Blog Archive - May 2008

Back to the future

A few weeks ago I was at a meeting in Cambridge that discussed how (or whether) paleo-climate information can reduce the known uncertainties in future climate simulations.

The uncertainties in the impacts of rising greenhouse gases on multiple systems are significant: the potential impact on ENSO or the overturning circulation in the North Atlantic, probable feedbacks on atmospheric composition (CO2, CH4, N2O, aerosols), the predictability of decadal climate change, global climate sensitivity itself, and perhaps most importantly, what will happen to ice sheets and regional rainfall in a warming climate.

The reason why paleo-climate information may be key in these cases is because all of these climate components have changed in the past. If we can understand why and how those changes occurred then, that might inform our projections of changes in the future. Unfortunately, the simplest use of the record - just going back to a point that had similar conditions to what we expect for the future - doesn't work very well because there are no good analogs for the perturbations we are making. The world has never before seen such a rapid rise in greenhouse gases with the present-day configuration of the continents and with large amounts of polar ice. So more sophisticated approaches must be developed and this meeting was devoted to examining them.

The first point that can be made is a simple one. If something happened in the past, that means it's possible! Thus evidence for past climate changes in ENSO, ice sheets and the carbon cycle (for instance) demonstrate quite clearly that these systems are indeed sensitive to external changes. Therefore, assuming that they can't change in the future would be foolish. This is basic, but not really useful in a practical sense.

All future projections rely on models of some sort. Dominant in the climate issue are the large scale ocean-atmosphere GCMs that were discussed extensively in the latest IPCC report, but other kinds of simpler or more specialised or more conceptual models can also be used. The reason those other models are still useful is that the GCMs are not complete. That is, they do not contain all the possible interactions that we know from the paleo record and modern observations can occur. This is a second point - interactions seen in the record, say between carbon dioxide levels or dust amounts and Milankovitch forcing imply that there are mechanisms that connect them. Those mechanisms may be only imperfectly known, but the paleo-record does highlight the need to quantify these mechanisms for models to be more complete.

The third point, and possibly the most important, is that the paleo-record is useful for model evaluation. All episodes in climate history (in principle) should allow us to quantify how good the models are and how appropriate the our hypotheses for climate change in the past. It's vital to note the connection though - models embody much data and assumptions about how climate works, but for their climate to change you need a hypothesis - like a change in the Earth's orbit, or volcanic activity, or solar changes etc. Comparing model simulations to observational data is then a test of the two factors together. Even if the hypothesis is that a change is due to intrinsic variability, a simulation of a model to look for the magnitude of intrinsic changes (possibly due to multiple steady states or similar) is still a test both of the model and the hypothesis. If the test fails, it shows that one or other elements (or both) must be lacking or that the data may be incomplete or mis-interpreted. If it passes, then we a have a self-consistent explanation of the observed change that may, however, not be unique (but it's a good start!).

But what is the relevance of these tests? What can a successful model of the impacts of a change in the North Atlantic overturning circulation or a shift in the Earth's orbit really do for future projections? This is where most of the attention is being directed. The key unknown is whether the skill of a model on a paleo-climate question is correlated to the magnitude of change in a scenario. If there is no correlation - i.e. the projections of the models that do well on the paleo-climate test span the same range as the models that did badly, then nothing much has been gained. If however, one could show that the models that did best, for instance at mid-Holocene rainfall changes, systematically gave a different projection, for instance, of greater changes in the Indian Monsoon under increasing GHGs, then we would have reason to weight the different model projections to come up with a revised assessment. Similarly, if an ice sheet model can't match the rapid melt seen during the deglaciation, then its credibility in projecting future melt rates would/should be lessened.

Unfortunately apart from a few coordinated experiments for the last glacial period and the mid-Holocene (i.e. PMIP) with models that don't necessarily overlap with those in the AR4 archive, this database of model results and tests just doesn't exist. Of course, individual models have looked at many various paleo-climate events ranging from the Little Ice Age to the Cretaceous, but this serves mainly as an advance scouting party to determine the lay of the land rather than a full road map. Thus we are faced with two problems - we do not yet know which paleo-climate events are likely to be most useful (though everyone has their ideas), and we do not have the databases that allow you to match the paleo simulations with the future projections.

