May 30, 2003

SARS - slight return

I am getting some great feedback on the modeling stuff, but I am feeling a bit frazzled tonight so I am going to shift gears briefly and let my thoughts on modeling simmer for a while.

SARS is back in the news. It seems like the disease has the potential for a bit of a second wind. The figure below summarizes my understanding of the disease. In individuals, there were reports of recurrence if the disease was not fully conquered in the first go-round. In communitities, there seems to be the potential for new outbreaks as well. Toronto is seeing a pretty good resurgence. Part of the bump in Toronto seems to have to do with how SARs is defined.

What is the relationship between the progress of the disease in individuals and in populations? The evolution of the disease in individuals is the domain of medicine; the evolution of the disease in populations is the domain of public health. My guess is that the stubbornness of the virus in individuals is related to the potential for new outbreaks. In part I think this because of the importance of restricting exposure in controlling spread - in order to contain the disease, each victim must infect less than one other person.

When I wrote about SARS previously, it looked like the mortality rate was reasonably low. Turns out that the mortality rate is higher than previously thought it may be as high as 17 - 20%. As might be expected, mortality is higher in younger and older people. For people over 60, the mortality is quite high. I am quite interested in the age structure of the mortality - is it typical for infectious diseases or is it unusual?

As I noted earlier, SARS is a coronavirus and it does seem to have moved between animals and humans.

May 29, 2003

Too Many Knobs?

As I have written about models, I have talked about comparing models to observations of the processes that they are meant to represent. I talked briefly about model parameters and how they could be tuned to make an individual model better represent the data at hand. Each parameter is like a knob that can be turned to adjust the details of the given model.

For example let's consider the linear model illustrated below. In this model, factory output is assumed to be proportional to the input of labor. For a given increase in the hours worked, the factory produces a corresponding increase in output. The constant of proportionality (a, the slope of the line) and the amount of labor necessary to simply maintain the factory at zero output (the labor-axis intercept (b is actually the output-axis intercept)) may be different for different factories. A factory characterized by the red line will be more efficient and more productive than one characterized by the green line.

The dots in the figure are observations of the relationship between output and input from some factory. While the data are pretty linear, it is easy to imagine a line that would fit those data better than the ones I have drawn. The better fitting line would be described by adjusting the slope (a) downward and shifting the intercept to the right.

In the example above there are more data points than there are parameters and we may find that the best fitting line does not actually pass through any of the observations. The extent to which the data are close to the best fit model is a measure of how good the model fits the data; it can also be a measure of the certainty with which the model can be used to predict behavior in the future. The case where there are more data points than there are parameters is called over-determined; over-determined is good because it gives you a measure of certainty regarding the fit of the model to the data.

Now imagine we had only two data points. In that case there is exactly one line that fits the data exactly. This is ok, but we can fit those data equally well with any two-parameter model and we have no measure of certainty. It is generally true that you can exactly fit N data points with a model that has N parameters.

Good models have considerably fewer parameters than there are observations to constrain the model. As models become more complex they acquire more tunable parameters. In the case of GCMs there are many many tunable parameters, but there are also many many observations to constrain the models.

In using models to help us think about how Earth functions, we must trade off the simplicity of a model that significantly abstracts Earth systems by modeling them with a small number of easily understood parameters with the complexity of models that attempt to include more detail of Earth functioning but contain a larger number of parameters with more technical meanings and interconnections. Choices about this tradeoff will be different depending on our purpose. Climate modelers who use models to test their detailed understanding of Earth functioning will obviously choose to work with more complicated models. Decision makers who have have to include many factors beyond the climate in there work, may be better served by simpler models that capture the well understood behavior of the climate.

May 28, 2003

Predicting the Future

Someone once said, "Predicting is hard, especially the future." That said, much of the rhetoric around relating science to policy making is based on the hope / belief that scientists and their models will be able to predict the future and it is the job of the policy maker to move society out of harm's way or to alter the future in beneficial ways. There are at least tow interesting things here: First, can scientists predict the future? and second, can policy makers alter the future?

Can scientists predict the future?
Consider climate: The US Global Climate Research Program (USGCRP) has invested more than a billion dollars in the development of General Circulation Models (GCMs).

GCMs are a class of computer models that attempt to simulate the circulation patterns of the oceans and the atmosphere. These models vary in how they represent the underlying physical processes. These variations reflect choices on the part of the modeling groups and in turn effect the kinds and details of the output produced by the model. Intercomparison of models and efforts to understand why model results differ is a major area of research.

GCMs are becoming more detailed with respect the processes that are included and with respect to the output that is produced. These models are often tested by hindcasting. In hindcasting, models are initialized with known conditions from some time in the past. The model output is then compared with observations from the subsequent climate history. The thinking is that if a model successfully "predicts" the past, it might be trusted to predict the future.

I said a while ago that weather prediction is not likely to go further out than it currently does (although I recently read an article suggested that understanding certain long wavelength waves in the atmosphere may extend certain kinds of weather prediction out beyond the current 5-7 days). So assuming we do trust GCMs to predict the future, the future of what? Well in the case of GCMs it would be climate with its inherently time and spatially averaged characteristics and related uncertainties. In general, the finer the spatial or temporal resolution we ask of a model the greater the uncertainty associated with the output.

Much of this line of thought is driven by conversations with Dan Sarewitz. In particular, beneath this description of models are some very fundamental questions having to to with the relationship between models and the systems that they represent.

Can policy makers alter the future?

Implicit in our faith in model-as-oracle is one of the following two conditions: either 1) the mdoel adequately represents all of the important processes; or 2) assumptions about external conditions remain true through out the prediction period.

