More Unusual Weather in December, 2010, and January, 2011

More unusual weather events! Probably only a coincidence.

Heavy snows in United Kingdom, enough to shut down Heathrow airport for several days. They've had three years in a row of unusually cold, snowy winters there. "Normally" they have little or no snow in London; but they are considering investing in snow removal equipment in defense against what they call a "step change" in weather.

Huge rainfalls in Los Angeles, washing away hillsides and homes. Well in excess of 10 inches of rain in 2 or 3 days.

Deep freeze on the east coast of the US, down to Florida, endangering the citrus crop. Christmas storm in New York and New England that dumped a lot of snow and produced hurricane force winds off the New England coast.

Winter tornadoes in Arkansas and Missouri, followed closely by snow that virtually blanketed the south, from Florida to Texas.

Massive flooding in Australia, putting the northeast state (province?) of Queensland under water. Water covered an area the size of France and Germany combined. Snakes infested the flood waters.

Massive flooding in Brasil, rivers raging, at least 500 people killed.

Wish all these coincidences would just stop! It is greatly inconveniencing us.

Some Thoughts on Exponential Growth

We hear the phrase, "exponential growth" a lot these days, because the phrase describes the manner in which a number of quantities are increasing in time. For example: bank balances; debt; the economy; world population; the extinction of species; the amount of carbon dioxide in the atmosphere; the melting of ice reservoirs are all increasing exponentially with time. The amount of water vapor that the air is capable of holding increases exponentially with temperature. Something grows exponentially when it increases in amount by the same fraction (or percentage) during each successive equal unit of time. Thus a bank account that earns 5% per year interest increases in size each year by 5%, or the fraction 0.05. You will here it said that exponential growth involves increase at a constant rate. This is inaccurate. Rate is the change in amount of something per unit of time. Thus if you travel 10 miles in 10 minutes, you are traveling at a rate of 1 mile per minute, or 1mile/min. Something that grows at a constant rate increases linearly, not exponentially, in time. Exponential growth results in a graph of amount versus time that inexorably curves upward. The increase is much more rapid than linear.

For example, suppose you are growing bacteria in a petri dish. Bacteria grow exponentially. Let's say that at the beginning, you start with 1 bacterium in the dish, and that these particular bacteria divide every minute. After 1 minute, you will have 2; after 2 minutes, you will have 4, and so on:

Time, minutes          Number of bacteria in dish

0                                  1

1                                  2

2                                  4

3                                  8

4                                 16

5                                 32

6                                 64

7                                128

You can see that with each successive minute the number of bacteria doubles from the number in the preceding minute. Here's a graph of number of bacteria on the vertical axis and number of minutes on the horizontal axis. Notice the inexorable upward curving. This curve is sometimes called a "hockey stick."

Generally, if a quantity is growing by a certain fraction, f, in each successive equal unit of time, the size of the quantity after n of these units of time have passed is calculated using the following relationship:

Size after n time units = Initial size * (1 + f)^n.

The symbol ^ means that the n is an exponent. As a concrete example, suppose that you start with $100 in a savings account and that you earn 4% interest compounded annually (yeah, I know--dream on!). How much will you have in the bank after 5 years?

Amount after 5 years = $100*(1 + 0.04)*(1 + 0.04)*(1 + 0.04)*(1 + 0.04)*(1 + 0.04) = $121.66

Yeah, 4% is a lousy interest rate. Note that we have multipled by (1 + 0.04) 5 times , which is what (1 + 0.04)^5 means. After 5 more years, your balance will be $148.02. Note that the amount of increase is bigger than the amount of increase in the first 5 years.

An interesting thing to calculate for a given fraction of increase is the amount of time required for the original quantity to double. In other words, how many time units must pass before the quantity is twice as big as it was initially? This can be estimated pretty easily from the following formula:

Number of time units for doubling = 70/percentage of increase = 0.7/fraction increase = 0.7/f

It will take about 17 years for your balance to double. It will double again in another 17 years, and will then be about 4 times larger than the starting balance.

The key thing about exponential growth is that quantities grow along a path that curves upward in time. Things can get unmanageably large pretty quickly. People don't get too concerned at the idea of an economy that grows at the rate of 5% per year, because most people think in terms of linear growth when they see this statistic. But this meant that 14 years, from now, the economy will be twice as large as it is now. And 14 years after that, it will be 4 times larger than it is now. If the economies of all of the developed countries are growing exponentially (most of them are, particularly those of China and India, which are growing at double digit percentages), doesn't it make sense that the raw materials (metals, wood, fossil fuels, minerals, rock, etc) consumed in this growth will be used up in very short order? What will happen to our growing economies then? Think about it.

