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Lucia has a bad day with partial derivatives

Partial Derivatives, dependent variables

Here’s a lesson in when to post and when to email. Over at the Blackboard, Lucia couldn’t make sense of David Evans’ post on partial derivatives, but instead of emailing us or commenting here, she published her unresearched thoughts and and asked her readers instead. Only most of them didn’t know either and it didn’t help that the quotes were misattributed, and Lucia’s assumptions were wrong. Together they generated a thread of fog, arguing about irrelevant points in maths and models that didn’t apply.  Having admitted that she is confused about what David was saying, in comments she went ahead and called him confused, declaring he didn’t understand maths, and was spouting nonsense. (Steady on Lucia.) In the nicest possible way David explains he’s right, she’s wrong. And he had defined and cited everything correctly too (it was all in the post, or linked to it).

Her post is titled: “Questions to David Evans: What do you mean about partial derivatives?”. Lucia had my email, but posted: “I’m hoping David or readers who understand his point can clarify for me”. However she didn’t email us after that either. So by the time I tripped over the thread there were already scores of pointless comments. I emailed her to correct things and connect David and Lucia, but evidently she didn’t want an answer to her query direct by email. She wants it all out in public so people can learn, which is a nice sentiment, but we would rather post new research than run classes.  (Sorry Part 11 is delayed — It took hours to read and unpack the misguided comments.)

We all could have saved a lot of time if Lucia had read the post carefully, or just asked before publication. We’ve tweaked my introduction to the post to clarify things, but all the scientific points and equations David raised remain the same. She is, of course, welcome to come here and comment. We hope the Blackboard will give us more useful feedback next time.

Just to remind everyone, the point of Post 4 was that the implacable confidence of climate modelers who say it’s “basic physics” is based on partial derivatives of dependent variables that might be close enough, or might be quite wrong, no one can tell. The advertising doesn’t fit the product.

- Jo

—————————–

My Reply To Lucia

Dr David Evans, 12 October 2015, David Evans’ Basic Climate Models Home

 

Lucia Liljegren thinks I made a mistake with partial derivatives in Eq. (2) of post 3 of the “New Science” series of blog posts when describing the conventional basic climate model. She also had difficulty understanding post 4 about the use of partial derivatives in the basic model, and thinks Eq. (1) of that post or the text just around it is definitely wrong.

Having read carefully through her post and its comments, I fail to see she found any mistakes in my posts or even made any informed criticism of them. Joanne and I have emailed her and tried to point out her mistakes, but she ignores any content and insists only that I made a mistake with partial differentials and that she only wanted to discuss it in public. Ok, now we are discussing it in public.

Background

Lucia is principally responding to post 4, which criticizes the conventional basic climate model for relying heavily on parameters that were partial derivatives that do not technically exist — because it is impossible to hold all but two of the relevant variables constant in climate, due to their web of inter-dependencies. The partial derivatives are not empirically verifiable; hence, an unknown error is incurred by using them.

In post 2, the main two partial derivatives in question are defined and discussed in the derivation of the basic model in its simplest form, with values from AR5 quoted:

  1. The Planck feedback, the change in OLR with surface temperature, when all is held constant. (Not quite everything else is held constant. The generally accepted way of doing this is described in Soden & Held, 2006, pp. 3355-56.  The Planck conditions are that all else besides tropospheric temperatures and OLR are held constant—so there are no feedbacks, all tropospheric temperatures (including the surface temperature) change in unison, and stratospheric temperatures are unchanged. There are some arbitrary choices to be made, such as whether it is the specific or the relative humidities that remain unchanged as the tropsphere warms, or what happens at the tropopause.) Value: 3.2 W/m2 per K.
  2. The change in OLR when the CO2 doubles, holding all else constant. Value: 3.7 W/m2.

So, there is a specific context, a specific model, and two specific partial derivatives.

Basic Models or GCMs?

In her post, Lucia says “If by “climate model”, David means the current generation of AOGCM’s (and in the following I will assume he does mean that.)” and ““These days, these sorts of 1-D lumped parameter models are, at most, used by those attempting to estimate climate sensitivity based on the time series for temperature, aerosol loadings and such. My impression is these are not the type of models David Evans is criticizing.”

The blog series is about the conventional basic climate model, as explained in the introductory post 1. That model is described and derived in post 2 and post 3. While there might have been some misunderstanding from Joanne’s introduction to post 4, any doubt would be dispelled by the first sentence of my article in post 4: “There are three significant errors with the conventional basic climate model (which was described in the basic climate model core part 1,and  basic climate model in full part II)”.

Lucia also says the claim that “effectively climate models model a hypothetical world where all things freeze in a constant state while one factor doubles” is untrue. No, the second partial derivative in the background above, the change in OLR when the CO2 doubles, does that, which is entirely consistent with the derivation of the basic model in posts 2 and 3.

Partial Differential of G

Lucia, in Comment 139694, says that “He [David] seems to mean G is a function of two independent variables:

This seems to be the root of Lucia’s misunderstanding of the partial differentials. G is the the net top-of-atmosphere downward flux, first introduced in Eq. (1) of post 3. The section that defines G also introduces the variables: the surface temperature TS, the n driver variables V1,…,Vn, and the m feedback variables, U1,…,Um. The next section is quite explicit: “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, …” Thus, schematically,

This definition of G does not change at any stage in my posts. In Comment 139725 Lucia claims that “And he [David] seem to alternate between definitions of G or whatever“, but I cannot see how any reasonable reading of the series of posts could lead to that conclusion.

Lucia’s version of G is absurd: Why does G only depend on one driver, and not the others? Which driver — what is the value of i? G obviously depends on the feedbacks, which depend in turn on the temperature TS, but I chose to explicitly include the feedbacks as arguments of G, following Eq. (1) of Held and Soden 2000[1].

We need to find the total differential of G, namely dG. From the MIT course notes linked to in post 4, Auroux 2010:

Total differential rule from Auroux

Auroux’s “fx” notation is a standard shorthand for “∂f/∂x“. Applying this rule to G:

as per Eq. (2) of post 3. This result is essentially the same as Eq. (6) of Held and Soden 2000[1].

Lucia, in Comment 139691, says however that “Evan’s equation (2) in his “part 3” post is incorrectly formulated. The consequence is that muchof what follows is either unnecessary, confused or possibly wrong. (I’d say there’s a mix there.)“, and that dG is

Lucia's version of G
Lucia has restricted the partial derivatives of G with respect to the drivers to only hold the surface temperature constant, which is absurd in any formulation because obviously the other drivers also need to be held constant.

In Comment 139699 Nick Stokes tries to slow Lucia down: “Lucia, Actually, I think his Eq (2) is OK. If he had read to the bottom of p2, he’d know to use suffices. If on the RHS he had suffixed the first term U,V and the second T,U and the third T,V he’d be OK, and it’s actually not a bad way of treating feedback.

Existence of the Partial Derivatives

Lucia, in Comment 139725, says “But I definitely think this bit contains quite a bit of stuff that is wrong no matter how you interpret the notation“, and reproduces the entire section entitled “The Required Partial Derivatives Do Not Exist” from post 4. Not a very specific complaint.

The section applies the formal definition of a partial derivative (such as in this Wikipedia article) to the partial derivative of G with respect to TS‍ at the initial steady state. The section makes the point that the climate states in that definition do not technically exist because they contain a changed surface temperature but all the other variables remain the same (surely Lucia is not suggesting they do exist?). The limit of non-existent numbers also does not exist; hence the conclusion that “the partial derivative does not exist, technically”. Seems pretty straightforward.

Conclusion

The genre of the New Science posts is a bit experimental. High level maths/physics ideas are being circulated for feedback among a very mixed audience. So Jo does a casual intro for everyone, ahead of the heavy maths. Lucia mistook the intro for the maths, and carelessly missed the links and context below. She didn’t read the mathematics correctly either. The entire thread at the Blackboard is a scientific rabbit-hole (though Rud Istvan admirably tried to lift the standards, thank you Rud). We got some useful feedback about communication, but there are better ways to do that.

 

Related Blog Posts

David’s post 3: New Science 3: The Conventional Basic Climate Model — In Full

David’s post 4: New Science 4: Error 1: Partial Derivatives

Lucia’s first post on our posts, at the Blackboard: Questions to David Evans: What do you mean about partial derivatives?

Our response to Lucia’s first post: Lucia has a bad day with partial derivatives

Lucia’s second post, at the Blackboard: Held & Soden without “hypothetical partials”

Our response to Lucia’s second post: Lucia has a bad week on partial derivatives

 

References

[1^] Held, I. M., & Soden, B. J. (2000). Water Vapor Feedback and Global Warming. Annu. Rev. Energy. Environ., 25:441–75.

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164 comments to Lucia has a bad day with partial derivatives

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    graphicconception

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    Eric Worrall

    I actually really liked the MIT example provided – makes it really clear why a description of a problem based on partial derivatives quickly degenerates into nonsense, if you don’t know the full relationship between all of the variables.

    No wonder alarmists were always so keen to demand we accept CO2 is the only independent variable of consequence – at least some of them must have known all along, that any other condition makes their models a complete nonsense.

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      Roy Hogue

      The gas law example makes the partial differential equation problem easy to understand. I wonder why a mechanical engineer would have such difficulty understanding it. I guess she never designed an air or refrigerant compressor. If she had she would know that the volume pressure and temperature are very dependent and be able to follow David’s argument about the climate models.

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      “I actually really liked the MIT example provided – makes it really clear why a description of a problem based on partial derivatives quickly degenerates into nonsense, if you don’t know the full relationship between all of the variables.”

      It doesn’t do that at all. In that example all the relationships are known. He’s simply introducing his students to a standard notation which allows the derivative to be unambiguously described. David makes much of where he quotes Auroux as saying ‘a partial derivative of the quantity “has no definite meaning”’. But Auroux is not saying no meaning exists. He is just saying that you need to add suffices to say exactly what you mean. Here is the conclusion to that section:
      “There is only one way out of our difficulty. When we ask for ∂w/∂z, we must at the same time specify which variables are to be taken as the independent ones…”

      It has a definite meaning, provided you use adequate notation (suffices).