In looking at the paleo record for useful model tests, there are two classes of problems: what happened at a specific time, or what the response is to a specific forcing or event. The first requires a full description of the different forcings at one time, the second a collection of data over many time periods associated with one forcing. An example of the first approach would be the last glacial maximum where the changes in orbit, greenhouse gases, dust, ice sheets and vegetation (at least) all need to be included. The second class is typified by looking for the response to volcanoes by lumping together all the years after big eruptions. Similar approaches could be developed in the first class for the mid-Pliocene, the 8.2 kyr event, the Eemian (last inter-glacial), early Holocene, the deglaciation, the early Eocene, the PETM, the Little Ice Age etc. and for the second class, orbital forcing, solar forcing, Dansgaard-Oeschger events, Heinrich events etc.

But there is still one element lacking. For most of these cases, our knowledge of changes at these times is fragmentary, spread over dozens to hundreds of papers and subject to multiple interpretations. In short, it's a mess. The missing element is the work required to pull all of that together and produce a synthesis that can be easily compared to the models. That this synthesis is only rarely done underlines the difficulties involved. To be sure there are good examples - CLIMAP (and its recent update, MARGO) for the LGM ocean temperatures, the vegetation and precipitation databases for the mid-Holocene at PMIP, the spatially resolved temperature patterns over the last few hundred years from multiple proxies, etc. Each of these have been used very successfully in model-data comparisons and have been hugely influential inside and outside the paleo-community.

It may seem odd that this kind of study is not undertaken more often, but there are reasons. Most fundamentally it is because the tools and techniques required for doing good synthesis work are not the same as those for making measurements or for developing models. It could in fact be described as a new kind of science (though in essence it is not new at all) requiring, perhaps, a new kind of scientist. One who is at ease in dealing with the disparate sources of paleo-data and aware of the problems, and yet conscious of what is needed (and why) by modellers. Or additionally modellers who understand what the proxy data depends on and who can build that into the models themselves making for more direct model-data comparisons.

Should the paleo-community therefore increase the emphasis on synthesis and allocate more funds and positions accordingly? This is often a contentious issue since whenever people discuss the need for work to be done to integrate existing information, some will question whether the primacy of new data gathering is being threatened. This meeting was no exception. However, I am convinced that this debate isn't the zero sum game implied by the argument. On the contrary, synthesising the information from a highly technical field and making it useful for others outside is a fundamental part of increasing respect for the field as a whole and actually increases the size of the pot available in the long term. Yet the lack of appropriately skilled people who can gain the respect of the data gatherers and deliver the 'value added' products to the modellers remains a serious obstacle.

Despite the problems and the undoubted challenges in bringing paleo-data/model comparisons up to a new level, it was heartening to see these issues tackled head on. The desire to turn throwaway lines in grant applications into real science was actually quite inspiring - so much so that I should probably stop writing blog posts and get on with it.

Butterflies, tornadoes and climate modelling

Many of you will have seen the obituaries (MIT, NYT) for Ed Lorenz, who died a short time ago. Lorenz is most famous scientifically for discovering the exquisite sensitivity to initial conditions (i.e. chaos) in a simple model of fluid convection, which serves as an archetype for the weather prediction problem. He is most famous outside science for the 'The Butterfly Effect' described in his 1972 paper "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?". Lorenz's contributions to both atmospheric science and the mathematics of dynamical systems were wide ranging and seminal. He also directly touched the lives of many of us here at RealClimate, and both his wisdom, and quiet personal charm will be sorely missed.

Ed Lorenz had a reputation of being shy and quiet, and this was indeed the impression he gave on first meeting. Indeed raypierre was interviewed by Ed at MIT in 1979 for his first faculty job — and remembers having to ask most of the questions as well as answer them. But he also remembers a lot of timely support from Ed that helped smooth over the somewhat rocky transition from basic turbulence theory to atmospheric science. The longer you were around Ed, the more you came to appreciate his warmth and sense of humor. He was an avid hiker, and many in the community (our own Mike Mann included) have recollections of time on the trail with him around the hills of Boulder and elsewhere.

