Mathematics Reform Initialized in Estonia

WSJ reports on reform of mathematics education combining the power of the human brain and the computer:

• Jon McLoone is Content Director for computerbasedmath.org, a project to redefine school math education assuming the use of computers. The company announced a deal Monday with the Estonian Education ministry to trial a self-contained statistics program replacing the more traditional curriculum.
• Schoolchildren in 30 schools in Estonia may be able to escape this misery, as they will shortly be embarking on a pilot for a new way of learning mathematics, computer-based mathematics, that reduces the emphasis on computation — doing sums — and increases the emphasis on understanding the uses of mathematics in real-world examples (“should I insure my mobile, how long will I live, or what makes a beautiful shape”).
• Estonia has been at the forefront of education reform. Last year it rolled out a trial to teach children from as young as seven robotics and how to program.

This is a signal to launch Mathematical Simulation Technology.

The "Hockey Stick" of the OLR Spectrum

As CO2 global warming alarmism is now losing credibility after 15 years of stationary temperatures and emerging fear of a coming ice age, it becomes possible for the first time scrutinize the core scientific evidence of the warming effect of CO2, which has been accepted by leading skeptics including Lindzen, Spencer, Singer and WUWT, namely the ditch between wave number 600 and 800 in the outgoing long wave radiation OLR spectrum produced by the IRIS and AIRS infrared spectrometers carried by satellites:

It is difficult to question evidence of this form, which bears the sign of hard physics as precise numbers produced by elaborate expensive instrumentation, because it requires knowledge of both instrument and processing of directly measured data, which both can be hidden in difficult technicalities.

Therefore the ditch in the spectrum, interpreted as a warming effect or "radiative forcing" from atmospheric CO2, has served CO2 alarmism as an "undeniable scientific fact" which cannot be questioned, with a warming effect of about 1 C upon doubling of atmospheric CO2. To refer to the spectrum has come to signify a deeper insight carried by both alarmists and skeptics, hidden to ordinary people not used to read spectra.

To question this "undeniable scientific fact" makes you into a "denier" destined to dwell on one of the lowest levels of Dante's Purgatorium.

In any case I have done so in a sequence of posts on OLR and I have come to the conclusion that the ditch in the spectrum attributed to CO2 is a misrepresentation of reality, or fabrication of fake evidence, similar to that of the "hockey stick", which started the fall of global warming alarmism.

I hope that skeptics are now read to question the OLR spectrum as the key evidence of CO2 warming with the same ardor as in the case of the hockey stick. Physicists have a special responsibility because the OLR spectrum is physics and not climate science.

But to be honest, very few seem to be interested in discussing the OLR spectrum, as if it is given once and for all by some superhuman intellect and thus beyond human understanding and scrutiny. But it is fabricated by people like you and me, and since it is the very basis of CO2 alarmism maybe some day someone will picks the thread. Since the first "hockey stick" attracted so much attention, may this new "hockey stick", if it is a "hockey stick", will deserve some as well.

Anyway, here are the key questions:

• How was the OLR spectrum produced? 
• What was directly measured by the sensors, and what was computed in post processing?
• Does the spectrum describe reality with radiation "blocked" by CO2?

These are precise scientific questions which can be answered by using basic physics and mathematics, if only there is an interest in doing so. Alarmists are not interested but skeptics should be.

Maybe Fred Singer will then find reason to reconsider his message:

• I am opposed to those who criticize the global warming scare, basing it on what I consider to be incorrect physics. CO2 is certainly a greenhouse gas and should produce some increase in atmospheric temperatures but it is so small we cannot detect it.

Singer is convinced that "CO2 certainly is a greenhouse gas", probably because he takes for granted that the OLR spectrum is correct science.  Singer is a physicist and should be able upon close inspection to tell if it is or not.  

If it is impossible to detect that "CO2 is a greenhouse gas", then it would be incorrect physics to declare that in any case "CO2 is a greenhouse gas". If ghosts cannot be detected, then it is not correct physics to nevertheless declare that "there certainly are ghosts" but they are "so small we cannot detect them". Right Fred?

