Guest Post by Willis Eschenbach
I love thought experiments. They allow us to understand complex systems that don’t fit into the laboratory. They have been an invaluable tool in the scientific inventory for centuries.
Here’s my thought experiment for today. Imagine a room. In any room dirt collects, as you might imagine. In my household I’m somewhat responsible for keeping the dirt down, so I get out the vacuum cleaner to clean up.
But suppose I had a magic way to handle that dirt. Suppose there was a class of beings such that whenever there was a concentration of dirt in some small part of the room, one of these beings would pop into existence, clean up the dirt, and then disappear. We’ll say this being is a rare relative of the Tasmanian Devil, call it a “Tasmanian Dirt Devil” (TDD).
Figure 1. One of the few authenticated photos of the elusive Tasmanian Dirt Devil (TDD) cleaning a floor in its natural habitat. PHOTO SOURCE: Annals of Cryptozoology, Vol. 6, 1954
After observing the room for a while, we realize that the TDD only appears when there is some small area of the floor with more than a certain concentration of dirt. However, we see that the TDD does not limit itself to that small concentration of dirt. It moves around and cleans out any other smaller concentrations of dirt around it as well. Once the area is cleaned to a certain level, the TDD vanishes, leaving the room somewhat cleaner. We also see that on days when traffic is heavy, often there are a number of Tasmanian Dirt Devils working on the room at once. No single TDD cleans the whole floor, but the floor is never dirty anywhere for long.
Now, here’s the question for our thought experiment: can we use a computer to model the effect of the TDDs, for example in order to calculate the rate at which dirt is being added to the floor, based on the average amount of dirt on the floor?
I say we cannot model it adequately if our only input to the model is the average level of dirt on the floor. Here are two circumstances to explain part of why the problem is ugly.
1. Someone spills a very small bit of dirt on one corner of the floor. Because the dirt is concentrated in one area, a TDD materializes, cleans up the dirt and the surrounding area, and vanishes.
2. Four people simultaneously spill a very small bit of dirt in all four corners of the floor. Four TDDs materialize, clean up the dirt and the surrounding areas, and vanish.
If all we have is the average dirtiness of the floor, a few bits of dirt which are rapidly cleaned up will make little difference in a daily average of floor conditions. Despite those small fluctuations, in one case there is four times as much dirt being added to the system as in the other case.
So I think we can agree that in our thought experiment, the average dirt level of the floor is not linearly related to the amount of dirt being added to the system. If we want to model what’s going on, it is very difficult to do it based on the average dirt level. We need much more detailed information in both time and space.
Here’s an illustration of a different problem. Again, two conditions.
1. Someone spills a very small bit of dirt on one corner of the floor. Because the dirt is concentrated in one area, a TDD materializes, cleans up the dirt and the surrounding area, and vanishes. Average dirt level on the floor ends up slightly below where it started.
2. Someone spills a very small bit of dirt evenly all over the floor. There is no concentration of dirt above the threshold level, so no TTD appears. The average dirt level on the floor ends up slightly above where it started.
Again, as you can see, average dirt levels and amount of dirt added show no correlation, even as to sign.
So what do Tasmanian Dirt Devils have to do with the climate? If we saw something like a TDD in our kitchens, we’d be amazed. However, something just as amazing exists in the climate. We’re not astounded by it all purely because are so familiar with it. However, let me take a small digression on the way to explaining the relationship between climate and Tasmanian Dirt Devils.
Emergent phenomena are a special class of things. They can be recognized by certain traits that they have in common. In general, emergent phenomena arise spontaneously at a certain time and place. Typically they exist for a definite duration and eventually dissipate at another time and place. Their appearance is often associated with some natural variable exceeding a threshold. Many times they involve a change of state of a variable (e.g. condensation of water vapor). Often they can move about somewhat independently. If so, although they have general tendencies, their specific movements are usually very difficult to predict.
One clear characteristic of emergent phenomena is that the properties of emergent phenomena are not apparent in the underlying stratum from which they arise.
