed specific humidity as the no feedbaback or reference condition before feedbacks.
George E. Smith; says:
June 12, 2012 at 4:16 pm
Well Dave, 98% of the solar spectrum energy lise between 0.25 microns, and 4.0 microns, with only 1% residual at each end, so there is no more than 1% of solar energy beyond 4.0 microns, and most of that comes between 4.0 and 5.0 microns, so basically there isn’t much of your 5 to 50 micron solar energy.
Gosh, only 1% directly heating the land and oceans and us? Because shortwave from the Sun doesn’t heat us.
It takes powerful heat energy to heat us, not lightweight light, so:
“NASA: “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.
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.”
So, shortwave can be chucked out of the equation? (Except as secondary source via photosynthesis and us eating the photosynthesisers and other eaters of the photosynthesisers).
Oh, rather that would be, how much of the upwelling thermal infrared is from the 1% direct beam heat energy, thermal infrared from the Sun, heating land and oceans and how much from the second step via photosynthesis?
garymount says: This was very distracting and is not helpful on the part of NASA. Shows their left leaning bias.
I’d be much less happy if they told my I had to spend loads of money on a platform that continually broken standards and screwed everyone around when a perfectly good (superior, more secure) product was available free of charge.
The free market of which you seem to be so keen would normally prefer a product with a better price/performance ratio.
Now you have let us all know you have a Wankdose Phone perhaps we can get back on topic.
Atonish me once, astonish me twice. Nice work Willis! Amazing that the 90 million a year poured into Oregon U cannot do something like this.
p.s. Willis, your thunderstorms cooling is then from the 1% direct beam thermal infrared as it’s the land heating which triggers it – the basic Water Cycle, which is missing from the KT97&kin, brings down temps 52°C from the 67°C the Earth would be without water.
For anyone using free Marxist / Lenninist software instead of paying out unnecessarily, I found I could use Willis’ xlsx file in open office with a couple of function replacements:
averageif() => sumif()/countif()
[2]!trendse() => slope()
all the slope() calls need an extra input, use the data from X13:X70
=SLOPE(Y13:Y70,X13:X70)*120*1.96
I can’t find any web reference to TRENDSE , so I think it may be Willis special that was defined in a separate file.
However, Willis , I don’t know if I am getting all that is expected.
I have four “charts”: two that would combine to make figure 3; one that seems to be your earlier Lissajous figures; and one that has labels like “∆SH TOA” that I do not recognise.
Is that all I’m supposed to get from that file?
Also, as a kind of parity check to make sure the above changes have not messed things up could you confirm the following cell results are correct:
AQ24=-77.6872125
Y4=7.66
Thanks.
Good work. I think this is another case where you might be better off with a 3-D graph foro figure 1: x coordinate being latitude, y coordinate being delta NetSun and z coordinate being delta ULR.
Myrrh, before you go on too much, please go and work out what happens to all the energy in the rest of the spectrum once it get past the ocean surface. Assuming it does not come out in Australia, there is the principal of conservation of energy that may give you a clue.
Please also bear in mind that while NASA has lots of really smart people , some of its sections have people that are seriously challenged with basic physics. No names, just saying.
(Due to the short length of the data, there is no statistically significant trend in either the actual or calculated datasets.)
The (time) length of the dataset doesn’t affect statistical significance, except to the extent it determines sample size. It’s always the case that more data (bigger sample) makes statistical significance more likely (assuming there is a real effect). Given the size of the sample here, if you don’t find a trend, then its because there isn’t one or it is very small (over the time period of the dataset).
<i.However, absence of evidence is not evidence of absence,
Surely, you do have evidence of absence. You have shown the longer term sensitivity can not be more than 10% of the shorter term sensitivity. Therefore, you have evidence of the absence of a greater sensitivity.
I see nothing Marxist at all about using a product freely produced by a group of individuals, not a government, that offer the product free of charge. I especially see nothing Marxist about the fact that this forces the producers of a product that there is a charge for to improve their product or lower their price.
I agree, however, that a US government website (NASA) should not restrict access on the basis of using one browser or another.
> It is in 1°x1° gridded format, so that each month’s data has almost
> 200,00 individual measurements
Is 200,00 a typo for 200,000?
[Thanks, yes it is, fixed. -w.]
“I agree, however, that a US government website (NASA) should not restrict access on the basis of using one browser or another.”
Does it? Where?
Willis, did you use some R code to make fig 1 & 2 ?
give,give 😉
Thank you Willis. I enjoy seeing true science in action. This along with the earlier topics and the comments is fascinating. True climate science is being performed voluntarily on sites like this and CA. Oh, how the internet has brought change we can believe in. You are certainly doing more than your fair share.
One Comment: BRILLIANT, EFFING BRILLIANT!
This pulls everything together. Too bad the data set isn’t longer.
Thanks Willis!