Lorenz launched the modern era of the study of chaotic systems, which has profound implications both within and beyond atmospheric science. We'll say more about that in a bit, but the monumental work on chaos should not leave Lorenz's other contributions to atmospheric science completely in its shadow. For example, in a 1956 MIT technical report, Ed introduced the notion of "empirical orthogonal functions" to atmospheric science, and this technique now plays a central role in diagnostic studies of the atmosphere-ocean system. He also pioneered the study of angular momentum transport in the atmosphere, and of atmospheric energetics. Among other things, he introduced the important notion of "available potential energy," which quantifies the fact that not all of the potential energy can be tapped by allowable rearrangements of the atmosphere.

Later, he pioneered the concept of resonant triad instability of atmospheric waves, an idea that has repercussions for the sources of atmospheric low frequency variability. As if that weren't enough Ed also introduced the concept of the "slow manifold" — a special subset of solutions to a nonlinear system which evolve more slowly than most solutions. The atmospheric equations support a lot of very quickly changing solutions, like sound waves and gravity waves, but on the whole what we think of as "weather" or "climate" involves more ponderous motions evolving on time scales of days to years. Ed's work on this subject launched the study of how such slowly evolving solutions can exist, and how to initialize a numerical model so as to minimize the generation of the fast transients. This is now part and parcel of the whole apparatus of data assimilation and numerical weather forecasting.

Ed was not a user of general circulation models. His essential approach was to crystallize profound phenomena into very small sets of equations for how a handful of variables change with time. He left behind him a dozen or so such models, each of which would repay many lifetimes of study. He was indeed a master of "seeing the world in a grain of sand." You can read about some of these models in the talk raypierre gave at the 1987 Lorenz 'retirement' symposium — not that this slowed him down!

Now let's take a closer look at that butterfly effect. Despite the fact that there are no butterflies or tornadoes in climate models, Lorenz's discoveries and their implications played a central role in climate modelling efforts and in the most recent IPCC report.

The notion of the butterfly effect itself was drawn from a simple but astute observation of the way the solutions of certain nonlinear equations behave when they are solved using a computer. Start with a greatly simplified representation of thermal convection, first formulated by Barry Saltzman using a technique called "low order modelling." If you run a simulation using these equations and then try and replicate it using starting values that only differ in the last decimal place, you will find that the simulations quickly diverge from one another - and by quickly, it means that the differences grow exponentially fast. Lorenz found this phenomenon by accident, but quickly recognised the profound implications. If the real weather system displayed the same behaviour, it meant that since however well one knew the initial conditions of the atmosphere, there would always be some uncertainty, that uncertainty would be quickly magnified, rendering weather forecasts useless after a few exponential doubling times. The practical implication is that - even if you had a perfect model - for every halving of the error in the initial conditions you only get one extra time period of useful forecast. Given this time period is only a few hours in many cases, the practicality of true weather forecasts for periods longer than two weeks or so, is vanishingly small.

The mathematically inclined reader who takes a look at Ed's early papers on what is now called the "Lorenz Attractor" will be astonished at the depth and modernity of his ideas about chaos. This line of work was no mere remark on a numerical exercise. Lorenz actually teased out the geometry of chaos — the many-leaved structure of the attractor — realizing that it was no simple geometric entity like a sphere or a folded sheet of paper. It was indeed "strange" in a sense which he made geometrically precise. This is why the work had such lasting impact on the area of pure mathematics known as dynamical systems theory. He went beyond that to develop or apply many fundamental concepts in chaotic systems, quantitatively formulating various measures of predictability and connecting the Lyapunov exponent — a certain precise mathematical characterization of chaos — with the structure of strange attractors. But that's for the mathematicians. What makes Lorenz's work interesting to the entity on the Clapham omnibus is the notion of sensitive dependence on initial conditions. Some have even seen in this deterministic chaos the resolution to the problem of free will!