Examples of natural emergent phenomena with which we are familiar include sand dunes, the behavior of flocks of birds, vortexes of all kinds, termite mounds, consciousness, and indeed, life itself.
Regarding climate, there is one particularly important class of natural emergent phenomena. These are the natural “heat engines”. Heat engines are able to turn heat into work. Examples of these natural emergent heat engines include hurricanes, thunderstorms, dust devils, tornadoes, and the Hadley Circulation itself.
The most common and most important of these heat engines are thunderstorms. Thunderstorms do two kinds of mechanical work. First, they power the deep tropical convection that is the driving force for the circulation of the entire ocean and atmosphere.
Second, thunderstorms drive what can be thought of as a sophisticated air conditioner, using a variation of the standard refrigeration method. This method, used in your home air conditioner, uses ambient heat to evaporate a liquid. This removes the heat from the area where the evaporation is taking place.
Then you move the evaporated liquid (and the latent heat it contains) to another location. In the new location, you condense the liquid, releasing the latent heat of condensation. The heat is then transferred to the surroundings, and the condensed liquid is returned to start the cycle over.
In the natural Hadley air conditioner that we call a thunderstorm, the same process takes place. Water is evaporated at the surface, cooling the surface. The water vapor rises to the clouds. There it is condensed. The latent heat it contains is released, rises, and is radiated out to space.
Meanwhile, in addition to losing latent heat through evaporation, the surface is further cooled by the fall of cold rain from the thunderstorm. This is accompanied by an entrained cold wind, which assists in the cooling.
In both cases (Hadley circulation and refrigeration) the net effect of a thunderstorm is to remove energy from the surface and move it up into the troposphere.
Having digressed, I return to what climate has to do with Tasmanian Dirt Devils.
Consider our thought experiment. If you replace TDDs with thunderstorms, replace the room with a climate model gridcell of the tropical ocean, and replace dirt with energy, you have an excellent description of the action of the climate system at the hot end of the climate heat engine, the Tropics.
Whenever there is a “hot spot” on the tropical ocean or land, if it is hot enough, a thunderstorm springs up and starts pushing huge amounts of energy vertically. As the thunderstorm moves across the surface, it moves towards the warmest area in its path. This preferentially cools the warmest areas. In addition, it continues to do so until the local surface temperature is a few degrees below the initiation temperature.
There are some conclusions that we can draw from this thought experiment:
1. In our thought experiment, increasing the rate at which dirt is added does not commensurately increase the average dirtiness of the floor. Similarly, increasing the rate at which energy is added to the Tropics does not commensurately increase the surface temperature.
2. Attempting to model our thought experiment using room-wide averages won’t work because Tasmanian Dirt Devils are driven by local conditions, not average conditions. Similarly, attempting to model our climate using gridcell-based averages won’t work because thunderstorms are driven by local conditions, not average conditions.
3. Modeling a system that contains simple linear feedback is not too difficult. In that case, average changes in the response variable are linearly related to changes in the forcings. Modeling a system with an active governor, like TDDs or thunderstorms, requires a much different type of model. As I showed above, in that case the response variable is not linearly related to the forcing.
4. Thunderstorms preferentially cool the warmest areas. Although the average temperatures might be the same, this has a different effect than a gridcell-wide uniform cooling. Again, this makes the modeling of the system more complex.
Let me be clear about what I am saying about models. I’m not saying that we can’t model the climate. I think we can, although it won’t be easy. But we have to model it the way it really is.
It is not a system with a linear relationship between forcing and temperature as conventional theory claims. It is a dynamic governed system with a complex, nuanced, non-linear response to forcing. Yes, we can model that. But as I show above, we can’t do it under the assumptions made by the climate models.
Could we model it parametrically, without having to model individual thunderstorms? Perhaps … but the model has to be designed to do that. And the current climate models either are not designed to do it or are not doing it successfully.
How do I know that they are not doing it successfully? Drift. Consider the room with the Tasmanian Dirt Devils. If there is no change in the amount of dirt being added per day, the system will rapidly take up a steady-state condition.
