Read the post to see it properly.
A feast. A feast! For those who want the meat, the math and the diagrams (don’t miss the diagrams). As far as we know, this is the first time the architecture of the basic climate model has been laid out in one place on the Net. This is the most math heavy post this series, but it has to be done, and properly. This is where the 1.2 °C direct effect of doubling CO2 gets amplified to 2.5 °C with fairly basic physics. If the equations are not your forte, look at the “the Establishment Case” below the equations to get some idea why establishment scientists find it mind-bendingly hard to imagine how climate sensitivity could possibly be much different.
For commenters who know there are problems with this model (don’t we all), one of the points of doing this is to get through to the establishment leaders — to speak their language instead of having separate conversations. Of course, for some minds it will not matter what skeptical scientists say, but for other, key people, it will. We would expect seeing the flaws laid out so clearly will undercut the implacable confidence of leaders, though they may not say so.
Again, this ties for Most Uncontroversial Post on this blog. Everything here, the IPCC would agree with (except maybe the last sentence).
Do admire the diagram –Figure 2. It’s no accident it is similar to an electrical circuit diagram. Modeling and feedbacks have been tested to the nth by thousands of electrical engineers around the world building things we use every day. Thinking of the climate model this way is a useful technique to figure out where it goes wrong.
In a sense this is where silicon chip wisdom starts to scrutinize the climate maze.
— Jo
3. The Conventional Basic Climate Model — In Full
Dr David Evans, 24 September 2015, David Evans’ Basic Climate Models Home, Intro, Previous, Next, Nomenclature.
Here is the conventional basic climate model, in full. It builds on the previous post in the series, which explained how the model worked in the case of no feedbacks and only a CO2 input. This post uses the same terminology, notation, and ideas, without necessarily explaining them again. This is “heaviest” post in the series.
Readers who don’t want to see details of the mathematical modeling might want to skip straight to the diagram and the calculation of ECS at the end — a general understanding of the previous post and of the model diagram below is sufficient to make sense of the ensuing posts in this series.
The Set-Up: Multiple Influences and Multiple Feedbacks
Consider the hypothetical situation where only the only things that can change are:
- Temperature. While some variables might alter the relativities between various mean atmospheric temperatures, we will take the temperature to be the one we are most interested in, the surface temperature TS.
- The n driver variables, V1,…,Vn, are the climate influences considered in the model, such as the CO2 concentration, the total solar irradiance (TSI), or the externally-driven albedo (EDA). The driver variables are not directly dependent on the temperature, each other, or the feedback variables.
- The m feedback variables, U1,…,Um, are the feedbacks that the model considers, such as the average lapse rate, the surface-driven albedo, or the average height of the water vapor emissions layer (WVEL). Each feedback variable is dependent on the temperature, but is not directly dependent on the driver variables or on the other feedback variables. Because they depend on temperature, as the Earth warms these variables further affect absorbed solar radiation (ASR) or outgoing longwave radiation (OLR), which affects warming, which further affects these feedback variables, and so on in a feedback loop.
The previous post is the special case where n equals one, m is zero, and V1 is the base-2 logarithm of the CO2 concentration L.
We are going to focus on the balance of radiation entering and leaving the planet, so it is helpful to explicitly focus on the net top-of-atmosphere (TOA) downward flux, namely
How Much Does the OLR Change?
If the temperature, the drivers, and the feedbacks all change, how much does the OLR change?
We generalize the process that led to Eq. (3) of the previous post. G depends on TS as well as on each of the driver and feedback variables, but on nothing else because everything else is held constant. The arguments of G are treated as 1+n+m independent variables, each of which varies by an incremental amount (using the “d” notation). We apply the well-known calculus rule for partial derivatives: the total change in G is the sum of the changes due to each variable, and the change due to a variable is the product of the partial derivative of G in that variable with the actual change in that variable —
(The Σ symbols means to sum what follows, one term for each value of the index i, whose values are in turn 1, 2,…, n or m. Thus each Σ is the sum of n or m terms, where each of the n or m terms in that sum is like what follows the Σ but with the appropriate value substituted for i.)
The Balance between Temperature and the Climate Influences
As in the simple case, we convert this description of how OLR changes into a description of a balance between increases and decreases in net flux, by considering a move between two steady states. Assuming the planet stays close to steady state as the climate influences do their work, the incremental changes dX become small changes ΔX, so Eq. (2) becomes
The radiation is balanced in a steady state (i.e. G is zero), so there is no change in net downward flux between steady states, so ΔG is zero. Also, because ASR is not directly dependent on surface warming, by Eq. (4) of the previous post,
Applying these two relationships to Eq. (3) gives the equation describing the balance:
Ignoring the feedbacks (by pretending all the Ui and their derivatives are zero), this says that the increase in OLR due to surface warming is balanced by an increase in net downward flux (i.e. increases in ASR plus decreases in OLR) due to changes in the driver variables V1,…,Vn.
Interpretation
Changes in the drivers can be viewed as a process with n+1 stages:
- In stage i, where i is in {1,2,…,n}, the climate driver variable Vi changes by ΔVi and everything else is held constant, which increases the net TOA downward flux G by
- In stage n+1, the surface warms by ΔTS holding all the drivers constant, which increases OLR by exactly enough to restore the net change in G to zero.
Or these n+1 stages can be viewed as n+1 processes that occur simultaneously, without significantly interfering with each other, and we add the OLR changes that each causes (the climate is linear for small changes, so processes and changes superpose).
Feedbacks
Feedbacks complicate the balance in Eq. (5) by adding yet more downward flux (which can be negative) due to changing values of the feedback variables U1,…,Um, which change in response to surface warming. These extra downward fluxes have to be balanced by yet more OLR due to surface warming, requiring more surface warming, which further changes the values of the feedback variables, and so on in a feedback loop.
Solving Eq. (5) for ΔTS, the surface warming is
where the total feedback f is defined as
This expression for ΔTS is the same as it is without feedbacks (i.e. with f equals zero) except that it is multiplied by
which is the distinctive form of a feedback f around a multiplier λ0 — apply Fig. 1 with a equal to λ0 and b equal to f.
Figure 1: The closed-loop and open-loop forms of a feedback loop are equivalent.
AR5 reports the individual and total feedbacks from the CMIP5 as (Table 9.5 and Fig. 9.43, and p. 591), in W m−2 °C−1:
- water vapor +1.6±0.3
- lapse rate −0.6±0.4
- water vapor and lapse rate combined +1.1±0.2
- surface albedo +0.3±0.1,
- cloud +0.3±0.7,
and the total feedback is
(Incidentally, the loop gain, the total amplification going once around the feedback loop, is
It is less than one. If it were greater than or equal to one then the infinite sum implicit in the denominator in Eq.s (7) and (9) would not converge and the computed surface warming would be infinite.)
Forcings (aka Radiation Imbalances)
In Eq. (7) the contribution to the surface warming by every driver shares a part in common: the Planck sensitivity λ0, modified by the feedbacks f. This inspires the concept of the “forcing” of a driver, as the part peculiar to the driver variable: the (instantaneous radiative) forcing of a change ΔVi in the climate driver variable Vi is the resulting change to the net TOA downward flux, namely
(see AR5, section 8.1.1.1 and Fig. 8.1; this is the appropriate form of forcing for changes between steady states). The contribution the change in climate driver Vi makes to surface warming, before feedbacks, is the product of its forcing and the Planck sensitivity:
The (total) radiation imbalance is the total change in downward flux before feedbacks, or the sum of forcings due to the drivers:
Diagram
The situation is illustrated in Fig. 2:
- The first driver, V1, is the no-feedbacks ASR ANF, the portion of ASR that is unaffected by feedbacks in the period under consideration. (Moving between steady states, changes in ASR are due either to ΔANF or to albedo feedbacks. Changes in ANF are caused by something external to Earth, such as a fluctuation in TSI or a change in externally-driven albedo.)
- The second driver, V2, is the logarithm of the CO2 concentration, L.
- The feedbacks are all combined into the total feedback f, see Eq. (10) above.
- The computational paths from the drivers to the surface warming ΔTS are provided by Eq. (7), noting that (see Eq. (5) of the previous post for the last)
Figure 2: Conventional basic climate model, for changes from one steady state to another. The radiation imbalances (or forcings) due to the drivers are added (the purple circle), then balanced by the responding increase in feedbacks-adjusted OLR due to surface warming that would occur if all else was constant.
Adding the forcings and applying the feedbacks in Fig. 2, the surface warming is
where
Each driver adds its forcing to the input of the Planck sensitivity.
The Conventional Calculation of the ECS
The equilibrium climate sensitivity (ECS) is the surface warming ΔTS when the CO2 concentration doubles (i.e. ΔL is one) and the other drivers are unchanged, which by Eq.s (16) and (17) is
This agrees with AR5 (p. 1033), which finds the ECS as likely to be 1.5°C to 4.5°C (for all greenhouse gases, not just for CO2, because it is for a doubling of equivalent CO2 concentration — AR5 p.1451, p.1452). Setting f to zero in Eq. (18) gives the no-feedbacks-ECS found in the previous post.
The Establishment Case
This calculation in Eq. (18) shows that the sensitivity of carbon dioxide is about 2.5 °C (though in AR4 (2007) the central value was higher, about 3.3 °C), though there is a pretty wide uncertainty. Note that the three parameters in Eq. (18) were obtained mainly by basic physics:
- DR,2X, the decrease in OLR if CO2 doubles holding all else constant, is based mainly on spectroscopy that can be replicated in laboratories.
- λ0, the Planck sensitivity, comes from Stefan-Boltzmann’s law (though it gets modified by 20% or so because we are concerned here with the surface temperature rather than the radiating temperature of the Earth). Stefan-Boltzmann’s law is based on replicated laboratory physics, and is almost certainly beyond reproach.