I would argue that condition 1) is unlikely to ever be true with respect to cliamte models. This is because human behavior is a fundamental element of the climate systemand human behavior cannot be modeled on the scales of GCMs. Current climate models inlcude human behavior as an input primarily in the form of scenarios of expected GHG emissions and other forcing behavior.

So policy makers can alter the future by putting in place structures that alter the human forcing of climate. This would violate condition 2) in our current modeling infrastructure.

One more detail to be cleaned up
In my initial formulation I not only had policy makers altering the future, but also altering it for the better. This is a pretty serious caveat to have brushed over. To be true it too requires two things (all 3 "tos" in one sentence!): 1) we can successfully predict the outcomes of our policies; and 2) we can agree on what "beneficial" means. (Now you can see why I brushed over them.)

At any given time there is a closed (?) set of possible futures. Some of these futures are more likely than others. More likely futures are "closer" to our current trajectory than less likely futures. As our society evolves, the probability distribution of possible futures changes; some become impossible (avoided disasters / missed opportunities) other become more likely. I think that one of our guiding ideas should be to keep the space of possible futures as large as possible and the probability map skewed in ways that reflect as best as possible our collective vision of better world.

May 24, 2003

Politics and Policy

Christie Todd-Whitman resigned last week from her position as Administrator of the Environmental Protection Agency. I was surprised she didn't resign the first time that the rug was pulled out from under her in the first weeks of her tenure. She was in the middle of a lot of scraps, but I always felt that she worked to advance her agencies missions by constructing the best policies possible based on what we know about interactions between humans and the environment. This often means moving away from a problem rather than solving it outright. She did some things I didn't agree with, but given the current administrations complete lack of understanding of the value of a healthy environment, I think she as good a job as possibly could have been done. I admire the fact that she didn't throw in the towel on many of the occasions when she was blind sided.

This is in the context of a distinction between means and ends. Whitman kept the common good that her agency was charged with in mind as she worked the politics of advancing her agency's mission. I thinks this sets her apart from much of the maneuvering that goes on in our government today. It is not clear that politics has not become the ends rather than the means.

Begin Aside
A lot of the following comes from conversations I have been having with David Gilbert-Keith.
End Aside

I read a more recent article by Lindblom this week. He continues to think that incrementalism is basically a good idea, but he is a bit more concerned about how common good is protected in the policy process. He sketches a scenario of tension among competing groups as a means to seek common ground and as a platform for developing policy. The problem comes when one group gains an overwhelming majority (the tyranny of the majority). I read an article in The New Yorker that follows this theme in the context of a discussion of Karl Rove; it seems that some of The Federalist Papers were also concerned with balancing the influence of "interests."

My question / concern is "How do we design policy processes that avoid tyrannies of interests?" As a member of an elite, it is not hard for me to entertain the value of a technocracy. As a liberal intellectual, I wonder how my far my ideas of societal good should be pressed in a highly heterogeneous society. We can no longer solve problems of difference by moving the frontier a little further west. We have reached the edges and are now filling in.

If we are going to be successful at managing Earth systems, then we will have to find ways to make trade-offs among competing interests. In building the necessary processes we will need to be careful the ends remain a healthy planet and that they don't contract to focus on strengthening the political power of "interests."

May 22, 2003

Initial Conditions

Well the little go-round I just had with html and my browser is as good a place to start as any. Bear with me as I go into a bit of detail about how my browser (Internet Explorer, you might use Netscape or any one of a number of other options but I think they all do the same basic thing). The browser does a number of things to make pages load faster. One of the things it does is that the first time it downloads a picture, it makes a temporary copy of that picture and stores it deep in your hard drive. Everytime you look at a picture on a web page, your browser looks to see if it already has a copy of that picture. If it does then it uses the copy on your hard drive rather than downloading it again - this makes pages load faster. It keeps track of pictures by their names.

Now my problem is that I often diddle with pictures as I go along but leave their names the same. Many times I have beaten my head against the wall trying to figure out why the changes I have made in the picture don't show up on my web pages. The reason is that I change the original and I change the web page version, but I forget to tell my browser to update its copy so it continues to use the copy of the initial version that it has stored on my hard drive.

The point here is that the browser initializes itself and then proceeds happily and I forget that the browser has this initial condition and beat my head against the wall.

Initial conditions are just that - they are the place that a system or a process starts from. They are the parameters of a model at the point that the model begins to run. In a baseball game, the initial conditions include the number and skills of the players available to play each position, the starting pitcher, the batting order, the umpiring staff, the size of the crowd, the weather and the score. As the game progresses each of these parameters can change and the details of how the game develops will be influenced by those changes. Changes in some parameters are more influential than others (pitcher vs crowd size).

Initial conditions have to do with time and answer the question "What is the state of the system of interest at the beginning of the time period of interest?" In the baseball example above, the period of interest was implicitly a single game. If I were interested in the history of a team or league, the parameters I choose to follow and specify as a starting point would likely be different. They would certainly include the management, the home town, and the ball park.

Begin Aside
Exercise for the reader: In the context of a single game, is the ball park an initial condition?
End Aside

Thus one person's initial conditions are another's intermediate state. In the context of weather, today's weather is an intermediate value in yesterdays 5-day forecast, but is the initial condition for today's 5-day forecast. Similarly the political state of an institution or nation provides initial conditions for the development of policy solutions.

Consider the activities of the EPA. Christie Todd-Whitman's initial conditions included US participation in the Kyoto protocol and she advanced from that condition. Unfortunately rate of change of that parameter was very high and negative. Her initial conditions also included much stronger political pressure to roll back environmental regulations that she had championed as Governor of New Jersey. Todd-Whitman's resignation changes the state of the EPA and will be part of the initial conditions that her successor inherits.
Policy Process - slight return

The figure from yesterday is kind of a joke. The joke has to do with the reduction of policy to a single instruction - "weigh all factors". Compare the following figures from Morgan and Henrion (1990):

Less Real

More Real

Morgan, M.G., M. Henrion, and M. Small, Uncertainty: a guide to dealing with uncertainty in quantitative risk and policy analysis, 332 pp., Cambridge University Press, New York, 1990.

