Archive for the ‘Blog Article’ Category

TRMM Satellite Reentering the Atmosphere Tonight

Monday, June 15th, 2015
Japan's Hayabusa satellite renters the atmosphere in June, 2011.

Japan’s Hayabusa satellite renters the atmosphere in June, 2011.

NASA’s very successful Tropical Rain Measuring Mission (TRMM) satellite will mostly burn up upon reentry tonight. The latest estimated time of re-entry from Space-Track.org right now is 4 a.m. GMT, give or take 1.5 hours.

To show you just how uncertain these predictions are, that time was moved up by 35 minutes from a prediction just 12 hours before, which is almost half a world away in terms of distance. In other words, it just about impossible to know where the satellite will reenter, except that it will be between about 35 N and 35 S latitudes.

Orbital predictions are very accurate when all you have to account for is gravity; once atmospheric drag comes into play, it’s a whole different ball game.

This news article from a couple days ago quotes NASA as saying that about 12 spacecraft components could survive re-entry and hit the surface. They also say the chance that one of these could hit someone somewhere is 1 in 4,200. I’m a little surprised it’s that high. But then there are a couple billion potential targets. ;-)

If I thought there was a decent chance it will reenter over the southeast U.S., I’d set my camera up for extended time lapse session tonight. But I’m pretty sure that would be a waste of time.

What Causes the Greenhouse Effect?

Saturday, June 13th, 2015

I’ve had a request to (once again) go through an explanation of the (poorly-named) Greenhouse Effect (GHE). Hopefully there is something which follows that will help you understand this complex subject.

The greenhouse effect usually refers to a net increase in the Earth’s surface temperature due to the fact that the atmosphere both absorbs and emits infrared radiation. (Our miniscule enhancement of the natural greenhouse effect with carbon dioxide emissions, and its possible role in global warming, is a separate issue).

This GHE temperature increase is frequently quoted as being around 60 deg. F, thus keeping the Earth from being an ice planet, since its average surface temperature is somewhere around 59 or 60 deg. F.

This 60 deg. F warming attributable to the GHE is actually incorrect; the greenhouse effect on surface temperature, if left to its own devices, would actually be at least twice that strong…more like 140 deg F average surface temperature…but most of that theoretical surface temperature rise is short-circuited by convective heat loss from the surface caused by convective air currents, in turn caused by the greenhouse effect, which also largely creates the weather we experience.

That’s right – without the greenhouse effect, we would not have weather as we know it. The greenhouse effect, energized by solar heating, creates weather.

The GHE is somewhat controversial among some skeptics, probably because we can’t “see it” the way we can see visible sunlight and the resulting heating of surfaces sunlight falls upon – a rather non-controversial cause-and-effect process. It instead involves infrared (IR) light, which we cannot see, but which is an essential part of the energy flows in our climate system…and in most other systems that generate heat. You can actually feel if it is sufficiently strong (e.g. radiant heat from a stove or fire).

I must preface the following discussion with this: The temperature of any object represents a balance between energy gained and energy lost by that object. Temperature is an energy balance issue. Unless phase changes are involved (e.g. melting ice), if more energy is gained than lost, temperature goes up. If more energy is lost than gained, temperature goes down. Understanding this is fundamental to understanding weather and climate, as well as the following discussion.

The atmosphere contains “greenhouse gases” (GHGs), which means gases which are particularly strong absorbers and emitters of IR radiation. In the Earth’s atmosphere, the main GHGs are water vapor and carbon dioxide. Absorption and emission of IR go together because anything that is a good absorber of IR is also a good emitter, although in general the rates of absorption and emission are not the same since absorption is mostly temperature-independent but emission is very temperature-dependent.

In the classical Kiehl-Trenberth global energy budget diagram, the energy flows I have marked with an “X” would not exist without GHGs:

greenhouse-gas-and-KT-diagram

Now, recall I said that temperature is a function of rates of energy gain and energy loss. Thus, those energy flow arrows marked with an “X” in the above diagram represent huge flows of energy which can affect temperature, if they really exist.