- f, the total feedback, comes from the large computer models, but its main components are arguably based largely on known physical properties of water vapor and so are surely about right. Although the possibility exists that there is a large and unknown negative feedback that has inadvertently been omitted, it hasn’t been found despite decades of searching.
The first doubling of CO2 from pre-industrial levels level might occur by around 2070, and it is widely thought that the CO2 level will top out at most after about three doublings, in the next century or two. If three doublings from pre-industrial occur, the expected surface warming by Eq. (18) will be 7.5 [4.5,16.5] °C. Even 4.5 °C would be pretty disruptive, while the upper end possibilities would be disastrous. Hence the alarm.
Looking Ahead…
Skeptics who are familiar with the conventional model have mainly accepted Eq. (18) but queried the value of f, arguing that because the model’s implications don’t match a lot of empirical evidence there must be a large negative feedback missing from f.
In this blog series we accept the parameters, including f, as roughly correct, but argue that the logic in arriving at Eq. (18) is faulty, and that when the modeling is done correctly the ECS is an order of magnitude lower.
Japanese physical chemist Kyoji Kimoto shows a basic mathematical error in calculation of the Planck feedback parameter (false assumption of constant atmospheric emissivity) alone reduces ECS down to 0.1-0.2C
http://hockeyschtick.blogspot.com/search?q=kimoto+Planck
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No he didn’t. He unrealistically assumes all OLR comes from a single emissions layer at 5 km (the characteristic emissions layer, a viable concept but too simplistic an approximation to use for this purpose), then applies his own theory about how lapse rate changes affect the ECS (which differs substantially from the conventional model and what the IPCC does). Simple but wrong.
It is unfortunate that there are so many underdeveloped attempts to show the model wrong. Most are easily dismissed by professionals familiar with the terrain, and disappear without trace. Which makes it a bit harder for a substantial critique. This series is different, as you will see.
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“No he didn’t. He unrealistically assumes all OLR comes from a single emissions layer at 5 km (the characteristic emissions layer, a viable concept but too simplistic an approximation to use for this purpose), then applies his own theory about how lapse rate changes affect the ECS (which differs substantially from the conventional model and what the IPCC does). Simple but wrong.”
That’s not what Kimoto did. Please take a look at his published paper (at the bottom of this post) and unpublished paper here:
http://hockeyschtick.blogspot.com/2015/07/collapse-of-agw-theory-of-ipcc-most.html
The section regarding the lapse rate in the unpublished paper is independent of the section on the miscalculation of the Planck feedback parameter, e.g. on pages 1060-1063 of the E&E paper Kimoto shows why the Cess et al assumption that atmospheric emissivity is a constant is incorrect, but is instead “a complicated function of Ts” and leads to an incorrect calculation of the Planck feedback parameter.
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Kimoto did as I described. He also, as you correctly point out, made some claims about emissivity and the Planck feedback calculation, which I politely ignored.
In Kimoto’s E&E’s paper at your link, he claims the Planck feedback is incorrectly computed because emissivity variation was not taken into account. The emissivity may well vary, but the variation is too small to matter. Here is why. The vast bulk of the Earth’s radiation to space is emitted by GHGs, which, being gases, have zero reflectivity in infrared and thus perfect absorptivity — and because their absorptivity is one, so is their emissivity. That is, the emissivity of GHGs is 1.00 because they do not reflect infrared. The surface of the Earth has a lower emissivity, around 0.96 on average across land, ice, and water, on all relevant wavelengths averaged appropriately, but only a modest percentage of OLR is emitted by the surface (less than 20%, and even most of that really comes from the water vapor continuum near the surface). Consequently the emissivity of Earth for radiation to space is over 99%, and doubling CO2 can transfer at most 3.7 W/m2 of OLR from being emitted by a GHG (CO2, emissivity of 1.00) to being emitted by the surface (0.96).
Kimoto’s treatment is unusual. He puts the surface temperature TS (288 K) into the SB equation, which is physically wrong because it is not the Earth’s surface that emits to space for the most part, but then compensates for that when getting the correct OLR by using an effective emissivity of 0.6 instead of the usual 1.0 or maybe 0.995. Then he computes the Planck parameter from this SB equation. On page 1060 he quotes Bony doing the computation correctly (using the actual radiating or effective temperature of radiation, 255K), but then says Bony is wrong and her “proposed values failed when tested mathematically.” Big claim, simply wrong.
Kimoto seems to believes that the Earth radiates to space from the surface, and that the Earth’s emissivity is 0.6. This is not right. His work looks good on the surface but doesn’t stand up to scrutiny.
Kimoto asked me to review his second paper, which I did, but he hasn’t resolved the issues I raised AFAIK.
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David, I sent your reply to Kjoji Kimoto and this is his reply.
“He misunderstood the mathematical treatment of Kimoto(2009)..
Cess(1976) used Ts=288K in the SB equation, not me.
When Cess’s equation OLR=Eeff x sigma x Ts^4 (see Eq.9) is differentiated with Ts as performed in Cess(1976),
we obtain the following results.
Labmda0 =-dOLR/dTs=-4Eeff x sigma x Ts^3 – (dEeff/dTs) x sigma x Ts^4 (see Eq.10)
The second term cannot be neglected mathematically as Cess(1976) did.
Further, Eeff is a complicated function as shown by Eq.(16) when evaporation and conduction fluxes are included at the surface.
He did not read Cess (1976), Manabe & Wetherald (1967) and Hansen (1981).”
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I rest my case.
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“Skeptics have mainly accepted Eq. (18) ”
Not a lot of the one’s that I know about.
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Fair point. Changed post text to “Skeptics who are familiar with the conventional model have mainly accepted Eq. (18)…”
From post 1: “Most skeptics arrived at their doubts in the carbon dioxide theory of global warming by noting the discrepancies between that theory and empirical evidence. They are empiricists. Consequently, many skeptics are unaware of the basic model, or its power, because it has been irrelevant to them.”
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I’m aware of it, although I’m grateful to you for putting it all in one place rather than the cut ‘n paste I’ve done over the last 5 years to assemble it. The discrepancy between the model output and empirical observation has distressed me (it is impossible to discuss this conflict in normal, polite society, as the huge majority of people are ignorant of the detail and irritated by anyone who isn’t)
I’m an empiricist by both training and instinct, and as you say, have rationalised the discrepancy between model theory (hypothesis ?) and observation by firmly postulating that feedbacks are misconstrued. I’ve even debated this with Andy Lacis on Judith Curry’s website
So I’m obviously interested to see whether you can reconcile this most vexatious issue. On which side of reconciliation the chips fall is not scientifically relevant – that they are seen to fall without “prompting” is critical
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ianl8888, I know were you are coming from. I think I have found a resolution, and as it happens the empiricists were right.
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Dr. Evans,
I understand the need to take all of the IPCC’s assumptions as correct in order to reach them as you show the flaw in the basics physics equations. But after this is accomplished, there is still the matter of finding the sensitivity by comparing it to the temperature records. Everyone who has looked at it knows the temperature records are adjusted to exaggerate the trends in temperature, whether intentional or by ignorance, and that they leave in (or add in) large amounts of Urban Heating and Local Heat Islands. So if ΔTS is exaggerated by 200-300% then climate sensitivity will be half or a third of what is estimated using the polluted ΔTS value.
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How does the urban heating/heat island effect reconcile with the record heat showing up across most of the world’s oceans?
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If we could measure the worlds oceans accurately enough to know that it was a record, then it would be worth reconciling.
One thermometer per 250,000 km3 of ocean. Only 12 years of records. We know nothing.
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Your hubby and all other Earth’s fine ‘engen-neers’ do understand the big difference between amplifiers and oscillators. Not so much for meteorologists, or Climate Clowns.
Your Dr. Evans is still thinking orders of magnitude above that of “momback” serfs/slaves. Those that claim to know, are the real dregs of society!
You have your democratic choice. Jump or be thrown into the volcano
All the best! -will-
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Much of the heat you spoke of has already left the planet…
August HadSST3 tropical temps were high but at the same time, SSTs in both the NH and SH were COLDER than July. All three are complied monthly with a global average too (if you can look past the absurdity of a single ‘global’ temperature. Know that the ocean is not warming BECAUSE the NH & SH SSTs did NOT increase in August, leaving only the tropics as the last place the warmth anomaly is still high, where the Nino regions are. This El Nino is on it’s way out.
See the latest SST image put out every few days by NOAA here http://www.ospo.noaa.gov/data/sst/anomaly/2015/anomnight.9.24.2015.gif“, look at previous SST images from several months ago and compare to the latest. See that the SST heat intensity is less NOW than previous months. The NW pacific warm water “blob” has really dropped off recently in these images. Satellite water vapor and IR imagery also indicate far less ocean evaporation lately vs earlier this year. US temps are down too.
As F10.7 solar flux (driven by sunspot activity) has averaged below 120 (my empirically determined threshold for SST warming/cooling) for three months, and TSI has dropped like a rock since Feb, there has been INSUFFICIENT solar activity for further ocean warming. The last half of 2015 is a cooling period as solar activity is unlikely to increase significantly for long until the next solar cycle.
Record temps earlier were simply built-up from the recent solar maximum. CO2 was not involved with that.
It’s all downhill from here temperature-wise Seamus. Haven’t you noticed it’s not hot?
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David
You say
“feedback, comes from the large computer models, but its main components are arguably based largely on known physical properties of water vapor and so are surely about right. Although the possibility exists that there is a large and unknown negative feedback that has inadvertently been omitted, it hasn’t been found despite decades of searching.”
