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.

The True Cost of Gasoline

What are you paying for gasoline now? Around $3 a gallon, give or take a quarter? Yeah, us too. Pretty cheap isn’t it? You don’t think so? Think of the effort needed to produce it. The crude oil has to be retrieved, loaded into transport vehicles, and taken to a seaport. Here it has to be pumped into tanker ships, which have to carry it from the middle east (or wherever, Mexico, Venezuela, pick your favorite unstable region) to a US seaport, where it is off-loaded into tanker trucks and taken to a refinery. Here huge amounts of energy are expended refining the crude oil into various products that we can’t do without: gasoline, diesel, kerosene, engine oil, asphalt. Then the gasoline is loaded into trucks and distributed to the network of filling stations around the country. And it’s only $3 per gallon? That’s cheap! How can they sell it so cheap you might wonder. Well, its because the government subsidizes the oil industry. In other words, the government pays part of the price so that the oil industry can sell it cheaply to us. Because of course we wouldn’t buy so much of it if it were more expensive, would we? But the government wants to keep us all trucking along in our vehicles, spewing CO2, because it’s good for the economy for us to be out on the roads. The bottom line here is that the price we pay is artificially low—it is fake.

Suppose the government stopped paying subsidies to the oil industry. The price of a gallon of gasoline might double (just a guess) to $6 or so. Would we still pay it? We’d grumble, but we’d pay it. It would cost about the same as a gallon of fancy bottled water. But we still wouldn’t be paying the TRUE cost of that gallon of gasoline. There are a lot of things that are not factored in to the price we pay at the pump. Some of these are:

1)The cost of environmental damage due to CO2 emissions during extraction of crude petroleum.

2)The cost of environmental damage due to CO2 emissions during transport of crude petroleum.

3)The cost of environmental damage due to CO2 emissions during processing of crude petroleum.

4)The cost of environmental damage due to spills of crude petroleum, either at the drilling station (recent Gulf of Mexico incident) or during transport (Exxon Valdez).

5)The cost of environmental damage due to CO2 emissions resulting from burning gasoline in automobiles.

6)The diminished quality of life for future generations who will have to survive on a diminished, depleted, hot earth. The diminishment/depletion is a direct near-future result of our continued insistence on using gasoline to support our selfish lives of constant consumption. This is a huge economic issue, but is even more a moral issue. We are committing crimes against future humans. If they were living now, we would be subject to a massive class-action lawsuit.

If we were to factor in all of these ignored costs (called externalities by the fossil fuel industry), the price of a gallon of gasoline would probably be 10 (or 20? Or 100?) times higher than it is now. So let’s consider ourselves lucky. We get to keep on ruining the planet and it won’t cost us much at all!

Wind Energy

Today, driving east on I-40 through the panhandle of Texas and the body of Oklahoma, I saw 3 wind farms. The two in Texas were moderately sized, perhaps 50 turbines each, and the one in OK was larger, somewhere between 100 and 200 turbines I'd guess. This is an ideal locale for wind farms, flat, treeless, and windswept. The turbines are magnificent: each blade is longer than the trailer on a flat-bed 18-wheeler. It was great to see those turbines facing into the wind and turning at uniform speed, generating clean electricity!

I've heard complaints to the effect that the turbines destroy the appearance of the landscape, but I find them much more appealing than the erector set towers that support the high-tension power lines of the grid. The fact that they give us non-polluting, non-CO2 generating electricity makes them beautiful.

Each turbine generates about 2 megawatts of electricity, so I saw about 400+ megawatts of electricity being produced today. Probably enough to completely power a small town or two.

There's plenty of room in these two states and in other states for wind turbines. Lets start installing them! Kudos to Texas and Oklahoma, both oil states, for moving in this direction.

Very Unusual Weather

Have you noticed, as I have, that in this fall and winter of 2010 we have had and are having "unusual weather events" with increasing frequency? Here are some examples:

Right now, there is a very unusual deep freeze covering about half of the geographical US and extending all the way down to Florida, where it is endangering the citrus crop. This deep freeze is accompanied by extensive snowfall in the midwestern states. Meteorologists admit that a cold wave like this so early in the winter season is unusual. In Minnesota, meteorologist say that it is the most powerful storm to hit Minnesota in "a long time." Within the past 2 weeks there was 3 feet of snow In Buffalo NY in a period of (I think) 48 hours, and 16 inches of snow in northwest Indiana.

