Jo Nova has a post today about an investigation of climate modeling mathematics by her husband David Evans. Evans believes he has uncovered a significant and perhaps major flaw in the mathematics at the core of the climate models.
She writes:
The climate models, it turns out, have 95% certainty but are based on partial derivatives of dependent variables with 0% certitude, and that’s a No No. Let me explain: effectively climate models model a hypothetical world where all things freeze in a constant state while one factor doubles. But in the real world, many variables are changing simultaneously and the rules are different.
Partial differentials of dependent variables is a wildcard — it may produce an OK estimate sometimes, but other times it produces nonsense, and ominously, there is effectively no way to test. If the climate models predicted the climate, we’d know they got away with it. They didn’t, but we can’t say if they failed because of a partial derivative. It could have been something else. We just know it’s bad practice.
…
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.
One might argue that the partial derivatives are good approximations, maybe all we’ve got and better than nothing. But this is an unknowable assertion because the partial derivatives are with respect to dependent variables. One might argue that certain climate variables are almost independent, in which case partial derivatives with respect to those variables are only slightly unreliable — and you’d be on more solid ground. But you wouldn’t really know how solid, so any model relying on these partial derivatives would have to be tested against reality — and if the model turned out not to work too well, it may be because the partial derivatives have the wrong values, or it might be because they are conceptually inappropriate, or it could be for some other reason entirely, and you wouldn’t know because said partial derivatives are not empirically verifiable.
It sounds to me as if that estimate is quite a wild card in this case, and perhaps it is this factor that creates such broadly different outcomes in climate models, as seen below:
![CMIP5-90-models-global-Tsfc-vs-obs[1]](https://wattsupwiththat.files.wordpress.com/2013/10/cmip5-90-models-global-tsfc-vs-obs1.jpg?quality=83)
Evans had previously done some work in this area that held some great promise, but in my opinion he released that work prematurely, and it was heavily refuted.
This looks like a much more concrete issue that will be hard to justify and/or explain away.
UPDATE: (9/29/15) Jo Nova adds this via email, with the request it be included here.
People are quoting us in comments with things we didn’t say, and getting caught by tangential things. It will make the discussion on WUWT more productive.
1. David didn’t say this was a “major error”. To summarize:
The partial derivatives used by the basic model do not,
mathematically, exist, and they are not empirically verifiable —
so they are a poor basis for a model. We use this clue in
later posts of this series to construct a better basic model.
2. This is part 4 of a long series. People need to read the
background to fully understand it. Some inferences are leading
to a pointless discussion. eg: of course partial differentials
can and do work in lots of models. In part 1, David pointed
out that most successful physical models get tested and either
dumped or improved in a short time frame. Climate models,
though, can remain wrong for decades. In parts 2 and 3 David
explains precisely what the basic climate model is.
3. David’s work last year was not refuted. We published one
correction, showing that the notch was suggestive of a delay,
but not mandatory as first thought. The delay (which is what
matters) is still supported by other independent studies of
empirical evidence which we cited. As this series will show,
the big findings from the last round stand up even stronger
than before. Publishing it then was very useful as we got some
useful feedback. The notch is real, it still suggests a delay
of one half a solar cycle, and that fits the data better than
any other explanation. We’ll be going through all that in more
detail.
4. The main point is the disconnect between science and “PR”:
their use of partial derivatives on dependent variables may be
partly right or wholly wrong — yet the IPCC says they are 95%
certain.
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ristvan September 28, 2015 at 3:54 pm
Your reply above discusses airplane wings, assuredly small scale. The part you haven’t dealt with is that computer weather models of large areas (e.g. Europe, see the ECMWF) give better forecasts than we got before such numerical computer weather forecasts were the norm.
So whether or not “the partials might approach constants”, I would strongly dispute your claim that their methods only work on small scales like airplanes, and that there is “no way they can” work for large areas like Europe … the weather models prove that their methods can and do work.
That’s not the problem. The problem is you can’t predict the climate by running a weather model for 50 years … no more than you can predict next years weather by running a weather model for one year.
w.
Propagated error of f(x1,x2,x3…) depends on partial derivatives df/dx1, df/dx2,… when variable x1,x2… are statistically independent. But when the are not covariances come to play. Is this what this note is about? I read all comments and had impression that every body just pretended they knew what the guy was talking about.
Almost everybody. Some of us actually used to know this stuff. Which is why Evan’s reminder is like a big Homer Simpson DUHOO! As embarassing as that is to admit.