Not so . Surprisingly Trenberth has found one. Here is another section from
“1.3.2
The IPCC climate models are further incorrectly structured because they are based on three irrational and false assumptions. First, that CO2 is the main climate driver. Second, that in calculating climate sensitivity, the GHE due to water vapor should be added to that of CO2 as a positive feed back effect. Third, that the GHE of water vapor is always positive. As to the last point, the feedbacks cannot be always positive otherwise we wouldn’t be here to talk about it. For example, an important negative feed back related to Tropical Cyclones has recently been investigated by Trenberth, see:
http://www.cpc.ncep.noaa.gov/products/outreach/proceedings/cdw31_proceedings/S6_05_Kevin_Trenberth_NCAR.ppt
See what he says says in Fig 2.
http://3.bp.blogspot.com/-ZBGetxdt0Xw/U8QyoqRJsWI/AAAAAAAAASM/ewt1U0mXdfA/s1600/TrenPPT.png
Temperature drives CO2 and water vapor concentrations and evaporative and convective cooling independently. The whole CAGW – GHG scare is based on the obvious fallacy of putting the effect before the cause. Unless the range and causes of natural variation, as seen in the natural temperature quasi-periodicities, are known within reasonably narrow limits it is simply not possible to even begin to estimate the effect of anthropogenic CO2 on climate. In fact, the IPCC recognizes this point.
The key factor in making CO2 emission control policy and the basis for the WG2 and 3 sections of AR5 is the climate sensitivity to CO2. By AR5 – WG1 the IPCC itself is saying: (Section 9.7.3.3)
“The assessed literature suggests that the range of climate sensitivities and transient responses covered by CMIP3/5 cannot be narrowed significantly by constraining the models with observations of the mean climate and variability, consistent with the difficulty of constraining the cloud feedbacks from observations ”
In plain English, this means that the IPCC contributors have no idea what the climate sensitivity is. Therefore, there is no credible basis for the WG 2 and 3 reports, and the Government policy makers have no empirical scientific basis for the entire UNFCCC process and their economically destructive climate and energy policies.
The whole idea of a climate sensitivity to CO2 (i.e., that we could dial up a chosen temperature by setting CO2 levels at some calculated level) is simply bizarre because the response of the temperature to Anthropogenic CO2 is simply not a constant, and will vary depending, as it does, on the state of the system as a whole at the time of the CO2 introduction.
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Missing link …. another section from
http://climatesense-norpag.blogspot.com/2014/07/climate-forecasting-methods-and-cooling.html
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Dr Norman Page,
I’m pretty sure this isn’t as much about CO2 as it is about pulling the basis for CO2 models apart one piece at a time in such a way that there can be no argument.
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Dr Norman Page, the quote “The IPCC climate models are further incorrectly structured because…” appears to be from Mike Jonas writing on Watts Up, not from Keven Trenberth as your text might imply.
Trenberth says in his Powerpoint that some effects of thunderstorms are significant and omitted from the climate models, and suggests directions for minor improvements in climate models. His implications for climate models is they under-predict changes in hurricanes and “SSTs may get too warm”. He does not say “massive negative feedback found, this changes everything” or even “our estimate of ECS might be too high”.
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David . Trenberth’s power point slide says quite clearly that the total global effects total – 1.49 W/m2 v CO2 radiative forcing of 1.5 W/m2. and that “it matters and it is not included in climate models.” Surely your calculations should include it?
http://3.bp.blogspot.com/-ZBGetxdt0Xw/U8QyoqRJsWI/AAAAAAAAASM/ewt1U0mXdfA/s1600/TrenPPT.png
The overall quotation is from my blog linked in my comment
http://climatesense-norpag.blogspot.com/2014/07/climate-forecasting-methods-and-cooling.html
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My background is in model output statistics (MOS). In weather forecasting, the original models were terrible. Trial and error made them better but they still suffer substantial biases and systematic errors which continue to this day. To get around this, MOS was developed. Model Output Statistics have been the gold standard now for over 40 years. Many weather forecasters will deny reliance on MOS, but they would be lost without it.
The relevance here is that raw model output is generally terrible at forecasting by itself. I would assume the same for climate models.
Climate models need CMOS (climate model output statistics)but this is not easily achieved. With weather, we have millions of forecasts and variables and timescales and locations to hone the statistics. With climate models, the data for fine tuning is sparse. Thus forecast skill is extremely hard to evaluate and a monkey throwing darts can achieve success (or failure) on a small data sample.
Climate models have been around for a third of a century or so now. If you compare “forecast vs observed”, the best fit is achieved with a coefficient of about 0.4. In other words, multiplying the forecast times 0.4 gives the best result on observed data suggesting the models have over-forecast by more than a factor of two. Before condemning this result too terribly, keep in mind that the verification sample is simply too small. We know the physics are solid and well established. We just don’t have enough cases to evaluate whether or not the model output is actually accurate. What data we do have is not encouraging.
Worse yet, I don’t see how this lack of verification robustness will be solved. I’m not sure what would convince me that the models have enough skill to bet trillions of dollars on them.
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I’m a bit worried about the distinction between the “large computer models”,and the “simple” models used to analyze their output.
The large computer models involve some quite fundamental physics of each of the discrete “blocks” of matter that are modeled, plus some dodgy simplifications about complex things like clouds.
Is this heading towards a shooting down of the simple analysis models, leaving the “large computer models” unscathed, in particular their warming “predictions”?
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The large computerized models have the same critical mistakes, and we demonstrate one of them using their public output later in the series. In a fair world, shooting down the basic model for those mistakes would also bring down the GCMs. Presumably they will try the defense that the “GCMS are different”, but it will be difficult to make it stick because their architecture of the basic model is the same as the GCMs — as reflected in many public statements. The GCMs can be repaired, but that would change their ECS estimates in a major way.
So, correctly shooting down the basic model also shoots down the GCMs.
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This series has been fantastic because it has exposed the extraordinary complexity of individual Components of the “model” equations to many of us who who have not seen them.
Several components are apparently replicable in a lab where it is easy to maintain control of the input and so get sensible analysis of
response but what happens in the real world is that the input factor may be at the mercy of another factor and that one of another and in the
end the whole chain of interaction is UNKNOWN.
The ONLY way to test any model is in the environment it is supposed to work in and it must be tested and calibrated.
There MUST be a demonstrated experimentally proven, real world link between T atm and CO2 levels for the “models” in waiting to achieve the status of Model.
David has shown the extraordinary complexity of the model, mathematically, but the errors inherent in the cross linkages between components
tells us that the T vs CO2 supermodels are not really models but dysfunctional computer simulations.
UNIPCCC smoke and mirrors.
KK
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David,
In equation (2) you have written
dU_i = (dU_i/dT_S) dT_S
which implies that the feedback variables U_i depend only on the surface temperature T_S. Isn’t it possible that the feedback variables could depend not only on the surface temperature, but also on the driver variables V_i and even on other feedback variables?
If that is the case, then
dU_i = (∂U_i/∂T_S) dT_S + Σ_k(∂U_i/∂V_k) dV_k + Σ_k(∂U_i/U_k)dU_k
Is there some physical justification for assuming that the feedback variables depend only on the surface temperature? Or is it just a simplifying approximation?
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The way I read it, David does it so because that’s the way the climate scientist do it. One cannot assume the governing feedbacks are linear either, although one might suppose so, and one would be wrong. For example water feedback might be nett negative or positive or anything in between depending on the form of the water in the atmosphere.
There is a point for example where the evaporation from the surface and the normal lapse rate results in the temperature at height being below the Dew point. The result is a large non linear negative feedback tipping point ( is actually a form of saturation ). In general this means that the atmospheric temperature above the ocean can’t exceed about 33 degrees for very long. As the average temperature rises, the tropical band where this happens must expand… This is why on equatorial islands the temperature hovers between about 23 and 33 all year around.
This cloud feedback is negative, non-linear and temperature /rh / wind speed and pressure dependent. There is potential for this factor also to be tidal, that is modulated by the atmospheric bulge caused by the moons gravity.
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nhill, I’m following the conventional basic climate model. This is what they do. We’ll get to this soon.
It’s a simplifying assumption; if they use the complications you suggest then they cannot solve the model.
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David.
I am not lost by your eqations, but i miss a fast way to see the definitions of the variables and constants.
When you state dA/dAnf, sorry for not using proper letters, i would like to check your definitions immidiately for what it means.
Some might be defined in the previous posts, or some former pages, but it does not help in the deeper uderstanding of the matter.
In a paper book you could put a finger in at the pages with the definitions, but that is not so easy with an e-paper, especially not when it is in an other post.
Please take it positively, but it is hard to follow all those variables and constants.
Just as an example:You have insolation (Suns input to earth), you have albedo from clouds, and you have albedo from the ground. All have infuence on what is converted to heat in the ground. So i need to check what is A and what is Anf.
See it that way: The readers are not immidiatly used to the meaning of the variables and constants as you are, who has worked a long time with the matter.
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I’m working on a nomenclature pdf that collects the symbols and definitions as we go along. Will put a link in the navigation line of each post, after author name and date.
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That would be *very* useful. I’ve forgotten so much of the maths I used to know, but can follow the gist of what you say.
This is a fascinating exposé, and I thank you for your integrity and perseverance.
I can’t wait for the next part…
60
This is solved by using multiple browser tabs or multiple browsers in virtual desktops, or multiple monitors, screen snaps, or any combination of these options. No printed book has as many options as your computer. This is also where mobile devices show their greatest weakness. They are not an improvement over a printed book.
00
Very observant. The presentation is likely much more important than what is presented!
All the best! -will-
00
AMEN!
I am using a getit note pad. However some of the variables and constants are not very clearly defined.