PS1 WUWT reports:

• Following last night’s State of the Union Address in which the president pledged to implement a job-killing climate change agenda, U.S. Rep. Blaine Luetkemeyer (MO-3) today introduced legislation to prohibit the United States from contributing taxpayer dollars to the United Nations Intergovernmental Panel on Climate Change (IPCC) and the United Nations Framework Convention on Climate Change (UNFCCC). 
• “The American people should not have to foot the bill for an international organization that is fraught with waste, engaged in dubious science, and is promoting an agenda that will destroy jobs and drive up the cost of energy in the United States,” Luetkemeyer said. “Unfortunately, the president appears to be ready to fund these groups, revive harmful policies like cap and trade, and further empower out of control federal regulators at a time when we should be doing everything possible to cut wasteful spending, reduce regulatory red tape, and promote economic growth.”

Apparently, Luetkemeyer has read the OLR spectrum and understood that the science is dubious...

PS2 Fred does not seem to be willing to answer my question about the reality of the OLR spectrum, but I think the question asks for an answer.

OLR Spectra Decoded as Fake!?

Consider the following outgoing long wave radiation OLR spectrum delivered by the Atmospheric Infrared Sounder AIRS flying on the Aqua satellite:

The graphs show the brightness temperature as function of wave number, with the brightness temperature the temperature of a blackbody with the same radiance at a given wave number as that recorded by the spectrometer (in principle bolometer) sensor, with in particular a zoom of the wave number interval 645 - 685 containing the main resonance at 667 of CO2.

We see a low brightness temperature of about 220 K and a peak at the main resonance at 667 of 250 K.  Both these brightness temperatures are lower than the temperature of 295 K in the atmospheric window between 800 and 1200, as if the sensor has recorded the presence of CO2 both at the tropopause (220 K) and in the middle of the troposphere (250 K).

We understand that a bolometer sensor measures radiance calibrated to blackbody radiance and thus cannot distinguish between low emissivity/high temperature and high emissivity/low temperature. This means that the assignment of brightness temperature is influenced by an unknown emissivity, which explains why the assigned brightness temperature is high at the main resonance 667 for which the emissivity is high, and low in the weak resonances surrounding the main resonance for which the emissivity is low. But it does not make sense that CO2 radiates from different temperatures for different frequencies, because all frequencies are assumed to have the same temperature.

The spectrum constructed is thus an artificial spectrum reflecting the sensitivity of the bolometer, which may be chosen so that resonances of CO2 are picked up before the continuous spectrum from the Earth surface, and then are assigned brightness temperatures according to radiance, as shown above. The weak resonances with low total emissivity of CO2 away from 667,  are then assigned a low brightness temperature (220 K) at full emissivity, as if all of the radiation from the Earth surface was blocked in the whole interval 600 - 800.

The OLR spectrum delivered by AIRS is thus an artificial spectrum constructed so as to hide that away from the main resonance 667, CO2 has small emissivity and thus cannot block all of the radiation from the Earth surface (even under doubled concentration from preindustrial level).

OLR spectra delivered by AIRS (and IRIS) are viewed as the key evidence of "heat trapping" or "radiation blocking" by atmospheric CO2. If these OLR spectra show to be fakes misrepresenting physics, the main scientific argument of CO2 alarmism evaporates.  So what does true science tell: fake or not fake?

PS To help discussion, recall the sparseness of the CO2 spectrum around 667 as pictured in the previous post.

Model of Atmosphere with CO2 shows Small Emissivity

Computed transmittance of atmosphere with CO2 with main resonance at wave number 667. Notice that the atmosphere is effectively transparent, except in a small interval around 667. The effect of CO2 is thus small.

Here is a another argument indicating that the effect of the atmospheric trace gas CO2 on the radiation balance of the Earth is small.

We recall the model of blackbody radiation studied on Computational Blackbody Radiation as a collection of oscillators with small damping with equal oscillator internal energy T representing temperature, with oscillator resonance frequencies n varying from 1 to a cut-off set at T and each oscillator radiating

• E_n = gamma T n^2    

where gamma is a universal constant, which is Planck's law. Summing over n from 1 to T, we obtain the total radiance

• E = sum_n gamma T n^2 = sigma T^4 

which is Stefan-Boltzmann's law with sigma = gamma/3. In the case of only one resonance frequency n = T, the radiance would be reduced to  

• e = gamma T T^2 = gamma T^3 ~ E/T

with the reduction factor 1/T. 

The radiance of an atmosphere which is fully opaque over the entire spectrum would radiate E, while an atmosphere opaque only for a specific frequency near cut-off T, would radiate e ~ E/T with a reduction factor  1/T. 