The models are subjected to a very similar test. In this test, called a “control run”, every one of the forcings of the model is held exactly steady. Then the models are run for a number of model years. Figure 2 shows the results from the Coupled Model Intercomparison Project (CMIP) control runs. We would expect the models to rapidly take up a steady-state condition.
Figure 2. Results of control runs for 16 coupled atmosphere-ocean climate models. SOURCE
Notice the drift in the surface air temperature in a number of runs over the 80-year simulation. The CERFACS model is the worst, but even a mainstream model like the NASA GISS model of James Hansen and Gavin Schmidt shows drift over the 80 years.
How much drift? Well, the trend in the NASA GISS model control run is a warming of about 0.7°C per century. This is about the same as the IPCC estimate of the warming over the last century, which is 0.6°C.
Now, you could look at that GISS model 0.7°C per century inherent warming drift with no forcing change as a bug. I prefer to think of it as a feature. After all, it lets Hansen and Schmidt simulate the warming of the 20th century without the slightest change in the forcings at all, and how many models can do that?
However, that drift does strongly suggest that they are not modeling the climate correctly …
As always, the quest for understanding continues. My best regards to all,
w.
Steve says:
December 17, 2010 at 10:01 am
“Willis explained that their is no direct causal relationship between average amount of dirt now, average dirt level added and future dirt levels (the “global kitchen climate”). There is no viable algorithm between these variables. The viable algorithm is between the current distribution of dirt, the distribution of dirt added and the future distribution of dirt. That was the entire point of his article – this climate can’t be (usefully) modeled without empirical data on the details.”
No, he did not “explain” it. He claimed it. And he’s wrong. In general there is a (noisy) causal relationship between those variables. I have actually performed a simulation that proves it. I will provide details later.
“Well, in your “experience as a scientist and systems engineer”, I suppose you didn’t learn that there actually is a standard scientific definition of predictive power. And your definition isn’t it. http://en.wikipedia.org/wiki/Predictive_power”
My definition of predictive power is in fact quite standard. Your reliance upon wiki to contradict me smacks of desperation, and is in any case futile, since it is here entirely in agreement with my explanation. From wiki:”The predictive power of a scientific theory refers to its ability to generate testable predictions.” As I stated. Any prediction at better than chance is statistically testable. “Theories with strong predictive power are highly valued …”, because obtaining statistical significance is easier; but note that this entails (as I pointed out) that predictive power is a matter of degree. It can be weak or strong. “The predictive power of a theory is closely related to applications”. Again, as I stated. A theory or model could have strong predictive power for global climate while having only weak predictive power for local weather, or vice versa.
“If I can guess the average dirt level of the floor for a given period of time and be correct 1 time in 1,000 , and a model comes along and correctly predicts the average dirt level correctly 5 times in 1,000, that model is 5 times more powerful than guessing. But it still would not be considered a powerful model, because 95% of the time it’s wrong!”
You still don’t seem to have grasped the difference between “predictive power” and a “powerful model”. You also don’t seem to understand the nature of predictions under noisy conditions. The strength of the prediction is measured by the accuracy of the estimates – the magnitude of the typical errors – not on whether any given estimated value will be “right” or “wrong”, because with continuous (or finely quantised) variables they will never be “right” (there will always be some error) even for very well understood and highly robust theories like ballistics.
Willis Eschenbach says:
December 17, 2010 at 12:39 pm
“Here’s the thing. Suppose we have positive feedback, such that any change in a variable ends up getting doubled in the output. We can see this and measure it. Then, as Paul suggests, we can use this to estimate the underlying algorithm. This method works great for a system with feedback.”
I did not claim that “we can use it to estimate the underlying algorithm”. We might or might not. What I have said – repeatedly – is that we do not need to know the underlying algorithm to get a useful empirical model. All we need is empirical data.
“But now let us suppose that we are in a “governed” system … We use that information to construct an algorithm for what’s happening regarding fuel and speed.”
That’s not a control algorithm. It’s an observational relationship connecting these two (or more) variables.