So, let’s now think through what happens as sunlight enters the climate system. As the Earth’s surface absorbs sunlight it warms up. As it warms up, it emits more and more IR energy, limiting its temperature rise (remember “energy balance”?).

If the atmosphere could not intercept (absorb) any of that surface-emitted IR energy, the energy would readily escape to outer space and as a result it has been estimated that the Earth’s average surface temperature would be only about 0 deg. F. But we really don’t know exactly because there would be a lot more ice, which would reflect more sunlight, which would make temperatures even colder. Also, we have no idea why kinds of clouds would exist under those conditions. Suffice it to say the Earth would probably be too cold for most life as we know it to survive.

But the atmosphere DOES absorb IR energy. The IR absorption coefficients at various wavelengths, temperature, and pressures have been measured for water vapor, CO2, etc., in laboratories and published for decades.

This absorption means the atmosphere also EMITS IR energy, both upward and downward. And it is that DOWNWARD flow of IR energy (sometimes called “back radiation”) which is necessary for net warming of the surface from the greenhouse effect.

(Technical diversion: This is where the Sky Dragon Slayers get tripped up. They claim the colder atmosphere cannot emit IR downward toward a warmer surface below, when in fact all the 2nd Law of Thermodynamics would require is that the NET flow of energy in all forms be from higher temperature to lower temperature. This is still true in my discussion.)

Now, some will claim the atmosphere’s decreasing temperature with height is also necessary for the greenhouse effect to occur. While this is true, the decrease in temperature with height in the troposphere is ultimately caused by the greenhouse effect itself.

You see, as long as an atmosphere (it doesn’t matter from which planet) has greenhouse gases, the temperature will decrease with height. Without convection, the temperature would decrease drastically with height…the so called “pure radiative equilibrium” case, first demonstrated by Manabe and Strickler (1964). The net effect of GHGs is to strongly warm the surface lower atmosphere temperature, and strongly cool the upper atmosphere temperature, compared to if those gases did not exist. The GHE makes the atmosphere so unstable that convection – weather – results, which restores the atmospheric temperature lapse rate to somewhere between dry adiabatic and moist adiabatic.

Remember, without greenhouse gases, the upper atmosphere could not lose the energy it accumulates from all sources, and would stay warm, and the atmosphere would not destabilize and cause convective overturning (weather).

This net result is not intuitively obvious. I sometimes use the (admittedly imperfect) analogy of insulation in a house in winter (even though heat conduction is a different physical process from radiation). Given the same rate of energy input into the home by its heating system, addition of insulation slows the net rate of heat flow from the warmer interior to the cold exterior, causing higher temperatures inside and lower temperatures outside, compared to if the insulation did not exist.

Again, temperature is the result of energy gain AND energy loss. If you reduce the rate of energy loss, temperature will rise…even if the energy input is the same. Extremely high temperatures can even be created with very little energy input…even from a tiny battery…if you can reduce the rate of energy loss to near zero. You cannot say anything about temperature based upon the rate of energy input alone, any more than you can say what the average level of a lake will be based upon the rate of water input alone. It just ain’t physically possible.

Analogous to insulation in a heated home, greenhouse gases reduce the net rate of infrared energy transfer from the surface and lower atmosphere to outer space, causing the surface and lower atmosphere to be warmer, and the upper atmosphere to be colder, than if greenhouse gases did not exist.

Since the effect is not entirely intuitive, years ago we programmed up the equations ourselves in a 1-D radiative-convective model for me to be convinced this is what actually happens. When the model is initialized with global average sunlight and atmospheric greenhouse gas concentrations, from any initial temperature profile you want (even absolute zero), it eventually equilibrates to the observed average vertical temperature structure of the atmosphere.

