CSCI 1210
Lecture notes on Modeling and
Sustainability
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.
This assumption implies (looking
at the picture below)
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.
The
location of the
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.
What
is causing reality to deviate from Hubbert’s
predictions? There are several possibilities:
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
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?
Non-conventional oil such as
tar sands (
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.
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.
Comparing estimates of oil in
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.
This sounds simple, but
Earth’s carrying capacity for humans is very hard to define.
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.
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.
These considerations show that
the ecological models discussed above, which might be somewhat valid for animal
populations, definitely are not adequate for humans.
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
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.
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.
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.
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, “
Now
look at the investment flow, “
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.
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.
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.
This chart shows that
available land declines somewhat, but land yield declines much more. So we will
now focus our investigation on 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.
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!
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.
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.
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: