Image Credits: NASA, BP.Blogspot.com, Wikimedia.org
By WUWT regular “Just The Facts”
NOAA’s State of the Climate In 2008 report found that:
The simulations rule out (at the 95% level) zero trends for intervals of 15 yr or more, suggesting that an observed absence of warming of this duration is needed to create a discrepancy with the expected present-day warming rate.
In 2010 Phil Jones was asked by the BBC;
“Do you agree that from 1995 to the present there has been no statistically-significant global warming?”
Phil Jones replied:
Yes, but only just.
In 2011, the paper “Separating signal and noise in atmospheric temperature changes: The importance of timescale” by Santer et al. moved the goal posts and found that:
Because of the pronounced effect of interannual noise on decadal trends, a multi-model ensemble of anthropogenically-forced simulations displays many 10-year periods with little warming. A single decade of observational TLT data is therefore inadequate for identifying a slowly evolving anthropogenic warming signal. Our results show that temperature records of at least 17 years in length are required for identifying human effects on global-mean tropospheric temperature.
In October 2013, the Remote Sensing Systems (RSS) satellite temperature data set reached a period of 204 months/17 years for which the slope is = -0.000122111 per year. For those not familiar, the RSS satellite temperature data set is similar to the University of Alabama – Huntsville (UAH) dataset that John Christy and Roy Spencer manage. Information about RSS can be found at here and the data set can be found here.
In November 2013, Dr. Robert G. Brown, Physics Department of Duke University wrote on WUWT:
This (17 years) is a non-event, just as 15 and 16 years were non-events. Non-events do not make headlines. Other non-events of the year are one of the fewest numbers of tornadoes* (especially when corrected for under-reporting in the radar-free past) in at least the recent past (if not the remote past), the lowest number of Atlantic hurricanes* since I was 2 years old (I’m 58), the continuation of the longest stretch in recorded history without a category 3 or higher hurricane making landfall in the US (in fact, I don’t recall there being a category 3 hurricane in the North Atlantic this year, although one of the ones that spun out far from land might have gotten there for a few hours). * Links added subsequently
While I must disagree with Dr. Robert G. Brown as to what one can and can’t be make into a headline, I do otherwise agree wholeheartedly. Unfortunately, with mainstream media outlets like PBS are running erroneous headlines like, “UN Panel: ‘Extremely Likely’ Earth’s Rapid Warming Is Caused by Humans” we are stuck reporting on average climate data. Amusingly, it has proven a quite effective method of informing the public and disprove erroneous alarmist claims and headlines, as Dr. Brown’s comment above attests.
For those not too familiar with the “Pause” in Earth’s warming, recommended reading includes: “Over the past 15 years air temperatures at the Earth’s surface have been flat while greenhouse-gas emissions have continued to soar.” The Economist “Global warming stopped 16 years ago, reveals Met Office report quietly released… and here is the chart to prove it.” Daily Mail “Twenty-year hiatus in rising temperatures has climate scientists puzzled.” The Australian “Has the rise in temperatures ‘paused’?” Guardian “On Tuesday, news finally broke of a revised Met Office ‘decadal forecast’, which not only acknowledges the pause, but predicts it will continue at least until 2017.” Daily Mail “RSS global satellite temperatures confirm hiatus of global warming, while the general public and mainstream press are now recognizing the AWOL truth that skeptics long ago identified…global temperatures are trending towards cooling, not accelerating higher” C3 Headlines
In terms of exactly how long the “Pause” has lasted, it depends on the data set and what it is being measured, e.g. in Werner Brozek’s recent article Statistical Significances – How Long Is “The Pause”? he showed that;
1. For GISS, the slope is flat since September 1, 2001 or 12 years, 1 month. (goes to September 30, 2013)
2. For Hadcrut3, the slope is flat since May 1997 or 16 years, 5 months. (goes to September)
3. For a combination of GISS, Hadcrut3, UAH and RSS, the slope is flat since December 2000 or 12 years, 10 months. (goes to September)
4. For Hadcrut4, the slope is flat since December 2000 or 12 years, 10 months. (goes to September)
5. For Hadsst3, the slope is flat since November 2000 or 12 years, 11 months. (goes to September)
6. For UAH, the slope is flat since January 2005 or 8 years, 9 months. (goes to September using version 5.5)
7. For RSS, the slope is flat since November 1996 or 17 years (goes to October)
Here’s what that looks like graphically;

However, to really see the big picture on “Earth’s Temperature” we must take into account many more measurements than just Surface and Tropospheric Temperatures. As such, the following is an overview of many of them. NASA’s Earth Observatory claims that;
“Global warming is the unusually rapid increase in Earth’s average surface temperature over the past century primarily due to the greenhouse gases released by people burning fossil fuels.”
so let us start there…
Global Surface Temperatures:
NASA’s Goddard Institute for Space Studies (GISS) Global Monthly Mean Surface Temperature Anomaly – 1996 to Present:

NOAA’s – National Climate Data Center – Annual Global Land and Ocean Temperature Anomalies:

UK Met Office’s – Hadley Center – Climate Research Unit (CRU) Annual Global Average Land and Ocean Temperature Anomaly;

the UK Met Office – Hadley Center – Climate Research Unit (CRU) Monthly Global Average Land Temperature;

and HadCRUT4 Global, Northern and Southern Hemispheric Temperature Anomalies:

The Pause appears to apparent in Earth’s Land and Surface Temperature record. It is important to note that the reason that the IPCC claims to be;
“95% certain that humans are the “dominant cause” of global warming since the 1950s” BBC
is because prior to 1950 Anthropogenic CO2 Emissions from Fossil-Fuels were insufficient to have a significant influence on “Earth’s Temperature”, i.e. Anthropogenic CO2 Emissions from Fossil-Fuels;

and Cumulative Anthropogenic CO2 Emissions from Fossil-Fuels:

In May 2013, the Economist noted that;
The world added roughly 100 billion tonnes of carbon to the atmosphere between 2000 and 2010. That is about a quarter of all the CO₂ put there by humanity since 1750. And yet, as James Hansen, the head of NASA’s Goddard Institute for Space Studies, observes, “the five-year mean global temperature has been flat for a decade.”
Additionally, surface temperature records are burdened with issues of questionable siting, changes in siting, changes in equipment, changes in the number of measurement locations, modeling to fill in gaps in measurement locations, corrections to account for missing, erroneous or biased measurements, land use changes, anthropogenic waste heat and the urban heat island effect. Thus to see the Big Picture of “Earth’s Temperature”, it also helps to look up.
Atmospheric Temperatures:
Since 1979 Earth’s “temperature” has also been measured via satellite. “The temperature measurements from space are verified by two direct and independent methods. The first involves actual in-situ measurements of the lower atmosphere made by balloon-borne observations around the world. The second uses intercalibration and comparison among identical experiments on different orbiting platforms. The result is that the satellite temperature measurements are accurate to within three one-hundredths of a degree Centigrade (0.03 C) when compared to ground-launched balloons taking measurements of the same region of the atmosphere at the same time.” NASA
Here is RSS Global Temperature Lower Troposphere (TLT) – Brightness Temperature Anomaly- 1979 to Present;

and this is the University of Alabama – Hunstville (UAH) Global Lower Atmosphere Temperature Anomalies – 1979 to Present:

Note: Per John Christy, RSS and UAH anomalies are not comparable because they use different base periods, i.e., “RSS only uses 1979-1998 (20 years) while UAH uses the WMO standard of 1981-2010.”
The March UAH Lower Atmosphere Temperature Anomaly was .29 degrees C above the 30 year average and RSS Global Global Lower Troposphere shows a .127 degrees C increase per decade.
When we look at Earth’s “canaries”, i.e. RSS Northern Polar Temperature Lower Troposphere (TLT) Brightness Temperature Anomaly;

appears to have Paused for the last 18 years and RSS Southern Polar Temperature Lower Troposphere (TLT) Brightness Temperature Anomaly;

looks like it has been on Pause for its entire record.
To this point we’ve only addressed the Lower Troposphere Temperatures, the following Temperature Anomaly plots from RSS will increase in altitude as is illustrated here:
Here is RSS Temperature Middle Troposphere (TMT)- Brightness Temperature Anomaly- 1979 to Present;

According to Remote Sensing Systems, “For Channel (TLT) (Lower Troposphere) and Channel (TMT) (Middle Troposphere), the anomaly time series is dominated by ENSO events and slow tropospheric warming. The three primary El Niños during the past 20 years are clearly evident as peaks in the time series occurring during 1982-83, 1987-88, and 1997-98, with the most recent one being the largest.” RSS
Middle Tropospheric temperatures appear to show slow warming overlaid with the El Niño/La Niña Southern Oscillation (ENSO) cycle, including several comparatively large El Niño events. Middle Tropospheric temperatures appear to entered The Pause with the large El Niño in 1998.
Moving higher in the atmosphere, RSS Temperature Troposphere / Stratosphere (TTS) – Brightness Temperature Anomaly- 1987 to Present;

has been in The Pause since records began in 1987, with a trend of just -.004 K/C per decade.
The 1997-98 and 2009 – 10 El Niño events are still readily apparent in the Troposphere / Stratosphere plot above, as is a spike from the 1991 eruption of Mt. Pinatubo. Note that the effect of Mt. Pinatubo is the opposite in the Lower and Middle Troposphere versus the Troposphere / Stratosphere (TTS), i.e. “Large volcanic eruptions inject sulfur gases into the stratosphere; the gases convert into submicron particles (aerosol) with an e-folding time scale of about 1 year. The climate response to large eruptions (in historical times) lasts for several (2-3) years. The aerosol cloud causes cooling at the Earth’s surface, warming in stratosphere.”
Ellen Thomas, PHD Wesleyan University
It is interesting that, incorporating the impact of three significant surface driven warming events, Troposphere / Stratosphere Temperatures (TTS) have been quite stable, however there is a bit of regional variation here, e.g.:
RSS Northern Hemisphere Temperature Troposphere / Stratosphere (TTS) – Brightness Temperature Anomaly- 1987 to Present;

has been increasing by .047 K/C per decade, whereas the RSS Southern Hemisphere Temperature Troposphere / Stratosphere (TTS) – Brightness Temperature Anomaly- 1987 to Present;

has been decreasing by -.039 K/C per decade.
Moving higher still in the atmosphere, the RSS Temperature Lower Stratosphere (TLS) – Brightness Temperature Anomaly – 1979 to Present;

“is dominated by stratospheric cooling, punctuated by dramatic warming events caused by the eruptions of El Chichon (1982) and Mt Pinatubo (1991).” RSS
The eruptions of El Chichon and Mt Pinatubo are readily apparent in the Apparent Atmospheric Transmission of Solar Radiation at Mauna Loa, Hawaii:

“The stratosphere” … “in contrast to the troposphere, is heated, as the result of near infrared absorption of solar energy at the top of the aerosol cloud, and increased infra-red absorption of long-wave radiation from the Earth’s surface.”
“The stratospheric warming in the region of the stratospheric cloud increases the latitudinal temperature gradient after an eruption at low latitudes, disturbing the stratospheric-troposphere circulation, increasing the difference in height of the troposphere between high and low latitudes, and increasing the strength of the jet stream (polar vortex, especially in the northern hemisphere). This leads to warming during the northern hemisphere winter following a tropical eruption, and this warming effect tends to be larger than the cooling effect described above.” Ellen Thomas, PHD Wesleyan University
The Lower Stratosphere experienced “dramatic warming events caused by the eruptions of El Chichon (1982) and Mt Pinatubo (1991).” RSS “The long-term, global-mean cooling of the lower stratosphere stems from two downward steps in temperature, both of which are coincident with the cessation of transient warming after the volcanic eruptions of El Chichon and Mt. Pinatubo.” … “Here we provide observational analyses that yield new insight into three key aspects of recent stratospheric climate change. First, we provide evidence that the unusual step-like behavior of global-mean stratospheric temperatures is dependent not only upon the trend but also on the temporal variability in global-mean ozone immediately following volcanic eruptions. Second, we argue that the warming/cooling pattern in global-mean temperatures following major volcanic eruptions is consistent with the competing radiative and chemical effects of volcanic eruptions on stratospheric temperature and ozone. Third, we reveal the contrasting latitudinal structures of recent stratospheric temperature and ozone trends are consistent with large-scale increases in the stratospheric overturning Brewer-Dobson circulation” David W. J. Thompson Colorado State University
Above the Stratosphere we have the Mesosphere and Thermosphere, neither of which have I identified current temperature time series for, but of note is that on “July 15, 2010” “A Puzzling Collapse of Earth’s Upper Atmosphere” occurred when “high above Earth’s surface where the atmosphere meets space, a rarefied layer of gas called “the thermosphere” recently collapsed and now is rebounding again.”
“This is the biggest contraction of the thermosphere in at least 43 years,” says John Emmert of the Naval Research Lab, lead author of a paper announcing the finding in the June 19th issue of the Geophysical Research Letters (GRL). “It’s a Space Age record.”
The collapse happened during the deep solar minimum of 2008-2009—a fact which comes as little surprise to researchers. The thermosphere always cools and contracts when solar activity is low. In this case, however, the magnitude of the collapse was two to three times greater than low solar activity could explain.
“Something is going on that we do not understand,” says Emmert.
The thermosphere ranges in altitude from 90 km to 600+ km. It is a realm of meteors, auroras and satellites, which skim through the thermosphere as they circle Earth. It is also where solar radiation makes first contact with our planet. The thermosphere intercepts extreme ultraviolet (EUV) photons from the sun before they can reach the ground. When solar activity is high, solar EUV warms the thermosphere, causing it to puff up like a marshmallow held over a camp fire. (This heating can raise temperatures as high as 1400 K—hence the name thermosphere.) When solar activity is low, the opposite happens.” NASA
In summary, “the Pause” is apparent in Earth’s atmospheric record, Lower and Middle Troposphere appear to have warmed slowly, overlaid with the El Niño/La Niña Southern Oscillation (ENSO) cycle, including four comparatively large El Niño events, and tempered by the cooling effects of the eruption of El Chichon (1982) and Mt Pinatubo (1991). Lower and Middle Tropospheric temperatures appear to have paused since the large El Niño in 1998. Tropospheric / Stratospheric temperatures appear to have been influenced by at least three significant surface driven warming events, the 1997-98 El Niño, and the eruptions of El Chichon in 1982 and Mt Pinatubo in 1991, but have maintained a stable overall trajectory. Stratospheric temperatures appear to have experienced two “dramatic warming events caused by the eruptions of El Chichon (1982) and Mt Pinatubo (1991).”, and “unusual step-like behavior of global-mean stratospheric temperatures” which has resulted in a significant stratospheric cooling during the last 30 years. Lastly, “during deep solar minimum of 2008-2009” “the biggest contraction of the thermosphere in at least 43 years” occurred and “The magnitude of the collapse was two to three times greater than low solar activity could explain.”
Ocean Temperatures:
“The oceans can hold much more heat than the atmosphere. Just the top 3.2 metres of ocean holds as much heat as all the world’s air.” Commonwealth of Australia – Bureau of Meteorology
From a surface perspective Hadley Center’s HadSST2 Global Sea Surface Temperature Anomaly;