And I suppose it is the non-intuitive nature of the process (I required a model demonstration to finally believe it) that breeds so much controversy and alternative ideas. I get that.

Now, I know that this post will cause a few people (you know who you are) to object with hand-waving arguments involving technical jargon that what really happens is something different. But until they put their ideas in the form of physical equations based upon known (and laboratory-measured) processes, which conserve energy, in a time-dependent model that also produces the observed average temperature profile of the atmosphere, I will not believe them.

What those people need to do is go read a book on atmospheric radiation, say Grant Petty’s A First Course In Atmospheric Radiation. I know Grant, and he is a brilliant and careful scientist. If you disagree with him (and the many other experts who agree with him), you’d better have some pretty good evidence to back your case up.

The bottom line, then, is the Greenhouse Effect, due mostly to greenhouse gases, is largely caused by the fact that the atmosphere emits IR energy downward, the so-called “back radiation”. This single component of the whole GHE process basically then determines all of the other features of the greenhouse effect and leads to net GHE warming of the Earth’s surface.

You can measure the greenhouse effect yourself with a handheld IR thermometer pointed at the sky, which measures the temperature change caused by a change in downwelling IR radiation. In a clear sky, the indicated temperature pointing straight up (“seeing” higher altitudes) will be colder than if pointed at an angle (measuring lower altitudes). This is direct evidence of the greenhouse effect…changes in downwelling IR change the temperature of a surface (the microbolometer in the handheld IR thermometer). That is the greenhouse effect.

If I’ve make a mistake in the above, I’ll fix it. I realize some might not like the way I’ve phrased certain things. But I’ve been working in this field over 20 years, and the above is the best I can do in 1-2 hours time. From some of the objections you will see in the comments, you will find it is a complex subject, indeed.

Greenpeace? Or Greendeceit?

Friday, June 12th, 2015

I just about made it out of Heartland’s 10th International Conference on Climate Change, now winding down near Capitol Hill, without having to deal with one of the 25 media outlets registered there known to be antagonistic to the view that global warming is neither all human-caused nor dangerous.

Then, a sharply dressed, very young man introduced himself (from Greenpeace) and asked if we could talk. Hmmm…

Oh, OK, I know we won’t agree, but maybe he wants to report on what was happening at the conference. I try to give everyone the benefit of the doubt. (Except the BBC…they burned that bridge twice).

The conversation began innocently enough, but then after 10 minutes of smiling accusations and baseless assertions, I was getting a little annoyed.

He even asked me if I considered him a “global warming Nazi“. I said, no, and explained the history of my use of that label (which I still stand by).

I said it’s obvious we are at opposite ends of the spectrum and tried to extricate myself from the conversation.

Then one of the conference staff and a security guard approached and said, basically, do you know this young man has a mic on him, and the young lady sitting across the way has a video camera recording your conversation?

Well, no I didn’t! How utterly delightful…and professional!

I said, well, my opinion of Greenpeace just went down a notch.

Did I ever have a positive view of Greenpeace, they asked me?

Well, yes, I’d say I once did.

And I said Patrick Moore (one of the Greenpeace co-founders) once did, too.

They both groaned. :-)

It’s too bad that Greenpeace now has to resort to deception to achieve their goals.

At the next conference I think I am going to agree to an interview with anyone…and make my own recording. If what Greenpeace did was illegal (I have no idea if you can record someone in DC without their knowledge), then I will let the interviewer know I will record them if they are recording me.

Then, if they cut and paste together pieces to make me look bad, I’ll have evidence of what really transpired.

UAH V6.0 Global Temperature Update for May 2015: +0.27 deg. C

Monday, June 8th, 2015

NOTE: This is the second monthly update with our new Version 6.0 dataset. Differences versus the old Version 5.6 dataset are discussed here.