Precisely. Or even next month’s weather by running a weather model, or a weather model many times with perturbed initial conditions, out for one whole month. One can do just about as well reading the probable weather from an almanac or assuming that it will be like the weather in that month last year, which is sort of the lowest common denominator seasonal average sort of prediction one can hit without much of a model at all besides the known annual/monthly variations in the weather.
I would say that we might be able to predict the climate by running model 50 years, but that the burden of proof that we can is absolutely upon anyone who would assert otherwise as it isn’t likely to work based on what we have observed from the efforts so far. We are decades to a century of hard work away from where we might be able to.
The latter in my opinion, of course. Who knows for sure? Surprise me.
rgb
Jim G1 –
the script writer tells the story,
the producer determines the end of the story.
Whatever the producer decides –
‘they confuse the observation of an actual factual material
called dark matter when they are actually
observing unexplained gravitational effects.’
is a fascinating summary of the plot.
Thx – Hans
All this is a fancy way of saying they guestimate the unknowns.
In the plot of 90 CMIP5 model projections/predictions, the plot of observed UAH lower troposphere temperatures stops just short of 2013. Of course, the ‘pause’ continues beyond that, albeit that 2015 no doubt will appear warm, and much will depend upon whether a La Nina follows in 2016/7.
But one can see that there are only two models presently tracking below observed UAH lower troposphere temperatures. Perhaps of more significance is what those two models project/predict circa 2018. At around 2018, those two models project/predict rapid warming. If the ‘pause’ continues through to and beyond 2018, those two models will be tracking above UAH lower troposphere observations. By 2020, none of the 90 models will remotely be in line with observations should the ‘pause’ continue through to 2020.
I have often said that 2019 is crunch time for the IPCC and AR6 if the pause continues as it will be impossible to simply ignore the fact that all the models are running warm, the majority very significantly so.
It is obvious that the very warm models are way off target. No one would realistically support their projections, but they are being included because of their impact on averages, ie., the averaged assemble. They permit the averaged assembly to stay on track for circa 2degC warming.
If the warmest running models were ditched, as they should be, the average will come down to a not scary figure and this will end the CAGW scare. How is the IPCC going to treat this? This is why Paris is so significant for the warmists and the proponents of CAGW. It is likely to be their last chance saloon, since if the ‘pause’ continues, mother nature is about to kick them where it really hurts.
if the ‘pause’ continues
And if the ‘pause’ does not continue, what do we say then?
Let me say it now. The pause will definitely not continue but where it goes afterwards is very much up in air, so to speak.
Based on what? Other than wishful thinking…
Shut the door, it’s cold out there ; )
lsvalgaard September 28, 2015 at 7:37 pm
if the ‘pause’ continues
And if the ‘pause’ does not continue, what do we say then?
//////////////////////
We have 90 model projections/predictions all of which show different outcomes. This reminds me of the Dire Straight’s song (Industrial Disease) “…two men say they’re Jesus, one of them must be wrong…” We know as fact that 89 of those 90 models must be wrong, what we do not know is whether one of them is right. If these models was based upon fully known and understood physics, and if the science was truly understood and settled, one would not have 90 different models. One would only have 3 based upon the 3 different future scenarios for CO2, or possibly 9 based upon the 3 different future scenarios for CO2 as altered by the 3 diff3erent scenarios for manmade aerosol emissions. People like making comparison with the aviation industry, and in that industry one does not get 90 different scenarios as to how the plane may fly in usual operation.
I am not making any prediction as to whether the ‘pause’ will or will not continue. Predicting the future makes fools of us all, especially when we know so little and understand even less as to the workings of the Earth’s climate.
What I am pointing out is the trajectory of the two models that are currently running cooler (but close to) the UAH lower troposphere observations in around the year 2018. If the ‘pause’ continues beyond 2018, it will a crunch time for those two models such that all models will be running warm.
If those two models had in 2006 (which I understand to be the date of the model and the date of the forward projection) been zeroed at the then observed UAH lower troposphere temperature, those two models would already be running warm in relation to the UAH lower troposphere observations, but my point is the projected/predicted warming (one of them very rapid warming) post 2018 so we may soon get a chance to look at their projections/predictions and to see what extent they correspond with reality (it always being possible that the UAH lower troposphere will show warming like one of the two models – obviously both models cannot be right since they project/predict different future rates of warming so we know that one of the two is definitely wrong).
I repeat:
if the ‘pause’ does not continue, what do we say then?