We conclude that the emissivity of transparent atmosphere with a trace gas like CO2 with only a few isolated resonances, would scale like 1/T and thus be small as soon as T is bigger than say 100 K.  

We thus find theoretical evidence from a basic model that the emissivity of the Earth's atmosphere with the trace gas CO2 would be small, and thus that CO2 would have little effect on the Earth's radiation balance.

Note that the sparseness of CO2 as a trace gas, gets expressed as a spareseness of absorption spectrum rather than small mass fraction because of the universality of blackbody radiation as being independent of the mass of the oscillators.

Story of Vanishing Evidence of CO2 Warming

In the late 20 century as the cold war was coming to an end, the fear of nuclear war was replaced by a fear of anthropogenic global warming caused by emissions of CO2 from burning of fossil fuels.

Governments united under UN gave massive support to science for producing evidence of global warming by CO2, evidence which governments could use to motivate a special tax on CO2, which would lead society into a new world without CO2-emissions, with lots of tax money to be spent by politicians.

Scientists started, with great enthusiasm stimulated by generous government grants, searching for evidence of a warming effect of CO2 in the form of a  "greenhouse effect" with CO2 named "greenhouse gas" because of its capability of absorbing and emitting infrared radiation at isolated specific frequencies, because of its unsymmetric molecular structure, as observed in an early study by the Swedish Nobel Laureate Svante Arrhenius from 1896.

But finding evidence was difficult because CO2 is an atmospheric trace gas (now 390 ppm) and it is always difficult to find evidence of a big effect from a small cause, because this can only happen in unstable systems and such systems have no permanence allowing study.

An idea which developed was that doubling of CO2 would cause a "radiative forcing" of extra 2 - 4 W/m2 to be added to the 240 W/m2 received from the Sun, which was connected to a global warming of 1 C. Of course 1 C would be barely noticeable, but that was the best that could be squeezed out of CO2 alone, but with feedback from the system under "radiative forcing" from doubled CO2, the warming could be inflated to 3 C, which would enough to motivate a tax on CO2 to save the world.

The whole story of global warming by CO2 then rested on finding evidence of "radiative forcing" of  2 - 4 W/m2 from doubled CO2 and scientists were ordered to construct instruments for recording radiation spectra, which could show this effect.

But this turned out to be virtually impossible, because 2 - 4 W/m2 was too small to be measured: It required an accuracy below 1% which was impossible to achieve in practice. The difficulty of a big effect from a small cause showed its real face.

To counter this "small cause - big effect" syndrome, new physics of "back radiation" was invented showing a warming of 300 W/m2 of the Earth surface from the colder atmosphere as a big cause, but the new physics violated the 2nd law of thermodynamics and thus belonged to fiction.

What then remained of scientific support of CO2 alarmism based on observation, was a recorded global warming 1970 - 1998 of 0.5 C, which was connected to an increase of atmospheric CO2 from 330 to 370 ppm during the same time.

But this connection disappeared during 1998 - 2013, which went by without global warming, while CO2 continued to increase to 390 ppm.

The evidence of global warming by CO2 has thus today crumbled to nil,  which presents a difficult case for the new report by IPPC under UN in charge of CO2 alarmism, to be presented in September. Without scientific support, a CO2 tax cannot be motivated and the whole BIG BLUFF project of unprecedented  dimensions, collapses.

... and All the King's Horses and all the King's Men Couldn't put Humpty together again...

This is a summary of a study I was led into starting in 2009 and I have reported on this blog.

Radiative Heat Transfer as Resonance Phenomenon

The analysis of blackbody radiation exposed on Computational Blackbody Radiation suggests that radiative heat transfer is a phenomenon of near-resonance between bodies communicating through electromagnetic waves combined with a phenomenon of high-frequency cut-off, which effectively leads to one-way heat transfer from warm o cold.

Vieving radiative heat transfer this way removes the non-physical aspects which appear when viewing radiative heat transfer as a two-way exchange of photon particles carrying heat energy back and forth from warm to cold and from cold to warm. The latter view is common in e.g. climate science with in particular downwelling long wave radiation DLR from a cold atmosphere supposedly warming the Earth surface. The non-physical aspects concern the idea of infrared photons and violation of the 2nd law in heat transfer from cold to warm.