May 21, 2003

Muddling Through

In 1959 Charles Lindblom published The science of "muddling through". It was destined to become a classic and muddling through is now a term of art in much of the public policy world. Lindblom's paper starts out with a sketch of what a rational process of policy making would look like. Part of the first step is to "list all related values in order of importance." This step is followed by a comprehensive analysis of all possible policy outcomes. With this thorough analysis in hand, the policy maker makes a choice that maximizes her values. Something like the following diagram (note especially the policy box toward the bottom of the diagram).

This process of policy making requires assembling and integrating tremendous volumes of data and knowledge Beyond the simplest, and not very interesting, policy problems Lindblom argues that this commonly articulated approach to policy making is not even possible. Herbert Simon's bounded rationality and his work with James March on the work of organizations point out that what in fact happens is that people use a limited amount of the information that they have available at any given time to actually make decisions.

In Muddling Through, Lindblom contrasts the fully rational approach with one in which the policy maker chooses one objective that is of primary importance and then, making choices from a small portfolio of policy approaches that she has experience, designs a next step in the evolution of the policy history of her agency. Lindblom argues that in making these choices the policy maker is choosing from differences at the margin. In this incremental approach to policy making, value tradeoffs and policy tradeoffs are intertwined.

Among the advantages of this approach is the fact that values do not have to be agreed upon among policy makers. "Agreement on policy thus becomes the only practicable test of the policy's correctness." The failure of a given analyst to consider all possible values is addressed by the fact that there is a portfolio of policy making agencies, each with its own primary values; interactions at the margins works to protect undue impacts of one policy on values that are not within its immediate scope. Muddling through recognizes that policy problems will never be solved comprehensively and thus policy solutions will advance toward better states by an ongoing process of iteration.

There is a notion of democratic principles in Lindblom's model. In particular by ensuring that values are advanced and prioritized through interactions among agencies with differing sets of priorities, he seems to assume that the portfolio of agencies in some ways reflects the societal parsing of problems and priorities.

The ideas of muddling through have been expanded upon by a school of environmental management called adaptive management. The primary difference is that in adaptive management, policies goals are made explicit and policies are treated as experiments. The experiment is successful if progress is made toward the goal; thus another explicit element of adaptive management is the inclusion of a measurement program in all policy regimes. It is this measurement program that allows statement to be made about whether a policy is successful or not.

Begin Aside
Of course it is a management axiom that "if you can't measure it, you can't manage it"
End Aside

So Lindblom sketches a policy landscape that moves incrementally and recursively from its current state to a new one according to a limited set of rules. Policy agents interact in a loosely couple ways that ensure that a wide range of values are represented and advanced in aggregate. In some ways this looks alot like the cellular automata models I was constructing of earthquake processes.

May 19, 2003

Weather vs. Climate

The difference between weather and climate is summed up in the following:

Climate is what you expect, Weather is what you get
If you don't like the weather, wait a few days; if you don't like the climate, move

So let's deconstruct...

Expect vs Get
The statistical part of weather vs. climate is captured in this one. Simply put climate is the average weather over some period of time. I spent a string of summers at the far end of the Alaskan peninsula on a set of islands sticking out into the Pacific Ocean. There was a map of Alaskan weather that turned up on post cards and T-shirts; the weather in the Shumagins was characterized as Always Shitty (as opposed to Mostly Shitty, Occasionally Shitty etc in other parts of that great state). You get the picture. In the Shumagins we would watch the Weather Channel precursor called "Alaska Weather" it was a brilliant 1/2 hour weather forecast for the region and you could often see the low pressure systems lining up to the west along the Aleutians. The Lows would bring the weather, the lining up is the climate.

Wait vs. Move
This one captures another piece of the story. Different places have different climates, Everywhere has weather. Weather is variable on the time scale of days or weeks. At best climate is variable on time scales of years or decades. So if you don't like "Shitty" weather, it is best not to live in Alaska (if on the other hand a really good storm on a regular basis through out the summer is your cup of tea, then the Shumagins are just the place (I spent my summers there because my adviser was an Englishman (Welsh really) who like the northern bits of the UK and the Shumagins were a good subsitute and had more active tectonics (or so we thought...))). If you like a really good down-pour 'long about mid-afternoon everyday through out the summer and fall followed by a really steamy evening, then South Florida is just the place for you. Sometimes you get hurricanes in South Florida, sometimes you get thunderstorms in Alaska, but the expectation is different.

Begin Aside
So then what is all the fuss about "climate variability" that we have been making in the National Assessment of Climate Variability and Change. Well here is the rub, sometimes you don't get what you expect. We have warm winters, wet springs, dry summers, and cool falls. It all comes down to the base line. One major factor in the variability of climate is El Nino. Another may be that human activity is changing some of the fundamental dynamics that we have come to take as normal (At the 100,000yr time frame, you get climate variability on the scale of glaciers vs no glaciers). (If your mind is starting to bend that is ok) But as I love to say that is a future topic...
End Aside

May 18, 2003

This Weekend's Weather

Soccer this spring has hammered by the weather. It seems that at times in the year, spring being one of them, the weather can run in roughly 7 day cycles and this year the 1 or 2 days of that cycle that were rainy and raw tended to fall on Saturday. This weekend it looked to be another rain-out. The Weather Channel multi-day forecast called for rain on Friday tapering off into showers Saturday morning. This is a recipe for canceled games, because the fields don't drain so even if things are off by 1/2 of a day, the fields can still be rendered unusable.