This is what I have so far: (I hope they are correct)
>>>>>>>>>>>>>>>>
ASR = A = Absorbed solar radiation (energy from the Sun that is not reflected)
CO2 = C = Carbon dioxide
OLR = R = Outgoing longwave radiation (heat/energy from Earth to space)
TOA = Top of the atmosphere
TSI = S = Total solar irradiance (energy/heat from the Sun, incident on Earth)
T_S Surface temperature (global average air temperature at the surface)
ECS = Equilibrium climate sensitivity (the increase in TS when CO2 doubles)
EDA = Externally-driven albedo (albedo independent of surface warming)
L = Base-2 logarithm of the CO2 concentration C
W_VEL = Water vapor emission layer (average height of optical top of water vapor)
λ0 = the Planck sensitivity λ0,
D = the “Planck feedback”, The first partial derivative, of OLR with respect to surface temperature
V = n driver variables, V1,…,Vn, are the climate influences considered in the model
U = m feedback variables, U1,…,Um, are the feedbacks that the model considers
G = the net top-of-atmosphere (TOA) downward flux,
F = the resulting change to the net TOA downward flux
A_NF = Changes caused by something external to Earth, fluctuation in TSI, a change in externally-driven albedo
NF = no-feedbacks, the portion of ASR that is unaffected by feedbacks
I = Radiative Imbalance
10
There is now a Nomenclature pdf, linked from the author line below the title (after Joanne’s intro).
00
Not that it matters for present purposes, but I’ve always questioned this is my own mind. I have no doubt as to the spectroscopy, but taking into account, e.g., the range of tropopause heights, I wonder how much confidence we can have in the calculations based on that spectroscopy.
60
Professional skeptics have checked this pretty closely, and say it is correct. It was an obvious first point to check, and but seems to have been done a decade or more ago to everyone’s satisfaction. I just accept it.
50
Spectral absorption/emission lines of a gas irradiated by a source at the same temperature as the gas appear in what manner? Unless the gas is changing temperature, such is invisible for any instrumentation even in a laboratory! Absorption of moderate frequency flux modulation can be measured to about four decimal places, via synchronous demodulation. the flux itself remains unmeasurable.
All the best! -will-
114
That was a lovely breakfast, thank you Dr Evans & Jo.
Warmest Regards
Climate Heretic
PS I know, Puns intended. 🙂
110
I think this work is incredibly valuable, furthering our understanding of climate will always be worthwhile. As for swaying the alarmists – no chance. They did not get where they are using logic and science and won’t be swayed by it. If your goal is to turn warmists ad hominems , arguments from authority, and logical fallacies are the key.
72
As mentioned in post 1, the conventional basic climate model is the real reason the establishment scientists believe, in most cases. They often mention “basic physics” as their rock.
Showing that it is erroneous might shake things up, in the longer term. In the shorter term it may gives pause to the politicians etc. if they see that their climate scientists based their convictions on faulty logic.
120
OT, but it is beyond belief what a dream run Turnbull’s ABC is giving him. Listening to them talk about him on ABC-RN now.
40
I know I get slammed for criticising David, but I post my thoughts as I have them in the hopes that my criticisms infect your ideas and we end up with something useful. There are two points of possible error.
You nominate four main sources of feedback, then you proceed to superpose them in spite of the fact that they have different periodicity (lags). You can’t do that except in the dc case. At certain response frequencies the feedbacks could reinforce. It would be more appropriate to apply each feedback in series and consider the negative and positive gains separately when assessing the effect of the loop gain because it’s the total of only the positive feedbacks and potentially even the sum of the positive gains and the inverse of the negative gains that will cause instability given that you can’t superpose feedbacks with different lags. That is: can we assume that the feedbacks are phase stable with frequency – probably not.
Finally these are averages, but the stability of any feedback system is NOT governed by it’s average feedback, if feedback is dynamic then the stability is governed by the PEAK feedback! Since the climate is remarkably stable (hasn’t varied by more than 3 degrees or so in 288 degrees) ie more than about 1% over millennia large peak positive loop gains are nigh on impossible to support. The idea that a climate as stable as this has high levels of peak lagged positive feedback (loop gain approaching unity) in it is impossible to fathom, the assumption about gain and feedback MUST be wrong.
Also, a question
When the surface lights from any cause, the surface heats and there is a large portion of that heat that is directly reradiated either as reflected light or by the fact that the light is converted to heat and then broadband IR ( after being thermalised it is reradiated over a broad frequency range including the region where the atmosphere is transparent to IR ). If Will Kinimonth is to be believed about 80% of thermalised energy is reradiated this way. It follows that the same portion of the CO2 generated warming fraction that is thermalised at the surface will be lost to this cause. This constitutes a feedback of (1/1-(ab))= 1/5 ie 1/( 1 – 1×-4) ie b=-4.
The way I understand it the model seems to assume that all the CO2 energy is recycled through the same process, IE that the wavelength of the CO2 derived energy is not changed through the thermalisation and reradiation process.
Where does the model account for that loss?
101
Whoops,
I should say that the assumption about gain and feedback must be wrong OR there are saturation effects that constrain the temperature to this range (there are large non-linear feedbacks that are temperature dependent – for example cloud formation over ocean at 33 degrees)
61
“The way I understand it the model seems to assume that all the CO2 energy is recycled through the same process, IE that the wavelength of the CO2 derived energy is not changed through the thermalisation and reradiation process.”
You seem to be implying that atmospheric CO2 is somehow thermalized by surface EMR flux.
Is this only to go along with David’s presentation of the CAGW scam, as they present it, or do actually believe that radiation rather than convection determine the temperature in the troposphere?
713
No,
What I am saying is that if the physical surface is irradiated by IR reradiated from CO2, ie the back radiation, at that point the radiation is thermalised as physical surface warming that is indistiguishable from direct warming. The now thermalised CO2 emission is then subject to being radiated out the atmospheric window according to S-B.
Direct radiation to space is a real loss/feedback it is temperature dependent, it is what causes frost where the surface can become colder than the atmosphere above it. In fact if you consider things properly a reduction in frost aught to be one of the first effects of global warming, but globally that hasn’t happened.
101
bobl: You’re not criticizing me, but the conventional model, which I am merely presenting at this stage.
In steady state, and thus between steady states, issues of feedback timing (phases etc.) are irrelevant. In any case, this is what the IPCC says the feedbacks are and I’m accepting their figures.
Notice that, by focusing on changes in OLR from one steady state to another, the model mainly sidesteps around issue of back radiation and details of what happens under the layers that emit to space at the various wavelengths — these details are reflected in the feedbacks parameter, in so much as they need to be attended to.
80
Yes, my criticisms are of the basic model, and I am putting them on the record so potentially we can pick them up later.
Yes, thats what I would have thought, but in my discussion with Will, it was clear that there aught to be a negative feedback with gain 0.2 somewhere. I don’t understand why that is missing. It could be in the lapse rate feedback element but that seems far too small to represent the loss and direct surface loss to space would (to me) be independent of the lapse rate. Anyway, it’s on the record now to pick up later, something to think about.
Also on the record, I don’t think you can compute two steady states and assume that the path from state A to B is irrelevant where you have lagged feedbacks. If I have an oscillator from 1V to 9V the average output is 5V but does that describe the output properly – no since the output of the oscillator is only at the average twice per cycle.
The impulse response of the feedback network is going to be relevant.
Save for later discussion…
22
I don’t understand that, at least if you’re talking about linear models and focusing only on the initial and final quiescent states.
If before feedback whose transfer function is F(s) a system has an open-loop gain whose transfer function is G(s), the closed-loop transfer function H(s) will be given by H(s) = G(s)/[1+F(s)G(s)]. This is true even though the feedback transfer function F(s) is one, such as F(s) = f / (1 + s tau), that implies a lag.
So long as the equilibrium (origin) values F(0) and G(0) are respectively f and g (and sometimes even when they aren’t), therefore, the output-y change delta_y ultimately caused a change delta_x in the stimulus x between two otherwise-constant values will be h delta_x, where h = H(0) = g / (1 + f g). That value will be independent of what those feedback and open-loop transfer functions F(s) and G(s) are and thus of what state-space path the system took from the initial quiescent state to the final quiescent state.
So, at least as far as the linear-model world is concerned, I don’t quite understand your comment.
00
Is such a model applicable to a system that appears to tend toward an elusive equilibrium/steady-state, while continuously adjusting all 200 Navier-Stokes coefficients in some unknown manner. Is the operation of this atmosphere even bounded? How/by what?
All the best! -will-
214
Joe,
Even in electronics where you have dynamic feedback systems the steady state can depend on the direction from which you approach it ( hysteresis ) I also am pointing out that the steady state says nothing about the actual climate. Consider two 1 volt square waves one with 50% duty cycle and another 75%. The average in one case is 0.5 v in the second case 0.75 v but in each case the average is never actually experienced.
In the climate consider say Melbourne which varies from 0-40 average of 20 and Brisbane about 5 – 39 an average of 22. Brisbane is on average 2 degrees warmer than Melbourne but is it hotter? No, Brisbane maximum is limited to about 39 while Melbourne can get up to 41 – 45. Melbourne is hotter.
Equatorial islands have temperature ranges from about 23 – 33, a mean of a scorching 28! 8 degrees warmer than Melbourne, but maximums are limited to about 33
they are much cooler than Melbourne in summer in spite of the min max mean being 8 degrees warmer. The dynamic behavior at any given climate state is central to the perceived climate.
Finally, let’s consider a hypothetical situation where instability causes a temperature oscillation, the temp monetarily drops, such that freezing occurs, the path that the climate has taken between state a and state b has changed albedo which aborts the oscillation at a different temperature than the static situation would suggest, this of course wouldn’t happen if the temp overshot, melted ice and decreased albedo. In either of these cases the final steady state would be dependant on the path the climate took between states
10
I’m afraid I don’t follow what you’re getting at with the duty-cycle stuff. But, sure, if you want to talk about hysteresis and so forth, then, yes, the history makes a difference.
