CSCI 1210

Lecture notes on Modeling and Sustainability

 

Prologue: the end of Cheap Oil

This part of the lecture finishes an incomplete previous lecture, but also leads into the main topic. As we will see, one possible threat to the sustainability of human civilization may the shock of running out of nonrenewable resources such as oil.

The Hubbert Peak

M. King Hubbert was the American geologist who, in 1956, correctly predicted that oil production in the 48 contiguous states of the US would peak in 1969. This was quite an accomplishment because it is very unusual for models to make such precise predictions of future events. Hubbert’s model was based on the following assumption:

n   Oil production follows bell-shaped curve

This assumption implies (looking at the picture below)

n   Maximum production occurs when 50% of total oil has been extracted.

In the bell-shaped curve below, the height of the curve represents the rate of oil production in barrels per year, and the total area under the curve is the total amount of oil produced. The point of maximum production is the highest point of the graph. You can see by the symmetry of this graph that half the area lies to the left and half to the right on the maximum point.

 

Hubbert’s original estimates

This is an illustration from Hubbert’s article in Scientific American in 1971. Here Hubbert was trying to predict the year of peak oil production in the entire world, not just the lower 48 states.

The location of the Hubbert Peak depends on the (unknown) ultimate amount of oil present. The graph above shows two bell-shaped curves, based on two different estimates of the total amount of oil originally present. The blue curve represents an estimate of 1,350 billion barrels and the black curve, 2,100 billion barrels. These are estimates of the total amount of oil originally present on the whole Earth, including oil which has not yet been discovered.  As you can imagine, this number is hard to estimate and there are differing opinions as to its value.

Note that the blue curve has a much higher peak than the black curve, but the peak comes only a few years later.  The larger original stock of oil allows society to continue increasing its oil consumption at nearly-exponential rates, which quickly burns up the extra 700 billion barrels of oil.

Also note that even the optimistic blue curve shows world oil consumption peaking in 2000, which is not what actually happened. Clearly, some unexpected real-world factor is creating deviations from Hubbert’s model.

Deviations from Hubbert model:

What is causing reality to deviate from Hubbert’s predictions? There are several possibilities:

n   Hubbert’s Basic model (bell-shaped curve) could be wrong

n   The model could be basically correct, but external factors such as the OPEC cartel could skew the results

n   There could be much more “conventional” oil and gas than in the blue curve estimate

n   There could be extensive “non-conventional” oil supplies: oil shales, tar sands, converting coal into oil, etc.

The OPEC effect: delaying the peak

 

The left side of this graph shows a “notch” in the rising Hubbert curve that occurred in the 1970’s. This was the time that the OPEC oil cartel was able to control the market and jack the world oil prices way up. The result was that oil consumption was slowed down for about 10 years. Meanwhile, the world made a concerted effort to find new sources of oil outside of OPEC’s control.

Eventually, enough non-OPEC oil sources came in line so that OPEC was no longer able to control the market. At this point you can see that oil production begins to rise at nearly the same rate as it had been before the OPEC interruption.

The OPEC factor was completely missing from M King Hubbert’s original model, which dealt only with the inherent limits posed by the original oil inventory. We might assume that aside from such “oil shocks” that result from factors outside the Hubbert model, the model may continue to predict the long-term trends of oil consumption.

Note also that the OPEC shock basically pushed most of the curve about 10 years to the right. Thus, we might now expect a Hubbert peak approximately 10 years later than Hubbert’s original estimate, or about 2010. (It will be less than 10 years because even with reduced oil consumption, a substantial amount of oil was consumed in the 10-year “notch” period).

The graph shows two possibilities for future oil production. The sharp peak is a classic Hubbert peak. The flat plateau is based on the possibility of a second OPEC shock that would suddenly raise oil prices. Higher prices would decrease consumption and make the world’s supply of oil last longer.

Why is a second OPEC shock considered a possibility? Because we know that most of the world’s remaining oil is in the Middle East (see below). As other sources run out, the world will become increasingly dependent on Middle East oil. The ability of OPEC to raise prices depends on how much they control the market. Some experts believe that whenever OPEC has at least 30% of the total world production, they are potentially in position to launch another big price hike.