But the rain never developed. In fact as the Friday got closer, the forecast changed from rain to showers, but continued to call for precipitation over the crucial field-soaking period. So Friday dawned, and sure enough the clouds came in, but noontime came and went without any rain, and then so did mid-afternoon. I went to bed with dry streets, peaked out the window at 3a (says something about my sleeping these days) and saw dry sidewalks. The sun rose behind a pretty raw overcast on Saturday, but everything was dry; so the Rockets got hammered in a 0-4 blowout (better game actually than the score).

The rain we were supposed to get was from a low that was to head northeast up the coast from the Carolinas. In this case there was also a high over New England that was to steer it out to sea. Based on watching my barometer, it looks like the high won and held the low further south than the forecasters expected. We have had seasonally pretty high pressure for the last few days.

Weather forecasting these days, at least in New York, is pretty good. The five day is not bad and by the time you get within 3 days it is pretty reliable in its main features (e.g rain vs no rain, warm vs cold). This is actually why the lack of rain this weekend impressed me. The forecast continued to call for showers long after they had failed to materialize as expected midday on Friday. The best I can do to explain it is the pressure story above and the observation that on the maps, New York was always on the northern edge of the region with predicted precipitation, so small changes in what actually happened could make a difference between getting rain and getting hammered.

In talking about the lack of rain with another soccer parent who spends a lot of time in England, she noted that in England nobody pays any attention to the weather forecast. Thus it would seem that the weather is more predictable on the East Coast of the US than it is in England (it is not that we are better at it, because the UK has one of the world's best Met Services). This is probably because the weather on the East Coast pretty much is all leftover from what was in Minnesota 24-36 hours earlier. Basically we can see it coming. England on the other hand is basically an island at the intersection of two or three serious oceans and its weather comes at it from all directions. (The geography of our weather also accounts for the pretty stable spring time period of 5-7 days.)

That said weather forecasting has still gotten pretty good. At least part of this skill is attributed to the fact that weather forecasters make literally thousands of predictions every year and with the success or failure of those predictions they learn a little bit more about how to make predictions. There are theoretical reasons why weather forecasting is not likely to go much further into the future than the 5-7 days that they now attempt. These reasons have to do with the complexity of weather systems and their sensitive dependence on initial conditions.

In fact, one of the founding scientists of the field of chaotic systems, Ed Lorenz, discovered sensitive dependence on initial conditions as he was developing the first very simple computer models of atmospheric dynamics. He was puzzled by the fact that if he restarted the model using output values of the model's parameters at some time, then the second run of the model would rapidly diverge from the first run. It turns out that in writing out the computer model's parameters, he was rounding them off and the round off mattered.

So weather predicting is probably at its limit as far as how far out it can go. Inside of the theoretical limits I expect we will get better at predicting the details of when the rain will start and stop and how much we will get etc. Next weekend looks like a soaker, but it is Memorial Day weekend so no soccer game. What the following weekend holds with respect to the weather is anyone's guess, but the twins have another commitment so the Rockets will be weakened up front and in the mid-field.

May 15, 2003

Some thoughts on Determinism

At one time I spent a fair amount of time investigating the behavior of a certain kind of computer model. These models consisted of simple grids of squares. Each square had a value associated with it that would increase slowly. If at some time the value of two adjacent cells differed by more than some threshold, the values of all the cells would be redistributed until the entire system was once again below the threshold. It turns out that such a model can produce very sophisticated patterns of behavior (at the time, I was thinking about the sizes of earthquakes) if there is also a certain amount of randomness in the system (for example, error in how the system re-equilbrates when the threshold is crossed).

In the models that I was working with all of the values were integers (whole numbers like 1,2,3...). In doing the re-equilibrating values from a cell are distributed between the neighbors and thus there is a division. I would round off all of my division back to integers and it turns out that this rounding was enough randomness to drive the model into the region of interesting behavior.

So what does this have to do with determinism? The behavior that was interesting is commonly associated with complex systems, sometimes called the edge of chaos. This behavior is very difficult or impossible to predict; it has sensitive dependence on initial conditions. In my models (and many others) it was also completely deterministic. That is, from the moment I started the program running, the entire path of its evolution was determined (using integers made this transparent (well to me anyway)) even though the next step cannot be predicted.

This is interesting in the context of the machine / organism debate. Clearly the models I was working with were machine-like, while they were interesting, they were completely deterministic. On the other-hand, looking at them from the outside, you would not necessarily know that. Furthermore, computer models can be constructed that modify their internal workings and the relationships amoung their pieces as they attempt to achieve certain (externally set) goals. One class of these codes is called genetic algorithms.

It is also interesting in the context of the "what do we do now" question. Consider humans as part of the system. We can change how we interact with each other and with the natural systems. But given the difficulty in predicting or understanding the impact of any given change, how should we decide what to do? In many ways answering this question is the task that I have set myself. I have the following thoughts as a place to start:
  • Incrementalism is probably a good default approach.
  • Plans should include monitoring impacts and contingencies for when things go wrong.
  • We must recognize that Earth systems are dynamic. To the extent that there is any balance in nature, that balance is likely due to tension rather than stasis.

May 14, 2003

Microwave Popcorn

Begin Aside
a bit of late night contemplation...
End Aside

Consider microwave popcorn:

$0.80 / bag (cheap, what is the margin on this stuff?)
the bag (let steam out, don't burn etc)
the popcorn (probably hybrid)
the grease / flavor (I don't really want to think about it)

not mention the ubiquitous oven itself

it is all technology...
The Idea of Wilderness

I am reading a book called The Idea of Wilderness by Max Oelschlaeger (1991, Yale Univ Press). Max spends a chapter on "Ancient Mediterranian Ideas", but I jumped straight from the paleo and neolithic to his discussion of the Modern. In making that jump it seems that one of his main points is that the earliest humans did not seperate themselves from the wild, but saw themselves as part of the natural cycles. While he doesn't say so explicitly, part of the cycle image is also a sense that our linear or forward notion of progress was absent from earliest human cultures.