I questioned your original comment because Dr. Evans seemed to be talking about using a linear model for transitions from one quiescent state to another, and you seemed to be emphasizing lags in that context. There the quiescent states depend only on the forward- and feedback-path DC gains, not on what their transient properties are.
But if your point is that history cannot in general be ignored, I agree.
00
At the risk of calling what looks to be a rather complicated model simplistic, it really is.
One of the greatest flaws of the ‘radiative greenhouse model (RGM)’ is that it assumes that the earth sun system is in ‘steady state’, or static equilibrium. At the overall level of total energy in = total energy out the system is steady state, however the RGM assumes that the earth is in STATIC equilibrium with the sun which it self evidently is not. The earth is in DYNAMIC equilibrium and any realistic model needs to take this into account.
It is probably OK, in the short term of decades or centuries (maybe not millennia though), to ignore seasonal differences and changes in orbital geometry of the solar system. It is however most definitely not OK (IMHO), to ignore the daily rotation of the earth and the clearly different processes by which the surface of the earth loses energy obtained from the sun, during the day and night and at different latitudes.
It may not be possible to construct an accurate model taking all of the above (and considerably more, for instance a reasonably correct model would not assume that the earth is an SB black body receiving an average insolation equal to one quarter of the maximum at every point of the earth’s surface), into account.
There are too many things about the RGM which remind me of the old story about averaging, which sees a man with one foot in a bucket of iced water and the other in one of boiling water, as being at a bearable average.
70
There are an awful lot of factors left out, aren’t there?
As Albert Einstein famously opined, “Everything should be as simple as possible, but no more so.”
Models necessarily approximate reality by simplifying it, trying to capture the essence (the factors that make the most difference) and to omit the insignificant clutter. Problem is, it’s hard to know which is which in advance, and the only real way to tell is to test the model against reality. Climate models take decades to test, so it’s taken awhile to be sure that this model fails.
I will show that the conventional model is simplistic in a couple of crucial respects, fix those aspects, and thereby make an alternative model. Maybe that alternative model also, in the fullness of time, will be shown to fail to capture the essence of the climate.
The GCMs are an attempt to take into account all the factors. However they have the same architecture as the basic model, and make some of the same simplistic errors.
90
Also, it “feels too linear” and/or “not chaotic enough”. It would seem to me that the drivers would not only affect temperature, but each other at times. So that “holding everything else constant” may not be a reasonable thing to do. Building a model of a chaotic system may not be possible at all. Especially one as complex as the climate.
50
Dr. Evans and Jo,
Thank you for a wonderful 65th birthday present!
I will probably not be able to follow all the math but I will try.
So Thanks again
Gai
Happy Birthday Gai! — Jo
140
Many happy returns gai, thanks for your excellent comments also, you’ve really been kicking warmist butt lately.
Regards Y. Stone. 🙂
30
A Galileo presenting his case,
Would by warmists be called a disgrace,
Then forced to retract,
His denial of ‘fact’,
That Earth was fixed central in space.
190
@Ruairi
I just love your ability to capture the essence of a post with a limerick!
Every one a gem.
BRgds,
-P.
40
There was a young man, David Evans,
Who assiduously modelled the heavens,
In warmist maths he indulged
With coming flaws yet divulged
To which they’ll reply, “Good ‘eavens”!
70
The center of the universe must be always elsewhere/when!
011
Dr. Evans,
In New Science 2: you refer to this book/paper;
Principles of Planetary Climate
R. T. Pierrehumbert July 25, 2009
Is this because the CAGW folk use it as reference, or do you think it is a valid reference for thermodynamics or electromagnetics?
I downloaded a copy and cannot believe that anyone would accept such meteorological nonsense! It simply has no scientific physical relevance at all!
I would like to follow what you present. What I find is your bold agreement with the underlying concepts that are all invalid.
No matter how the invalid is pieced together, it is still invalid. You seem to be agreeing that some points are valid, only because that is what is claimed.
Your presentation here;
“DR,2X, the decrease in OLR if CO2 doubles holding all else constant, is based mainly on spectroscopy that can be replicated in laboratories.”
What is measured/replicated in laboratories is not at all what is measured/replicated,. in this atmosphere. In this atmosphere there is no way to determine the source of unmodulated exit flux so no way of determining attenuation of flux at any frequency. WV and CO2 attenuate nothing. This is fallacy #1.
“λ0, the Planck sensitivity, comes from Stefan-Boltzmann’s law (though it gets modified by 20% or so because we are concerned here with the surface temperature rather than the radiating temperature of the Earth). Stefan-Boltzmann’s law is based on replicated laboratory physics, and is almost certainly beyond reproach.”
Only when applied to near blackbody surfaces with no intervening dissipative media. Both Planck’s equation and the S-B equation are for a theoretical maximum. The S-B equation gives only the maximum one way flux plus direction normal between two flat surfaces at any two temperatures. The parenthesis containing the difference between functions of temperature must be evaluated before any other algebraic process. None of this applies to this planet in any way. This is fallacy #2
“f, the total feedback, comes from the large computer models, but its main components are arguably based largely on known physical properties of water vapor and so are surely about right.”
You seem to agree with the concept of radiative feedback, This is what hasn’t been found despite decades of searching. This is fallacy #3.
All the best! -will-
416
Pierrehumbert’s 2010 textbook, Principles of Planetary Climate, is considered the gold standard of climate textbooks. This link to a 2009 pdf copy seems to be legit: http://cips.berkeley.edu/events/rocky-planets-class09/ClimateVol1.pdf.
It is thus an authoritative source of establishment climate thinking. I recommend it — it’s not perfect, but neither is our state of knowledge.
201
“It is thus an authoritative source of establishment climate thinking. I recommend it — it’s not perfect, but neither is our state of knowledge.”
Thank you! and all success
I can now see how very wrong their thinking must be. This source treats thermodynamics as mechanics and electromagnetics, EMR, as basic thermodynamics.
There is no science, or any kind of our state of knowledge, in it. It appears total fantasy. Of all that is known in engineering of these two subjects, none appears!!
All the best! -will-
517
Sorry David have to agree with Will about Pierrehumbert’s book. If that is the establishment take on the engineering subjects of thermodynamics, heat & mass transfer, fluid dynamics and reaction kinetic they do not have a great understanding of the basics of engineering science.
Not sure if you mentioned the radiation window in part 1 or 2 but I have just put a post https://cementafriend.wordpress.com/2015/09/ which gives a value of 66 W/m2 from satellite measurements and agreed by Dr Trenberth. Plugging that in a energy balance shows that there is no need for the backradiation assumption. Also note that Max Planck proved the 2nd law of Thermodynamics in a book titled “Treatise on Thermodynamics” 1903
217
CAF,
Zenith flux at 8-13.5 microns can reach over 60 W/(m^2 sr) over 30 N lat on clear nights! However the 85% cloud cover in this band much reduces this. The largest contributor to exit flux power comes from the continuous solar evaporation of existing airborne H2O condensate, when this is released as the WV re-condenses it airborne condensate on the dark side.
Never even mentioned by Trenberth and his University Corporation for Atmospheric
ResearchNonsense!All the best! -will-
117
Will wrote: “What is measured/replicated in laboratories is not at all what is measured/replicated,. in this atmosphere. In this atmosphere there is no way to determine the source of unmodulated exit flux so no way of determining attenuation of flux at any frequency. WV and CO2 attenuate nothing. This is fallacy #1.”
Totally wrong! Given the composition and temperature of the surface of the earth, we know that it emits an average of 390 W/m2 of thermal infrared radiation. We have satellites in space that measure an average of 240 W/m2 of thermal infrared escaping to space from the top of the atmosphere. The outward flux from the surface is “attentuated”. Quantum mechanics and measurements in the laboratory tell us how WV and CO2 interact with this flux by both emitting and absorbing photons.
Planck’s Law and the derived S-B equation apply to radiation in equilibrium with the medium through with it is passing. Those who treat the earth as a black or gray body with a single temperature always run into problems because the radiation flowing through the atmosphere often has not come into equilibrium with an atmosphere whose temperature changes with altitude. Radiation transfer calculations in such non-equilibrium situations are handled by the Schwarzschild equation. This is how the forcing for 2XCO2 is calculated.
121
Environment Minister claims responsibility for ending an Abbott government proposal to investigate climate modelling.
The Australian newspaper today
80
I know The Australian calls it modelling but it reads more like it was about their homogenisation of temperature records, as many were calling for.
20
He should be held responsible for the billions of dollars of wrong decisions being made on the basis of “adjusted BoM” data. This adjusted data will basically alter in a major way the future of this country due to high energy cost further destroying industry; causing inappropriate investment in expensive unsustainable energy; loss of coal export markets as investment in coal industry being discouraged; inappropriate water projects such as desal plants because someone told government it would never rain again; loss of standard of living for consumers because of expensive domestic energy; downsizing of housing to make it more energy efficient which lowers standard of living; over investment in public transport and bicycle lanes supposedly to save “greenhouse gases” etc. etc.
21
might be useful to define G for clarity
G = balance of radiation entering and leaving the planet
especially as it is then used in subsequent equations
30
David,
“CO2 influence” in your diagram does not exist in reality. It is a product of the so called “greenhouse effect” that is supposed to raise the temperature of the surface of the Earth above what the Sun can possibly do, and that without any other more powerful source of energy. This is physically impossible, because it violates the law of conservation of energy. Such a warmer surface would radiate more energy away than it gets from the source of heat. This is equivalent to energy production out of nothing, which is not possible.
519
Greg, we’ve been through this topic to the nth. Greenhouse gases are just working to slow the heat loss of energy flowing from a very hot sun, through the Earth to very cold space. They work like an insulator. They are not “generating energy” which of course would be silly (or nuclear).
see Why greenhouse gas warming doesn’t break the second law of thermodynamics
and
So what is the Second Darn Law?