The model analyzed on Computational Blackbody Radiation consists of a system of bodies with each body consisting of a set of oscillators subject to small radiative damping, which communicate by sharing a common force carried as an electromagnetic wave. In equilibrium the bodies share a common temperature and there is no heat transfer between the bodies.

Each body is like a radio receiver/sender communicating with the other bodies through resonance transmitted by a  force carried by electromagnetic waves, thus interacting over distance by resonance.

If one body is heated (e.g. internally), then its oscillator amplitude increases and so the corresponding balancing force and the residual force is transmitted to the other bodies which in resonance restore force balance reaching a common temperature. The result is that the heated body transfers heat energy to the surrounding colder bodies, by resonance over distance.

With this view, the functioning of an infrared thermometer can be understood as a set of oscillators which by resonance assumes the same temperature as a target at distance.

Similarly a selective infrared thermometer can be conceptualized as an oscillator with a specific resonance frequency with capability of at distance measuring at the temperature of a body with the specific resonance. It will operate like a sensitive radio sensitive receiver which can tune in on a weak sender at a specific frequency.

The Interferometric Reflectance Imaging Sensor IRIS carried by the Nimbus 4 satellite can be seen as such a selective infrared thermometer capable of measuring the temperature of the atmospheric trace gas CO2 through its main resonance at wave number 667, which produced the following spectrum supposedly demonstrating the warming effect of CO2 as the ditch around 667:

But as discussed in previous posts on emissivity, it is not all clear that the above spectrum constructed from measuring the temperature of the trace gas CO2 describes the emission spectrum of the Earth + atmosphere in the range of resonance of CO2. Most likely, it does not.

PS Here is a transmittance spectrum of CO2 from Scienceofdoom computed with spectralcalc illustrating the sparseness of the absorption away from 667. It does not seem plausible that the transmittance of a O2 - N2 atmosphere with a trace of CO2 is close to zero in the whole interval 600 - 800.

Here is a close-up of computed transmittance through 1 m atmosphere with typical CO2 concentration at 0.1 bar showing the sparseness of absorption:

Inflated Modtran Effect of Atmospheric Trace Gases

What is the effect of the atmospheric trace gas CO2 (390 ppm or 0.039%) on global climate? The answer by IPCC consensus is given in the following graph:

which shows the spectrum of the outgoing longwave radiation OLR from the Earth with atmosphere as computed by the software Modtran on the basis of certain satellite measurements.

The idea is that the ditch in the spectrum in the wave number interval 600 - 800 can be attributed to the main absorption line at 667 of CO2.  The total effect is then supposed to be the area between the Planck curves for 288 K and 220 K in the interval 600 - 800, which comes out to be about 40 W/m2. The total "radiative forcing" of atmospheric CO2 is thus supposed to be about 40 W/m2 (disregarding overlap with H2O),  which by Stefan-Boltzann's Law can be connected to a temperature rise of about 10 C.  The total effect of CO2 as the main cause of the ditch, would thus be global warming of 10 C. (With half the ditch attributed to CO2, the effect would be 5 C,  which by Lindzen is cut down to 2.5 C without disclosing the reason). PS With 20 instead of 40, and half of 20 attributed to CO2 one would get 10 W/m2 and thus Lindzen's 2.5 C.

If CO2 was complemented by other trace gases together covering the whole spectrum, the warming effect would be 288 - 220, that is a whopping 68 K, from the mere presence of trace gases.

Is this reasonable? Is it possible that trace gases, making the atmosphere opaque for certain wave numbers, can make the full atmosphere opaque over the entire spectrum?

No, it does not seem to be reasonable, as detailed in an earlier discussion, which means that the above spectrum computed by Modtran does not seem to describe reality.

Yet the Modtran spectrum is the very basis of CO2 alarmism as the core evidence that the presence of of a trace gas can cause substantial global warming.

So there is the question: Can the presence of trace gases make the atmosphere fully opaque?

AGW vs WMD

NASA is now spending big money on projects such as CERES to find instrumental evidence of anthropogenic global warming AGW, but finds nothing. It is similar to the fruitless efforts by CIA to find evidence of weapons of mass destruction WMD in Saddam Hussein's Iraq. Is this an expression of paralyzed US politics?

LB Överger IPCC: När Kommer KVAs Avbön?