NOAA’s – National Climate Data Center – Global Sea Surface Temperature Anomaly;

Reynolds OI.v2 Global Sea Surface Temperature Anomaly

all appear to be well into The Pause.
Obviously Sea Surface temperature only scratch the surface, thus changes in Ocean Heat Content are important in understanding “Earth’s Temperature”. Here is NOAA’s NODC Global Ocean Heat Content from 0-700 Meters – 1955 to Present;

and here is the same from Ole Humlum’s valuable climate data site Climate4you.com, NODC Global Ocean Heat Content – 0-700 Meters – 1979 to Present:

It seems apparent from the plots above that Global Ocean Heat has increased over the last several decades, and has not paused per se, however the rate of increase seems to have slowed significantly since 2004.
Sea Level:
“Global sea level is currently rising as a result of both ocean thermal expansion and glacier melt, with each accounting for about half of the observed sea level rise, and each caused by recent increases in global mean temperature. For the period 1961-2003, the observed sea level rise due to thermal expansion was 0.42 millimeters per year and 0.69 millimeters per year due to total glacier melt (small glaciers, ice caps, ice sheets) (IPCC 2007). Between 1993 and 2003, the contribution to sea level rise increased for both sources to 1.60 millimeters per year and 1.19 millimeters per year respectively (IPCC 2007).” Source NSIDC
Global Mean Sea Level Change – 1993 to Present:

Global Mean Sea Level Change Map with a “Correction” of 0.3 mm/year added May, 5th 2011, due to a “Glacial Isostatic Adjustment (GIA)” – 1993 to Present;

While it appears that Sea Level Rise has continued recently;

it is important to note that Sea Levels were increasing at a similar pace during the first half of the 20th century, before anthropogenic CO2 emissions were sufficient to have a significant influence on “Earth’s Temperature” and Sea Level:
Snow and Ice:
A proxy often cited when measuring “Earth’s Temperature” is amount of Snow and Ice on Earth. According to the United States Geological Survey (USGS), “The vast majority, almost 90 percent, of Earth’s ice mass is in Antarctica, while the Greenland ice cap contains 10 percent of the total global ice mass.” Source USGA
However, there is currently no generally accepted measure of ice volume, as Cryosat is still in validation and the accuracy of measurements from Grace are still being challenged. Sea Ice Area and Extent are cited as proxies for “Earth’s Temperature”, however there is significant evidence that the primary influences on Sea Ice Area and Extent are in fact wind and Atmospheric Oscillations.
With this said, Global Sea Ice Area;

had it’s largest maximum in 2013, since 1996 and has remained stubbornly average for the entirety of 2013. Antarctic Sea Ice Extent has remained above the 1981 – 2010 “normal” range for much of the last four months;

we had the third most expansive Southern Sea Ice Area measured to date;

and Southern Sea Ice Area has remained above average for almost all of the last two years:

At the other pole Arctic Sea Ice Extent has remained within the 1981 – 2010 “normal” range for the entirety of 2013;

and Northern Hemisphere Sea Ice Area had it’s smallest decline since 2006:

There appears to have been a negative trend in Northern Hemisphere Sea Ice Area and Extent, a positive trend in Southern Hemisphere Sea Ice Area and Extent, thus the resultant Global Sea Ice Area trend appears to be slightly negative. However, in the last 6 years there does appear to be a Pause in Global Sea Ice Area.
In terms of land based data, here is 20 Year Northern Hemisphere Snow Cover with 1995 – 2009 Climatology from NCEP/NCAR;

Northern Hemisphere Snow Cover Anomalies 1966 – Present from NCEP/NCAR;

Northern Hemisphere Winter Snow Extent – 1967 to Present from Rutgers University;

Northern Hemisphere Spring Snow Extent – 1967 to Present:

Northern Hemisphere Fall Snow Extent – 1967 to Present:

While none of the Snow plots offers a global perspective, when looking at the Northern Hemisphere, there appears to have been a slight increase in Winter Snowcover and Snow Extent, a decrease in Spring Snow Extent and no change in Fall Snow Extent over the historical record.
Based on the limited Global Ice and Snow measurements available, and noting the questionable value of Sea Ice Area and Extent as a proxy for temperature, not much inference can currently be drawn from Earth’s Ice and Snow measurements. However, there does appear to be a Pause in Global Sea Ice Area.
Conclusion:
The Pause in “Earth’s Temperature” appears in many of Earth’s observational records, it appears to extend for between 6 – 16 years depending on the data set and what it is being measured.
Additional information on “Earth’s Temperature” can be found in the WUWT Reference Pages, including the Global Temperature Page and Global Climatic History Page
Please note that WUWT cannot vouch for the accuracy of the data/graphics within this article, nor influence the format or form of any of the graphics, as they are all linked from third party sources and WUWT is simply an aggregator. You can view each graphic at its source by simply clicking on it.