There have been 2 recent incidents of cruise ships caught in intense storms causing huge waves that tossed cabin contents and people around in their rooms for as long as 2 days. One occured South of Cape Horn involving a ship returning from an Antarctic cruise, which experienced 45-foot waves. The other involved a ship in the eastern Mediterranean Sea in which there were hurricane force winds and huge waves. The latter has been called "unprecedented."

Over the past few years there have been increasing numbers of increasingly strong tornadoes, not only in the usual places (midwest) but in unusual places (like Arizona). Similarly, hurricanes seem to be increasing in number and strength. The worst year was 2005 when there were 27 named tropical storms (a bit more than our alphabet can handle). Katrina hit in August, then Rita in September, then Wilma hit in October. All were very destructive storms hitting various Caribbean areas. We all know the Katrina story.

Over the last few winters, large snowstorms have been happening in the northwest, where conditions are usually pretty mild in winter.

There are persistent droughts in large regions of Africa (Sahel region in particular), while in other places (recently Pakistan) there are deluges of rain and floods.

In 2003, a long heat wave in Europe resulted in the deaths of 30,000 people (this number varies according to where you read it, so I have picked the smallest estimate of deaths)

The decade of the 1990s was the hottest on record. How about the decade of the 2000s?

In Alaska, average yearly temperatures have risen 5 degrees Fahrenheit in summer and 10 degrees Fahrenheit in winter since the 1970s. Wonder what effect this has on the livlihoods of Alaskans?

California has experienced a very large number of very destructive forest fires. This is a result of drying out of the forests, which is in turn weather related.

Huge swaths of mountain forest in Colorado, Utah, Wyoming have been devastated by the pine bark beetle (Cathryn and I saw this during an RV trip this past summer-both campgrounds in Rocky Mountain National Park looked like RV parking lots full of stumps). This also is weather related in two ways. First, the trees had dried out enough to make a comfortable temporary home for the beetles. Second, the reproductive effectiveness of the beetles has been enhanced by warmer average temperatures in the mountain regions.

What is responsible for this escalation in severe and unusual weather? Actually, this is one of the predicted (as early as the 1980s) consequences of the gradual and persistent increase in average global temperature caused by the accumulation of greenhouse gases in the atmosphere. This is called global warming--you all know about it. Many of you don't "believe in it", asking things like "How is a cold wave in the midwest consistent with global warming?" The answer is to be found in understanding the difference between weather (a daily, local phenomenon) and climate (average weather over the entire globe and over a relatively long period of time, usually a year or a decade).Global warming refers to the average temperature of the surface of the earth over, say, the period of a year. Weather in a given location varies widely from season to season, even day to day, as it always has, and is unpredictable. Climate, on the other hand, is quite predictable, precisely because it is an average of weather over a long period of time. You can read about this.

Rising average temperature has consequences, many consequences. One of these is that oceans warm up. This of course means more rapid evaporation of water from the oceans and soils. This means more water vapor in the atmosphere. This means more precipitation (rain, snow, sleet, hail). This also means more intense hurricanes and tornadoes, both of which gain energy from the heat released when water vapor condenses. Larger amounts of water vapor mean more available heat to fuel storms. It all ties together in a way that is quite logical at the same time that it is quite scary. Even if we completely stopped producing CO2 right now, average global temperature will continue to increase gradually for at least a century, due to the time lag involved in the huge oceans to heat up to the point that the earth gives up energy to space at the same rate that it receives it from the sun. This means things are going to get worse weather-wise even if we stop CO2 production cold right now. As the oceans warm up, they will release come of the CO2 that is now dissolved in them (gases get less soluble in water at higher temperture), exacerbating the greenhouse effect. This is called a positive feedback (phenomenon A causes phenomenon B causes phenomenon C which enhances phenomenon A).

Just more food for thought as you continue to pump CO2 into the atmosphere by driving (very bad), using your cell phone, using your computer, turning on a light, running your washing machine and your dryer (very bad), your refrigerator, your microwave, your oven, your stove (very bad), your toaster, your power tools, your TV, your sound system, your radio, your shower, your lawn mower, your dishwasher, your flashlite, your motorcycle, your automatic garage door, your vacuum cleaner (very bad), your coffeemaker, your coffee bean grinder, your electric carving knife, your blender, your toaster oven, your ipad, your kindle, your...

Is there anything we can do that does not make our situation worse?