Jumping to the Modern as I did I missed alot of transition but here is what I have gleaned about the difference (remember this is what I think Max thinks and I am still early on in the book...):
  • Christianity has a dominate the Earth element to it. How that manifests has evolved but it has been an important part of the development of Western thinking about the relationship between humans and nature. In general though it requires that humans understand and dominate nature to know God or to return to a state of grace.
  • Within the Modern there is an important split between nature-as-machine and nature-as-organism. This split is presented as an evolution from organismic to mechanistic and Oelschlaeger traces its origins back to Galileo. In part Galileo's use of the telescope introduced science as measurement and nature as the thing to be measured.
  • Of course a crucial element of the Modern is that humans stand outside of Nature. Even the romantic poets stood outside. They longed to get back in and they looked to Modernity to return them to the Garden.
  • The nature-as-machine metaphor is traced back to Descartes and his mind / body split.
  • The finalization of the split between civilization and wilderness is laid at Adam Smith's feet.
    Wealth of Nations represents the realization of Merlin's dream: the base and valueless could not, with the facility of natural science and industrial technology, be transformed into a Heaven on earth. Consumption, and its never-ending growth, is the summum bonum of the Wealth of Nations, an ideal yet living today in the relentless pursuit of economic development. Through legerdemain, Smith transformed the first world from which humankiind came into a standing reserve - a nature of significance only within a human matrix of judgment, devoid of intrinsic value. (p.94)
  • The machine vs organism view continues to be important. In the machine causal relationships are linear and direct. In the organism they can be non-linear and complex.
More on this soon...

May 13, 2003

Data, Results and Observations

Tonight's entry is an editted excerpt from a paper I wrote for my PhD thesis, but in the end it wasn't included there.

The terms, "data", "results" and "observations" are often used interchangeably. This reflects the fact that in the evolution of a field of study, the distinction between data, results and observations can become blurred. As work on a topic progresses, assumptions that were clearly stated in the beginning become taken for granted; they are no longer stated and exceptions to them are easily dismissed as mistakes. In an effort to see through the blurring, the following section presents some definitions ...

Begin Aside
The following are proposed definitions. They are how I would like to see the terms used not necessarily how they actually are used. In particular, computer modelers often talk about the data that their models produce.
End Aside

Data are things that are accepted as being facts; this is analogous to being accepted as independent of any model. It is this characteristic which makes data useful in constraining models. Unfortunately, as noted yesterday, it is not possible for anything to be completely model independent; the very act of perception involves assumptions about what is likely to be seen. To accommodate this fact, data can be defined as things whose model we are willing to ignore or at least to accept without question. What is and is not data is a decision that is made in the context of the problem that is being considered. An example of something that I would consider data are the measurements of CO2 concentration in the Keeling curve.

Results are the output of some operation on data; results cannot be model free. Any sort of manipulation of data is done with some purpose and that purpose is determined by the choice of model. In the case of data reduction (e.g., averaging several measurements) the model is usually so widely accepted that the results are once again considered data. The fact remains that even averaging assumes something about the nature of the process which is being measured. An example of results would the the average temperature of Earth.

Observations are generalizations from data or results and, like data, they are meant to be model free. Also like data, it is not possible for them to be so. Observations are the most pernicious of model hiders. It is in generalizing or expounding upon data or results that our preconceived notions are the most invisible. An example of an observation would be to note that both CO2 concentration and the average temperature of Earth are increasing.

End Excerpt

So there you have it - some definitions. In the remainder of the paper that those come from I worked very hard to be consistent with how I used the terms. The problem is that the rest of the world hasn't read my paper and doesn't maintain the same vigilence in how they use these terms. I think what I am hovering around here is that even as we investigate how the world works, we make assumptions about how it works. Those assumptions influence what we find etc.

In reaction to my Eqn 0 piece last night a reader pointed out that politics can also have a strong influence on what is model and what is data. (Is that a fair paraphrase David?) No question about that and that is why this whole problem is so insidious. Politics are buried even deeper than assumptions about linearity or homogeniety. Obviously there is much more to say on this ...

May 12, 2003

Equation 0

My favorite equation is the following:

data = model + residual (Eqn 0)

When it was first presented to me it was in the form:

residual = data - model (Eqn 0')

In the 0' form it is a way to compare your understanding of a problem (model) with the way that the world actually works (data). Another way of thinking about eqn 0' is that the model is the part of the world that you understand and the residual is the part of the world that remains to be explained. Your model of the world is acceptable to the extent that your residual is acceptable. In general, acceptable resduals are very much like low volume white noise (they have no structure and low amplitude).

Begin Aside
Notice that I have not said that the model is true or false, it is only accepable or unacceptable.
End Aside

If your model is not acceptable there are two things that can be done. The first is to refine the parameters of the existing model. Lets say that our model of how much CO2 a car puts into the atmosphere is a linear function of how many miles it is driven. We might write that down as follows:

CO2 = a * miles + b (Eqn 1)

a and b are the parameters of the model. a is the slope of the line and b is the "0 intercept". The values of a and b are choices we make and can be adjusted based on the make and model of the particular car. Cars with better gas mileage will have a lower values of a. The intercept value, b, will be very close to 0 and will vary with the driver of the car; in my quick thinking tonight it might reflect the time that a driver allows her car to warm up before starting off.