Jim Cripwell, No feedback climate sensitivity is just an approximate value for adding 3.7Wm-2 of insulation to the atmosphere. It depends on the average temperature of the surface and the TOA outgoing radiation. So any forcing that changes the average surface temperature or the outgoing radiation would change the estimate. There is no magic energy. In fact the estimate is pretty easy to do yourself.
http://redneckphysics.blogspot.com/2012/06/why-is-sensitivity-08-degrees.html
You may even be able to do a better job:
P. Solar says: “Does it? Where?”
The claim was made that the site in question complained about using EI. I don’t know if it is true. To be honest I doubt it as well. But if such I thing were going on, I’d be opposed to it. Wouldn’t you?
Well, anyway, the main point of my post was that if people want to offer something they have produced for no charge, there is nothing un-capitalist about it. You don’t agree with the assertion that free browsers are “Marxist”, do you?
Sorry Willis, I don’t get the need to do an area adjustment for Fig 2.
Well, anyway, the main point of my post was that if people want to offer something they have produced for no charge, there is nothing un-capitalist about it. You don’t agree with the assertion that free browsers are “Marxist”, do you?
Early open source proponents, such as Richard Stallman, had a clear and stated agenda of undermining software copyright, that is, software property rights. Although, I’d characterize them as anarcho-socialists, rather than Marxists. Otherwise, you are correct. There is nothing un-capitalist about free software competing with commercial software.
Hi Willis: Interesting stuff. I looked a bit into these simple energy balance models when I was looking at the evidence for Lockwood’s claim that the oceans equilibrate very rapidly in response to changes in forcing.
http://errortheory.blogspot.com/2011/03/does-solar-activity-have-to-keep-going.html
That evidence evaporated when a two heat sink model was used instead of a one heat sink model. Without a very long data set, all can be determined with surface temperature data is how long it takes for the upper ocean heat sink to equilibrate to the change in forcing, revealing next to nothing about how long it takes for heat to transfer in and out of deeper ocean depths.
That is the part of the problem I was looking at: what can we say about time to equilibration. Now you are looking at a different part of the problem: the implied climate sensitivity. But perhaps the one can inform the other.
For a given measured time constant tau, the reason the implied climate sensitivity goes up when the heat capacity of the system goes up (as it does dramatically when moving to a two heat-capacity model), is because some of the increase in the net incoming solar radiation would be getting stored in the secondary heat sink, in effect siphoning it off, decreasing the effective increase in forcing that is causing whatever warming is observed. Thus for a given amount of observed warming, the implied climate sensitivity is higher.
But notice how the impact of the second heat sink will vary depending on its history (its initial condition at the time the forcing is changed). If it is very cold compared its long run equilibrium temperature for the new level of forcing then it will suck a lot of heat from the upper ocean. If it is near equilibrium, it will draw very little.
You are only looking at five years of data, creeping down into the profound solar minimum of 2008 and creeping back out. Is the lower ocean heat sink anywhere near equilibrium for that level of forcing? Probably not by long shot. You are looking at a period of historic lows of solar activity after an 80 year “grand maximum” of solar activity (or 80 years of medium-high solar activity at the very least).
The expectation in this case is that the global lower ocean would be divesting stored heat across the entire 5 year period. That tells you on which side your calculations are going to be erring. In general, climate sensitivity is going to be overestimated. There is heat coming into the measured surface temperatures from below as well as above. Once that is accounted, the implied feedback multiplier is reduced.
Am I making sense? If so, ocean heat content data might help to resolve this issue, but that gets us into the thorny problem of whether we can trust that data after our best measure of ocean heat content–the stearic sea level–just had its last several hears of data switched from falling to rising by members of the same “consensus” that is responsible for the hockey stick and the severely manipulated HadCrut GISS etc.
In any case, the relation between tau and lambda might not be so simple after all, once the state of the deeper ocean heat sink is considered.
Kasuha says:
June 12, 2012 at 3:49 pm
I’m sorry, Kasuha, but T^4 is far, far from enough to explain the difference shown in Figure 2. Run the numbers yourself and you’ll see.
w.
Another fine post Willis. Where do you get the time and energy and the great insights? I guess talent will out, huh?
rgbatduke says:
June 12, 2012 at 4:02 pm
Thanks as always for your comments, Robert, always appreciated. The earlier dataset that I used covered 14 years. Surely this would be enough to reveal at least something of a longer-term time constant.
Again, I have to reiterate that in my earlier analysis, when I included a second longer time constant in the equation, I get a slightly shorter short time constant, along with a longer time constant on the order of two years for both hemispheres.
But the sensitivity associated with the longer-term time constant is only about a tenth of the sensitivity associated with the shorter time constant.
Go figure … that’s the problem I have. I have no issue with the possibility of a second much longer time constant. My problem is, whenever and however I include one, the sensitivity comes out much smaller (~ a tenth of the size) than when I use only one time constant.
All the best,
w.
P. Solar says:
June 12, 2012 at 6:12 pm
My bad, I forgot to take out my custom functions. Averageif is does what you say. Trendse, however, actually calculates the trend standard error after adjustment for autocorrelation.
w.