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        gai

        “There is only one way out of our difficulty. When we ask for ∂w/∂z, we must at the same time specify which variables are to be taken as the independent ones…”

        And if you declare a variable to be ‘independent’ and the variable IS NOT what then? Seems like your are playing word games especially since CO2 was declared the “Control Knob” and everything else is then dependent on CO2.

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          “And if you declare a variable to be ‘independent’ and the variable IS NOT what then?”
          Chain rule. You can take account of the dependence. The silly thing is that David’s G example, that he’s emphasising in this post, is differentiating both dependent and independent variables explicitly.

          The CO2 stuff is a pointless distraction. This is an introductory math lecture. But it illustrates that despite all the huffing about partial derivatives, I don’t see an example where an actual climate scientist has supposed to have used them wrongly.

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            Rud Istvan

            Nick, I gave very specific examples at Lucia’s by equation number from the CAM3 technical notes. Chose deep comvection, section 4.1. She could not be bothered to even look them up. Clear examples of chain rule partial differentiation of variables that are not independent. I gave up on Lucia’s thread. You are just factually wrong, period. Go see for yourself.
            Sent Dr. Evans a copy of the CAM3 documentation. Very complex. What he has done is abstract the kernel in IMO a clear and useful way.

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            “I gave very specific examples at Lucia’s by equation number “
            What you didn’t specify is what is wrong with them. Eq 4.2 is a standard energy conservation. Rate of change of sensible heat is proportional to divergence of flux. The daddy of all such is this:
            ρc ∂T/∂t = ∂q/∂x, where flux q = k ∂T/∂x, k=conductivity, c=specific heat
            The heat equation – goes back to Fourier. And is q independent of T? No, it’s the derivative of T.

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              Andrew McRae

              Nick,
              Aside from the triviality that you forgot the negative sign in front of k, I’ve been able to follow why that heat equation example is not problematic. In that particular example the derivative of T is in terms of another derivative of T. Luckily that example is so simple that the 1st derivative is with respect to the same variable as the 2nd derivative. It is then just the 2nd-order derivative of T with respect to x, which is why in Fourier’s heat equation it is also written as the Laplacian of T with respect to x.
              There are no other variables, independent or otherwise, to be held constant, so this simple example is not the same class of problem as the OLR feedback problem. You cannot defend the more complex case by proving the simpler case has been acceptable.

              In support of David’s criticism, Rud implies CAM3 TN eqn 4.2 is the same class of problem as the OLR derivative problem. In other words, it was a partial derivative of an equation having a mixture of independent and dependent variables, in which the real value of dependent PDs is unknowable. From your comments on Lucia’s blog I see you’ve placed a screenshot of the relevant eqn, which is helpful only if the notation is also explained.
              The notation implies that the subscripts u and d refer to upward and downward components of vertical mass flux and “dry static energy”. The c subscript appears to mean the net of upward and downward components, for both mass flow and “dry static energy”. The subscript listing the independent variables of the differential, “cu”, is then somewhat nonstandard because there are no variables called “c” or “u” in the equation, leaving some ambiguity. But I guess they mean any variables which have c or u as subscripts are considered independent and constant for the purpose of differentiation. Therefore M_c and M_u are independent. By definition that should mean M_d is also independent but they have not included d on the LHS subscripts.
              Same with C and E, which will have to be treated as an independent constant (there’s no Legendre del applied to it) despite not being listed in the subscripts on the LHS which were supposed to list all independent variables.
              So even as a matter of precise definition and mathematical communication the CAM3 example given here is not a great one. But it’s worse than that, and I can see Rud’s point.

              The radiative environment affects the Temperature. They have explicitly treated upward flux as constant when a different radiative environment should affect convection rates. It’s the same with C and E where the condensation rate also should be affected by the radiative environment. They are modeled as constant, but in reality they are dependent.
              This is why your solution of adding the suffices is beside the point. The concern is not a lack of clear meaning in the mathematical description, that’s just communication. This is a lack of physical meaning in the equation even when precisely described with your nominated “adequate notation”.

              I can’t comment on how much difference this actually makes to the simulations, but you have missed the point that David was making.

              The problem is, does the real value of

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                Andrew,
                This is completely muddled. Eq 4.2 differentiates with respect to t and z only. And the only issue of dependence is between those variables. The only way there can be a dependence is if the frame of reference is moving. And it is – they are using a Lagrangian frame moving with the updraft, as indicated by the cu suffix on time. In a different frame, there would be an extra term for advecting sensible heat (ρcv.∇T).

                Dependence of the other variables is irrelevant. There is no differentiation wrt T. All that matters is conservation. The rate of change of sensible heat must be equated to the divergence of all energy fluxes, whatever they depend on. As in the heat equation.

                “the error will accumulate”
                There is no error – at least due to variable dependence.

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                ” equated to the divergence”
                OK, -divergence, with your sign convention.

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              Andrew McRae

              (continuation of above comment 2.2.1.1.1, which was fine in preview but after posting was truncated at the first extended Unicode character.)

              The problem is, does the real value of Σ∂G/∂V_i actually matter or can it be elided when computing dG. (Analogous argument for ∂T/∂t in CAM3 deep convection.) To actually counter David’s point would require finding a paper which showed the independence approximation was valid because either (a.) the error introduced is a very small factor (say 1/1000) of the true value, or (b.) that the parameterisations in conventional models account for it, or (c.) that the error is exactly canceled out in the way the equation is applied. Even when the error is small these PDEs are being integrated over at least 3.5 million timesteps, so the error will accumulate.

              _ _ _ _ _ _

              (Having said that, of all the changes that could be done to improve the accuracy of climate models, adding the variable solar activity influence on ozone, cloud condensation, and meridional flux should be their number one priority. When all the proven major climate drivers are modeled to first approximation, then they can worry about how good the approximations are, such as dG/dT or ∂T/∂t.)

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                gai

                Thank you Andrew for putting that thought into rigorous mathematics. I had been hoping Dr Evans or some one else would.

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                Andrew, I didn’t want to comment on matters outside the basic model, but if your interpretation of the equation Rud pointed out are correct, then yes it seems like a similar case to the post (such as for the Planck feedback, for instance). If the formal definition of a partial derivative becomes the limit of a series of climate states that cannot exist, then the partial derivative is suspect. (While you might make an estimate of the partial derivative that you are confident in, it cannot be empirically verified, even in principle, so how would you really know your estimate was correct? If you are confident that the actual changes in something you are holding constant are in fact very small, then such an approximation is probably ok.) And yes, the problem lies in the physical meaning, so it cannot be fixed merely by stating more clearly what is held constant.

                An example of a ∂G/∂V_i is the decrease in OLR from CO2 molecules when CO2 doubles, thought to be about 3.7 W/m2 per log-doubling. If the log-base-2 CO2 concentration L changes by dL, it contributes (∂G/∂L) * dL to dG (setting V_i to L). This is pretty crucial because it is the change in CO2 concentration widely thought to be driving climate change, so it cannot be omitted from dG.

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            Nick Stokes October 13, 2015 at 5:09 am · Reply

            (“And if you declare a variable to be ‘independent’ and the variable IS NOT what then?”)

            “Chain rule. You can take account of the dependence. The silly thing is that David’s G example, that he’s emphasising in this post, is differentiating both dependent and independent variables explicitly”

            The error is trying to take the partial derivative of the ultimate result with respect to the ultimate result, even indirectly! There is no chain rule for such, nor is there any necessary requirement for convergence of such. Another grand display of intentional SCAM! :-(

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              “The error is trying to take the partial derivative of the ultimate result with respect to the ultimate result, even indirectly!”
              Well, give an example. What you say doesn’t make sense.

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                Why? You figure it out!!! :-(

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                It’s babble. But ∂x/∂x is perfectly meaningful. The answer is 1.

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                James Bradley

                Nick,

                You seem to be in a bit of a panic about this, if indeed David Evans is wrong you’d be sitting back laughing until he compounded all his errors publicly, then you’d come out with your evidence and vilify him.

                You got nothing, but the believers hand book of tricks, your credibility is crumbling.

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                “You got nothing, but the believers hand book of tricks”
                You got nothing at all.

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                Nick Stokes October 13, 2015 at 6:32 am

                “It’s babble. But ∂x/∂x is perfectly meaningful. The answer is 1.”

                At what point in time space or cycle need such ever be true? This is your nonsense of formula.

                Measure ∂x, then measure 1/∂x at any location in space-time. Never has a product of one. The variance is called thermal noise power! Please go somewhere and buy a clue! ;-(

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                Nick Stokes October 13, 2015 at 8:16 am

                (“You got nothing, but the believers hand book of tricks”) “You got nothing at all.?”

                You seem to refer to yourself! Which some read and then shake head sideways. :-(

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                “Measure ∂x, then measure 1/∂x at any location in space-time. “
                So when you were asked in a maths exam to differentiate x² you said – well, first you have to measure dx², then go measure 1/dx, then, well, dunno. You must have been a star student.

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                James Bradley

                Nick,

                True to form you merely repeat the words of others.

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                James Bradley

                Wow, Nick,

                Most red thumbs I’ve received since the last time you used sock puppets.

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                gai

                However ∂x/∂x is not perfectly meaningful because it is too close to zero divided by zero.

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                Nick StokesOctober 13, 2015 at 9:08 am

                (“Measure ∂x, then measure 1/∂x at any location in space-time. “)
                “So when you were asked in a maths exam to differentiate x² you said – well, first you have to measure dx², then go measure 1/dx, then, well, dunno. You must have been a star student.”