The second option if your residuals are not acceptable is to change models. In the context of the example above perhaps the amount of CO2 emitted by a car is some more complicated function of its average speed:
CO2 = c * sqrt(avg speed) (Eqn 2)

In this case c is our adjustable parameter but we have also introduced a non-linear element (the square root) and an aggregate factor (average speed). (I am not going to into this further tonight, the important point is that there are alternate possiblities for our explanations of how the world works).

OK that is all fine and good, but what does it have to do with my preferred formulation of this equation, Eqn 0? Well my preferred form suggests that the data we actually collect reflects what we expect to find plus some surprises. This is a variation on Kuhn's ideas of a paradigm and pardigm shifts. In times of normal science, experiments are designed to explore the details (refine the values of a and b in Eqn 1) of the paradigm (model); we only look for what we expect to find. In times of pardigm shift, the surprise part cannot be ignored and we must replace our models (Eqn 1 vs Eqn 2).

The key issue here is that Eqn 0 and Eqn 0' are the same equation. Each form has surprise in it and models and data are acceptable to the extent that our level of surprise remains acceptable.

Begin Aside
Notice that I have not said that the model is true or false, it is only accepable or unacceptable.
End Aside

May 11, 2003

SARS slight return

I am getting some great feedback on the modeling stuff, but I am feeling a bit frazzled tonight so I am going to shift gears briefly and let my thoughts on modeling simmer for a while.

SARS is back in the news. It seems like the disease has the potential for a bit of a second wind. The figure below summarizes my understanding of the disease. In individuals, there were reports of recurrence if the disease was not fully conquered in the first go-round. In communities, there seems to be the potential for new outbreaks as well. Toronto is seeing a pretty good resurgence. Part of the bump in Toronto seems to have to do with how SARs is defined.

What is the relationship between the progress of the disease in individuals and in populations? The evolution of the disease in individuals is the domain of medicine; the evolution of the disease in populations is the domain of public health. My guess is that the stubbornness of the virus in individuals is related to the potential for new outbreaks. In part I think this because of the importance of restricting exposure in controlling spread - in order to contain the disease, each victim must infect less than one other person.

When I wrote about SARS previously, it looked like the mortality rate was reasonably low. Turns out that the mortality rate is higher than previously thought it may be as high as 17 - 20%. As might be expected, mortality is higher in younger and older people. For people over 60, the mortality is quite high. I am quite interested in the age structure of the mortality - is it typical for infectious diseases or is it unusual?

As I noted earlier, SARS is a coronavirus and it does seem to have moved between animals and humans.

May 09, 2003

A course I'd like to teach

Tonight I am going to do something a little different. Rather than a mini-essay, I am going to present the syllabus for a course that I think would be fun to teach someday. In keeping with the spirit of the blog, it is a first pass not a finished product.

Introduction to the Science of the Environment

I. Introduction to Scientific Thinking (2 weeks)

  • Brief history of Cosmology
  • The Calculus
  • Kuhn, Popper, Feyerbend (or why the extreme postmodern doesn't matter)
  • Reductionism and Determinism

II. Cycles and Systems (4 weeks)

  • Rocks (how old is Earth and how do we know?)
  • Hydrologic Cycle
  • Ocean and Atmospheric Circulation
  • Carbon & Nitrogen Cycles
  • Industrial Ecology

III. Models (1 week)

  • Conceptual models
  • Analytic models
  • Comuter models
  • Data, Models and Results (chickens and eggs)

Review and Mid-term exam

IV. Introduction to Ecosystems (2 weeks)

  • Trophic structures
  • The work of the Odum Brothers (energy flows through natural systems)
  • Types and Distributions
  • Urban Metabolism and Ecologic Footprints

V. Introduction to Public Health (3 Weeks)

  • Aggregate vs Individual health
  • Toxicology
  • Epidemiology

Begin Aside
This is a topic that could use some more thought. Clearly it is the one I am least familiar with.
End Aside

VI. Wrap up / Tie it all together (1 week)

Final Paper - Write an intellectual history of a major environmental concept (chosen from a list e.g. Sanitation, Clean Air, Climate Change etc.)

May 08, 2003

Systems, Systems, Systems

In my "Name Change" entry a few days ago I wrote about singular vs plural Earth systems. But what is all this noise about systems? What makes "systems thinking" so important?

Systems thinking is usually contrasted with reductionism. Reductionism is the mode of inquiry that has taught us most of what we know about how Earth works. A reductionist approach to a problem considers the problem in isolation from all other problems and influences. It takes the problem apart bit by bit and then takes the bits apart (turtles the rest of the way down). At the heart of a reductionist approach to learning is the assumption that if all of the bits are understood, then the whole will also be understood. Just as it isolates the problem, the reductionist approach isolates the understanding of each of the component bits from each other (OK - I am bashing a bit here, but as I noted early on, I do that sometimes). Reductionism works well to the extent that problems and bits are actually fairly isolated from each other and that understanding of the bits in isolation is neatly related to the understanding of the bit when it is put back into the whole.

However when bits interact with other bits in non-linear (unexpected / interesting) ways in the context of the whole, then reductionism does not work as well as a mode of inquiry because understanding the bits in isolation only tells you about its behavior in isolation. It doesn't tell you the complete story of how the bit contributes to the function of the complete (here it comes...) system.

So systems thinking is an effort to understand problems in their entirety complete with all of the messy interactions among bits. I sometimes think of the systems approach being one which considers a problem from the perspective of black boxes. Where in a reductionist approach one would relentlessly deconstruct the boxes, a systems approach focuses on the function of the box. How does the box transform a given input into an output? Where does the box get its inputs? Where does a box send its output? The detail of how the box transforms an input into an output is ignored in favor of understanding the interconnection of black boxes and the transformation of signals as they move through the system.