The Version 6.0 global average lower tropospheric temperature (LT) anomaly for May, 2015 is +0.27 deg. C, up considerably from the April, 2015 value of +0.06 deg. C (click for full size version):
UAH_LT_1979_thru_May_2015_v6

The global, hemispheric, and tropical LT anomalies from the 30-year (1981-2010) average for the last 5 months are:

YR MO GLOBE NH SH TROPICS
2015 1 +0.26 +0.38 +0.14 +0.12
2015 2 +0.16 +0.26 +0.05 -0.07
2015 3 +0.14 +0.23 +0.05 +0.02
2015 4 +0.06 +0.15 -0.02 +0.07
2015 5 +0.27 +0.33 +0.21 +0.27

I suspect that the May warming is due to El Nino-related warmth in the Pacific.

The global image for May, 2015 should be available in the next several days here.

The new Version 6 files, which should be updated soon, are located here:

Lower Troposphere: http://vortex.nsstc.uah.edu/data/msu/v6.0beta/tlt
Mid-Troposphere: http://vortex.nsstc.uah.edu/data/msu/v6.0beta/tmt
Tropopause: http://vortex.nsstc.uah.edu/data/msu/v6.0beta/ttp
Lower Stratosphere: http://vortex.nsstc.uah.edu/data/msu/v6.0beta/tls

Temperature Update Delayed (so watch my cool video instead)…

Friday, June 5th, 2015

Sorry for the delayed temperature update for May, as I’ve been in Alameda, CA on family business. I’ll post the update when I get to work on Monday, June 8.

But in the meantime, check out the time lapse video I did of the full moon rising over San Francisco and the Golden Gate Bridge, as the lights come up in the city. Best viewed full-screen, since there are a lot of things happening:

TRMM Satellite Coming Home Next Month

Friday, May 22nd, 2015

Japan's Hayabusa satellite renters the atmosphere in June, 2011.

Japan’s Hayabusa satellite renters the atmosphere in June, 2011.

NASA’s Tropical Rain Measuring Mission, the first satellite to carry a rain radar, has been on-orbit since late 1997, but last year it finally ran out of the fuel required to keep it maintained at its relatively low altitude, 400 km.

So, TRMM is “coming home” after a very successful mission measuring tropical rain systems for over 17 years.

Back when the TRMM concept was being pitched by NASA-Goddard scientists at HQ, I was pitching the competing mission representing NASA-Marshall. In retrospect, John Theon (the Program Manager at the time) made the right decision and gave the go ahead to develop TRMM.

I helped campaign for the design of the TRMM Microwave Imager (TMI), but by the early 1990s our global temperature monitoring work was taking up most of my time and to everyone’s surprise (since my original expertise was rainfall measurement from satellites), I chose not to be part of the TRMM Team.

TRMM also carried one of the CERES Earth radiation budget instrument packages, which allowed researchers to document the diurnal cycle in cloud effects on reflected sunlight since TRMM was placed in a non-sun-synchronous orbit, as well as the Lightning Imaging Sensor (LIS) which was developed here in Huntsville, and a Visible and InfraRed Scanner (VIRS).

I’ve been tracking the fall of the TRMM satellite, and as can be seen it is now descending rather rapidly:

TRMM-altitude-since-Jan-2014

If we zoom in, we get a better idea of it’s trajectory in the last couple months, and Space-Track.org is now calculating a reentry date of June 19:

TRMM-altitude-since-April-2015

Once the satellite reaches about 90 km altitude, it reenters very quickly. Because the rate of descent is nonlinear, and depends upon the satellite orientation, which might be tumbling and causing variable amounts of atmospheric drag, it is almost impossible to determine where the satellite will fall…it could be anywhere between 35N and 35S latitude, as suggested by this single day of TRMM radar coverage:

TRMM-orbits

The June 19 date could also change substantially…it might be many days off. For example, in just one day, the reentry date was moved up by a day by the Space-Track folks.

I’d like to congratulate all of the many engineers and scientists here in the U.S., in Japan (which provided the radar), and throughout the world, who made the TRMM mission such a great success.