                Interesting, not! x starts as, = absolute surface temperature!!!
                Now say x = sin^2(x) + cos^2(x). for a new temperature. as you and other Clueless Climate Clowns (CCC) do often, while never checking!!

                You say “∂x/∂x is perfectly meaningful. The answer is 1.”

                Would you like to demonstrate a value of 1? :-(
                Troll!

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          John B

          All Nick Stokes ever does is play word games. Every site he visits he contaminates with distracting nonsense. He has become the ultimate TROLL.

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      OriginalSteve

      I come back to Dr John Christies 2012 work whereby he effectively shredded all the 40+ IPCC models by disproving them with basic surface temperatuer data.

      As Einstien said ( paraphrasing ) – “hey if I was wrong, one scientist would be enough to prove that”

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    William

    OT and I apologise, but it seems the alarmists are starting to panic about the pause and potential cooling – By using an atmospheric general circulation model known as ECHAM, Professor Sybren Drijfhout found that for a period of 20 years, Earth would cool if global warming and a collapse of AMOC were to occur simultaneously.

    The study, published in the journal Nature, said such a scenario would “obliterate” global warming for the roughly 15 to 20 years, offsetting global temperatures by 0.8C. The resulting surface cooling would last for 40 to 50 years. The paper goes onto note that such a scenario would result in heat flow from the atmosphere into the ocean which is something that has already been witnessed over the last 15 years during a period of climate hiatus — also referred to as a global warming slowdown or global warming pause.

    So global warming may cause global cooling. The bets are hedged, if it warms it is because of rampant AGW, they win, if it cools, it is because of rampant AGW. Either way, they win.

    But at least they acknowledge the pause/hiatus/peak!

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      Roy Hogue

      If you pay someone to find something they’re going to go all out to find it.

      I wonder what would happen if the same group of people were suddenly paid not to find the same thing. Would they not go all out to find that global warming isn’t there at all? The models would be just as complicated, the partial differential equations just as subject to error and the arguments just as convoluted but there would be no global warming.

      Climate change by whatever name you use has become the cause du jour for anyone who has to find a problem of some kind in order to get paid. After all, who will be satisfied to read your research paper that finds NOTHING TO WORRY ABOUT? Who will provide that precious grant money to find nothing? How will the talking heads have an audience if all they can say is, Gee folks, there’s no problem today?

      It’s time for us to realize who own’s these professors, these scientists… …time to holler, foul!

      Dr. Evans has embarked on a project to actually explain observed climate behavior whatever it may be. He isn’t trying to prove there is a problem and he isn’t trying to prove there isn’t a problem. That will anger and confuse a lot of the world. But I hope that this time the chips will fall where they fall because that’s the way they should fall, not because someone has a vested interest in a certain outcome. Evans is in the unique position that he isn’t beholden to anyone when it comes to what his findings are.

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        Anton

        “If you pay someone to find something they’re going to go all out to find it.”

        Dead right, and for my money the worst are Racial Equality organisations who are government-funded. If they said that racism was mild in Western countries compared to many places then they’d be out of a job, so they go round telling minorities how oppressed they are, and generally making community relations worse instead of better. They are the walking definition of worse than useless.

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          OriginalSteve

          Yes, and apply the same to the sudden “domestic violence epidemic”……

          Been there all along, and I’ll bet you based on some stories I’ve heard from people now in their 80s about how widespread it has been in society for years, but back then it wasnt talked about. I’m not excusing it, but anything can be “mined” when you pay people to “find” it….

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        Roy Hogue October 13, 2015 at 12:13 am

        “If you pay someone to find something they’re going to go all out to find it.”

        Roy,
        I agree this has all the earmarks of money and political pressure. this is much more deep seated than that! This reflects the personal integrity (or lack thereof) of the highest levels of scientific academia. There likely is no recovery for the now disgraced sciences.

        Today’s scientists have substituted mathematics for experiments, and they wander off through equation after equation and eventually build a structure which has no relation to reality.”— Nikola Tesla

        It seem to me that understanding has been replaced by algebraic formula. Formula comes way after understanding learned by making own mistakes, not reading of those by others. The formula without understanding is like the formula for ‘weight” (W). W=mg. easy to remember but must remain abstract to remain mathematical. Weight as we know it is never symbolic algebra, it is the concept of heaviness and all that goes with it! The abstract W = mg, must allow g = W/m which is conceptually nonsense as the gravity of large mass (Earth) is not at all affected by small mass within that gravitational field. With proper understanding a measured weight divided the measured mass (force acceleration) can be used to estimate the mass of the Earth. None of this is ever mentioned in academia. only the formula, with no understanding. Especially by the professor, that can only profess, but can not do! :-(

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          Alfred

          Acts 16″16
          16 And it came to pass , as we went to prayer, a certain damsel possessed with a spirit of divination met us, which brought her masters much gain by soothsaying :

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        Greg Cavanagh

        We have examples of where this is true. Debating competitions. Your team is given a subject not of your choosing, and you must debate its merits to win the competition. Exhibit A:
        http://nypost.com/2015/10/07/national-title-winning-harvard-debate-team-loses-to-ny-inmates/

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          Roy Hogue

          Greg,

          I’m glad I’m in the habit of looking into the past threads to see if someone has replied to me so I can decide whether I need to answer back.

          In this case I would love to have witnessed that debate, not only for the sake of the debating skill but for the subject matter which is a very hot, very touchy thing at the moment. Given the current political climate it must have been tough for the inmates to pull off a win, especially against Harvard, where the whole team would have been literally indoctrinated in theory and practice against the proposition being debated — such is our world at the moment.

          Hat’s off and more power to those inmates and their mentors.

          I’ll leave you to guess what my personal position is. But if you know me at all you won’t have any trouble figuring it out.

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      “The bets are hedged, if it warms it is because of rampant AGW, they win, if it cools, it is because of rampant AGW.”

      Yes, and if there is temperature stasis, it means these yin-yang forces of rampant AGW are locked in a to-the-death struggle for climate supremacy! :)

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        OriginalSteve

        Er…hang on….how the dickens can you have global cooling caused by global warming?

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          jorgekafkazar

          You have to be a spittle spewing pseudoliberal to grasp the concept.

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          Tom O

          It goes something like this – global warming causes the polar icecaps to melt. The infusion of cold water into the ocean then causes colder air to flow down over the continents, precipitating out the water vapor as snow, cooling the atmosphere. How this doesn’t prevent the icecaps from melting still is beyond normal but well within the bounds of psychotic logic, so, you see, global warming causes global cooling. Easy, right? that’s taught in CAGW 101.

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          OriginalSteve October 13, 2015 at 9:47 am

          “Er…hang on….how the dickens can you have global cooling caused by global warming?”

          The same way the Clueless Climate Clowns (CCC) do. Simply make it look hard to take the partial derivative of surface with respect to surface temperature! See easy! ;-)

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    bob sykes

    Apparently I am missing something. The whole argument over partial derivatives seems to be a red herring. The GCM’s perform a numerical integration of the transport equations. The only questions are: (1) Are the transport equations properly formulated? (2) Are the initial and boundary conditions properly stated. (3) Is the numerical integration scheme appropriate?

    Of all the questions, the numerical integration scheme is where people often make substantial errors. And generally the errors (and arguments about them) are concerned with the size of the time and space steps, the appropriate averaging over steps and cells, the shape of the cells, the handling of curvature and angular momentum, etc.

    There are also the issues of freely adjustable parameters and curve fitting. Apparently some of the models are quite adjustable. I note that of the hundred or so models is use around 3 or 4 or so actually do represent the pause. Somewhere someone has stated that those models use the adjustable parameters to force a data fit. But I have no idea.

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      Bob: What you are missing is mentioned in the sections “Background” and “Basic Models or GCMs?” in the post above.

      To repeat, there is a specific context, a specific model, and two specific partial derivatives. By your comment, you are unaware of what they are.

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        Robk

        Your patience is admirable David.
        It’s been 30 odd years since I last did calculus. I found your bite size presentions well described and well laid out. I read Lucia’s posts last week and it was clearly a response to poor comprehension.
        I look forward to reading the MIT link when I have some time.
        Thank you Jo and David for some clear and concise science communication.

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      bob sykes October 12, 2015 at 11:42 pm

      “Apparently I am missing something. The whole argument over partial derivatives seems to be a red herring.”

      David’s example of the widespread misuse of partials is key to understanding of the deliberate intentional deception of all the climate models, basic, or gigantic! They all simply do not represent anything at all of what is the operation of this Earth’s atmosphere.

      “The GCM’s perform a numerical integration of the transport equations. The only questions are:
      (1) Are the transport equations properly formulated?
      (2) Are the initial and boundary conditions properly stated.
      (3) Is the numerical integration scheme appropriate?”

      The obvious answer to all three is no!!! The structure of your grand GCMs or basic climate models, have no relationship to the physical operation of this atmosphere. All such is nonsense. All is but a deliberate intentional SCAM!

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    Random Comment

    I just read Lucia’s post and all the comments (phew!). I look forward to the misunderstandings being resolved.

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    The problem is not the understanding of partial derivatives; the problem (listen up, Lucia, this is for you) is dogmatic avoidance behavior, and a confusion between two definitions of “debate”: 1) a competent “scientific” debate, whose purpose is to find the truth, and 2) a “public” debate, whose purpose is to control the masses. With respect to the latter, everything “public”–debate, election, whatever–is no more than a beauty contest, with “beauty” defined as that which the public, on balance, likes best (without any study, any consistent logic). The system is broken and we are in a war atmosphere, not a “debate” atmosphere.

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      So true Harry.

      I am wondering what would have become of so many important discoveries and mistakes of science if the debate through history was always so charged with fear, misrepresentation and hatred. I always thought scientists were more than happy to have their life’s work debunked/re-interpreted, provided the new information or interpretation was correct. That is at the end of the day what scientific progress is all about.