Now clearly systems can have subsystems. (I really must write get the hierarchy thread started soon!) And deconstructing a system into subsystems definitely has a reductionist quality to it. I tend to think that one of the fundamental differences is that reductionism has an inherent assumption of linearity underlying it. In a reductionist frame, the bits have to go back together again in such a way that what you learned in isolation is still the dominant thing to be known, this seems to obviate any cross terms or feedback relationships. In a systems approach it is not assumed that the role of any box can be understood completely on its own. It might be useful to send signals through a box in isolation in order to understand its transforming properties, but by keeping track of and focusing on connections in a systems approach, the "putting back together" problem is always under consideration.

Begin Aside
If any one is actually reading this, I would love some feedback on my equating reductionism with linearity!
End Aside

So wrapping up for tonight - Reductionism has taught us a lot about how the world works and it will teach us more. But by adding a strong measure of systems work to our knowledge producing endeavors, we can gain an richer understanding of problems by focusing on interactions among subjects of interest.

May 07, 2003

The Grey Area

It is remarkable that I have gotten this far without introducing the following diagram. I call it a disciplinary map and use it to help me think about how to design interdisciplinary teams to address Earth systems problems.

The traditional disciplinary organization of the university is represented by the lobes in the figure. My own discipline, geophysics, maps into the blue lobe along with the other physical sciences such as physics and chemistry. The magenta lobe represents the life science which primarily are biology and medicine. These two lobes together make up what is traditionally thought of as the Natural sciences. The yellow lobe labeled "Human Processes" is the region of Simon's artificial and contains the social sciences, engineering and the humanities. At the intersections of the main lobes are regions that represent interdisciplinary enterprises. Of particular notice is that I map ecology into the purple region between physical and biological processes.

Begin Aside
Exercise for the reader: Where does mathematics map?
End Aside

An example of how problems might progress through the diagram as we learn more about how Earth works is provided by climate change. The problem of increasing CO2 concentration in the atmosphere was first noticed by atmospheric chemists (blue lobe). Understanding the resulting greenhouse warming requires understanding both the CO2 chemistry of the atmosphere and the human processes associated with fossil fuel burning (yellow lobe) and thus maps into the green region. Continuing on with the problem to understand the resulting impacts and the carbon system as a whole requires that we also understand the biological systems that sequester and otherwise move carbon around; this is an Earth systems problem and maps into the grey area.

As you move from the edges of the diagram to the center, interactions among process studied by different disciplines become increasingly important. As we progress we need to work in all regions of the diagram, but as human impacts on the functioning of Earth systems become increasingly important, we must pay increasing attention to the grey areas.

May 05, 2003

Natural and Artificial

The Natural and The Artificial

Herbert Simon makes a distinction between the Natural and the Artificial that I have found useful over the years. To first cut, the Natural is everything that can be separated from human intentionality and the Artificial is that which reflects human intentionality. In more detail:

  • Artificial things are synthesized by humans

  • Artificial things may imitate appearances of natural things

  • Artificial things can be characterized in terms of functions, goals, adaptation

  • Artificial things are often discussed, particularly when they are being designed, in terms of imperatives as well as descriptives

  • Natural things are everything that is leftover

    Over the last several decades the Artificial has encroached steadily on the Natural. It is sometimes stated that there are no ecosystems on Earth that are untouched by Human influence (indeed to the extent that those systems have plants that have physiological response to the concentration of CO2 in the atmosphere, this statement must be true). But untouched does not imply that the systems themselves are now artificial; the details of their function may be changed, but it is still independent of human intentionality. That distinction and argument is fairly straight forward in the Arctic, but what about in Manhattan?

    As I have thought about the urban environmental systems, I have begun to question the usefulness of Simon's distinction in such highly engineered environments. I can not quite convince myself that the Natural has been completely swamped (after all the winds still obey the laws of fluid dynamics), but at some level it seems that the distinction has been thoroughly blurred.

    Consider the trophic structure of a city. To what extent does it reflect human intentionality? The biodiversity is extremely low with a small number of very hearty species dominating the biomass. Those hearty species depend in large part on human refuse for their food. Thus we might argue that while very large parts of the urban ecosystem imitate the appearance of natural ecosystems (albeit sick ones perhaps), they are in fact synthesized by humans. The ecosystem of a city is in large part the a by product of the rest of the city's designed elements. The trophic structure of the NYC subway is an unintended consequence of the need to move a remarkably large number of people around a very small and congested environment; it trophic structure in that environment natural or artificial? In terms of imperatives, we try to destroy it constantly.

    There has been a lot of discussion about whether humans are parts of the natural system. To my mind that is a question that does not have a useful answer. Humans are clearly a part of the singular Earth system, but we are a special part. We have intentionality that is of particular importance to us. So where there was a time during which humans might consider themselves apart from nature, we are now increasingly intertwined with nature despite (or perhaps because) of our efforts to isolate ourselves from the vagaries of Earth's natural systems.

    Wrapping up, I think that it is important that we carry the notion of a distinction between that which reflects human intentionality and that which is independent of it, but that we also recognize that that distinction maybe coming increasingly difficult to discern. This blurring increases the importance of developing decision-making processes that recognize the potential for far reaching human impacts on Earth's functioning.

  • May 03, 2003

    Name Change

    I change the name of my blog today from Planetary Management to Earth Systems Management. The change reflects a couple of things. First I did a Google search on "planetary management" and got a lot of stuff that was oriented to imaginary planets rather than to the very real one we currently (and for the foreseeable future) live on. I want to steer clear of fictional enterprises because I believe that we really are making management decisions (through action or inaction) at the scale of Earth and I do not want my ideas to be confused with fiction (despite that fact that I have on occaision been known to make things up).

    The second reason that I changed the name is that I wanted to get a plural noun into the title. The expansion of the number of disciplines studying Earth's functioning clearly indicates that there is more than one system at work on our planet. The disciplinary focus has taught us much about those systems. It is now time to work on understanding the interaction of those systems.

    In particular our management decisions are likely to reflect the mode of our inquiry. For example fisheries managment decisions in the mid-20th Century focused only on the lifecycle of individual species primarily because that is what fishery biologists were interested in. We now know that environmental factors such as El Nino variations and inter-species interactions such as trophic structures are also important in fish stock dynamics and our management strategies are beginning to reflect this.

    Begin Aside
    Imagine a surface of constant but very low nitrogen concentration. If that concentration is low enough, most of Earth's atmosphere would be inside of it. For all intents and purposes, that surface would define a closed system with respect to mass (that is all of Earth's stuff would be inside of that surface (this ignores some gasses going up and some rocks coming down). Energy would cross that boundary and in the long run the balance of the energy fluxes that cross that surface are is all that we have to go on.
    End Aside

    I mentioned that I wanted to get a plural noun into the title to call attention to the fact that there are multiple systems to be considered. But as I have also alluded to, at some large scale there is a single Earth System. How we parse that singular system is crucial to how we will understand it and how we will make decisions that affect the evolution of the singular and plural systems.

    May 02, 2003


    I referred to the "outlaws of Guangzhou" a few nights ago (SARS entry) and would like to return to that briefly. In Kingdom of Fear Hunter S. Thompson quotes Pablo Escobar, "the difference between a criminal and an outlaw is that an outlaw has a following." Thompson goes on to note that perhaps Escobar's only real crime "was that the the product his business produced was seen as a dangerous menace by the ruling Police & Military establisments of the U.S. and a few other countries that were known to be slaves and toadie of U.S. economic interests."

    Begin Aside

    I think that Hunter S. Thompson is one of our unsung brilliant writers. He can be over the top, but his writing is often brilliant and his political anaysis is very good.

    End Aside

    The reason I bring this up is that the image I have of the activites of Guangzhou is of lawlessness not in a gangster sense, but in an operating-outside-of-the-norms sense. That was what I was going for in juxtaposing Guangzhong and Zhongnanhai.

    In a recent Wired magazine article Arthur Kroeber characterizes the Guangzhou region as follows: "An untamed technology boom is sweeping through China's Pearl River Delta, where cheap labor, mass production, police thugs, and get-rich-quick dreams rule. It's a terrible, horrible, lawless frontier. And it works." The image is one of raw capitalism in the shadows of communist China and within commuting distance of Taiwan. In this teeming economic cauldron new products, ranging from inexpensive computers to hybrid viruses, are being exported to all parts of the globe with little or no overarching framework.

    So the point tonight is that strong systems can emerge in the absence of guiding frames, but there are costs associated with such unfettered, large scale activites. (I can see that I am going to have to return this yet again, but enough for tonight.)

    May 01, 2003

    Finiteness of Earth

    One of the major changes that has occurred in the relationship between humans and our planet is the realization that Earth is finite. I placed a scale on Earth’s size a few days ago – the radius of a sphere of equal volume. With a radius of about 6000km, that sphere has finite volume. Now that volume is large and for most of human history it was so large as to be essentially infinite. Resources could be extracted and wastes disposed of at no apparent cost to the present or future. This was true because the rates of extraction and disposal were small compared to the overall size of our planet.

    As our numbers and capacities have increased, the fluxes of material through our societies have increased to the point that we can now “feel the edges” of Earth’s capacity. Assumptions of infinite sources and sinks must now be replaced with boundary conditions on capacity.

    If we assume that there are 5 billion (5e9) people (I know there are more than 6 billion, but 5 is such a nicer number to work with) and that Earth has 1e14 square meters of ice-free land, then everyone gets about 2e4 square meters of land (about 4 American football fields) to produce and absorb all of the inputs and outputs that they need to survive.

    Water is another resource that is limiting for humans (actually all life on Earth). Earth has a lot of water, but 97% of it is in the oceans. Of the remaining 3%, 70% is tied up in glaciers and permanent snow. This leaves about 1% of the total water on Earth for all of human needs. Indeed a significant proportion of Earth’s inhabitants do not have access to adequate water resources.

    Nitrogen provides an example of human capacity to rival that of natural systems. I don’t have the exact numbers at hand at the moment, but very roughly, human activities are responsible for a doubling of the magnitude of the nitrogen cycle. In the case of nitrogen, humans have overwhelmed the natural system and we do not yet know what the effects of this impact will be.

    Finally consider food. I sometimes start a discussion of environmental policy with our cheery friend Malthus. He certainly was concerned about issues of finiteness and rooted his policy recommendations in the assumption that our ability to reproduce would soon outstrip our ability to produce food. The doom and gloom that he expected has, for the most part, not developed because he did not consider the impact of technological innovation on the productivity of farmers. Ignoring infrastructural issues related to the distribution of food, we have the capacity to produce enough food for Earth’s current population.

    This leads to the question of whether there is a largest number of humans Earth can support. Certainly there is an upper limit related to the physical space that each person must occupy, but well before that limit, is there a limit based on the ability of Earth systems. Joel Cohen addressed this topic in his book How Many People can the Earth Support? His answer is that it depends on how well you want those people to live. Thus while there are certainly physical limits, there will be cases there our values and desires establish the upper limits of our activities.

    The case of Malthus brings up and interesting counter argument to what I have written so far. There are those who will argue that Earth is in fact not finite. There argument is rooted in the idea that technological will always advance faster that resources are depleted and provide substitutions etc. I find these arguments to be hopeful by ultimately not helpful. It is true that the Malthusian disaster has been steady pushed into the future by technological innovation, I think it is overly optimistic to believe that we have nothing to worry about because technologists will always save the day.