PS. When I am suggesting that a model may be right, I merely mean that it is corresponding (for the time being) with reality (ie., real world observations). Of course it may be corresponding with real world observations merely by fluke. It does not necessarily mean that the model has got the science and the maths right. Of course, those that have already diverged significantly, have obviously got something wrong.
lsvalgaard September 28, 2015 at 10:19 pm
I repeat:
if the ‘pause’ does not continue, what do we say then?
//////////////////////////
That depends upon what happens, and whether we are able to identify a possible reason for what has happened.
Say over the next 5 to 8 years, the globe begins to cool at a slightly greater rate than it is presently cooling according to satellite temperature data. That would reinforce the view that the two models were wrong.
If the pause comes to an end, but there is simply a step change in 2015/early 2016 much like the step change in temperatures seen in and around the 1998 Super El Nino, the satellite data will appear flat between say 1979 and the run up to the 1998 Super El Nino, flat from post that event through to the run up to the 2015/6 El Nino, and flat post that even through to say 2023/4. This will suggest that there is zero first order correlation between temperatures and CO2 and that there are two warming episodes to be seen in the satellite data which warming episodes coincide with natural events (El Nino) which do not appear to be driven by CO2. Of course, we might not know what drives Super El Ninos, what causes some El Ninos to release significant energy/heat into the atmosphere which energy/heat is not quickly dissipated.
I accept that we do not know or understand sufficient about the climate and what drives it. The question is whether we can start eliminating things, or whether we can start assessing how much various things influence and drive the climate.
The problem is all down to the quality of data sets and their short period, and the love by some to over extrapolate poor quality data.
I would suggest that unless there is first order correlation between temperatures measured by the satellites and CO2, then all we can say is that the signal to CO” is so small that it cannot be detected by our best measuring devices within the limitation of those devices and their error bounds. That does not mean that there is no signal, merely that it cannot be detected.
Of course, there could be some second order correlation, but to wean that out, one would have to know considerable detail and accuracy on whatever it is that is being claimed to mask the first order correlation. But of course, this is where data sets are hopelessly thin on the ground and of poor quality so one can never address the second order correlation point.
“And if the ‘pause’ does not continue, what do we say then?”
Why just pick the best match in the huge spread of climate model prognostications, yell loudly “See we got it right” and keep drawing the tax funded paychecks.
regarding predictions of future temperature. i stick by the adage (and historical temperatures) that what goes up,must come down.
Jo Nova has a post today about an investigation of climate modeling mathematics by her husband David Evans.
————
Husband? Damn!!! 🙁
“Partial differentials of dependent variables is a wildcard — it may produce an OK estimate sometimes”
I can’t remember exactly but I think I remember Tennekes covered this and how it might affect climate modeling. The basic idea is that it is generally okay to neglect high order terms as long as the spatial and temporal discretization is fine enough. To figure that out one has to reduce the fineness then make it more coarse and compare the results. They should be reaching an asymptotic limit. To improve things, i.e. to use a more course grid or longer time step, some of the more significant HOT’s are included. It’s kind of an art to figure out which ones to keep and which ones to neglect.
Now (again – I think) climate modelers do not do this. Their models have implicit (not solver implicit but just generic English word implicit) self stabilizing mechanisms and they end up not having to make a very fine grid nor taking very find time steps. They then do not check to see if their result is robust to discretization size and hence never really know. As long as they get the “right” answer, everything is good enough.
ristvan September 28, 2015 at 10:27 am
Thanks for the link to your reference. My earlier comment stands. The way that the CAM model handles the physics seems (to my semi-tutored eye) to be the same way that weather models handle the physics, and the weather models get tested every day. However, the devil is in the details …
So for Dr. Evans to show his claim is valid, he’s got to show that the climate models are doing it DIFFERENTLY than the weather models.
Now, it is quite possible that I’m not understanding just how the climate models are doing it differently. But as near as I can tell, Dr. Evans has neither made the claim that the climate models do it differently than the weather models, nor has he explained why weather models work and climate models do not.
Me, I say the reason is not to be found in the physics core, but in the fact that the important emergent thermal regulatory phenomena are sub-grid-scale.
Finally, you say:
How does this show the “fatal partial derivative problem”? This supports my claim, which is that the physics is correct (enough), but some of the basic assumptions are incorrect. If the physics were fatally compromised as Dr. Evans claims, there’s no telling what the addition of the “adaptive iris” would have done. But in the event, it worked just as expected. It greatly reduced climate sensitivity, meaning that the physics is working but reality is not correctly modeled because important aspects are omitted … and that’s only one of the thermal regulatory phenomena that the climate models omit.
Best regards,
w.
I have explained it several times on this thread. Not again. Too boring. Figure it out for yourself.