“But when we repeat our experiment in a governed system like a car with cruise control, we see something surprising. Fuel use goes up and fuel use goes down, but the average speed doesn’t change at all! (Note that this also happens with the Tasmanian Dirt Devils, where dirt input goes up and down, but the average dirtiness of the floor stays constant.)”
This is one of your unproven claims, which turns out to be false. Even fully regulated systems do not in general maintain a constant average output for different inputs. The behaviour of such control systems is much more subtle and surprising than you imagine. Your Tasmanian Dirt Devils will not hold the average dirtiness of the floor constant under different dirt inputs. Try it yourself – as I already have.
Even if your tropical thunderstorms did constitute a temperature governor (they don’t, they constitute a temperature difference governor) this would not prevent the global average temperature from varying over potentially quite a wide range.
Here are the results of a numerical experiment on the properties of systems utilising “dirt devils”.
Take an 8×8 grid (chessboard). Let units of dirt (draughts pieces) be placed randomly on the board, and choose a simple detection threshold of dirt (pieces) present in any two or more contiguous or superposed squares. Then remove the dirt from those squares.
For a deposition rate of one unit of dirt per move, the average total dirt = 5.8+/-0.2 units (filling factor 9.0%).
For a deposition rate of two units of dirt per move, the average total dirt = 3.7+/-0.4 units (filling factor 5.8%).
This is a gradient, between those values, of -2.1 moves. This is a predictive empirical model (approximately linear within this range) with differences of the same order as the move to move fluctuations, and thus quite a strong predictor even over surprisingly short timescales of say ten moves or less. Over longer periods of course it should be considerably more robust.
At lower and higher rates, the correlation asymptotes to about 10% at the bottom end and 5% at the top, with increasingly strong fluctuations as the rate increases. In other words, there’s about a factor of two in output as a function of changes in the input rate.
This analysis is based on a scenario in which the devils work (infinitely) fast. If we modify it to let each devil remove only a single unit of dirt per move, this increases the average level accordingly; the greater the deposition rate, the greater this increase.
So, for 1 unit/move, the average total dirt becomes 6.3+/-0.2 (10%),
for 2 units/move, the average total dirt becomes 5.1+/-0.4 (8.0%),
and for 3 units/move, the average total dirt becomes 7.4+/-0.6 (11.6%).
Note how the curve has turned up again at the high end. It does not asymptote (except at ~100%).
This assumes an unlimited number of devils (one per simultaneous detection). If, more realistically, the number of devils is limited, then the curve will rise even more steeply, becoming vertical when the deposition rate equals the total number of devils (who will then be unable to keep up even when working flat out).
A pseudo-random number generator on my calculator was used to generate the coordinates, to give a random distribution of dirt. If instead the dirt is more clustered, this has the effect of moving the curves upwards and to the left (as if from a higher deposition rate). Similarly, if the dirt is anti-clustered, the curves move down and to the right (as if from a lower deposition rate).
Note that if one selects a particular algorithm to minimise the dependence of the output on the input in a given range, one can, with only modest changes, also produce one that will have either a positive or negative dependence (decreasing the speed or reaction time of the devils increases the gradient, increasing them decreases it).
This is all in line with the sort of behaviour I expected; as indeed I stated earlier in the thread, only for what has turned out to be my sound scientific intuition to be pooh-poohed.
Here is the raw data for rates 1 and 2:
Omit starting transients (5 moves):
Delta=+1 – (0 0 0 0 0) 2 0 2 0 2 0 0 0 2 2 0 0 2 0 2 2 0 2 0 0 0 2 0 0 0 2 2 2 3 2 0 2 0 0 0 2 2 0 2 2 0 2 0 2 0 0 2 0.
Delta=+2 – (0 2 0 2 2) 0 3 2 0 2,2 0 2,2 4 2 2 3 2 2 2 3 0 0 0 3 2 2 2,3 0 2,2 0 2 2 2 3 3 3 2 2 2,2 0 0 2,2 2 0 2 0 2 2 0 2,3 2 2 2 0 2,2 2 2.