The blanket on your bed is cooler than 37C but still works to keep you warmer without breaking the second law.
250
A blanket does not allow you to cool on a hot day !
Please please please do not use the blanket analogy… ever. !!!
920
Analogies can be troublesome when not taken for what they are. They are only simplifications to help those not getting the basic idea, of slowing the rate of cooling in this case, and not meant to stand up to rigorous scrutiny or nitpicking. I often found my Chemistry teacher’s analogies annoying, bless her, but that’s how it is if you don’t need them , like blankets.
30
“Thermodynamics applies to net flows of heat, not to each individual photon, and it does not prevent some heat flowing from a cooler body to a warm one.”
Thermal EMR flux is never detached from an emitter in a direction of higher radiance at any frequency!!
This has nothing to do with thermodynamics, only electromagnetics. No physical realization of such flux has ever been demonstrated. Total fantasy.
All the best! -will-
819
Thanks for that ray of sanity Will’
Much appreciated.
KK
312
A ray or a flow ?
20
A blanket increases the temperature gradient between the inside and the outside of the blanket. There’s no hotspot at the outside edge. That’s why the analogy isn’t that good.
The lapse rate is set by convection so I don’t get why ∂R/∂L should be negative. That from the surface must be negative but from the TOA should be positive and equal in magnitude when there is a steady state because downward convection is so slow, and back radiation doesn’t get far. I’d expect the energy to be spread over the broad emission bands of water, liquid and gas, so not actually observing that is not a problem since it would be difficult.
20
” A blanket increases the temperature gradient between the inside and the outside of the blanket. A blanket increases the temperature gradient between the inside and the outside of the blanket. There’s no hotspot at the outside edge. That’s why the analogy isn’t that good.”
Only better than the GCMs.
Think of the blanket as being the atmosphere rather than a layer within it.
More of a duvet perhaps 😉
20
An increase in carbon-dioxide concentration, and thus in its base-2 logarithm L, increases the tendency of the atmosphere to retard radiation from the surface to space, i.e., to reduce the rate R at which, if all else remained equal, the earth would radiate to space. Of course, not everything else remains equal, but ∂R/∂L is the everything-else-is-equal rate at which the outgoing longwave radiation changes with a change in the concentration’s logarithm. So it’s negative.
This is not inconsistent with lapse rate, whatever its cause. Since the optical depth increases with CO2 concentration, the effective emission altitude does, too, making it–again, before other system responses–colder in accordance with the lapse rate and thus less radiative.
Now, that cooling is a transient effect; other effects make the new effective radiation altitude’s temperature tend to rise to the old one’s and thereby return the net radiation to zero. But those effects (e.g., the earth’s accumulation of heat in response to the transient radiation imbalance) are separate from the one captured by the first partial ∂R/∂L of outgoing radiation R with respect to the base-2 logarithm L of CO2 concentration.
10
Just saying that the accumulation of energy is at the TOA and increased radiation to space from there, over a very broad emission spectrum, rather than more heat energy being accumulated at the surface. If the heat can by-pass the filling of your duvet and warm the top very easily, the effect of the filling is to insulate the bottom of the duvet from the top and it doesn’t do its job very well.
00
Not sure I follow you.
Perhaps you’re saying that increased surface temperature increases effects such as thunderstorms that make heat latent heat “tunnel” through the optical barrier and thus compromise carbon dioxide’s retarding effect. If that’s what you mean by “accumulation at the TOA,” I guess maybe there’s sense in which it’s true. But energy has to accumulate at the surface for its temperature to rise, so I don’t see how you’re ruling out energy accumulation there.
Again, though, I don’t think I followed you.
00
“But energy has to accumulate at the surface for its temperature to rise, so I don’t see how you’re ruling out energy accumulation there.”
Insolation power is distributed throughout the troposphere and surface maintaining a linear lapse as modified by latent heat of evaporation, at a rate in excess of possible convective transfer. How this is done is poorly/not understood.
This effect, however, must be completely spontaneous from the measurements, as is EMR exit flux to space.
Any change in near surface temperature is but an indication of the atmospheric volumetric expansion with increasing insolation at that location.
Please stop trying to stuff this atmosphere into your preconceived shoe-box, it doesn’t fit.
014
There was an interesting 1/2 hour perspective on what went before the 1st and 2nd Darn Laws on BBC Radio 4 last night , in Perpetual Motion, of the first and second kind. A relaxing antidote too when tiring of or for anyone not following the Maths.
20
Jo, I thought this was a good post on the subject from a post on Tallbloke’s blog here (and posted below).
Sorry it’s so long, but it’s definitely worth reading.
82
Joanne Nova said: “Greenhouse gases are just working to slow the heat loss of energy flowing from a very hot sun, through the Earth to very cold space. They work like an insulator. They are not “generating energy” which of course would be silly (or nuclear).”
=======================
Dear Joanne,
no, the “greenhouse effect” as established in “climate science” and the IPCC reports accordingly is not about “slowing the heat loss of energy” as you put it. It is exactly that thing that you rightfully called silly. You just need to actually read the sections in the IPCC reports where they reveal their “physical basis”. A critical look at their “Earth energy budget” should be sufficient actually. It is like cooking the books in the finance. If they were caught doing such a thing in the finance they would have to do some jail time, but hey, it is just “climate science”!
In short, first they molest the Stefan-Boltzmann equation and come to the (wrong) conclusion that the Sun can only do -18°C on average on the surface of the Earth. Then they look around and say “Hey, but it is not so cold, it is much, much warmer! This is the GREENHOUSE EFFECT! 33°C!” Then they go on to calculate the CO2 share and this share is what David put in as “CO2 influence”. Of course, it is physically impossible, like I said, because such a warmer surface would radiate away more energy which is equivalent to energy production out of nothing. But “climate science” is so exiting, I guess, why should they care about such a boring thing as the law of conservation of energy!
So yes, it is that silly. All that talk about blankets etc. is just a distraction. Maybe they initially fooled themselves by that false analogy, I do not know. Perhaps it was not a fraud really back then, like 100 years ago, just a mistake.
220
Greg, I was responding to your sentences. Quote: “This is physically impossible, because it violates the law of conservation of energy. ”
“Such a warmer surface would radiate more energy away than it gets from the source of heat.”
Read the posts I linked. Think about net flows of energy.
GHG’s are not creating energy. The energy comes from the sun. The sun is hotter than Earth. No laws of physics are broken.
GHG’s slow the heat loss like any insulation does.
The blanket analogy is not a distraction, for this semantic argument it is extremely useful. Its there to show how the sentence “a cooler object can’t warm a warmer object” is meaningless without context. It’s obviously wrong, because it happens all the time for 7 billion people who sleep under a blanket at night. We are warmer with a blanket than without it, the blanket is not generating joules. The surface of our skin is hotter than it would be if we did not use a cooler blanket around us, therefore the cooler blanket can be said to be “warming us” even though it does not generate energy.
Consider the whole system, not just the “two objects” which are part of a larger heat flow. Both our skin and the Earth have a another source of heat that is not the insulation. Our skin is warmed by chemical reactions of food with us. The Earth is continuously heated by the sun.
210
Joanne, you wrote: “GHG’s are not creating energy. The energy comes from the sun. The sun is hotter than Earth. No laws of physics are broken.”
Right, IN REALITY the so called “greenhouse gases” are not creating energy, of course.
Unfortunately, they do exactly that in “climate science” and the IPCC reports accordingly. Maybe you need to read their “physical basis” sections. Just take some time to do that. Again, their “greenhouse effect notion” is in fact not about slowing cooling, it is about raising the temperature above what the Sun can possibly do. You understand, as I can see, that such a notion is absurd, so let us just clarify what THEY really say. They do mention the blanket analogy as well, which is misleading and helps the readers to swallow the main absurd concept.
319
You can convince yourself of the greenhouse effect by using a simple radiation-only one-dimensional model of photons’ being emitted in random directions (just up or down in 1D) by discrete atmospheric layers, which with some probability intercept photons that traverse them.
It’s hard to follow that action in your head–well, it’s hard for me, anyway–but running it on a computer will demonstrate the effect nicely. For this purpose it makes things easier to consider all photons as having the same energy and to keep track of heat in terms of photons absorbed minus photons emitted.
01
Joe Born September 26, 2015 at 1:18 am ·
Just what is the potential or potential difference that will allow such flux, that you call photons’ in random directions?
Has such ever been observed, anywhere, at any time? Why promote such fantasy?
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I’m told that excited gas molecules radiate isotropically. If you can cite compelling evidence to the contrary, I will be happy to entertain it.
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I will cite nothing!! Gas molecules at a lower temperature than their environment only absorb EMR flux and increase in temperature asymptotically toward that higher temperature where all radiative flux ceases. No thermal radiative flux to a higher radiance has ever been detected nor demonstrated.
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Joe says “I’m told that excited gas molecules radiate isotropically. If you can cite compelling evidence to the contrary, I will be happy to entertain it.”
>>>>>>>>>>>>
Paraphrasing Dr. Robert Brown of Duke wrote over at WUWT:
Dr Happer in his lecture agreed (see comment #28) and further stated that the time to radiate is about ten times slower than the time to the next collision in the troposphere. Dr Happer in his lecture also answered my question about where CO2 energy is radiated instead of being handed off via collision. Experimental data shows barely any radiation at 11 KM and that radiating is in the stratosphere ~ 47 KM above the surface.