Global Warming Effects of Breathing

This morning I did a very interesting calculation of the total amount of carbon emissions produced by the breathing of human beings. I came up with 3.1 billion tons of carbon (not CO2) per year, assuming 6.7 billion people in the world, a lung tidal volume of 0.5 liters, 15 breaths per minute, that air is 1/5 oxygen, and 100% efficiency in converting inhaled oxygen to exhaled CO2. Note that this amounts to about 1/3 of the annual world fossil fuels emissions of 9 billion tons of carbon! Assuming further that 50% of our exhaled CO2 enters the atmosphere, it would increase atmospheric CO2 concentration by 0.75 ppm per year. Even if we didn't burn any fossil fuels, would our breathing alone cause global warming? Is this another argument for limiting population growth?

Some Amazing Facts About Fossil Fuel Use, GW, and Other Things

As of 2000, total annual global emissions from fossil fuels were 8.7 billion tons of carbon (1 ton = 2000 pounds). About ¼ of this was from the US. This is 800 times more than in 1800.

Since 1750, the total CO2 emissions from fossil fuel use has been 280 billion metric tons of carbon (1 metric ton = 2200 pounds).

The global per capita emissions average is 1.23 metric tons of carbon per person per year. The average in the US is 5.6 metric tons of carbon per person per year.

In the US, half of the electricity is produced by burning coal. A billion tons of coal (6700 pounds per person) is burned in US every year.

In 2005 US coal-fired power plants generated about 50 tons of mercury.

Coal burning is the largest producer of greenhouse gases (GHG). It also produces soot (which kills 24000 people/year in US), mercury, lead, sulfur oxides (acid rain, aerosols). Annual health costs resulting from coal soot problems is $167 billion.

Atmospheric CO2 levels were 280 ppm in 1780, are 382 ppm now, and at the current rate of growth in use of fossil fuels will reach 950 ppm by 2100. To cause a 1 ppm increase in CO2 level, 2.12 billion tons of carbon (7.8 billion tons of CO2) must be added to the atmosphere.

19 of the 20 hottest years in the past 150 years have occurred since 1980; 2005 was the warmest year on record in the northern hemisphere.

Whereas average global temperature has increased 1.4 deg F during the 20^th century, the average temperature in Alaska has increased by 4 deg F since 1950, and 7 deg F during the winter in the interior.

11 deg F of global warming wiped out 95% of all species at the end of the Permian era, 250 million years ago.

Energy use in the US rose by 50% from 1970 to 2006. The population of the US also increased by 50% in this time period.

The Greenland and West Antarctic ice sheets are shrinking at more than 100 cubic kilometers (24.4 cubic miles) per year.

In the US, there are 225 million cars; this is 1.2 cars per licensed driver.

Burning 1 gallon of gasoline produces 17 pounds of CO2. A car getting 20 mpg and driven 15000 miles/year produces 6.4 tons CO2 per year.

The average human being produces 1.7 tons CO2 per year in the act of breathing. So the world population of 6 billion produces 10.4 billion tons CO2 per year (calculation assumes 0.5 liters of CO2 expelled per breath, 15 breaths per minute, and 2 grams CO2 per liter).

As of the end of 2010, about 85 million barrels of oil per day are produced (and consumed) globally.
Only 1% of travel in the US is by public transit (bus, train).

In 2007, 21% of the US corn crop was diverted to make ethanol for cars.

There are 17000 dams in the US producing 2.6% of the electricity.

A golf-ball sized piece of uranium fuel is energy-equivalent to 8000 barrels of oil, or 1200 tons of coal, or 22 million cubic feet of natural gas.

17% of the world’s energy comes from nuclear reactors.

For every terawatt-year of energy use, the number of worldwide fatalities was 8 for nuclear, 85 for natural gas, 342 for coal, 418 for oil, 884 for hydro, and 3289 for LNG. A terawatt is a trillion (a million million) watts.

Mankind used 16 terawatt-years of energy in 2005. Running at a power level of 1 terawatt for sixteen years produces 16 terawatt-years of energy.

There is sufficient uranium to power us for 50000 years at the current usage rate.

To provide 80% of our energy from nuclear power by 2050 would require building 100 2.5-gigawatt (1 gigawatt = 1 billion watts) plants per year between 2015 and 2050, giving a total of 3500 plants generating 8.75 terawatts of energy. This would cost $17 trillion, much less than our current total debt.

The single most important thing you can do to decrease your own CO2 emissions is to stop flying in airplanes.

The US has 4% of the world’s population, yet is responsible for 25% of the world’s greenhouse-gas emissions. In addition, we incarcerate 25% of the world’s prisoners.