Katternö-tidningen rappoterar att Lennart Bengtsson är på god väg att överge den CO2 alarmism han tidigare har har framfört för som ansvarig för KVAs uttalande till stöd för IPCC:

• Temperaturhöjningen är så liten att någon knappast skulle märka den, om inte vi meteorologer hade upplyst om saken.
• Jag vill snarare jämföra med katolska kyrkans medeltida avlatsbrev, vilket var ett effektivt sätt att få en förskrämd allmänhet att betala för att undslippa helvetets fasor. Dåtidens katolska kyrka visade här stor skicklighet. Vi får vara tacksamma att Luther lyckades få stopp på detta oskick, åtminstone i våra protestantiska trakter.
• Jag är inte bara surprised, jag är astonished!
• Att oroa sig för att Antarktis är på väg att smälta är nästan på samma nivå som att oroa sig för att jorden och Venus kan komma att kollidera inom så där en miljard år [vilket vissa modellberäkningar visar].

Nu väntar vi bara på att LB skriver om KVAs uttalande från stöd till avståndstagande från IPCCs CO2 alarmism. När kommer detta LB? Sveriges folk och regering väntar på besked för att kunna gå vidare! 

Kanske t o m LB skulle kunna börja uppskatta en person som jag, och inte bara anse att det jag skriver  är "rappakalja" enligt tidigare uttalande i DN? Kanske klockan har gått ett varv.

CERES and Radiative Forcing

      The Earth's energy budget according to CERES showing unphysical "back radiation" of 340 W/m2
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An overview of the CERES project is given in CERES, a review: Past, present and Future (2011):

• The Clouds and Earth Radiant Energy System (CERES) project’s objectives are to measure the reflected solar radiance (shortwave) and Earth-emitted (longwave) radiances and from these measurements to compute the shortwave and longwave radiation fluxes at the top of the atmosphere (TOA) and the surface and radiation divergence within the atmosphere. The fluxes at TOA are to be retrieved to an accuracy of 2%. 
• The first objective of CERES is to measure OLR radiances to an accuracy of 1% and reflected solar radiances to 2%. The global mean OLR flux is approximately 240 W/m2, so the requirement is 2.4 W/m2 accuracy. Likewise the global mean reflected flux is 100 W/m2, thus the requirement for shortwave flux is 2 W/m2.

We compare the accuracy of 2-3 W/m2 with by IPCC supposed "radiative forcing of  CO2" of 1.8 W/m2 and "total anthropogenic radiative forcing" of 1.6 W/m2 during 1750-2005 and 3.7 W/m2 from doubled CO2. 

We conclude that the accuracy of CERES even at the lower level of 1% for OLR, would not be good enough to detect effects of "radiative forcing" by CO2. 

That the "radiative forcing" of doubled CO2 would be 3.7 W/m2 is a wild guess by IPCC without experimental support, which serves as the following cornerstone of CO2 alarmism:

• Without any feedbacks, a doubling of CO2 (which amounts to a forcing of 3.7 W/m2) would result in 1 °C global warming, which is easy to calculate and is undisputed. 

Here the "easy undisputed calculation" is dQ = 4 dT, where dQ is "radiative forcing" and dT corresponding global warming as a differentiated form of Stefan-Boltzmann's Law Q = sigma T^4. 

The number 3.7 or 4 W/m2 is so chosen by IPCC that the global warming would be 1 C, according to the "easy undisputed calculation", which is not too big to not be possible and not too small to be negligible. The basic argument of CO2 alarmism is that with feedback 1 C can become 3 C which is alarming. 

The whole idea of "radiative forcing" lacks sound physics basis since the forcing comes from the Sun and only from the Sun, and this is reflected by the fact that it cannot be discovered by instruments measuring physical phenomena, that is, it is fiction of a BIG BLUFF.

PS CERES is selling itself e.g. on a video telling us

• When you add greenhouse gasses such as CO2 and methane you change that radiation balance on the top of the atmosphere and you change the amount of outgoing radiation so that imbalance means more energy in the system...part of it goes into the ocean...and part of goes into actually warming the Earth...all of those things should give you a coherent picture of how things are changing as we warm the climate...

The purpose is obvious: Use CERES to show global warming by radiative forcing from CO2. The only trouble is that CERES shows nothing of this sort...all attempts to measure radiative forcing by CO2 seem to fail miserably...the scale of the BIG BLUFF with its organized governmental science support, is really impressive...