The idea that small causes can have large and disproportionate effects is not at all new of course. The poem: "For the want of a nail, the battle was lost" (medieval in origin) encapsulates that well, and popular culture is full of such examples, "It's a wonderful life" (1946) and Ray Bradbury's "A Sound of Thunder" (1952) for instance. Curiously, Bradbury's story also involves a butterfly, and since it predates Lorenz's coining of the phrase by a decade or so, people have speculated that there was a connection to Lorenz's choice of metaphor (he started off with a seagull in his 1963 Trans. N.Y. Ac. Sci. paper). But that doesn't appear to be the case (see here for a history). It's worth adding that all of Lorenz's papers were exceptional in their clarity and are well worth tracking down as an example of science writing at its best.

However, the difference between the long-standing popular conception and Lorenz's work is that he demonstrated this effect in a completely deterministic system with no random component. That is, even in a perfect model situation, useful predictability can be strongly limited. Strictly speaking, Poincaré first described this effect in the classic three-body problem in the early 1900s, but it was only with the onset of electronic computers, as used by Lorenz, that this became more widely recognised. To throw in another popular culture reference, Tom Stoppard's Arcadia has a character, Septimus, who drives himself mad trying to calculate chaotic solutions to the logistic map by hand.

So what does this have to do with the IPCC?

Even though the model used by Lorenz was very simple (just three variables and three equations), the same sensitivity to initial conditions is seen in all weather and climate models and is a ubiquitous phenomenon in many complex non-linear flows. It is therefore usually assumed that the real atmosphere also has this property. However, as Lorenz himself acknowledged in 1972, this is not directly provable (and indeed, at least one meteorologist doesn't think it does even though most everyone else does). Its existence in climate models is nonetheless easily demonstratable.

But how can climate be predictable if weather is chaotic? The trick lies in the statistics. In those same models that demonstrate the extreme sensitivity to initial conditions, it turns out that the long term means and other moments are stable. This is equivalent to the 'butterfly' pattern seen in the figure above being statistically independent of how you started the calculation. The lobes and their relative position don't change if you run the model long enough. Climate change then is equivalent seeing how the structure changes, while not being too concerned about the specific trajectory you are on.

Another way of saying it is that for the climate problem, the weather (or the individual trajectory) is the noise. If you are trying to find the common signal that is a signature of a particular forcing then averaging over a number of simulations with different weather works rather well. (There is a long standing quote in science - "one person's noise is another person's signal" which is certainly apropos here. Climate modellers don't average over ensemble members because they think that weather isn't important, they do it because it gives robust estimates of the signal they are usually looking for.)

The ensemble approach, and indeed the multi-model ensemble approach, used in IPCC then derives directly from Lorenz's insights into his serendipitous numerical problem.

Impressions from the European Geophysical Union conference 2008

Last week, the European Geophysical Union held its annual general assembly, with thousands of geophysicists converging on the city of Vienna, Austria. It was time to take the pulse of the geophysical community.

When registering at the conference, we got a packet called 'Planet Earth; Directions for Use'. As far as I know, this is a new feature apparently offered by the EGU. The box says 'EGU cares…' and it contains 4 sheets: Biosphere, Hydrosphere, Litho- and Pedosphere, and the Atmosphere. The Biosphere sheet is concerned about the biodiversity, the hydropshere discusses water shortage and loss of marshland issues, the litho- & pedosphere mentions the fact that fossil fuels are finite and soil erosion, and the atmosphere discusses AGW.

Of course this is a gimmick, and perhaps it is even aimed at the wrong target group. These issues are more or less taken as given by the majority of the EGU community by now, it seems. It's more pressing, however, that the rest of the world population understand the problems.

Actually, it was refreshing arriving at the harbor of sanity in the EGU meeting, after the the insane climate-change debate circus in Norway at the moment – lead by a number of academics who start to look more and more like crack pots, and a right-wing populist political party taking after Inhofe.

What were the highlights? It's impossible to cover everything, and I only sampled some talks which are most relevant to my own work. But one important talk was about setting the global climate models' initial state (ocean) to describe the current climate. The intention was to capture subsequent slow natural variations (decadal variation) associated with the thermohaline circulation (THC, not to be confused with other meanings according to a recent article in Eos: VOLUME 89 NUMBER 11 11 March 2008).

Apparently, if the global climate model is initialized with the current state, then the global mean temperature may not rise much over the next decade or so, and then suddenly bounce up and converge with the current scenarios. But some critiques argue that forcing models to have a prescribed state, will trow them off balance, and that the model will try to recover its balance for the next few model years.

Another presentation discussed the possibility for slow climatic variations to be predicted 10 years in advance (potential decadal predictability), and concluded that there is a potential for over the North Atlantic regions – associated with the THC. But an increasing AGW may destroy this possibility, as the predictability reduces when the world gets warmer.

There are some interesting and newish data coming of age: radio occultation. This involves measuring the bending of GPS signal through the atmospheric limb, as measured between different satellites. The atmospheric temperature and humidity affect radio signals refractive index. But there is only short data series (~10 years), but so far the temperature trends are consistent with the models for similar intervals. But these are independent to the satellite MSU data, and do not suffer in the same way from differences between satellite instruments, etc.

My personal favourite this time was a talk on 'recurrence based transition analysis'. The presentation was subtly slick and so nicely executed that it can only be done on a Mac. The talk was very clear, no excess number of words, and to the point.

There were many good talks, but some common mistakes. Well, at least I'm a bit slow when having attended a few dozen presentations, so presenters speaking fast or too crowded Powerpoint slides risk losing me. There is supposed to be a golden rule called 'Seven by seven': no more than seven bullet points, consisting of no more than 7 words! And one should speak slowly and repeat the important points.

So what did people talk about? What was 'The buzz-word'? There was no obvious paradigm shift, and I didn't catch one single theme that was the vogue of the day, but there were some issues that kept popping up: decadal predictability, cryosphere and the polar regions, model ensembles and probabilities, regional modelling and extremes.

What I find striking with such monster conferences is the sheer scale of diversity in terms of geo-subjects that people study. There were rows upon rows of posters in several large rooms, in addition to the talks.

There seems to be a great secret of Powerpointerism: the programmers at Microsoft designed a right mouse click option to show a presentation straight away without showing the subsequent page. There is a systematic neglect of this functionality, so that the Microsoft guys must have implemented this one in vain.

The best quote that i heard on this conference was: 'A trend is a trend is a trend …'. In other words, there is no definite definition of a trend, at least not to statisticians who like to use more complex lagged correlation models. Something to bear in mind for those who fit linear lines to data points - in order to study trends - and then use the goodness of fit to say whether the trend is 'significant' or not.

Another bad habit is showing latitudinal profiles of zonal mean values as if the points at high latitudes are equal to those near the equator. What they really compare are oranges and apples, as the low latitude zonal means involve higher degrees of freedom than at high latitudes. I have explained this in more technical details in a GRL article from 2005, but such graphs can be found even the latest IPCC report. Though it may be a minor point, it makes models look worse than they actually are, as part of the spread towards the poles can be attributed increasing statistical fluctuations when the number of degrees becomes less. Thus, the results would stand stronger taking this aspect into account.

I was pleased to hear that some colleagues in the German weather service sometimes use RealClimate for inspiration to their monthly seminars. What was more unexpected, however, was being met with a slide showing 'Natural Trendy?' on a session that I had been invited to give a talk.

Furthermore, it turned out that LiCohn and Koutsoyiannis, one of them the author of the very paper that I had criticized, sat down next to me. We nevertheless had a very civilized and friendly chat, deciding to disagree on the matter of natural trends.

But Dr. Koutsoyiannis commended us for being respectful in our reply to his comments. I think this is a very important issue – we have to be respectful, sincere, and show courtesy in our criticism, even when we argue why we think that a paper has flaws. This brings us back to the discussion on blogs and journals.

I think that we have built up a reputation only because we deliver relevant quality analysis. We are very much aware that we some day may be mistaken, so it's important to be humble and check our drafts amongst ourselves. But when a question was asked about the importance of blogs like RealClimate in the session, the answer was that they were good entertainment.

Vienna is a pleasant city with many pretty sights. The only annoying thing is that one often has to breathe in local pollution from the next table when dining in restaurants. Austria is one of the few western European countries that has not introduced a smoking ban in restaurants it seems.