New Satellite Upper Troposphere Product: Still No Tropical “Hotspot”

Thursday, May 21st, 2015

One of the most vivid predictions of global warming theory is a “hotspot” in the tropical upper troposphere, where increased tropical convection responding to warming sea surface temperatures (SSTs) is supposed to cause enhanced warming in the upper troposphere.

The trouble is that radiosonde (weather ballons) and satellites have failed to show evidence of a hotspot forming in recent decades. Instead, upper tropospheric warming approximately the same as surface warming has been observed.

It has been also been pointed out, with some justification, that our lower tropospheric temperature product really can’t be used to find the hotspot since it peaks too low in the troposphere, and our mid-troposphere product might have too much contamination from cooling in the lower stratosphere to detect the hotspot.

A recent paper by Sherwood and Nishant in Environmental Research letters presented a reanalysis of the radiosonde data and claims to find evidence of the hotspot. I’ve looked through the paper and find the statistical black box approach they used to be unconvincing. I’ll leave it to others to examine the details of their statistical adjustments, what what the physical reasons for those adjustments might be.

Instead, I want to introduce you to a new product that is made possible by the new methods we now use in Version 6 of our UAH datasets (links at the bottom).

Since we now have a tropopause (“TP”) product, we can combine that with our lower stratosphere (“LS”) product in such a way that we pretty well isolate the tropical upper tropospheric layer that is supposed to be warming the fastest.

The following plot of the satellite weighting functions shows that a simple linear combination of the TP and LS weighting functions (from MSU3/AMSU7 and MSU4/AMSU9, respectively) gives peak weight in the layer where the strongest warming is expected to occur, approximately 7-13 km in altitude:

UT-weighting-function

If we apply the coefficients (1.4, -0.4) to the TP and LS products, the resulting “UT” (upper troposphere) product for the tropical oceans (20N-20S) produces monthly anomalies since 1979 as shown by the bright red line in the following plot (I have added offsets to all time series so their linear trend lines intersect zero at the beginning of 1979):

Upper-troposphere-vs-tropical-SST-sat-vs-CMIP5

Note that the linear warming trend in the UT product (+0.07 C/decade, bright red trend line) is less than the HadSST3 sea surface temperature trend (light green, +0.10 C/decade) for the same 20N-20S latitude band, whereas theory would suggest it should be about twice as large (+0.20 C/decade).

And what is really striking in the above plot is how strong the climate models’ average warming trend over the tropical oceans is in the upper troposphere (+0.35 C/decade, dark red), which I calculate to be about 1.89 times the models’ average surface trend (+0.19 C/decade, dark green). This ratio of 1.89 is based upon the UT weighting function applied to the model average temperature trend profile from the surface to 100 mb (16 km) altitude.

So, what we see is that the models are off by about a factor of 2 on surface warming, but maybe by a factor of 5 (!) for upper tropospheric warming.

This is all preliminary, of course, since we still must submit our Version 6 paper for publication. So, make of it what you will.

But I am increasingly convinced that the hotspot really has gone missing. And the reason why (I still believe) is most likely related to water vapor feedback and precipitation processes, which largely govern the total heat budget of the free-troposphere (the layer above the turbulently mixed boundary layer).

I believe the missing hotspot is indirect evidence that upper tropospheric water vapor is not increasing, and so upper tropospheric water vapor (the most important layer for water vapor feedback) is not amplifying warming from increasing CO2. The fact that UT warming is indeed amplified — by about a factor of 2 — during El Nino events in the above plot might be related to the relatively short time scales involved, since convective heating and radiative cooling are far out of balance during short term variations, but are much closer to being balanced in the long-term with global warming.

The lack of positive water vapor feedback is an especially controversial assertion to make, given that (1) SSM/I satellite measurements of water vapor have indeed been increasing in lock-step with SST warming, and (2) probably a unanimous opinion in the IPCC climate community that water vapor feedback is positive.