Paul Birch says:
December 18, 2010 at 7:40 am (Edit)
I take a car with cruise control. I drive sixty miles up Pike’s Peak. I note the mileage, I see I’ve burned three gallons. My average speed is 30 miles an hour.
I take the same car and drive sixty miles on the flat. I note the mileage. I see I have burned two gallons. My average speed is 30 miles an hour.
That is analogous to the climate situation. We don’t have detailed moment by moment observations. We have observations at the start and at the end of a period. From that we need to see if we can develop some kind of algorithm (which I seem to use in a much general sense than you do) that relates the fuel used to the speed.
OOPS. Can’t do that. Since 30 mpg and 20 mpg both give us the same speed, the situation is non-invertible. So we can’t address it directly, we have to use other information to try to figure out the situation.
Now, as you point out, in a real system there are small signals from the transient response to the control forcing. And you keep saying, over and over, that using those small signals we can construct a rough model of the system.
And you are right about that, you can do amazing things with very small measurements … but here in climate science we have nowhere near the number and accuracy of measurements that we would need to try to tease out such a small relationship. If you truly think it can be done, perhaps you could tell us the frequency of observations and the amount of detail that we would need to do it … my point is that while you are right in theory, in practice at present it’s not possible. To make it worse, computer models have a “black box” called a gridcell. Within that box, there is absolutely NO DETAIL. The gridbox may be 100 km on a side, and within it, we don’t know where anything is. We don’t know if the heat is in the north or south of the gridbox. We don’t know if the wind is stronger in the east or west.
So yes, as you point out, if we had fine detailed measurements of all the relevant variables we might be able to tease out the tiny signal that you truthfully say is there.
But in the real world, we have nothing like that. We have few measurements, scattered in time, with plenty of gaps and missing data. The data to date, for example, is not sufficient to answer questions like how long carbon resides in the atmosphere. Answering questions like yours? Doubtful … and we can’t use the current generation of models to figure it out.
In addition, you have missed the main point. This is that if there is a feedback system governing the planet, we will neither find it nor understand it using the current climate models.
Finally, regarding your comment:
It is that kind of comment, the sly dig to try to establish just how dumb we all are and how much smarter you are, that makes it so unpleasant to read what you post.
My friend, you don’t have a clue what other people know or what they imagine. You’ve never met me. You don’t know me. You don’t know what experience I have had. You don’t have a clue what “subtle and surprising” thing I can imagine.
The truth is that it is other people that are “much more subtle and surprising than you imagine”. You’d get more traction if you kept that in mind.
Willis Eschenbach says:
December 18, 2010 at 3:22 pm
“I take a car with cruise control. I drive sixty miles up Pike’s Peak. I note the mileage, I see I’ve burned three gallons. My average speed is 30 miles an hour. I take the same car and drive sixty miles on the flat. I note the mileage. I see I have burned two gallons. My average speed is 30 miles an hour.”
This is yet another unwarranted assertion. In general, you will not get the same average speed in the two situations. You would not do so unless the governor (cruise control) were able to react infinitely rapidly, infinitely strongly and with infinitesimal hysteresis, which it won’t. Typical regulated systems are likely to show quite significant – and predictable – changes in average output as a function of input conditions – as much as a factor of two, or more. In my previous comment, I proved that experimentally for systems utilising your dirt devils.
If the dirt devils were indeed an appropriate analogy for your tropical thunderstorms, then we might expect global temperatures to range over a similar factor as the dirt level. Or perhaps, making the analogy more directly with energy fluxes, by only the fourth root of it – which would still mean that average global temperatures could vary over a 55K range! This is not a negligibly small effect.
“Now, as you point out, in a real system there are small signals from the transient response to the control forcing. And you keep saying, over and over, that using those small signals we can construct a rough model of the system.”