davidmhoffer says on November 16, 2013 at 1:47 pm:
“O H Dahlsveen;
I do suspect that you are using one of the editions of “Kiehl & Trenberth’s
>>>>>>>>>>>>>>>>> .
Your suspicions would be completely wrong”.
= = = = = = = = =
If my suspicions are completely wrong, which is – of course – very possible, then I am very interested to learn where you do get your numbers from. I am always willing to learn more. The only way to do that is to ask. – So, please tell.
Shawnhet says:
November 16, 2013 at 8:02 pm
Respectfully, you’re way off here. The reason you are dividing by 4 is because of the geometry of the Earth and not because of some “Warmist” conspiracy. If the Earth was a flat disk you would be dividing by 2.
>>>>>
Shawnhet, respectfully, you’re way off here. If the Earth were a flat disk, there would be no “dividing by 2”. An “ideal absorber” would indeed be a flat surface, and there is no “divide by 2” in the SB equation.
I think maybe you are trying to use the SB equation to find an “average”. You cannot do that because the equation is non-linear.
For your questions about Earth’s total energy and surface area, the values at wikipedia are close enough.
Genghis says:
November 16, 2013 at 8:03 pm
“Hmm, you can only get that 360K temp directly under the noonday Sun at the equator. It is not even an average temp of the earth, not to mention that it isn’t an equilibrium temperature and you can even get a higher temp than that there because the albedo is less there too.”
>>>>>
Genghis, be aware that the SB equation does not give you an “average temp”. At equilibrium it gives you an EXACT temp for the solar radiation.
“Also albedo doesn’t matter if emission = absorption, albedo only affects the rate at which equilibrium is reached. And since the Sun has been roasting the Earth on a spit for 4.5 Billion years, equilibrium has long been reached.”
>>>>>
Albedo DOES matter because it affects the amount of solar radiation reaching the Earth. You will not find 360K on the surface of the Earth due to the cooling mechanisms. Equilibrium has NOT been reached, nor is it likely to ever be reached, due to Earth’s rotation.
“Don’t discount the simple direct S-B approach too quickly. It almost completely eliminates the greenhouse affect. Remember the warmers claim it is 255K by some weird calculations that violate Kirchoffs Law.”
>>>>>
The “simple direct S-B approach” is to use the equation exactly as it is supposed to be used. Any other usage renders results invalid. Consequently, 255K and 279K are both invalid.
Mario Lento:
In my message to you of Nov. 16, 2013 at 11:01 pm, I erred: the statistical significance level was 94%.
geran says:
November 17, 2013 at 5:10 am
“Genghis, be aware that the SB equation does not give you an “average temp”. At equilibrium it gives you an EXACT temp for the solar radiation.”
———
Yes, but because the Earth is rotating and the surface has mass that has to be warmed it is absorbing more radiation than it is emitting. Therefor it is not in equilibrium by definition. It isn’t even in a steady state.
“Also albedo doesn’t matter if emission = absorption, albedo only affects the rate at which equilibrium is reached. And since the Sun has been roasting the Earth on a spit for 4.5 Billion years, equilibrium has long been reached.”
>>>>>
Albedo DOES matter because it affects the amount of solar radiation reaching the Earth. You will not find 360K on the surface of the Earth due to the cooling mechanisms. Equilibrium has NOT been reached, nor is it likely to ever be reached, due to Earth’s rotation.
—————-
You are correct again, equilibrium for that particular spot or any particular spot is never reached and that is why 360K is never seen, but it has nothing to do with albedo or a cooling mechanism.
“Don’t discount the simple direct S-B approach too quickly. It almost completely eliminates the greenhouse affect. Remember the warmers claim it is 255K by some weird calculations that violate Kirchoffs Law.”
>>>>>
The “simple direct S-B approach” is to use the equation exactly as it is supposed to be used. Any other usage renders results invalid. Consequently, 255K and 279K are both invalid.
——–
I am using the S-B equation properly, by assuming equilibrium. It is the same 340 watts/m^2 Trenberth uses for the energy balance. The difference is that they claim that 30% of that number never gets absorbed. The problem though and the error that they are making is that reflected is exactly the same as emitted in an equilibrium condition.
A proof that they are wrong is the average temperature of the ocean, which is 6˚C (279K) or 340 Watts/M^2. Exactly the temperature predicted by the Stefan-Boltzman Law.
O H Dahlsveen;
If my suspicions are completely wrong, which is – of course – very possible, then I am very interested to learn where you do get your numbers from.
>>>>>>>>
I didn’t “get them” from anywhere. I learned how to apply SB Law in order to predict the temperature of components in a system during the design process for various pieces of equipment. For those applications the problem was considerably more complex. A current running through a resistor for example results in a certain amount of power (P in watts) being input to the resister. If I know the surface area of the resister, I ought to be able to calculated P in w/m2 and determine the temperature of the resister. Except that doesn’t work because the resister is also exposed to radiant energy from its local environment. So, I also need to know the average temperature of the immediate environment to calculate the base line temperature of the resister, and then calculate the amount the temperature of the resister will rise above the ambient temperature. But that number is also wrong because the resister is physically mounted in some manner to a circuit board or other apparatus, so there is going to be conduction between the resister and the apparatus. Now I need to also know the temperature of the apparatus under a range of conditions, and determine from there if conduction is going to increase, decrease, or not affect the temperature of the resister. With any luck the whole thing is inside a small closed container where the ambient temperature of the air rises to an equilibrium point during operation because it if isn’t, I then not only need to know the temperature of the air, but I have to calculate how much convection is going to be introduced during operation that will have a cooling effect beyond all the factors I’ve already listed. Plus that needs to be done across the operating temperature expected for the device in all use cases. For a control module in a car that could be sold anywhere in the world, I might have to do that set of calculations across a range of temperatures from -60C to +60C. With any luck the input voltage is DC. If it is AC, I’ll need to consider the frequency. For example, if the AC current is 60Hz, the average current would be zero. I’d use the RMS (root mean square) current instead to come up with an “effective average”. However, if the AC frequency is very low (say 1 Hz) and the temperature response of the component very rapid, that approximation would be invalid. I’d have to use peak voltage instead to determine maximum values.
Working out the math to come up with the effective black body temperature of earth is by comparison rather trivial.
geran says:
November 17, 2013 at 5:06 am
“Shawnhet, respectfully, you’re way off here. If the Earth were a flat disk, there would be no “dividing by 2”. An “ideal absorber” would indeed be a flat surface, and there is no “divide by 2” in the SB equation.”
You are right that there is no divide by 2 in the S-B equation – this comes from the fact that a disk(in this case) has a light side that at a given time absorbs light and dark side that does not. The dark side will still have a temperature though, and, thus, per S-B still emit energy to space. As such, you would treat a flat disk Earth as though it absorbed energy as though it was a single sided disk and *emitted* energy as though it was a double sided disk. Per S-B the temperature of an abject is determined by the amount of energy it emits, of course.
“I think maybe you are trying to use the SB equation to find an “average”. You cannot do that because the equation is non-linear.”
I am trying to find an average and I agree that the equation is non-linear but all your argument can do in this regard is *increase* the size of the apparent GHE, it does not decrease it or get you to a temperature of 360K that has to be cooled. As a hypothetical, imagine that through a network of mirrors or whatever most of the Energy hitting the Earth is focussed on a square kilometer of the Earth raising it to one million K. In order to energetically balance, the rest of the Earth’s temperature would have to be substantially less warm. If you were to take the average temperature calculated (by a comprehensive set of thermometers) on our hypothetical Earth and compare it to the calculated S-B one for our Earth the S-B must be higher (this is direct consequence of the non-linearity you mention).
The point here is that we can measure through our own set of thermometers that the average temp of the Earth’s surface is ~15C and what you mention above makes it impossible to return an answer above ~ -18C, we still have to explain where the 33C differential comes from. It can’t come from the non-linearity in S-B that would just increase the differential.
“For your questions about Earth’s total energy and surface area, the values at wikipedia are close enough.”
Cool. From the “energy budget of the Earth” page I get A. a total solar energy of 173 petawatts and B. From the main page on the Earth, i get a total surface area of the Earth of 5.1 X10^14 m^2 – by dividing A by B I get 339 W/m^2 which is pretty close to the 342 W/m^2 predicted under the standard derivation.
Cheers, 🙂
Genghis;
The problem though and the error that they are making is that reflected is exactly the same as emitted in an equilibrium condition.
Absorbed energy does work. Reflected energy does not. Hence absorbed and reflected are not exactly the same in an equilibrium or any other condition, and hence the logic behind removing reflected from the calculation,
A proof that they are wrong is the average temperature of the ocean, which is 6˚C (279K) or 340 Watts/M^2. Exactly the temperature predicted by the Stefan-Boltzman Law.
You can’t predict the temperature of the ocean strictly from SB Law. You have to account for cooling via evaporation and convection. You also have to account for energy on a seasonal basis from sea ice melting and cooling. Then there’s rain. Then there’s wind from over land which may bring warmer or cooler air into contact with the ocean depending on any number of conditions. Evaporation and convective processes are the big ones though.
I notice that my reply to Jquip above from November 16, 2013 at 11:20 pm had some muddled language.
The sentence “The area under a cosine curve as you described above is 2 which shows that the average flux hitting a flat disk is F the average hitting the side facing the sun is F/2 which is exactly what the purely geometric solution says.” should read:(** denotes changes to previous).
The area under a cosine curve as you described above is 2 which shows that ** when** the average flux hitting a flat disk is F **per unit area** the average flux hitting the side **of a sphere** facing the sun is F/2 which is exactly what the purely geometric solution says.
Cheers, 🙂
You also have to account for energy on a seasonal basis from sea ice melting and cooling
I meant melting and freezing.
@Shawnhet: “the average flux hitting a flat disk is F **per unit area** the average flux hitting the side **of a sphere”
Couple things. F is ‘watts per unit area’ already. You’re getting confused on ‘average.’ If we postulate a wall in space, perpendicular to the vector of the radiation, then F incident on the surface is identical to F projected at the surface. And as it is planar and perpendicular, then F anywhere is F everywhere. So we only need F projected at, but not on, and can plug it into SB and derive the temp anywhere and everywhere on that plane. But at which point the dimensions of the plane are completely meaningless.
@See – owe to Rich: “It is invalid because the value is…”
No, you didn’t show it was invalid. You produced a valid proof about a different subject. We are not talking about the total wattage incident on the circle describing the base of the hemisphere, nor of the area->area conversion. We are talking about the watts per unit area incident on the surface of the object. This is, beyond question, necessary as that’s the unit that SB takes and gives. And without question the Earth is not a wall in space.
This is a problem where reality is wrong or your model is. If you state that neither is wrong, then it is incumbent on you to show how you can reduce the geometry found in reality, to that of the preferred model you like, without introducing greater errors. This is, or should be, a remarkably trivial thing as it is a first business issue of modelling. For example, Newton or Gauss and the math that permits us to treat a spherical mass as a point mass. And if they had just said: “Imagine a cubic mass” therefore the average gravitational acceleration of a sphere is…” You’d be quite right in calling them charlatans. This is, of course, not what they did. They started with the geometry as found, and showed why and how it could be treated as a point mass.
davidmhoffer says:
November 17, 2013 at 8:55 am
Genghis;
The problem though and the error that they are making is that reflected is exactly the same as emitted in an equilibrium condition.
Absorbed energy does work. Reflected energy does not. Hence absorbed and reflected are not exactly the same in an equilibrium or any other condition, and hence the logic behind removing reflected from the calculation,
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That isn’t correct. A black object is exactly the same temperature as a white object in equilibrium and absorption = emission is exactly the same. Test it, I have.
Where albedo matters is in the time it takes to reach equilibrium. A black object will reach equilibrium very quickly while a highly reflective object will take a long time to reach equilibrium. The earth has had 4.5 billion years to reach equilibrium, time enough I think.
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A proof that they are wrong is the average temperature of the ocean, which is 6˚C (279K) or 340 Watts/M^2. Exactly the temperature predicted by the Stefan-Boltzman Law.
You can’t predict the temperature of the ocean strictly from SB Law. You have to account for cooling via evaporation and convection. You also have to account for energy on a seasonal basis from sea ice melting and cooling. Then there’s rain. Then there’s wind from over land which may bring warmer or cooler air into contact with the ocean depending on any number of conditions. Evaporation and convective processes are the big ones though.
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The processes you describe, evaporation, convection, conduction are energy flux within the system and do not effect the energy flow into or out of the system, only radiation can go into or out of the system. The Oceans contain over 90% of the total energy in the system so yes the S-B equation is a very good predictor of the oceans energy and temperature.
Jquip;
This is, beyond question, necessary as that’s the unit that SB takes and gives.
>>>>>>>>>>>>>>>
No it is not. SB Law is predicated on the energy absorbed by the object in joules per second being equal to the energy radiated in joules per second. Using w/m2 and the area of incidence is just a short cut to calculating the joules/s. The same goes for calculating the energy radiated. Using the total area times the w/m2 is just a short cut to determining the joules/s total.
http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
Genghis: “Therefor it is not in equilibrium by definition. It isn’t even in a steady state.”
True, but as a first order issue we not only desire, but need, a fixed base to start from. One that allows us to reduce confounding factors in a *non destructive* manner. From which we can then add back in the confounding factors properly without making everything go loopy. There is, in this, a notion of dead-end trivia values. That is, output that is interesting for comparison between non-interacting objects, but which is so thoroughly bodgered, that we cannot use it for inputs to other models about that object. Which, if done, becomes the GIGO problem so commonly mentioned here about Climate folks using dead-end trivia values as input, to produce more dead-end trivia values.
” The difference is that they claim that 30% of that number never gets absorbed.”
This derives from albedo. The significant problem with the radiation budgets is that they posit the F/4 model as something other than a dead-end trivia value. Such that when that is then used as input, they then compare it to what the averaged measured temps are. (To the degree that this is advisable at all.) Quite unsurprisingly they get a difference between these to numbers. But as they have an absolute number for temp, and a simple difference between the two, then they back fill the difference with IR feedbacks. If you assume that none of the numbers are dead-end trivia, then it isn’t really relevant whether it’s IR feedback or not, it is necessary that there is feedback of some wavelengths.
The problem in this is that T derived from F/4 is not representative of any geometry or average at all. And further does not represent a manner similar to how the average measured temp is derived. So at the absolute beginning the difference between these numbers is a GIGO value; dead-end trivia. And so the IR feedbacks remain a GIGO problem. And it just continues to pile on from there.
davidmhoffer: “SB Law is predicated on the energy absorbed by the object in joules per second being equal to the energy radiated in joules per second.”
Yes, I’m perfectly aware of this. But that’s not at all the whole story is it? For if that were the case we could simply consider the total Joules on the cross section to be the Joules/m^2 for a single unit area. I hardly need point out how absurdly wrong that would be.
jquip
The sun emitts a flux which is measured as joules/s/m2 which is intercepted by a disk of radius R, and re-radiated by a sphere of the same radius R. The ratio of area of the disk to area of the sphere is 1/4. It is as simple as that.