But the SSM/I measurements are largely insensitive to the very low levels of upper tropospheric water vapor, so they can’t tell us anything about upper tropospheric vapor. And while lower-tropospherc water vapor is governed mostly by SST, upper tropospheric vapor is governed by precipitation processes, and we don’t even understand how those might change with warming, let alone have those physics included in climate models.

Instead, I suspect the models have been adjusted so that precipitation systems detrain more water vapor into the upper troposphere with warming, simply because that’s what we see on short time scales, say during El Nino events, and so the convective parameterizations in the models are adjusted to meet that expectation.

As part of a DOE contract we have, we will be examining 183 GHz measurements of upper tropospheric vapor, but those are available only since 1991 from the DMSP satellites, and late 1998 from the NOAA satellites. And from what I’ve read, it might not be possible to get meaningful trends from those data. So, at this point it’s not clear that we can get long term trends from water vapor…although there has been some tantalizing evidence of upper tropospheric drying since the 1950s in radiosonde data.

You can read more about the issues involved in determining water vapor feedback, and why I think it might not be amplyfing global warming, here.

For those interested in combining the TP and LS products themselves, the new Version 6 files (look for “beta2″ in the filenames) are located here:

Lower Troposphere: http://vortex.nsstc.uah.edu/data/msu/v6.0beta/tlt
Mid-Troposphere: http://vortex.nsstc.uah.edu/data/msu/v6.0beta/tmt
Tropopause: http://vortex.nsstc.uah.edu/data/msu/v6.0beta/ttp
Lower Stratosphere: http://vortex.nsstc.uah.edu/data/msu/v6.0beta/tls

Iraq’s Largest Oil Refinery Still Burning After 5 Weeks

Tuesday, May 19th, 2015

The latest NASA MODIS satellite imagery from today shows that the huge Baiji oil complex continues to burn as the Islamic State torches the facilities there.

The MODIS thermal infrared sensors first indicated fires there on April 11, and by April 18 the black clouds of smoke had drifted almost 300 miles, well past Baghdad:

Baiji-refinery-fire-MODIS-4-18-2015

To give some idea of the size of the smoke cloud, here’s a wide angle view from April 18 stretching from Israel and the Mediterranean Sea to Baghdad (click image for full-size):

Baiji-refinery-fire-MODIS-4-18-2015-wide

Here’s today’s imagery (May 19, 2015); the size and extent of the smoke cloud changes daily depending mostly on wind conditions:

Baiji-refinery-fire-MODIS-5-19-2015

From what I’ve read, even if Iraqi forces regain control of the refinery, the complex is so expansive that IS can render it largely unusable by continuing to attack critical portions of the complex.

Nearly 3,500 Days Since Major Hurricane Strike… Despite Record High CO2

Friday, May 8th, 2015

Subtropical Storm Ana forming off South Carolina on May 7, 2015 (NASA MODIS image).

Subtropical Storm Ana forming off South Carolina on May 7, 2015 (NASA MODIS image).


As Subtropical Storm Ana churns off the southeast U.S. coast, the global atmosphere has exceeded 400 ppm carbon dioxide content for the first time in…well…who knows?

And also on tap for this month (May 25th, Memorial Day) is another milestone: 3,500 days since the last time a major hurricane (Cat 3 or stronger) struck the U.S., which was Hurricane Wilma in 2005.

Maybe we can all pause to remember the “good old days”, when hundreds or thousands of people died in major hurricanes. /sarc

You remember 2005, right? Hurricane Katrina? So many hurricanes that the National Hurricane Center ran out of names? The next year, Al Gore blamed it all on humanity’s carbon dioxide emissions in his movie, An Inconvenient Truth.

You might not remember that 2 years ago news reports also were reporting we hit record CO2, at 400 ppm. So why the latest report regarding 400 ppm? Well, because now we’ve exceeded 400 ppm, rather than just hitting 400 ppm.