      I think one of the main problems here is that trillions of dollars are now invested in the basic models being infallible and when that kind of money is on the line, people will defend their slice of it to the death. The alarmist industry rushed headlong into forcing policy changes both social and economic, without ever really gathering enough evidence to justify those positions. Now in order to maintain those positions they must fight on any battlefield, except the one that challenges their flawed work. So the debate will always and inevitably be taken back to insults, red herrings, straw men and Ad Hom. When you also consider this is the only part of the debate the gen. pop. actually understands, it further fuels the propensity for simplistic public dismissal of contra ideas and evidence as the easiest way to avoid discussing the science.

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        Greg Cavanagh

        You are an optimistic one aren’t you Safteyguy. The past has been a lot more fiercely debated, protected and fought over than the present day. When you start getting into the details of history it’s amazing just how fierce the egos really were.

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          True enough Greg, but I guess the difference I was aiming at but failed to explain was… It wasnt quite so “24 hour news cycle”. You didnt have the daily bashing of your detractors on a personal level playing out on the news.

          But yes I am an optimist when it comes to professional conduct.

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        Tom O

        The problem has become one described, in part, by Tesla in the comment posted earlier. Science always has been “the search for the truth,” if you will. Science does not KNOW the truth, nor can it define it, only search for it, but you find a lot of nice nuggets along the way. Climate science, the “settled science,” has forgotten that nothing is settled since there may yet be some factor not understood.

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      PeterS

      Well put Harry Dale Huffman. I like the description that we are in a war atmosphere, not a debate atmosphere. I would go one step further and say the war is over and they have won, unforutnaly. It certainly looks that way according to what’s happening everywhere in the political arena. Of course there’s always an opportunity to fight another war. Only time will tell how that eventuates.

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      Wayne Job

      This global warming science stuff is a made up paradigm ,that non can change but must be proved at all costs. Those outside this paradigm will not be supported but derided.

      It is no different in the other set paradigms of physics the outsiders get nothing but ridicule.

      ” We can say with some finality, however, that the Big Bang and the Standard Model are to physics of the future as Phlogiston is to modern chemistry”
      D.L. Hotson.

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    Most advancement does come from questioning the assumptions, so this would seem useful.

    However, problems with the formulation ( and other implicit assumptions ) of
    1. Planck feedback and
    2. RF from CO2 doubling

    would not appear to be large sources of error.

    I write that because calculating the RF from CO2 doubling does not vary greatly
    spatially, seasonally, or diurnally.

    When I calculate the spatial variation of RF, for a fixed atmosphere, using a radiance code,
    I find small spatial variance from global average RF in the sub-polar mean:
    ( lower levels of net radiance mean lower levels of RF ).

    So, whatever the variances in other factors ( clouds, lapse rate, humidity, et. al. ),
    that might arise from the formulation, by the spatial analog, would not change global RF much.

    What I believe is much more significant wrt climate models are the equations of motion.

    We are still stuck with problems of formulation laid out by Lorenz.

    Fluctuations appear on the synoptic, seasonal, decadal, and at least centennial scales and the relative variance
    appears to increase from the biennial to the centennial scale.

    Perhaps RF from 2xCO2 would exceed the variance from chaotic flow, but it would certainly
    limit any pronouncements on sensitivity because natural variation in multiple parameters and even net radiance, will continue.

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    dp

    Is it not the point of the derivative conversation is that they reveal the models allow what nature does not? That is what I took away from it.

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    LarryT

    I remember sitting in my partial Diff class with my professor with 2 higher math phd’s going over a proof in class. He was reading from a proof in our text that stated “It is intuitively obvious that” and stopped. He stood there for a few minutes and then dismissed class. The next class he handed out 10 pages of math to go from that step to the next.

    Just because Lucia did not see the “intuitively obvious” may be in an inadequate explanation not an inadequate understanding.

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      Mark D.

      OK Larry T but then that doesn’t explain why she had to drag it down over on her site instead of asking the polite (oh were they polite?) questions here when and where they might have been helpful. She perhaps has inadequate understanding of more than maths.

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        jorgekafkazar

        Lucia is a lukewarmist. While there was a time when I considered that a tenable position, science has moved on and it’s beginning to look as if she’s out on a limb.

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      Anton

      ‘Clearly’ is a lot neater than “It is intuitively obvious that”…

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    Yonniestone

    Has the forum for utilizing the scientific method shifted with technology?, if so probably an ‘old school’ phone call or ‘snail mail’ would have sufficed instead of making an ass of U and me.

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    John in Oz

    From David’s resume:

    David consulted full-time for the Australian Greenhouse Office from 1999 to 2005, and part-time for the Department of Climate Change from 2008 to 2010, and was the lead modeler in developing FullCAM, the world-leading carbon accounting model that Australia uses for analyzing the carbon in Australia’s biosphere for the Kyoto Protocol.

    It seems to me that whether David is right or wrong, Government policy is based on error.

    If his current writings are wrong then his previous, and all subsequent work based on it, is suspect and should not be used to formulate policy.

    If he is correct then all previous work that disagrees with it is suspect.

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      I think what that shows John is that the Govt. of the day in any given country is far more interested in the revenue opportunities presented by AGW than the voracity of the reasoning that underpins it. Thats why AGW has become a political not a scientific topic. It basically does not matter anymore who is right, the wheels are so fully in motion now, the race to collect the dollars is all that matters.

      The only part remaining of this predictable saga is that when the cooling starts, the IPCC and the Govts. who bent over the lowest will claim they fixed the world by their actions. Then we will move on to the next scare campaign which looks to building up now in the form of a second phase of nuclear war scaremongering.

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      Bill Burrows

      David’s FullCAM model was developed within the Australian Greenhouse Office (AGO) to provide estimates of net CO2 arising from this country’s Land Use, Land Use Change and Forestry sector. It allowed Australia to fulfill reporting requirements under the Kyoto Protocol e.g. FullCAM gave the AGO estimates of CO2 released following huge land clearing episodes in Queensland and NSW. These estimates satisfied bureaucrats checking country wide reports for the Protocol – but they were rarely, if ever, backed up by actual measurements in the field.

      So Australia soon became the greenies pariah and was (and still is) vilified for having the worst net CO2 emissions in the world. Indications that the continent was more likely to be a net sink of CO2 were essentially ignored e.g. see Global Change Biology (2002) 8, 769-784. Now the IBUKI satellite data (http://wattsupwiththat.com/2014/07/05/the-revenge-of-the-climate-reparations/)and the OCO2 satellite (http://wattsupwiththat.com/2015/10/04/finally-visualized-oco2-satellite-data-showing-global-carbon-dioxide-concentrations/) show Australia is indeed a net sink for CO2.
      Both the GCMs and FullCAM highlight that relying on model outputs for making policy decisions can be a dangerous and very expensive practice if the outputs are not backed up by actual field measurements, or quantitative observations. The current hiatus in observed global troposphere temperatures, despite GCM projections to the contrary, is a case in point.

      And FullCAM is currently being used to determine the number of Australian Carbon Credit Units (ACCUs), generated from native vegetation regrowth, that are submitted for auction – either through a Carbon Abatement Contract or on the secondary market. Hundreds of millions of taxpayers’ dollars have been set aside for this progressive auction (next one in November) under the Coalition’s Direct Action Plan. Yet no objective data (field measurements) are required to substantiate the FullCAM model output for any particular Carbon Estimation Area. So the validity of the claimed ACCUS, generated over potentially thousands of hectares for some individual contracts, is not backed up by field sampling. Poor fellow my country.

      Models are commonly designed to produce estimates (predictions/projections) of what is occurring in the real world. But no credence should be placed on their outputs unless these are endorsed by actual measurements, accompanied by the associated sampling error (%).

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        Hi Bill,

        What you say is correct, AFAIK. (For onlookers, Bill is familiar with FullCAM — an author of this report).

        In FullCAM’s defense, it replaced a system of national carbon accounting (still used by nearly all nations) that simply partitions the country into three or six zones, estimating the typical carbon per hectare within those zones (in the trees, crops, debris, mulch, and soil on the hectare, and products derived from the hectare), and applying it across the entire zone. But vegetation isn’t neatly quantified. It varies slowly as one moves 3,000 km from say the tip of tropical northern Queensland through rainforest and inland through savannah and semi-desert to temperate Tasmania, in response to a wealth of factors. FullCAM attempted to capture those factors, and to estimate the carbon per hectare based on temperature, soil type, rainfall, dominant plant species and the properties of that species, etc etc (over a thousand inputs all up), with estimates of which parts were “cleared” or “forested” in any year provided by satellite.

        Both FullCAM and the system it replaced were theoretical estimates of carbon per hectare. Presumably FullCAM was a better estimate — it was certainly more bureaucratically defensible, and it sounded great to politicians. Very scientificy sounding. Can anyone else make a better sounding estimate? Taking all those factors into account? (Sound like a GCM?)

        I asked if field trials were being done for validation. There were some, but they were pitiful in number. They generally said FullCAM was correct to within 10%, but the testing was only on a limited range of conditions and the tests were limited by expense and difficulty — how do you measure the weight of the fine roots (thinner than your little finger) of a tree? Or all the carbon in the soil? Not to worry I was told, just get on with modeling.

        FullCAM had severe shortcomings, even in a theoretical modeling sense. The initial philosophy was to make an estimate, even if poor, and refine it later with more work and more data. However, once the first national carbon inventory was estimated, for political reasons it could not be altered by more than a small percentage each year — or it would undermine the credibility of the program in the eyes of our political masters! So corrections and fixes were not necessarily made, and in some cases FullCAM was deliberately run with broken versions. You can imagine the bureaucratic problems — better not to validate. I eventually resigned, in large part out of the way it was all going.

        The FullCAM experience has left me very sensitive to issues of theoretical estimation versus validated or interpolative models. Yes FullCAM was a better estimate, and in time with enough data and work and willingness to chase only the truth it would probably converge on the truth in a reasonably timely matter. But politics and money intervened. I might add that there was only a limited amount of money in the Australian rural research scene, and FullCAM sucked oxygen out of some rooms — I gather one either contributed to the FullCAM effort, or funding flowed elsewhere.