No, this is not what I’ve said. First, the inputs are not in general “forcings”. A forcing is an oscillating signal at a frequency other than the resonant frequency of the system forcing the system to oscillate at that frequency. Turning on a tap or blocking a drain is not a forcing. This is another of those terms, like anomaly, that the AGW “climate scientists” misuse. Second, I wasn’t talking about transients, but about the long-term averages. Third, there is no reason to suppose that these signals will be “small” and, as I have proved for the dirt devils scenario, often they are not.
“To make it worse, computer models have a “black box” called a gridcell. Within that box, there is absolutely NO DETAIL. ”
If all we want is the average global temperature, we simply don’t need detail. Any more than we need to know the location and variety of every plant in every field in the country to predict the harvest. The details don’t much help and don’t much matter.
“So yes, as you point out, if we had fine detailed measurements of all the relevant variables we might be able to tease out the tiny signal that you truthfully say is there.”
I said no such thing! What I said was almost the diametric opposite: that we do not need detailed measurements to get a useful model, and that the dependence of even regulated (or “governed”) systems on input conditions is often considerable (far from tiny, and sufficient for good empirical models).
“In addition, you have missed the main point. This is that if there is a feedback system governing the planet, we will neither find it nor understand it using the current climate models.”
I have not missed this point. I’m saying that your claim is false. There are many feedbacks present and they can all – in principle – be included in the models. None of them holds the average global temperature constant. Overall, they simply reduce (or in some cases increase) the amount it varies. There is no need to assume that any of those feedbacks comprises a global temperature governor; and tropical thunderstorms certainly do not (because the regulated variable is a temperature difference, not the absolute temperature; and because their range is not global but is itself variable); nor does the tropics to polar “heat engine” (for similar reasons).
PB: The behaviour of such control systems is much more subtle and surprising than you imagine.
“It is that kind of comment, the sly dig …”
It wasn’t a “sly dig”, it was a directly pertinent remark (perhaps with a touch of frustration). You yourself had demonstrated in your post and comments that you were unable to imagine how a governed control system could show a strong dependence of average output on average input, or how general observations could lead to useful empirical models of the overall system behaviour even without specific knowledge of the control algorithm or underlying physics. You still seem unable to imagine this, even after I have proved the point by experiment.
Paul Birch;
That the speeds are not identical (to how many decimal places?) is actually irrelevant. Up front we design the feedback system to react to variance of a given amount, just as a thermostat allows temperature to drop a degree or two below its setting before firing up the furnace, and raises it a degree or two above the setting before shutting it off.
As for your overwhelmed Devils, you could attempt to drive a car up too steep a grade for it to sustain 30 mph, but that is also irrelevant.
Brian H says:
December 21, 2010 at 5:36 pm
“That the speeds are not identical (to how many decimal places?) is actually irrelevant. Up front we design the feedback system to react to variance of a given amount, just as a thermostat allows temperature to drop a degree or two below its setting before firing up the furnace, and raises it a degree or two above the setting before shutting it off.
As for your overwhelmed Devils, you could attempt to drive a car up too steep a grade for it to sustain 30 mph, but that is also irrelevant.”
These features are not in the least “irrelevant”. Not only do they directly contradict Willis’s false and simplistic claims, but as common control system behaviours they are also likely to be found in the global climate systems that he wishes to explain by analogy with his dirt devils and cruise control. Even if there exist global temperature governors (which I rather doubt), as distinct from merely ameliorative negative feedback, it does not follow that their hysteresis range must be small; it could easily be ~50K or more. Nor does not follow that they cannot be close to overload; indeed, systems such as tropical thunderstorms are quite likely to be near overload near (some of) the margins of their geographical extent.
Note, by the way, that the cruise control analogy is considerably poorer than the dirt devil one, because there is only a single, accurately known (measured) speed of the car, under a known and fairly restricted range of conditions, being regulated by a single governor (control system). It would not be particularly hard to make the hysteresis range quite small (for other than improbably extreme stresses – like running into a brick wall!). By contrast, dirt devils, and tropical thunderstorms, are regulating dirt levels and temperature differences in multiple locations simultaneously. One should not expect these to have the same system dynamics as a single control loop.