The minor distinction illustrates an important fact: it takes a huge amount of CO2 emissions to raise the atmospheric CO2 concentration by even a tiny amount.

It took nearly a century to raise atmospheric CO2 concentrations from 3 parts per 10,000 to 4 parts per 10,000. That’s right, nearly a century to add 1 molecule of CO2 to every 10,000 molecules of atmosphere.

Most people aren’t aware that the atmospheric concentration would have gone up twice as fast if not for the fact that nature loves the stuff. No matter how fast we produce it with our cars and planes and power plants, nature sucks up half of it, like a starving dog that has just been fed dinner.

In fact, without CO2 life as we know it on Earth would not exist.

More CO2 has led to global greening. Increased agricultural productivity. It probably has contributed to recent warming, in my professional opinion, but that warming has been relatively benign, with no observable increase in severe weather.

Which brings me back to hurricanes. There is a huge amount of natural variability in global hurricane activity from year to year, and even decade to decade. For example, see Dr. Ryan Maue’s charts here.

This extreme variability would happen with or without humans, just like it happens in tornado activity. Yet, many people tend to anthropomorphize everything that happens in nature. Changes in nature are seen as an extension of changes in human behavior, specifically our use of fossil fuels. It really isn’t much different from medieval witches being blamed for bad things that happened.

Eventually a major hurricane will strike the U.S. again. Maybe it will be this year, maybe next year. No one knows.

But you can be sure that when the current drought in U.S. major hurricane strikes ends, that, too, will be blamed on humans.

Mystery Climate Index #2 Explanation

Friday, May 8th, 2015

Yesterday I presented this time series of climate data and asked if anyone could determine any physical causes based upon it’s character:

mystery-climate-index-2

I like the example because it shows realistic variability compared to, say, global average temperature variations.

I created it with a very simple function that actually has some basis in how the real climate system operates. Lance Wallace came closest to the right explanation. Bob Tisdale even gave a prediction of how politicians and environmentalists would have used it to call for energy policy changes. :-)

But the time series, with its multi-decadal warming trend, was created entirely from a monthly series of random numbers. It’s what I call a “constrained random walk”.

How Does this Relate to the Real Climate System?
If you had random monthly cloud variations over the earth, it would cause a monthly random climate forcing as more or less sunlight was absorbed by the system. That effect is cumulative, since the heat is stored by the land and the ocean. So, every month’s value is just the previous month’s value plus a new random number (I used +/-0.5 as the range of random numbers in Excel). BUT…this would just produce a random walk, which almost always wanders away from the average state over time. This is in contrast to the real climate system, which has net negative radiative feedback (the more it warms, the more infrared energy it loses to space, restoring the system to an average state).

You can mimic this negative feedback by just subtracting off 10% of the previous month’s value from the next month’s value. In other words, instead of each month being the previous month’s value plus a random number (which would produce a random walk), use 0.9 times the previous month’s value instead. This is actually an approximation to the time-dependent energy budget equation in a 1D global energy balance model.

The reason for this example is to show that relatively rapid (monthly) forcing in the form of just random cloud variations can cause low-frequency climate variability…even multi-decadal temperature trends. You don’t need variations in solar activity. The reason why is the climate system’s “memory” — its ability to store energy. Certain preferred time scales of temperature variability tend to show up because of certain characteristics of the system — the depth of the ocean mixed layer, the time it takes the tropical atmosphere to overturn, etc.

This kind of variability is contained, to a lesser or greater extent, in all of the IPCC climate models. The cloud variations aren’t really “random” because they have physical causes, but they can seem random because the causes are myriad and complex. This is also the type of simple climate model forcing we used in our papers demonstrating how cloud feedbacks in the climate system have likely been misinterpreted, because researchers tend to assume cloud variations are caused by temperature variations while ignoring causation in the opposite direction.

Thanks to everyone for offering their ideas. I hope you are beginning to appreciate how some of the structure we see in global temperature variations might simply be just nature flipping a coin.