Why is the possible second shock represented as a plateau rather than a notch? Because there is no model for predicting the detailed “history” of a second oil shock. A plateau is the simplest possible scenario, but who knows what would actually happen?

Adding non-conventional oil

Non-conventional oil such as tar sands (Alberta) and super-heavy crude (Venezuela) is more expensive to extract than conventional oil.  The chart above includes 750 billion barrels of non-conventional oil added to the original 2000 billion barrels of conventional oil. Note the OPEC “notch” in the 1970’s.

You can see that the purple curve (non-conventional oil) peaks far to the right of the black curve (conventional oil). This is because we would extract the conventional oil first (it is easier and cheaper).  The green curve represents total oil, conventional and non-conventional.

 Note that adding the additional 750 billion barrels makes the peak of the green curve much higher, but shifts the peak only a few years to the right. Again you see the effect of exponential growth: even substantial additional supplies will be quickly burned up if exponential consumption growth continues.

How much oil is there??

This graph shows 65 published estimates ultimate global oil resources from 1942 to 2000. Note that apart from the early period (before the magnitude of the giant Middle Eastern deposits was appreciated), most of the estimates have been close to 2 trillion barrels (that’s 2000 billion barrels).

Recently the United States Geological Survey (USGS) estimated total world resources at 3.3 trillion barrels. As you can see from the comparison of estimates, this is an unusually optimistic number. Recall that the size of ultimate global oil resources is the key unknown for predicting the Hubbert peak.

Where is the Oil?

This chart from the US Department of Energy shows how the Middle East dominates known oil reserves. Notice these are reserves (known oil in the ground) rather than resources (oil that is yet to be discovered). Less-explored regions such as Africa could have a surprising amount of oil. Still, it is likely that Middle Eastern oil will increasingly dominate the global picture.

Future political developments in Iraq could have a major influence on the possibility of a second OPEC shock (see above). If the future government of Iran sided with America, Europe and Japan rather than with OPEC, the power of OPEC to control world oil prices would be greatly reduced. Also, the political stability of Saudi Arabia is a matter of concern.

Our government claims the war in Iraq had nothing to do with oil. Whether you believe this statement or not, it is inevitable that considerations of oil will affect US national security policy in the Middle East.

 How much oil in Iraq?

Comparing estimates of oil in Iraq gives a sense of the uncertainties involved:

n   Saddam Hussein’s deputy oil minister: 300 billion barrels (bbl)

n   Council on Foreign Relations: 220 bbl

n   US Geological Survey: 120- 160 bbl

Years of poor management under the Saddam Hussein regime may have reduced the ultimate amount that can be recovered from Iraq’s oil fields. See http://www.occupationwatch.org/article.php?id=2005

How long till the Hubbert peak?

 

This chart shows the Hubbert model fitted to two widely different models of ultimate recoverable oil resources. The vertical axis represents world oil production in millions of barrels per day.

Once again, exponential growth rears its ugly head. The difference between the two curves is 2000 billion barrels, or about 2.5 times the total amount of oil produced from the first oil well in 1859 through 1998. As you can see from the graph, this gigantic amount of extra oil would move the oil peak forward only about 20 years.

Part I: Sustainability, Dynamic Systems, and the World3 Model

What is sustainability?

n   Humans living in a way that does not diminish Earth’s capacity to sustain life

n   Alternatively: living within Earth’s ecological carrying capacity

This sounds simple, but Earth’s carrying capacity for humans is very hard to define.

Are we going through a global ecological crisis? In the US, this question was much more prominent in the 1970’s and 1980’s than it is today. In my opinion this reduced level of public concern is due to a more conservative political culture, not to a more optimistic scientific assessment of environmental problems.

Results of logistic model

n    Population makes a “soft landing” right on the carrying capacity

n    When population is small, positive feedback rules

n    As population increases, negative feedback takes over -- the system feels its limits.

The logistic is our simplest model of a dynamic system that cannot undergo continued exponential growth. Compared to the other possibilities discussed below, this is the most optimistic scenario for future population growth.

Negative Feedback with Delay

n   System responds to the limit, but only after a delay.

n   Result: system overshoots and oscillates around the limit.

This is the next-simplest dynamic model we have studied. If the future human population curve looked like this, it would probably be a very evil future. The peaks in the graph would be global overpopulation events, and the dips would be periods of mass famine returning the human population to within Earth’s carrying capacity. Not good.

Overshoot and collapse

   

n    Previous model assumes carrying capacity is constant

n    What if a severe overshoot degrades the environment?

n    Carrying capacity might be permanently reduced

n      Image:http://www.dieoff.com/page80.htm

If this is what the human future looks like, it would be a total nightmare scenario: a wasted planet with a residual human population, likely reduced to barbarism. Quite a few science fiction movies are based on this theme, which suggests that this fear is more present in our hearts than we would like to admit.

 

Humans are different…

Human carrying capacity is hard to define, because…

n          Technological changes affect food production

n          Complex social factors affect reproduction and  population

These considerations show that the ecological models discussed above, which might be somewhat valid for animal populations, definitely are not adequate for humans.

UN world population projections:

This graph from the United Nations Population Fund shows optimistic projections of the future growth of world population. (We discussed this in more detail in an earlier lecture). Note that although world population continues to increase, it is no longer increasing exponentially.

The latest estimates project a future world population leveling off at about 9 billion. This is about 50% more than our current world population of 6 billion. Note also that North Americans and Europeans will make up an increasingly smaller portion of the total world population. This is because our population is already leveling off, while the populations of Asia, Latin America, and Africa will continue to grow for some time.

n   World population may have passed its inflection point in 1970.

n   Herman Kahn called this time “The Year Zero”

Kahn, who was a bit of an unusual scholar (see his classic, “On Thermonuclear War”), nonetheless had an interesting point here. A society to the left of the inflection point is dominated by exponential growth into an apparently limitless environment. To the right of the inflection point, society is dominated by the approach to the limit. Kahn was very optimistic about this period, which he saw as characterized by increasing global affluence, democracy, and human well-being due to economic development.

The key point to take home from this chart is that the human “population explosion” is not the key threat to Planet Earth. Although accommodating an additional 3 billion Earthlings will challenge our creativity, we have 100 years to accomplish this task. Problems with over-consumption may be a much greater danger, as we will see below.

 

World3: The Nightmare Scenario

n     World3 model created by MIT systems group for the Club of Rome

n     Model updated, 1990

Graphic: www.dieoff.com

This graphic is based on the book Limits to Growth, which appeared in 1972 shortly after the first Earth Day. The authors were the first to raise the possibility of an overshoot-and-collapse scenario for global human civilization. To get an idea of the magnitude of this disaster, recall that the worst human calamity of the 20th century was World War II, which killed perhaps 50 million people. On the scale of this graph, the death of 50 million people would be a blip in the curve of about 2 pixels. You would not even notice it unless you looked closely.

The World Model nightmare scenario burst into human consciousness 30 years ago and has haunted the dreams of millions of people, including myself,  ever since. In what follows we will deconstruct the World Model (the current version is called World3) to find the source of the nightmare prediction. Then we will discuss what, if anything, needs to be done to make this prediction not come true.

World3: A complex model

This is the population submodel of World3. It resembles the age-structured population model that we discussed earlier in this course. Note that the population is broken into age classes 0 to 14, 15 to 44, and so forth. This is a much coarser grid than we used in our Excel model. Even though World3 is very complex, it is also extremely oversimplified. That’s because the world system is so big!

World3 Natural Resources

The purple sub-model represents nonrenewable resources. These are represented by the purple box (a stock in Stella). The flow “natural resource use rate” is one-way, gradually emptying the original stock.

The green sub-model represents resource efficiency technology. As resources are used up, the system responds by adding technology to improve efficiency. Notice there is a delay in applying this technology, which means that the system will tend to overshoot. In other words, by the time resource depletion becomes a serious problem, the system reacts but it is too late to prevent the crash.

World3 Industrial production

Industrial production is primarily dependent on the accumulation of industrial capital. More production enables the system to accumulate more capital, which in turn accelerates production. This is the primary positive feedback loop driving World3 to disaster.

Take a closer look at the flows going into and out of the industrial capital stock. The flow going out, “ind cap deprec,” is depreciation. That is, the stock of capital gradually wears out. The flow going in, “ind cap invest,  is investment. The stock of capital will grow as long as the rate of investment exceeds the rate of depreciation.