The Super Mandias has this illustration:
http://www2.sunysuffolk.edu/mandias/global_warming/images/stratospheric_cooling.jpg
The legend with the illustration:
Dr Happer’s information is illustrated by this image the Warmists use to say ozone is a greenhouse gas. The Figure is from Uherek, 2006. They even say it “show how carbon dioxide is cooling the stratosphere.” The black dotted line is the tropopause and you can see water is dumping energy just under the tropopause (the pink splotches surrounded by dark blue) while CO2 is dumping energy from just above the tropopause and up (the big yellow streak on the left) just as Dr. Happer, and Dr Brown stated. Ozone is the smaller yellow streak on the right.
………..
From this, based on experimental data we have:
#1. The outgoing long wave radiation only makes it a few meters before being absorbed by CO2.
#2.The time to radiate is about ten times slower than the time to the next collision in the troposphere.
#3. CO2 radiates 47 KM above the surface.
#4. Another very important point Dr. Happer brought up.
The Pound–Rebka experiment (VERY IMPORTANT because gases are moving randomly and in random directions)
This means depending on the direction the molecule was traveling at the time it emitted the photon it may or may not be the correct wavelength for CO2 OR WATER VAPOR to absorb on its way back towards earth. However the closer you get to earth the more likely the absorption because of the pressure-broadened absorption bands of CO2 in the lower atmosphere.
This means that while half the photons emitted at 47 kilometers up in the atmosphere are headed towards the earth, a significant fraction aren’t going to make it to the ground and are instead going to be absorbed by CO2 or H2O and handed off via collision to the rest of the atmosphere.
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Joanne Nova September 25, 2015 at 11:59 pm ·
Greg, I was responding to your sentences. Quote:
“Read the posts I linked. Think about net flows of energy.”
Joanne,
Since you are recommending thinking, Please at least consider for the moment “perhaps both Joanne and David have been brainwashed into accepting the notion that thermal EMR flux is actually dispatched in opposing directions proportional only to self-temperature^4 of such mass.” Perhaps this is not true, just as turnedoutnice has stated on your blog many, many times. Who profits from such misdirection?
Why is this notion so very widespread? Would not such, in order to rise from conjecture to hypothesis require some evidence? With most such conjecture a methodical means of falsification would be demanded. Why has such not been so demanded in this case? Can not all be explained more convincingly without breaking the S-B equation into two mathematically incorrect so called S-B laws in opposing directions? Just what is being offered to convince, except CO2 BS?
All the best! -will-
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Thanks for this JN, It answers a previous query of mine. So the principle is insulation – the slowing of heat transfer to space. Can this be explained for a simple mind like mine in terms of physical principles since the mechanism as I see it seems different than that of the blanket you mention. The insulators I am familiar with seem to require enclosure of a low thermal density material (air trapped in a blanket or even better a vacuum trapped in the walls of a thermos) in such a way as to create a barrier to conduction (and possibly convection) of heat away from the heat source. How does gas in a fluid atmosphere that is absorbing and re-radiating the long wave radiation accomplish this insulating effect?
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Think, space blanket or reflective insulation since they work the same way as CO2, you produce energy, about 200 W of it, this warms you to a temperature where all the 200 W is lost at equilibrium. The reflective insulation reflects the ir you emit back to you even though the aluminium space blanket is cold because it has 97% reflectivity
This prevents you losing energy by radiation and reduces the loss of energy from 200 W to a lower value, you inside the blanket heat up because the retained energy difference between the new emission and 200 W until once again your loss of energy equals 200 W – energy conservation. The reason you heat up is because energy loss ( cooling ) is being prevented by the high reflectivity low emissivity aluminium blanket. There is no more energy involved. The blanket does not create energy it just recycles it, we have just changed the RATE of energy loss, nothing more.
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good outline
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My Latest experiment seems relevant here!
Can a body be warmed by its own radiation, reflected back? Does reflected radiation act like a thermal blanket, reducing radiation heat loss?
I tried to answer the second question. The answer from my experiment is; Yes, reflected radiation does reduce heat loss.
My apparatus consists of two cylindrical glass vases. One is smaller than the other and fits inside with about 1.5mm gap. The gap is sealed with styrofoam and the inner cylinder filled with hot water, then capped.
The water temperature is taken over time with an alcohol thermometer and the outside vase surface temperature measured with a thermocouple.
The rate of heat loss is reduced when the inner surface of the outer vase is silvered.
More details later. I am trying to get a heater coil inside to answer the first question.
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“I tried to answer the second question. The answer from my experiment is; Yes, reflected radiation does reduce heat loss.”
So nice that some are trying to check, rather than accept. Please consider a different explanation than reflected radiation (flux). The reflective surface reflects not flux but the potential for flux. this is called radiance. If the reflection of potential were perfect, there would be no difference in potential and no flux in either direction. The difference may sound trivial and physically is trivial with no dissipative matter between the surfaces (vacuum). With some matter like atmosphere in the path and convective heat transfer the whole concept of the S-B equation is never applicable! Such a combination is still analytical but fraught with error from assumptions.
The CAGW Clowns understand that difficulty so instead, just baffle you with bullshit.
All the best! -will-
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Joanne Nova September 25, 2015 at 2:49 pm ·
“see Why greenhouse gas warming doesn’t break the second law of thermodynamics”
Read the comments! No agreement!!
“and So what is the Second Darn Law?”
In this Joanne replies to Joe Postma:
“Can you at least acknowledge that in the Sun-Earth-Atmosphere system it is possible that energy flows which are always going from the hot sun to cold space, could be changed by a colder entity (GHGs) which would allow a warmer entity (Earth) to get even warmer, given that a third source (the Sun) is continually adding energy?”
Since Postma has gone to the dark side: Such is possible if solar power were delivered to the Earth’s surface directly, with no convection, and no latent heat!
This would be the case of multiple Willis Echenbach steel greenhouse shells. In this case the temperature of each inner shell must have a higher temperature than the next outer for any radiative exitance to occur from the inner shells. This is demanded by the complete S-B equation, involving two different temperatures. No difference in temperature, no flux in any direction.
This increasing inner temperature is the result of re-thermalizing each shell via initial EMR flux to create the progressively lower outer temperature and still provide the necessary radiative potential difference for flux generation from inner to outer shell.There is no increase in power transfered because of increased temperature of the inner. Work out the actual power transfered outward by the two temperature S-B equation. In every case,even with increasing surface area outward, it is precisely that of external power delivered to the innermost shell.
This Earth’s atmosphere works much differently!! Here the decreasing outward temperature gradient is not set by the re-thermalization of EMR exit flux. Instead the thermal gradient is set by the gravity induced pressure/density gradient of this atmosphere, as modified by diurnal latent heat.
This non radiative temperature gradient results in a higher ‘at altitude’ temperature, and an increase in maximum possible exit flux to space.
The actual question that the CAGW crowd cannot answer is “To what reference does this atmosphere adjust airborne H2O, for such a fine control over weather”. And just the temperature that baby bear likes at all surface locations.
All the best! -will-
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Um no, the gravitational well does NOT by itself establish a thermal gradient if the gases involved were at absolute zero then then gases would freeze energy would minimise ( not be absent since the frozen gases still have a minimal potential energy) add heat energy to a gas in a gravitational well though and the added energy will apportion itself between kinetic and potential energy such that a lapse rate is established.
The lapse rate is caused by energy apportionment between potential and kinetic in a gravitational well, there must be a source of energy present to have a lapse rate.
The flow of heat from hotter at the bottom to colder at the top means that the kinetic energy equilibriates through the gas and the gas at the top then has more total energy than at the bottom, without the tendency for energy to move from hot to cold the lapse rate would be 9.8 C per km instead of 6 odd and the surface would be much hotter than it is.
Slow the rate of energy loss and the lapse rate will increase making the surface hotter.
This though is a kicker for me, adding CO2 increases radiative loss to space which decreases stratospheric temperature increases the difference between surface and stratospheric temperature. This must INCREASE energy flow and decrease the lapse rate cooling the earth.
This is a bit of physics hard to reconcile. If CO2 RADIATES I R TO SPACE THEN MORE OF IT MUST RADIATE BETTER assuming that nothing else is rate limiting the energy flow.
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“Um no, the gravitational well does NOT by itself establish a thermal gradient if the gases involved were at absolute zero then then gases would freeze energy would minimise ( not be absent since the frozen gases still have a minimal potential energy)”
You describe a situation of no atmosphere. Please discover for yourself the expression of gravity in a compressible surrounding fluid.
“add heat energy to a gas in a gravitational well though and the added energy will apportion itself between kinetic and potential energy such that a lapse rate is established.”
You cannot establish any kinetic or potential energy in an atmosphere except for the thermal noise power of each molecule (kT/t). From a thermodynamic standpoint the atmosphere is everywhere isopotential. All force of the gravitational field is expressed as a logarithmic decrease of both pressure and density with altitude. The ratio of these two (P/rho), is called the isentropic exponent, a constant of 1.4 for Earth’s troposphere. This PV constant is the part of the (kT/t) power attributable to the linear increase in ‘pressure power’ with decreasing altitude and the linear increase in ‘temperature’.
“The lapse rate is caused by energy apportionment between potential and kinetic in a gravitational well, there must be a source of energy present to have a lapse rate.”
You appear to have been throughly brainwashed! Think for yourself! The lapse rate is a thermostatic temperature gradient with no thermodynamic potential of either temperature differential or pressure differential. Both are spontaneously, dynamically, canceled by gravity, at sound-speed. J. Loschmidt “Uber den Zustand des Warmegleichgewichtes”
Atmospheric ‘motion’ within the atmosphere requires no ‘work’ whatsoever. Acceleration of mass is a different story.
All the best! -will-
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The problem with “reducing ” each effect in the model is that it does not take into account the distributive effects of feedback and sensitivity.
looking at Figure 2. what becomes apparent is that the feedbacks are applied post drivers +solar influence+co2 influence.
and that the surface temperature is the output of the sensitivity and feedbacks with the radiative imbalance being the input.
The Climate models assume (because of the grid architecture) that net radiation flow is calculated from adjacent grids only.
I am not convinced that an average climate “sensitivity” can be applied to such a grid system
I wonder what role the scattering effect of the atmosphere plays in reducing the warming effect of CO2 both for inbound and outbound radiation.
but i am only guessing here..
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Not surprising but disappointing;
http://www.news.com.au/finance/business/winds-of-change-blow-as-turnbull-government-shifts-towards-renewable-energy/story-fnu2q2e9-1227543550114
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Yes I thought that little skunk Hunt was with it when he gave environmental approval to those large coal projects. His history of involvement with the UN is probably one source of his abysmal ignorance of the futility of expecting solar and wind power to be of any practical use in a modern economy like Australia which has vast supplies of coal. It seems Abbott was keeping him more or less on the straight and narrow.
Like Turnbull he is a lawyer so I don’t hold out much hope for scientifically informed decisions about AGW from either of them. In an excerpt from the Lateline interview, about his stifling the investigation into the BOM, I him heard say it was all technically above board and again, showing his profound ignorance, he referred to the satellite data as a confirming part of the BOM’s fiddling with the land based data.
During that interview he said that he and Turnbull were both passionate about dealing with climate change. Abbott better hang around in parliament as the Libs may yet need him when the polls start reflecting the large percentages of Lib supporters who are AGW skeptics.
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and again thank you to Jo and Dr. Evans … really enjoying your posts 😀
It is interesting to note that as we approach winter here in Utah, the ground will freeze and we will get seriously dumped on with snow… 😮
Somewhere on this planet is a town with the average global temperature, sea level, humidity, wind speed and rainfall and where the average family live.
I wonder if they vote for the Green party ?
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The heartland of the Australian Greens is Tasmania where their former leader and founder has a cottage in a farming community. It has been claimed in media circles that the cottage has a lovely garden and down at the bottom of that garden lives the Fairies that the Greens consult for policies.
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It’s known as the mid-North Coast, NSW, Aus (according to the CSIRO, that area has the most temperate climate on the planet)
They obviously don’t need to 🙂 🙂
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Not so sure about the last sentence Ianl, There are lots of green unthinking people at Byron Bay and in its Hinterland (eg Nimbin). Sure some have had their brain cooked by drugs but there are lots of others who have been brainwashed as it is the thing to do to keep up with the crowd.
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My brain hurts, Brian.
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Brian Damage
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David
When calculating feedback for water vapour do the climate models consider the heat of evaporation at the surface to be the same as the heat of condensation at the height (pressure) of cloud formation?
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I don’t know. I’m just using the feedback values reported in AR5; I don’t know all the details of how they got them.
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Sigh …. oh dear
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The answer to that is no, the water vapor transport is not handled right and is understated in models, the feedback is negative not positive. This is clear because the lapse rate decreases if the air is moist, moist air transports more energy which increases cooling
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As an observation, the Climate model architecture appears on the surface to have been designed from the bottom up, where much effort has been placed (and quite correclty) on getting the physics right.
However, what is interesting is that a look at any global temperature graph from the last 400,000 years reveals a definite “sawtooth” waveform of uniform periodicity that would raise the eyebrows and perhaps interest of any EE major.
Maybe it would be worthwhile studying climate change and thus modelling it from the assumption that this “sawtooth” profile holds some significance .
In geological time frames the polar regions have in the past been ice free and yet the Earth has moved to very cold temperatures despite this, in addition what surely must be of interest to Climate Scientists is a thorough understanding of such swings and not small perturbations .
The Fourier series for a sawtooth waveform is remarkable similar to these global temperature graphs.
uncanny almost 😮
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The Milankovitch cycles are supposed to be the cause of the sawteeth, both by empirical observation (eccentricity of earth orbit) and mathematical theory ?
However, my probably inadequate understanding is that the most recent and most intense of the glacial epochs did not co-incide with a Milankovitch cycle, although all the preceedings glacials did
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This may be of interest Ian,
Extract from ‘Tomorrow’s Weather’ Alex S. Gaddes (1990)
“The Rhythm of the Cycles from 3,064.31 BC to 1977.6 AD
(As derived through the ratio principle.
See Appendix for original empirical derivation.)
3,064.31(BC) to 1,277.75 (BC) = 6* cycles of 297.76 years
between minima
1,277.75 (BC) to 682.23 BC) = 2 cycles of 297.76 years
between minima
682.23 (BC) to 384.47 (BC) = 1 cycle of 297.76 years
between minima
384.47 (BC) to 806.57 (AD) = 4* cycles of 297.76 years
between minima
806.57 (AD) to 1,402.09 (AD) = 2 cycles of 297.76 years
between minima
1,699.85 (AD) to 1,977.60 (AD) = 1* cycle of 297 .76 years
between minima
_______________________________________________________________________________
The pattern of the rhythm of the cycles reveals a discreet falling off of the number of cycles displayed at the commencement of each ‘epicycle’.
Moreover, when one considers the figures at the beginning of an ‘epicycle’ against the formula for the inverse square law of gravitation, one’s interest becomes compounded.”
An updated version of this work,(including ‘Dry Cycle’ forecasts to 2055,) is available as a free pdf from dongaddes93@gmail.com
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Dr Evan answered this is accepted by sceptics.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
There is new work on this point by Dr Happer and a colleague using atmospheric measurements and he found the calculations incorrect for the Absorption wings. (Paper in the works)
The take away from his UNC lecture (9/2014) was the CO2 ‘modeling’ is a mish-mash of theoretical equations and experimentally derived data. Where the Climate models missed the boat is in using equations for ‘line broadening’ aka the ‘wings’ where the additional CO2 absorption ( at 400 ppm) is supposedly taking place. These equations produce results that do not match up to the experimental data. The lines are not as broad as theory would have it.
This was the point of the lecture. Why was the theory wrong?
Since the experimental data shows less broadening this flattens the CO2 log curve and essentially lowers the ‘Climate Sensitivity’ of CO2 for a doubling to 800 ppm to less than 1C===> 0C
David Burton put up an audio video and slides of Dr Happer’s presentation at this. link
SLIDES: link
Slides 16, 22, 42, 43 and 44 are the critical slides.
You can get useful background for the physics in these comments from WIKI .
SUBJECTS:
Mössbauer effect (recoil energy lost during absorption <==CRITICAL)
The Pound–Rebka experiment (VERY IMPORTANT because gases are moving randomly and in random directions)
Motional narrowing
Voigt effect
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GHG’s slow the heat loss like any insulation does.
GHGs do not slow the loss of heat energy from the planet as the irradiative loss must always equal the irradiative gain or the temperature rises uncontrollably. What GHGs do is to increase the atmospheric lapse rate making it warmer on the surface.
01
” GHGs do not slow the loss of heat energy from the planet as the irradiative loss must always equal the irradiative gain or the temperature rises uncontrollably. What GHGs do is to increase the atmospheric lapse rate making it warmer on the surface.”
Without the effect of H2O and CO2 the Earth’s atmosphere would have a higher laps rate. This must result in a higher surface temperature. Do you have anything but fantasy?
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So in spite of the partial differential equations, this is the model I’ve developed such a strong dislike for because it’s predictions do not match reality, don’t even come close.
Simplified, the model is just the sum of its components: energy in, feedbacks, forcings and energy out again add up to what the temperature should be but isn’t.
00
Extract from ‘Tomorrow’s Weather’ Alex S. Gaddes (1990) pp 54 -55
Flooding would be Inevitable
Obviously if the rising carbon dioxide level in the atmosphere were the only consideration one could predict, unequivocally, that inundation of the lowlands of the Earth would be inevitable in the immediate future.
However, (see Ref. Nos. 12 and 13) it [rising carbon dioxide level] could well turn out to be lucky for us, in the light of those other factors which act in the opposite way to carbon dioxide in the atmosphere. I refer to wind-blown and volcanic dust in the atmosphere and the ever-intensifying albedo factor.
May be glad of Greenhouse Effect
Who can say that sometime in the not-too-distant future, we will not be glad of the “extra blanket” provided by an enhanced “Greenhouse Effect?”
Apart from the anti-Greenhouse Effect factors mentioned above, there is another powerfully active component at work, which governs the amount of CO2 in the atmosphere.
According to Rankama and Sahama (Ref. No. 14) the oceans act as a sink for any build-up in carbon dioxide above a partial pressure (PP) in the atmosphere; that once the critical PP in the atmosphere is reached, the excess carbon dioxide is taken into solution by the oceans.
They note that the cold polar waters are capable of the greatest absorption of carbon dioxide. Apparently the equilibrium ratio of carbon dioxide in sea water to that in the atmosphere is 50:1.
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How do you translate the following: a[b,c]? My differential calculus class failed to cover this type of expression. Thanks.
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Try f(anything) = 1.7[0.97,2.43]/3.2 = 0.53[0.3,0.76]
Divide all!! That of course destroys all meaning, with just numbers! 🙁
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GM: That’s an uncertainty expression, not calculus! The number in front is a number, an estimate, while the numbers in the square brackets just give an idea of how precise the estimate is.
“a[b,c]” just means that “a” is the best estimate of the value, while the value could be as low as “b” or as high as “c”. (to within some probability, typically such as 90% — 2 standard deviations).
For example, “3.7 [3.5, 4.1] W/m2” is a number that we think is most likely 3.7 W/m2, and is very likely between 3.5 W/m2 and 4.1 W/m2.
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“Even 4.5 °C would be pretty disruptive, while the upper end possibilities would be disastrous. Hence the alarm.”
Disastrous for whom? I hate shoveling snow. The way I see it, there will always be winners and losers no matter what climate you have.
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Fascinating article, by the way!
00