        As the environmental bureaucracy dumbs down (the existing staff choose the new staff, and don’t want anyone too threatening, a common bureaucratic phenomenon), I’ve heard FullCAM is under threat and many want to return to the spreadsheet with six vegetation zones — basically because the new managers simply do not understand how FullCAM works or how to operate it. (No chance the govt will ever want to employ me again, so I can say these things now.)

        The parallels with the climate models are obvious. A very theoretical basic model (based almost entirely on lab data, not real world climate data), expanded into GCMs with great political and bureaucratic significance and momentum, failing validation (the pause, missing hotspot, etc etc). I often wonder if the climate modelers are experiencing some of the same pressures and problems as in FullCAM.

        As it happens, I am claiming in this series the the basic architecture of the conventional climate models is wrong (posts 5, 7 and 9) and that significant inputs have been omitted (post 10), with more to come…

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          Bill Burrows

          Thanks very much for your detailed comments David. They certainly needed to be said. Hopefully others will appreciate that you are one damn good modeller, who knows both the limitations of his models and what he is talking about. Keep up the good work and may the force be with you. The politico/bureaucratic system must be spitting chips knowing that one such as yourself and your deep inside knowledge has come in from the ‘dark side’. As a retired 40 year public servant myself I loved your “dumbing down” analogy. It is so true. But it should not be forgotten that this process was initiated by the politicians in the first instance. I tried to give good independent advice to my political masters throughout my career. The latter came to a sudden end (initiated by me) when I was asked to obliterate a report (commissioned by my Departmental CEO) and prepared for a Productivity Commission inquiry. I was also advised to delete it from my agencies server and my hard drive, as well as destroying all hard copies to boot. Lesson – never embarrass a politician with facts they do not want to hear!

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            doubtingdave

            Bill thats intriguing i hope you kept the evidence , are you subject to some official secret act or gagging order ?

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              Bill Burrows

              I will leave my reply to your imagination dd. Politicians can be quite subtle at times. My Departmental head (of a reasonably large and economically important Agency) also suddenly found himself transferred to the Agency at the lowest scale in the government’s pecking order. [And one for which he had no obvious discipline expertise. But he was a great guy and I think he acquitted himself well there in any event].

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                Michael

                Basically as good a modeller as you can be at this scale of modelling which still not very good- compares well to totally awful which is the normal standard.

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    pat

    worth noting!

    15 Aug: Physics Today: Questions and answers with Freeman J. Dyson
    What does the iconic physicist think about the Pluto flyby, the Iran nuclear deal, and how his scientific legacy might be affected by his contrarian climate-change views?
    PT: Are you ever concerned that your contrarian view of climate science will become as much a part of your legacy as all the other contributions you’ve made to science? Or do you embrace that possibility?
    DYSON: I do not care what my legacy will be. To me the most beautiful aspect of science is that it is a collaborative enterprise, with a multitude of people from all over the world taking part. In the long run, it does not matter who discovered what. We all share the joy of discovery even if we do not share the credit. I am happy to be skeptical about the prevailing dogma concerning climate change, whether or not it turns out that I am right. As a scientist, I can disagree vigorously with my colleagues and still remain friends…
    http://scitation.aip.org/content/aip/magazine/physicstoday/news/10.1063/PT.5.3026

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    pat

    also well worth noting:

    12 Oct: Daily Mail: Katherine Rushton: BBC ‘ignored public’s views on its future and instead used paid-for-study to represent the views of the population’
    Around 40,000 people responded to questionnaire from the BBC Trust
    Thought that governing body would pass their views onto Government
    Trust decided not to include survey results in official report on BBC future
    Those who took part said they were ‘outraged’ to have their views ignored
    The BBC Trust side-lined the views of the public from its official report on the future of the Corporation – despite lecturing everyone else that the public’s voice should be ‘heard loud and clear’.
    It also skewed the results of a survey, even after telling MPs that any decisions about the future of the broadcaster should be based on ‘evidence’ rather than any preconceptions…
    But instead of the 40,000 members of the public who filled in the questionnaire, the results are from a sample of around 2,900 people chosen by polling agency ICM.
    Last night, people who filled in the survey were outraged that they took the time and effort to set down their views, only to have them dismissed in the Trust’s official report.
    Caroline Levesque Bartlett, who runs a campaign to ban the licence fee, said: ‘I find it really irritating…we are allowed to share our view only once every ten years, and the BBC Trust rigs. What a sham.’ A BBC Trust source admitted that the results of the public questionnaire were not properly included in the official document, and hinted that it may have run out of time to do the analysis it wanted…
    http://www.dailymail.co.uk/news/article-3268840/BBC-ignored-public-s-views-future-instead-used-paid-study-represent-views-population.html

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      gai

      A BBC Trust source admitted that the results of the public questionnaire were not properly included in the official document, and hinted that it may have run out of time to do the analysis it wanted…

      Translation: We couldn’t figure out how to slant the analysis so the outraged public’s voice wasn’t ‘heard loud and clear’ to say SHUT THEM DOWN!

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    handjive

    Mea Culpa:

    The problem is, I was only accounting for a doubling of greenhouse gases, as opposed to the tripling or more under the current business-as-usual approach, and the models used for estimating future sea temperatures didn’t account for more frequent extreme El Niño.

    And if so, then my original projections of when the oceans become too hot for coral reefs are too optimistic!
    . . .
    Every climate model underestimates.

    Underestimate. Overestimate. Both are an example of failure.

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    TdeF

    For those who are interested, the French are excited about the Paris IPCC conference

    A letter from the Alliance Francaise

    “In 2015, France will be hosting and presiding the 21st Session of the Conference of the Parties to the United Nations Framework Convention on Climate Change (COP21/CMP11), otherwise known as “Paris 2015” from November 30th to December 11th. COP21 will be a crucial conference, as it needs to achieve a new international agreement on the climate, applicable to all countries, with the aim of keeping global warming below 2°C. France will therefore be playing a leading international role to ensure points of view converge and to facilitate the search for consensus by the United Nations, as well as within the European Union, which has a major role in climate negotiations.

    While the focus will be on Paris, the implications will affect all of us. Even though Melbourne is almost as far as it could possibly be from the site of the UN Convention, the decisions will also need our commitment and willingness to change in order for their objectives to be achieved.

    To encourage debate about the event, its purpose and its possible outcomes, the European Union Centre at RMIT is delighted to partner with Alliance Française de Melbourne [and with the French-Australian Chamber of Commerce & Industry (FACCI)] to host an event focused on Paris 2015.

    Speakers at the event will include
    Dr Hartmut Fuengeld, Centre for Urban Research at RMIT;
    Ms Amandine Denis, Head of Research at ClimateWorks Australia;
    and representatives from Victorian Government and French Industry.
    There will be plenty of opportunity for questions and discussion.
    Light refreshments will be served from 5:30pm for a 6pm start.”

    The Council Chamber, RMIT University
    Building 1, level 2
    124 La Trobe Street
    Melbourne, VIC 3000
    Australia
    Thursday, 15 October 2015 from 5:45 PM to 7:15 PM (AEDT)

    Yes, Europe really needs those Carbon Credits. Send cash now.

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    Anton

    The world’s senior judges get together to work out how to criminalise expressions of climate change skepticism:

    http://www.telegraph.co.uk/comment/11924776/Judges-plan-to-outlaw-climate-change-denial.html

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  • #

    I see the plague of Stokes has finally arrived down under. Consider yourself now added to the alarmist hit list David.

    Pointman

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    Bulldust

    One for the rank hysteria file – Ocean acidification will lead to species collapse according to Prof Ivan Nagelkerken of the university of Adelaide:

    https://au.news.yahoo.com/thewest/national/a/29794622/acidification-to-cause-species-collapse/

    I guess you can nail that to the church door (yes, I see what I did there…)

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      discussed in The Conversation

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      janama

      He’s done alright out of scaring people about climate change:

      From his Bio

      Vidi research fellowship (Netherlands Organization for Scientific Research ), Netherlands, 600,000 euro, 2005 – 2010
      Future Fellowship (Australian Research Council), Australia, 714,528 A$, 2013

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      TdeF

      No idea what this means. Ocean acidification. From CO2? The oceans are not acid and never will be. It is one of those fantasies which has become fact by repetition.

      The world’s oceans are alkali and buffered by billions of tons of limestone anyway. Besides, 98% of all CO2 is already in the oceans. Another 2% would hardly matter. Acid rain is about metals forming acids, as with high sulphur fuels from say South America and SO2 becoming H2SO4. The sulphur is extracted these days. So someone has conflated acid rain with acid oceans and blamed CO2? Utter nonsense and from a University Professor no less but a new breed of skin diving pseudo scientist.

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        gai

        Beat me to it, thanks TdeF.

        If I knew nothing about CAGW, Ocean acidification would convince me it was a scam before I read past those two words. Amazing what a solid base in geology and chemistry will do for you.

        No wonder there is such a big push to Dumb Down Education World Wide.

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    Hi David, I always understood partial derivatives to mean holding all other independent variables constant. In what way does adding a subscript to say which are constant add anything? If all the others are constant, that is what it means anyway, and if not, it isn’t a partial derivative. Just trying to understand the criticism of you.

    [this was caught by the spam filter for reasons unknown] ED

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      Ron, the subscript can be added if there is confusion about what should be held constant — it means only the subscripted variables are held constant. This typically arises when the arguments of the function being differentiated are dependent on one another. For instance a function might have three arguments, the partial derivative might be with respect to one of them, and another argument is subscripted to say to hold that one constant — which means the third argument is allowed to vary. See the first couple of page of the MIT text by Aoroux to see why one might want to do this.

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    Mike Flynn

    The problem with the endless palaver about models, is that Nature doesn’t seem to be paying any attention whatsoever.

    Nobody, anywhere, has demonstrated the ability of either of the major supposed “greenhouse gases ” – carbon dioxide or water – to warm anything at all.

    Amazingly, their supposed “warming” properties vanish after nightfall, or, in the Antarctic, pretty much all the time.

    The lowest recorded temperature on the Antarctic continent was recorded at the height of the Antarctic summer, from memory, and was below the freezing point of carbon dioxide. Some warming ability, eh?

    Given the aridity of Antarctica, and the Libyan desert regions, it seems that the warming and cooling properties of H2O gas are marvellous indeed. It has the ability to force extremely high temperatures when it’s hot, and extremely low temperatures when it’s cold!

    Does anybody of even average intelligence have any logical reason for believing this greenhouse nonsense?

    Anybody foolish enough to try to demonstrate the warming ability of CO2 in a laboratory, fails miserably. Hence the bizarre belief that models, based on poorly understood physics, can replace inconvenient facts.

    Burn lots of fossil fuel. Release the CO2 and H2O sequestered by Nature over the eons. Don’t starve. Don’t freeze. Enjoy life – that’s what it’s there for.

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    Ross

    O/T but I’ll follow nature any day compared to models. Interesting few months ahead in the Northern Hemisphere

    http://www.telegraph.co.uk/news/weather/11926752/Britain-faces-longest-winter-in-50-years-after-earliest-ever-arrival-of-Siberian-swan.html

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    Ross

    No doubt the Paris-ites are hoping it isn’t going to happen.

    Anti Paris-ites maybe not so much

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    Steve McDonald

    That Pope scorns capitalism.
    What country has the highest per capita income on the planet?

    And how much tax do the inhabitants of that country pay.

    Like the rich on the left the Vatican has one God and that is money.

    Once a week they will demand in a shameful way the last few dollars from Worlds poorest.

    The absolute worst capitalist is a hypocritical capitalist

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    crakar24

    Hello David,

    I don’t understand the math but i do understand the context in which they are being used, i asked my son who is in his third year of Mech eng “Do the words partial derivatives mean anything to you?” He responded by saying “Yes a head ache” i wonder if Lucia got one of those when critiquing your work?

    Anyway for what it is worth when i try and go to Lucia’s site i get a polite message “Blocked by the defence gateway” so there you have it not even the Dept of defence rate her, your site of course gets a free pass :-)

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      Bob Fernley-Jones

      @ Crakar,
      You prompted me to actually visit Lucia’s site and I entered it with no problem.

      Have you been naughty over there and caused some offence?

      I think there may be slight amelioration in her opening paragraph to which I’ve added my bold emphasis:

      Recently, David Evan’s wrote a post at Jo Nova. Oddly, I saw the post today after following a link to Anders blog. I then read Davids post: David’s post left me rather puzzled. In fact, I can only conclude that I either don’t understand what David is trying to say or David’s argument is confused. But it could be me.

      With that, I can imagine (without looking far) that the sky is the limit in open comments.

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    When the mathematics of the climate models is settled, then maybe we can talk about the extreme paucity of data that is available for input.

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    Harry Twinotter

    “Over at the Blackboard, Lucia couldn’t make sense of David Evans’ post on partial derivatives, but instead of emailing us or commenting here, she published her unresearched thoughts and and asked her readers instead.”

    I wish some would do that when they do not understand the data and methods used by the Australian BOM.

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      Rollo

      I wish some would do that when they do not understand the data and methods used by the Australian BOM.

      Harry you visit this site often enough to know that the BOM has been approached many times by sceptics. I suggest you google before you post.

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      James Bradley

      Oh no, Harry Twatter, Svante Callender or is it Art Vandelay now – you finished the Penske file yet?

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      Bob Fernley-Jones

      Harry T,

      Sorry, see below (probably #27) I forgot to hit reply.

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      Geoffrey Williams

      Sorry Harry Twinotter but you’ve got you’re “otters in a knot’ again.
      There is no real comparison between the two matters you have referred to.
      I must concur with Rollo above – you are out of order and clearly showing your bias!
      Geoff W Sydney

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      RB

      cc: “Shoni Dawkins”
      date: Fri, 7 Sep 2007 08:28:03 +100 ???
      from: “David Jones”
      subject: RE: African stations used in HadCRU global data set
      to: “Phil Jones”

      Thanks Phil for the input and paper. I will get back to you with comments next week. Fortunately in Australia our sceptics are rather scientifically incompetent. It is also easier for us in that we have a policy of providing any complainer with every single station observation when they question our data (this usually snows them) and the Australian data is in pretty good order anyway.

      Truth be know, climate change here is now running so rampant that we don’t need meteorological data to see it. Almost everyone of our cities is on the verge of running out
      of water and our largest irrigation system (the Murray Darling Basin is on the verge of collapse – across NSW farmer have received a 0% allocation of water for the coming summer
      and in Victoria they currently have 5% allocations – numbers that will just about see the death of our fruit, citrus, vine and dairy industries if we don’t get good spring rain).
      The odd things is that even when we see average rainfall our runoffs are far below average, which seems to be a direct result of warmer temperatures. Recent polls show that Australians now rate climate change as a greater threat than world terrorism.

      Regards,
      David

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        Harry Twinotter

        RB.

        “Fortunately in Australia our sceptics are rather scientifically incompetent…”

        Not only in Australia.

        I assume that was a reference to the Millenium Drought.

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        RB

        Three thumbs down? You did read the bit

        It is also easier for us in that we have a policy of providing any complainer with every single station observation when they question our data (this usually snows them

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    Bob Fernley-Jones

    Dear Harry,

    I’ve had the BoM enquiry desk correct some algorithm errors on what was their formerly labelled HQ Site. More recently I’ve indicated what are severally embarrassingly corrupted data to that same desk and all follow-ups were ineffective. I went to higher levels including The Hon Bob Baldwin MP (For minister Greg Hunt). However, after referral by Baldwin, the then acting BoM CEO evaded addressing the issues, but indicated that they would investigate it if I provide funding to do so.

    You were saying Harry?

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      crakar24

      Did you respond by asking what the BOM funding is used for if not for the purpose of ensuring the data set is accurate and free of errors?

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        Bob Fernley-Jones

        @ Crakar,

        I’m not sure what you are asking, but I sort-of gave-up when they suggested that I should pay them to correct their bad data which was very clearly corrupted. E.g. step-change “corrections” in ACORN-SAT that had no correlation with recorded site changes or prolonged sharp step-changes for what were progressive events etcetera

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          crakar24

          star commentSorry Bob,

          I tend to reach conclusions i assume others have already arrived at.

          1, The BOM are paid handsomely by the governement to management among other things the temperature data set, the word manage implies it is maintained as accurate as one could possibly make it and routinely checked for any errors either through software (algorithms) or perhaps faulty equipment and so on.

          2, You approached the BOM with legitimate concerns about the data set in an attempt to assist them to achieve what they are paid handsomely to do.

          3, The BOM responded by asking you to provide funding to allow the BOM to achieve something that they had already been paid handsomely to achive. Ergo if they are not spending the money on maintaining the dataset then what are they spending all that money on?

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          Griffo

          It might be a good joke to initiate a crowd funding project to make the bom face up to their cynical avoidance of their duty to provide accurate information to interested and informed members of the public. How much do they want ?

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      Harry Twinotter

      Bob Fernley-Jones.

      Not sure what your point is, and we only have your word for what you claim.

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    Bob Fernley-Jones

    Maybe Lucia will clarify/comment domani?

    Whatever, when David’s work is peer-review-published, perhaps the controversy will die down?

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      crakar24

      In order for Davids work to be peer reviewed one would need to find several people that A) have a firm grasp of math and B) have an understanding of the inner workings of a climate model. Throw in a basic understand of code writting and you have someone worthy of the title of “peer”.

      How many people would have that skill set? I can see many problems here for David as most reviewers will suffer from Lucia syndrome.

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      Greg Cavanagh

      There have been many papers published that call into question, or turn upside down, CAGW papers. The controversy continues unabated. Being correct (whatever that is) doesn’t win the argument.

      Something the Law Judges should consider before they outlaw scepticism of Catastrophic Anthropomorphic Global Warming (<—the whole point of reducing Carbon Dioxide emitions). PS: when catastrophy doesn't come, do they repeal the law? What is the threshold of evidence that the law is no longer needed?

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    pat

    re BBC’s apology for Quentin Letts’ “What’s the point of the Met” program:

    12 Oct: Bishop Hill: Has the BBC banned all non-alarmist views?
    Peter Lilley has just issued the following press release.
    BBC PUTS IMPARTIALITY AT RISK BY ATTEMPTS TO CENSOR AND DISCREDIT MPs
    The BBC is undermining its reputation for impartiality by apologising for “giving a voice” to two MPs and by putting a ‘health warning’ on the BBC website casting doubt on their credibility – even though the accuracy of what they said is not disputed: says Peter Lilley MP in a letter to the Director General…
    The letter in full:…
    COMMENTS: Alex Cull:
    Here’s a transcript of BBC Radio 4′s Feedback, broadcast on 9th and 11th Oct (h/t Mikky):
    https://sites.google.com/site/mytranscriptbox/2015/20151009_fb
    http://bishophill.squarespace.com/blog/2015/10/12/has-the-bbc-banned-all-non-alarmist-views.html

    surprised the program is still available…but it does havea NOTE added:

    BBC: The Met Office
    NOTE:
    This programme raises questions about the accuracy of previous long-term global warming forecasts by the Met Office and contains comment by MPs who are Trustees of the Global Warming Policy Foundation, which challenges government policies to mitigate anthropogenic global warming. We would like to clarify that the Met Office’s underlying views on climate change are supported by the scientific consensus.
    PROGRAMME SYNOPSIS:
    Quentin Letts begins a new series casting a critical but amicable eye across institutions at the heart of British life, asking the question ‘What’s the Point Of…?
    http://www.bbc.co.uk/programmes/b06418l5

    it is great fun, so listen while u can, if u haven’t already.

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    RB

    The heat equation – goes back to Fourier. And is q independent of T? No, it’s the derivative of T.

    Nick Stokes up there, somewhere.

    k needs to be independent of x and ΔQ≠cρΔT because of work done. The heat equation could go back to when Noah was learning to swim but you couldn’t just use it without checking if it were valid. I assumed that these things were dealt with properly but you, Nick Stokes, have me more cynical than ever.

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      RB,
      I wrote the heat equation in its conventional formulation for a solid rod. k would normally be constant, though dependence on x is no propblem. No P-V work. I put it as a counter to Rud’s apparent belief that there is an issue with fluxes being dependent on T.

      I say apparent, because Rud won’t say what he thinks is actually wrong with the equations he names. But at least he has nominated examples, however vaguely. Elsewhere I see no examples at all of actual alleged misuse by climate scientists. Just airy mutterings.

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        RB

        I realised that you might have been referring to something other than the atmosphere (as conduction is negligible). Still don’t think that you put up much of counter argument by saying that the heat equation is settled science.

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          KR

          That wasn’t the point Nick was making, although if you think there is scientific disagreement about basic heat equations you will be sadly disappointed.

          Rather, Nick was demonstrating that partial derivatives are quite manageable and well defined if you use them correctly, including notation indicating what is being treated as dependent and independent in the partial derivative. And that Dr. Evans claims that partial derivatives are “strictly hypothetical and not empirically verifiable” or “has no definitive meaning” are incorrect, as pointed out in the next few pages of the class notes Evans refers to.

          To clarify, the Auroux 2010 notes Evans quoted should be placed _in context_:

          “The answer is, that there is no one right answer, because the problem was not well-stated. When the variables are not independent, an expression like ∂w/∂x has no definite meaning.
          [...]
          There is only one way out of our difficulty. When we ask for ∂w/∂x, we must at the same time specify which variables are to be taken as the independent ones. This is done by using the following notation: …”

          See how much more information is available in context?

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            RB

            Nick was demonstrating that partial derivatives are quite manageable and well defined if you use them correctly

            assume that dk/dx=0?

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              RB

              I think people have missed my criticism of Nick Stoles comment. The heat equation has k as a constant.

              That is OK if dk/dt=0 then dq/dx=0 even when dt/dx≠0.

              Just thought that it was a poor example to use to show that “partial derivatives are quite manageable ” even if the problem would have been dealt with. Not intractable, just a very different result to ignoring it.

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            KR: You say “See how much more information is available in context?”. Here is what you quoted from me, in context:

            “But in climate there are many variables and they are not independent — they form a rich web of feedbacks and indirect interconnections. As a rule of thumb, “in climate, everything depends on everything”. Consequently it is not possible to hold everything constant except for only two variables, as required for partial derivatives to exist. For example, warming the surface affects nearly every climate variable, not just the OLR.

            The partial derivatives of dependent variables are strictly hypothetical and not empirically verifiable – like the proverbial angels on a pinhead. In climate, you cannot vary just one variable, hold everything else constant, and measure the change in the other variable of interest. Employing partial derivatives in climate therefore incurs unknown approximations – so it is unreliable.”

            In the context, the partial derivatives referred to are well stated — hold all other variables constant.

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              Andrew McRae

              So KR just mischaracterised your argument by taking a few words out of context, making a strawman generalization.

              Can you clarify whether at 2.2.1.1.1 I understood your objection correctly?

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              • #

                Yes. The problem is physical reality, not notation. I’ve replied above at Comment 2.2.1.1.2.

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                David Evans October 14, 2015 at 6:00 pm

                “Yes. The problem is physical reality, not notation. I’ve replied above at Comment 2.2.1.1.2″

                Please this physical (measurable) is enough. Reality must also encompass all of fantasy, religion, and conjecture.
                The horn on my orange unicorn has spiral flutes, how about your orange unicorn? Have you checked? Perhaps only female orange unicorn horn’s have spiral flutes, or summtun!
                All the best! -will-

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              KR

              You used a portion of a text describing how to get results with definite meaning from partial derivatives – out of context – to claim that results from partial derivatives lack definite meaning.

              I consider that inappropriate, as you’ve thereby distorted, and in fact reversed, the meaning of Auroux’s notes. Partial derivatives _are_ mathematically definite if you use the proper notation. And that includes between “Non-independent Variables”, the very title of the Auroux notes you quoted from.

              “Up to now in calculating partial derivatives of functions like w = f(x, y) or w = f(x, y, z), we have assumed the variables x, y (or x, y, z) were independent. However in real-world applications this is frequently not so. Computing partial derivatives then becomes confusing, but it is better to face these complications now while you are still in a calculus course, than wait to be hit with them at the same time that you are struggling to cope with the thermodynamics or economics or whatever else is involved. For example, in thermodynamics, three variables that are associated with a contained gas are its

              p = pressure, v = volume, T = temperature,

              and you can express other thermodynamic variables like the internal energy U and entropy S in terms of p, v, and T. However, p, v, and T are not independent variables…” (emphasis added)

              … and on to the proper notation and Chain Rule for correctly handling partial differentials of dependent variables.

              Now, do the physics have interdependencies, additional feedbacks, that are not accounted for in modelling (both simple energy models and more complex GCMs that evolve the thermodynamics and see what happens)? Perhaps, although the ranges of model results _are_ consistent with observations, and you would need to present some physical evidence otherwise. But there is absolutely no mathematic basis for objecting to partial derivatives, and IMO you should not have posed your objections in that framework.

              [Note: If you _aren't_ asserting that partial differentials are mathematically undetermined and hence problematic in climate science, you should consider rewriting that section of your arguments prior to any peer-reviewed publication. Because quite frankly I see no other way to interpret Post 4 in its present form.]

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                KR: I disagree. You are quibbling over semantics and are taking statements out of context, and I doubt if you have read posts 3 and 4 carefully. You seem to have a particular problem with this sentence:

                When a quantity depends on dependent variables (variables that depend on or affect one another), a partial derivative of the quantity “has no definite meaning” (from Auroux 2010, who gives a worked example), because of ambiguity over which variables are truly held constant and which change because they depend on the variable allowed to change.

                Obviously a partial derivative that is well-specified has definite meaning, but that is not what was being talked about, as indicated by the part of the sentence that says “because of ambiguity over which variables are truly held constant and which change because they depend on the variable allowed to change”. Yes, if it is well specified then that ambiguity is specifically eliminated, so that is not the what the sentence is about. As noted in the post above, post 4 has a specific context, a specific model, and two specific partial derivatives. The pd’s in question are not well specified, and are ambiguous for the reasons stated. The pd’s in question do not have “the proper notation”, so what you are saying does not apply to them. They are exactly what Aurox was talking about.

                You say I “need to present some physical evidence otherwise”. I did, in post 4, which talks about the physical impossibility of allowing only surface temperature and OLR to vary while holding all else constant, as required to compute the Planck feedback, one of the partial derivatives required by the conventional basic climate model. Note too that this series of blog posts is about basic climate models, the application of “basic physics”; it is not about GCMs.

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              KR

              Addendum, I neglected it in my previous post:

              The relationships derived from partial derivatives _are_ empirically verifiable, by observations, just like any other relationship.

              Your claim that they “are strictly hypothetical and not empirically verifiable” is therefore unsupportable. If you have issues with the consensus view of the physics, present your evidence in physics and observations. Incorrect mathematic claims of this sort are a very poor argument.

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                KR: Please read post 4 more carefully. Briefly, a partial derivative does not exist if it is a limit of a sequence of numbers that do not exist, because the climate states they purport to describe do not exist. The Planck feedback parameter (see post 3) is such a pd. It has not been empirically observed, and even in principle never can be, because it it the increase in OLR while the surface temperature is incremented but all other climate variables are held constant — which is physically impossible.

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                KR

                I don’t consider presenting a linked reference to support a claim of “lack definite meaning”, when that reference explicitly says the complete opposite, to be mere semantics. YMMV.

                .

                The so called Planck response is _never_ expected to be observed in _isolation_ – it’s primarily a computed value used in comparisons between forcings. Actual observations require dealing with feedbacks (differing ones depending on timescale) and efficacies, which scale the response to such forcings. And to the accuracy with which we can observe temperatures and feedbacks, and by the physics used in modelling, we are _in addition_ observing the Planck response. Chris Colose has an excellent discussion of Planck forcing, feedbacks, etc, here.

                But again, I see no support whatsoever for claiming a partial derivative “does not exist”. You’re mixing mathematic statements with physical observations, with a very strong implication that the math is wrong, and I consider that an unreasonable emphasis.

                The previous paragraph is indeed about semantics – and semantics do matter when presenting an argument to the layperson. It’s entirely too easy to convey a completely different picture than what the data, or a narrowed/restated interpretation of the argument, supports.

                If you are _not_ arguing that the math is undefined, then may I suggest making it clearer in your opening post. Since your last few posts have indeed clarified matters, I’ll consider that particular issue done with.

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              • #

                KR. Well we’ll have to agree to disagree on the aptness of the “no definite meaning” quote.

                No, not the Planck response (which includes feedbacks) but the Planck feedback (which does not) — which is defined as the partial derivative of OLR with respect to surface temperature holding all else constant in post 2 and discussed in post 4. The Planck conditions* are the generally accepted way of saying what to hold constant when computing it –and of course are physically unreal. Hence the Planck feedback is unreal and unobservable for physical reasons.

                Again, you are not discussing the actual partial derivative in question, despite it being amply clear in the posts and having had it pointed out to you several times.

                *Planck conditions (the conditions under which the Planck feedback or sensitivity applies): All else besides tropospheric temperatures and OLR are held constant — so there are no feed-backs, all tropospheric temperatures (including the surface temperature) change in unison, and stratospheric temperatures are unchanged (Soden & Held, 2006, pp. 3355-56). There are some arbitrary choices to be made, such as whether it is the specific or the relative humidities that remain unchanged as the troposphere warms, or what happens at the tropopause.

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    pat

    12 Oct: National Review: Rupert Darwall: Pseudo-Historians Erase Scientists’ Early Caution on Global Warming Read more at: http://www.nationalreview.com/article/425433/climate-mafia-rewrites-science-history

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  • #
    RB

    all tropospheric temperatures (including the surface temperature) change in unison, and stratospheric temperatures are unchanged.

    ∂T/∂x doesn’t equal 0 because of convection and the work done. That requirement kind of says that radiation adsorbed at the top of the troposphere from the surface must be lost to space as the air warms without rising.

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      RB – That’s the way it is traditionally done (e.g. the Held and Soden papers of 2000 and 2006). It is arbitrary and non-physical.

      The issue is the derivation (post 2 or post 3) requires one to hold all drivers and feedbacks constant while allowing a temperature (presumably the one of greatest interest, the surface temperature) to increase, and allowing OLR to change. It is highly non-physical, so what can you do? I am just relaying the traditional solution — the Planck feedback/sensitivity is under the Planck conditions, which are as described above.

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      RB

      Sorry if it came out as criticism of your work , David, but I was only stating my own spin on the fault in the logic behind the model. For the assumption to be true, there has to be a pipe from the top of the atmosphere that is independent of Ts, as the energy absorbed goes into making the air hotter. It can’t rise and cool to maintain the lapse rate near the tropopause.

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    2dogs

    I think the resolution of this confusion requires the adoption of the term “exogenous” as used by economists.

    i.e.

    1. The IPCC asserts climate sensitivity of 1.5 – 4.5 C per 2xCO2.
    2. This climate sensitivity is essentially a partial derivative extracted from the climate model.
    3. It is only one of many such partial derivatives that could have been determined, depending on which variables are held constant.
    4. What you are actually after is the co-efficient of response to an exogenous increase in CO2.
    5. David Evans asserts the IPCC didn’t get that, because they picked the wrong partial derivative.

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    • #

      1. The IPCC asserts climate sensitivity of 1.5 – 4.5 C per 2xCO2.

      Well that’s already broken, isn’t it. Because the logarithmic effect of adding more CO2, the increase from the alleged pre-industrial 280 ppm to the current 400 ppm is already a fair slice; but it seems not much warming at all; around 0.7°C. Less than half way on the lower edge of the range.

      Of course most of the CO2 in the 400 ppm is natural. Outgassing from oceans is substantial when they heat just a fraction of a degree under increased insolation when e.g. albedo drops a few percent. There’s also geological CO2 outgassing, variable. Variable it seems with the positon of the Earth relative to other celestial bodies.

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      2dogs: The ECS is an algebraic formula involving a couple of partial derivatives — see Eq. (1) of post 3., where lambda-0 (the Planck sensitivity) and D-R,2X (the fall in OLR from Co2 as CO2 doubles) are both partial derivatives.

      While the partial derivatives introduce some unknown amount of error because they cannot (even in principle) be empirically verified, I doubt if they are the major causes of error in the IPCC’s estimate of the ECS. I reckon it is mainly that the solar response is applied to the CO2 forcing (post 9), and that the rerouting feedback or something similar (post 5, post 7) is omitted from the conventional models (in both cases, both the basic model and the GCMs).

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    Richard Ilfeld

    Science: I think it is worth reminding folks that we wouldn’t be having this conversation if the data matched the theory. Rising tides and rising temperatures that were obvious would certainly quell debate, and ordinary folks would do what they have always done: change crops and move inland.

    My analogy for the maths challenged (myself included after all these years).

    There is enough underwater archeology to demonstrate inundations in history, and the Brits drinking local wines in the MWP but beer later shows one of many well-documented instances of crop migration.

    David’s science is no more threatening that the losing sports coach of a formerly winning team saying “folks, it’s time to go back to the fundamentals”. The prima donnas say “I’m perfect, trade me” and everyone else gets down to work because the scoreboard doesn’t lie.

    Defending a flawed model is like blaming the officials.

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    jim2

    If David and Lucia can clearly define the differences, and focus on it and only it, then the light generated will be good. If the differences are well defined, we will know when they have been resolved and can move on to the other points of the model.

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      Rud Istvan

      They have been, in principal. Even at this abstract level, even just skeptics cannoy agree.
      Politically pathetic. In terms of hard core science, shows the limits of blogosphere debate on same. Ignoramo opining do not advance understanding. And on this particular topic, ignorami seem to predominate. Very disheartening.

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        jim2, Rud: Sometimes good science eventually comes from these sort of scraps, regardless of motivations and the evolution of the dispute, because it motivates people to really examine matters closely.

        Lucia is clearly suspicious that the formulation of G above and in post 3 is suspect because it includes both the temperature and the feedbacks in the arguments of G, even though the feedbacks are in turn functions of G. So she will want to reformulate G as a new function, call it H, that is only a function of the temperature and the drivers. However pdG/pdT and pdH/pdT are quite different, as the former holds feedbacks constant while the latter does not.

        Her alternative path with H is interesting and perhaps worth investigating. However, the formulation of G is useful because it immediately arrives at the Planck feedback and the feedback loop, with very little computation — and is also legitimate, as Auroux’s Eq. (3) indicates. It is also the one in the textbooks — I don’t claim any ownership of it. Note also that the Planck “feedback” is computed holding (the real) feedbacks constant — that is, using the formulation of G as above.

        Even demonstrating the existence and viability of an alternative approach with H does not show that the approach with G is wrong, which was Lucia’s claim.

        The further point about the existence of the partial derivatives again flows from using G or H. The establishment model holds feedbacks constant, ergo they are using G, and simply applying a formal definition of a partial derivative to G shows that the partial derivative of G with respect to temperature does not exist. The partial derivative of H with respect to temperature does exist, but it allows feedbacks to vary and is not the partial derivative in the conventional basic climate model.

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        Oh woah are we! What is needed is to trash the whole concept of an Earth atmospheric/climaste model!!! Then as Pointman writes, isolate the pathogen (UN) to see if it will destroy itself, without further contagion! I guess many earthlings love to be SCAMMED! The next ice age will correct that. Bet of the roaches! :-(

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    Wally

    Unfortunately we seem to have a great many comments from people who have not done a tertiary applied maths degree.

    I have done degrees in both Applied Maths, and Engineering (Electronic and Electrical / power systems at honors level).

    The electrical / power systems engineering degree is (or was, back in my day) chock full of differential equations, so we had to know all this stuff.

    It is not until final year of an Applied Maths degree, or final year of an ELECTRICAL engineering degree (with the power systems focus) that a lot of this makes sense.

    IT’S HARD, FOLKS. And a first year undergraduate barely gets it.

    What David explains is in fact completely correct.

    There are numerous pedants who would like to correct on about notation, etc. This obscures the fundamental point.

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      crakar24

      Wally,

      As i said in a previous comment i understand the concept but the actual calculations are something i would have to (re)learn before i could bring more than just the coffee to the table.

      My son gets it i got him to look at the equations and he gave them a thumbs up and also gets how they cannot be applied to a “climate simulator”.

      The problem is most people dont get it even to my low level of understanding, these people are known as the herd, they look to thier authoritive figures for guidance, Lucia is an authoritive figure but even they are thrashing around in the dark grasping at shadows trying to discredit David and in the end that is all they really need to do.

      The authoritive figure has spoken and the herd has listened, they can now ignore Davids work because Lucia has. Pretty soon you will have some dippy herd member by day, climate eco tard by night telling you how partial derivatives work.

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      Wally October 14, 2015 at 11:50 am

      “IT’S HARD, FOLKS. And a first year undergraduate barely gets it.
      What David explains is in fact completely correct.
      There are numerous pedants who would like to correct on about notation, etc. This obscures the fundamental point.”

      Wally,
      I agree! Even the partials of circular trig functions are to hard to get by most folk! I cannot show a single easy to understand incorrect partial derivative that refuses to converge, it has been to long.
      Have you such an example? Perhaps some Laplace stuff without getting into Laplace stuff! I understand how to stay out of deep shit. Can you show how easy this is to do if not carefully aware of what not to do? Please. Such would be most helpful! Don’t worry about the know it all trolls. Those that wish to learn/understand may very well “ask” embarrassing questions. This is the other side of learning.
      All the best! -will-

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      gai

      “Unfortunately we seem to have a great many comments from people who have not done a tertiary applied maths degree.”
      ……..

      Yes, but that does not mean we can not grasp the concept. (Dr Evans is a good teacher.)

      I did a couple years of Calc in the Precambrian and have never used it since. However I did use fractional factorial (and full factorial) designs and am very familiar with the concept of confounding factors. Without that mathematical tool we never would have solve the question of what was causing bad product in several cases.

      So yes I understand the idea of dependent variables vs independent variables. For example if you let three dependent variables vary looking for a unique outcome you can get an unresolved mess. With a full factorial design for three variables you need to run twelve experiments to disentangle the effects. With a fractional design with only 4 experiments the main effects are confounded.
      ………..

      As far as “the authoritative figure has spoken and the herd has listened” goes, it does not necessarily work that way. I know I and several others ‘jumped ship’ from WUWT because the authoritative figure was not making sense.

      Skeptics are a contrary lot.

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    [...] Lucia has a bad day with partial derivatives [...]

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    abe

    The ONE thing you can ALWAYS know about a Magic Gas believer: they are BARELY able to proceed in FUNDAMENTALS of thermodynamics

    because they’re ALWAYS trying to REMEMBER WHERE to SWAP the HOTTER/COLDER VALUES so their RELIGION makes them unable to tell which

    direction a thermometer will go.

    00