Show your work. With the linked references to CAM3 you have apparently now managed to find after much criticism and some spoon feeding.
Did you read the above cited CAM3 PDs.? Do you realize their parameterizations are all constants? Do you realize the very real problem that some of those PDs cannot be constants? Again, please show your homework.
ristvan September 28, 2015 at 11:29 pm
ristvan, you have not explained how the weather models can use pd’s and get the right answer, while the climate models cannot. How and where are they different than the climate models, where you claim the error is “fatal”?
Seriously? You’re still sulking because I asked you for a LINK TO YOUR OWN CITATION???
Get real! Giving a link to your own citation is bog-standard everyday practice. For you to moan about being asked to do it is a joke. And for you to insist that everyone who wants to see what you are talking about should waste their time doing a google search and hoping for the best is the height of arrogance. You’re not special. Post a link to your supporting documents like everyone else does, and quit whining about doing it.
w.
“So for Dr. Evans to show his claim is valid, he’s got to show that the climate models are doing it DIFFERENTLY than the weather models.”
Why should the climate models do it differently than weather models to be wrong? As far as I (semi) understand it, the point is that on small scales the errors are unimportant but on larger scales they compound, a point that was made in comments earlier. Scales don’t just mean distances and volumes, they also mean temporal. Over short time scales the weather models might be ok given the initial conditions can be plugged in, but as time goes on the errors compound, making them untenable as models for climate – which is just the long view of weather.
Thanks, agnostic. It’s well known that the weather models cannot see too far into the future because the weather is chaotic. Note that it doesn’t matter how good your computer model is—starting from the same initial conditions, there are many possible future evolutions of the weather, and the further out you go, the wider the spread gets.
So the fact that current weather models can’t predict very far into the future is NOT a reason to assume that they are incorrect.
w.
Hear, hear.
True, the mere fact that partial derivatives can have the shortcoming that Dr. Evans identified does not establish that their shortcoming is significant in the climate-model context. But the arguable success of partial-derivative use in short-term-weather forecasting doesn’t establish that climate models use them accurately.
I look forward to more specificity in Dr. Evans’ argument that they don’t.
Willis Eschenbach says: September 29, 2015 at 1:31 am
So the fact that current weather models can’t predict very far into the future is NOT a reason to assume that they are incorrect.
——————————
I’d say that the fact that current weather models can’t predict very far into the future *is* reason to assume that they are incorrect for anything beyond the short term.
I once knew a mathematician once who proved that there were so many uncertainties in a model that the EPA used for some policy decisions that their results could actually be anywhere on the graph and still be within the goodness of fit.
I don’t understand such things, but the way he described it, they could fiddle with the models to get whatever results they wanted to justify whatever policies they had in mind.
After presenting his paper, he was taken off the workgroup and never invited to participate again, and the modeling continued apace.
Will Eshenbach
“So the fact that current weather models can’t predict very far into the future is NOT a reason to assume that they are incorrect.”
To the contrary. You can get away with incorrect models more easily explaining errors away as chaos.
Thanks, Peter. I see my remark wasn’t clear. Let me try again.
The fact that the weather is chaotic means that even a perfect model could not predict its future state very far into the future.
THEREFORE, the fact that a model cannot predict the weather very far into the future is NOT evidence that the model is flawed.
I hope that’s clearer.
w.
“The fact that the weather is chaotic..”
That is an assumption, and is in fact largely specious.
I note a comparison is being made with weather forecasts, but personally, I do not consider that weather forecasting is particularly good as far as countries which are subject to variable weather conditions.
For example, the UK is particularly fickle. I am unsure whether any forecast given at 11pm gets the next 24 hours right over the entirety of the UK. Do they get the morning, noon, evening night time temperatures right in each county, do they get the patterns of cloudiness right (ie., when the sun will shine through) in each county, do they get the amount of rainfall right in each county, do they get the wind, or patterns of fog or low lying mist right in each county. I bet that there is no day when such a 24 hour weather forecast has been correct for the entirety of the UK.. I certainly can’t remember one. It would be interesting whether the UK Met Office could cite one. And this is now why they say that there is a 10 or 20% or whatever chance of rain etc, so it is difficult to be wrong. What they will, not say is that it will rain in Birmingham at 11:30 for 45 minutes, then it will stop and the rain will onset again at 3.30pm until 10pm when it will stop again and during such time there will be 8 mm of rain.