Now look at the investment flow, “ind cap invest.” This depends on the total amount of industrial output, which makes sense: the more the economy is producing, the more it will invest. But what about the other factor, “fioa ind”? This mysterious variable is the fraction of industrial output allocated  to industry. In World3, industrial output must be allocated between investments in industry, investments in agriculture, and investments in extracting natural resources. This factor turns out to play a major role in causing the collapse, as we will see.

World3 Agriculture

The agricultural sub-model of World3 is quite complex. Basically agricultural production depends on:

n  The mount of arable land (land devoted to agriculture)

n  Agricultural investments: tools, fertilizer, etc.

n  Loss of land fertility due to erosion

n  Loss of land fertility from pollution

All of these are very hard to predict!

World3 Persistent Pollution

The red sub-model above represents the life and death of Persistent Pollution, which is defined as pollution that stays in the environment for a long time (such as carbon dioxide, which causes global warming). Because World3 is so oversimplified, the model contains only a single generic pollutant.

The green sub-model represents pollution control technology. Note the arrow leading from “ppoll index” into the green sub-model. The variable “ppoll index” represents the amount of pollution in the environment relative to the amount of pollution in the year 2000. The arrows from “ppoll index” lead to the flow that generates pollution technology. In other words, the model assumes that society reacts to rising pollution levels, instead of preventing pollution before it happens. Because of the inherent delays in deploying the new pollution technology, the system will tend to overshoot its goal of appropriate pollution levels.

Also note that pollution technology is represented as a stock. Think of big warehouses filled with filters, catalytic converters, and other pollution control technology. In World3, you can add more of these filters, but you cannot make qualitative changes: switching to new industrial technology that does not pollute in the first place.

Deconstructing the nightmare scenario:
what happened?

To investigate the root causes of population collapse, we use the Stella graph tool. This allows us to choose up to five of the 100+ variables to plot on a chart. This chart shows food and population. We see that the population collapse is apparently caused by a decline in the food per capita.

Note that for event A to “cause” event B, A must occur before B. Here we see that the drop in food per capita occurs before the population drops.

What factors affect food supply?

Returning to the model, we see that food supply is determined by the amount of arable land,  the land yield per acre, the fraction of available land that is harvested, and the amount of harvested food that is lost in processing before it is sent to consumers.

To investigate the cause of the food supply decline, we set up another chart to graph these variables.

Why does food supply decline?

This chart shows that available land declines somewhat, but land yield declines much more. So we will now focus our investigation on land yield.

What factors affect land yield?

We have skipped the step where we go back to the Stella diagram to see which factors affect land yield. That diagram showed that degradation of fertility due to factors such as erosion affects land yield. Land yield is also affected by the amount of agricultural inputs, such as fertilizer.

This chart appears to show a huge decline in fertility, but look at the scale on the right. Actually fertility only declines from 600 to 540. On the other hand, agricultural inputs collapse from a peak of nearly 170 to almost zero. So we will focus our investigation on agricultural inputs.

What happened to Agricultural inputs?

Here we see that the collapse in agricultural inputs corresponds to a collapse in industrial output. This makes sense: without industrial output, we cannot make fertilizer!

What factors affect industrial output?

Remember up above when we talked about available capital being allocated to agriculture, industry, and resources? Here is where that allocation problem comes back to cause the collapse, as we will see in the next slide.

What happened to industrial output?

Aha! Here at last is the root cause of the collapse, which has been buried under the complexities of the World3 model. What has happened is this: the model has been designed to make society absolutely dependent on nonrenewable resources. When these begin to run out, society directs more and more of its limited capital to extracting more nonrenewable resources.

Malthus in, Malthus out!

This is the primary critique of World3: it is programmed with the assumption that industrial output depends on a finite stock of nonrenewable resources. No matter what other assumptions you make, this model society will eventually collapse when the resources run out. In this case it happens this way:

1.    Nonrenewable resources run out…

2.    Capital is diverted to resource extraction

3.    Less capital for agriculture

4.    Yields fall, leading to famine and death

 

But is this realistic? In part 2 of this lecture we examine the key question: what, if anything, are the limits faced by human society?