Often times exponential growth is plotted as a straight line on a semi-log plot. The Y-axis is logarithmic and the X-axis is linear. Here is an example:
In exponential growth, the rate of growth may well change, but the growth is still exponential!
What kinds of things grow exponentially?
Clearly exponential rates of growth are an integral part of the planning process. Different aspects of a growing population have different exponential growth rates and these need to be considered.
For instance, suppose your urban area is growing
at the rate of 5% a year. How does this translate into the
Whenever schools get crowded, freeways get jammed, airline hubs get crowded, oil gets used up, there are no more available phone numbers, the federal debt goes beyond recovery, etc, etc is an indication of poor planning and trend extrapolation.
In a nutshell: there is no reason that we should ever be surprised at the rate of resource utilization. If we simply pay attention to past history, in general, its a fairly good guide for future resource use.
The difference between linear growth (constant number of units
growth per year) vs exponential growth (constant percentage
increase) is difficult to see initially, if the exponential
growth rate is small.
We can use the
Graphical Tool to help understand this.
Here is some data:
First we try a linear fit which will clearly be seen as bogus.
We can use the Statistical Graphical Tool to help understand this.
Here is some data:
Then we will try an exponential fit with 10% growth rate to see its much better.
So in this case its obvious that the growth rate is exponential but in some other case such as the population data for California its not so obvious!
What do the latest models show? Here we see the predicted temperature increases on the land surface when the data is analyzed in cumulative time slices.
Later we will compare the models with some data.
Current concentration of CO2 is 360 ppm
Current concentration of CH4 is 1.8 ppm or 25x1.8 = 45 ppm CO2 equivalent. This is 12% of CO2 concentration and its growing 2.0 -- 2.5 times as fast.
The methane content of our atmosphere has more than doubled since pre-industrial times and in the last few years has shown a small decrease (no one knows why). If the sources of methane deposition stay constant then we will not have a problem. This seems unlikely however as anthropogenic soruces of methane production (e.g. rice,cows,sewage) continue to rise. Eventually (100-200 years) these sources will dominate over natural sources of methane emission.
More About Methane:
Methane Removal Mechanism (some estimates suggest the methane residence time is up to 10 years so there is no short term equilibrium control):
CH4 + 2O2 CO2 + 2H20
Is this apparent reduction in the rate of methane build up due to a threshold effect that is does methane build up until the atmospheric chemistry is temporarily accelerated? Was Pinatubo to blame?
An expert's view
Ice Core Data:
An example of Myth Perpetuation: Deforestation of the Amazon Rain Forest greatly contributes to the Greenhouse effect:
Note - the biggest uncertainty with the whole carbon cycle is
the role of deep ocean transport:
uptake of CO2 primarily depends on how fast CO2 can be transported downwards from the ocean
surface; if "too much" CO2 accumulates in the surface layers at one time, absorption slows down.
Global data on the concentrations of CO2 in the oceans are still very sketchy, and many contributing
factors, such as ocean biology, are still not well understood. Absorption is also known to depend on
local weather conditions. For example, winter storms accelerate CO2 exchange by exposing sea-water
to the atmosphere through bubbles and spray.
The oceans' uptake of CO2 primarily depends on how fast CO2 can be transported downwards from the ocean surface; if "too much" CO2 accumulates in the surface layers at one time, absorption slows down.
Global data on the concentrations of CO2 in the oceans are still very sketchy, and many contributing factors, such as ocean biology, are still not well understood. Absorption is also known to depend on local weather conditions. For example, winter storms accelerate CO2 exchange by exposing sea-water to the atmosphere through bubbles and spray.
Simplest Prediction is increase in global mean temperature. Can We see evidence for this in the Data?
Role of clouds is crucial --> Net Cooling or Warming? --> There is general consensus that cloud cover will increase as the capacity for the atmosphere to retain water increases with increasing temperature.
What does the actual data look like?
Long Term Temperature Trends:
When positional data is combined with temperature data and timesliced in this way - it seems clear the Global Warming is occurring. This conclusion was reached by a National Academcy of Science panel in Sept. 1995 and is accepted by most.
What about Stratospheric Cooling?
The temperature of the stratosphere - an upper region of the atmosphere that extends from about ten to fifty kilometers (six to thirty miles) above the surface of the Earth - will be significantly COOLED.
The cooling comes about through the combined effect of increases in carbon dioxide and the observed depletion in stratospheric ozone, and the manner in which the two gases absorb and re-emit energy. Opposite in sign to what is expected near the ground, the change has been predicted by models and has now been OBSERVED. As such, it provides potential early evidence of greenhouse warming.
Some Additional Internet Resources:
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