davidmhoffer: “The sun emitts a flux which is measured as joules/s/m2 which is intercepted by a disk of radius R,”
Are the joules/s/m2 intercepted by the space-wall called Earth or the surface of the sphere called Earth? We’re done bargaining about unit areas, now we only need to finish bargaining about whether the Earth is flat or not.
Jquip says:
November 17, 2013 at 9:46 am
“Couple things. F is ‘watts per unit area’ already. You’re getting confused on ‘average.’ If we postulate a wall in space, perpendicular to the vector of the radiation, then F incident on the surface is identical to F projected at the surface. And as it is planar and perpendicular, then F anywhere is F everywhere. So we only need F projected at, but not on, and can plug it into SB and derive the temp anywhere and everywhere on that plane. But at which point the dimensions of the plane are completely meaningless.”
Respectfully, you are avoiding the issue I raised. You provided a framework such the solar flux incident at point C on the surface of the Earth was Fcos(BAC). This is perfectly valid but not very useful on its own and leads to the next obvious question: what does the framework that you provided us tell us about the average flux at the surface of the Earth?
I submit that your framework leads to the exact same answer for the average value or F from the surface of the Earth as the standard derivation (and I have provided math to back that up). If I am mistaken somehow, please tell me what the correct (per you) answer is and how you calculate it.
Cheers, 🙂
jquip
The cross section of the energy flux intercepted by the earth is flat. The earth is a sphere.
Shawnet: “Respectfully, you are avoiding the issue I raised. ”
Honestly, I don’t see how you get from there from here; so there’s not any manner in which I think I can properly address it to begin with. I understand you’re after a cosine curve, but I can’t fathom how you get from the average height of a hemisphere to the area under a cosine curve. If my notes didn’t clear things up for you, then you’ll need to clear things up for me 😛
As for the ‘same value’ on standard deviations: My only assumption here is that you intend to mean from -1 to +1 sd, which is certainly not the same as 2/3. As for what it tells us? That every average is valid for every data set, so long as your error bars are large enough and you’re not concerned if it’s useful for later modeling tasks. Since you mention statistics, simply take the average of a bimodal distribution and then see what you can claim as valid and accurate information that gives you about the distribution itself.
Specifically here, we’re using one arbitrary manner of producing an average flux to produce an arbitrary temperature. And in the other we’re using an average temperature to produce an arbitrary flux. But, for bonus points, the average flux used to derive the arbitrary temperature is based on an a priori model of self-contradictory conditions (In the use we’re trying to put it to) to justify an average flux from an arbitrary temperature. Which is a terribly tangled bit of circular nonsense and a bit hard to sort through. So apologies for that, but it wasn’t my creation.
What I’ve put forward here is little more than how actual photons hit an actual sphere. The average flux of which can be used to derive T. But if you’re interested in radiation budgets and the average T as measured on the surface, then it should be done as the intergration of T, rather than the flux. That computes both things in the same manner. So while there are always errors, both values are computed in the same manner. So we can state that, whatever the error is in these calculations, it is only one rather than a collection of them going goodness which directions.
jquip;
Honestly, I don’t see how you get from there from here;
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The fact that he got an answer that exactly matches the answer derived strictly from geometry ought to give you pause.
davidmhoffer: “The cross section of the energy flux intercepted by the earth is flat. The earth is a sphere.”
So since we’re all certain that the flux is intercepted by the surface of the Round Earth, then if the F/2 calculation for the lit side is correct then there is a proof that we can reduce 2F/3 to it. This is not a bit of vulgarity or asking too much of people producing physical models. And, as noted, is precisely the same thing that was done in justifying the ability to treat spherical masses as point masses.
There is no necessity that using global equilibrium on a volumetric body, or on a differentially irradiated body makes anything that is feasible, non-absurd, or violates other laws of physics. But if that cannot be shown, then we are attempting to use a theoretically model — an analogy — in a manner that stretches it beyond the breaking point. But if we are to state that it is perfectly cromulent, then there is a proof of it that we do not get absurd results. And all we need for that is the reduction from what actually occurs in reality as 2F/3 to the conceptual notion of a the area of a hemisphere in relation to a disc as F/2.
If Thermo has it’s big boy pants on, and the use of this by Astronomers, Cosmologists, and Climatologists isn’t violating Thermo and the rest of the laws of physics then: Such a proof exists.
So what is it?
davidmhoffer: “The fact that he got an answer that exactly matches the answer derived strictly from geometry ought to give you pause.”
Well, it’s a different answer than the one I got derived strictly from geometry. So since you’re active, perhaps you can square that circle for me.
sigh.
He got F/2 for a hemisphere which is exactly the same as F/4 for the sphere.
jquip;
So since we’re all certain that the flux is intercepted by the surface of the Round Earth, then if the F/2 calculation for the lit side is correct then there is a proof that we can reduce 2F/3 to it.
>>>>>>>>>>
sigh.
There is no 2F and there is no 3. If you agree that the lit side is F/2 then for the sphere as a whole F remains the same and the lit side plus the dark side comes to 4. Which gives you F/4.