I accept that weather forecasting has improved these past 40 years, but in the UK, a weather forecast is only good for about 2 days and in general terms only, unless there is particularly benign conditions (a blocking high) when it may extent for a longer period. I emphasise that it is only in general terms that the weather forecast is good, when you look at the detail and what is predicted for each county (the UK is divided into counties much like the US is divided into states, but of course each county is a rather small area), and when you look at each weather component (sun, cloud, rain, wind, mist, fog, temperature etc) for each county, then you quickly appreciate that the forecast is not as sound as the general thrust appears.
I don’t forget that weather computer forecasts are being constantly updated and tuned. The initial parameters are constantly being rechecked and updated and even so, they can’t ‘predict’ with accuracy good regional forecasts, but rather the most general of trends (perhaps splitting the UK up into say 7 areas, Scotland, the boarders, the Midlands, Wales, the South West, the South East, Northern Ireland, and they often have to say that rural areas will be cooler without mentioning what those rural areas will experience).
Personally, I consider that people are getting rosy eyed over the state of weather forecasting and not looking at the detail objectively.
We all know that CGMs do not do regionality well, and yet climate is regional not global, and until regionality can be done well, there is no hope for these models.
Looks to me like the models were built to match the real data for the 80’s/90’s, but do so only because they have been ‘adjusted’ to match, the equations they use bearing no relation to actual climatic input-output relationships.
I’d like to see a model that maps from the IPCC technical reports to the Summary for Policy Makers.
95% of nothing.
jimpoulos- Are you the same person who worked at JND in Atlanta in the 1980’s? Just curious. I knew you then and found it funny that a name from the past would show up so unexpectedly.
Willis said: “However, the devil is in the details …” Exactamente.
We know the limits of weather models — because we check their forecasts against observations.
We also know that climate models are not validated and are running hot. So everybody agrees there is room for improvement, I hope. I hope also that everybody realizes that this is a hard problem, perhaps even impossible, and it is not simple high school physics.
First, you have to get the physics right. No consensus there. Then you have to get the computation right, and this is not trivial. In HPC (high performance computing) there are Grand Challenge problems, i.e. those fundamental problems which would be very useful to solve but which are somewhat beyond our reach at the moment.
Quoting from one top Google hit,
https://en.wikipedia.org/wiki/Grand_Challenges
Everything done so far is not necessarily wrong and not necessarily right. Some details yes, some no. It depends on the details. Not all of the physics is in the climate models and even if the climate models were perfect, it’s still not clear that they could predict, any more than we can predict the stock market.
Exactly …. every single day we see the end of a 5 day forecast and can compare the forecast to reality. That means we’ve had over 20,000 review periods since 1960 when weather modelling began. If you want to limit it to the satellite era then we still have over 13,000 reviews.
If we say 5 decades in a climate forecast is the equivalent of a 5 day weather forecast we’ve had exactly zero since satellite data became available to verify predictions in 1979.
Since the claim as I understand it is we have not validated climate models, I think the comparison to weather models does not help the case.
The atmospheric CO2 level has been above about 150 ppmv (necessary for evolution of life on land as we know it) for at least the entire Phanerozoic eon (the last 542 million or so years). If CO2 was a forcing, its effect on average global temperature (AGT) would be calculated according to its time-integral (or the time-integral of a function thereof) for at least 542 million years. Because there is no way for that calculation to consistently result in the current AGT, CO2 cannot be a forcing.
Variations of this demonstration and identification of what does cause climate change (R^2 > 0.97) are at http://agwunveiled.blogspot.com
it’s funny to see all the allegations made at the start. When you read his article (and the former parts, he is not saying that climate models are useless, they are modeling multiple variables and of which a lot remain unknown in how they “cooperate”
that’s why the models the ipcc use are wrong, they don’t include factors that are yet to be discovered or that are known (AMO and PDO are not included in the IPCC models thus they are already wrong even if the rest is scientifically correctly built).
What i understood from the series is that he does not say the models are useless, but in order to work they need constant training, as such models reuire in order to become reliable and valid. If the models can’t reproduce the known measured past temperature and all other parameters, then you should put it again “at the schoolbanks and train it further” instead of saying that models predict X or Y degrees of warming at a point of time in the future Z.
This is what didn’t happen and still doesn’t happen so that makes these models scientifically incorrect as they are inconsistent with what is being observed. They should retrain them and see what variables do play a role as well together with increasing CO2. Saying that the models are right, while observations show differently is a complete blame to real science, it’s guesswork and i’m sorry then you don’t need models, then i can also say tomorrow the sky “WILL” look purple based on a model and then say it does look purple as my model said so while in fact it’s not the case.
So yes the models need training and maybe in 40 50 years they will have some validity. but now they are useless