Sea Level Projections vs. Tide Gauge Data

Carbon dioxide, climate change, disaster, SEA LEVELS WILL RISE!

You can see all kinds of sea level rise predictions for the 21st century, with over-wrought images of houses and buildings under water.  One of the favorite predictions of the hand wringers is “1.8 meters” of sea level rise for the 21st century.  A major purveyor of this lurid climate-porn prediction is Stefan Rahmstorf (see here, here, and here).

Consider the following points

• 75% of atmospheric anthropogenic CO2 arrived after 1950.
• There has been no obvious acceleration in sea level rise rates since 1950 as seen from tide gauges.
• Extrapolating tide gauge time series to 2100 would give about 15cm of sea level rise between 200o and 2100.
• Projections of 1, 1.8 or 2 meters of sea level rise between 2000 and 2100 would require extraordinary rise rate accelerations.

Let’s compare the sea level data of the 20th century with these wild prediction for the 21st century.  The movie below will show all the tide gauge data sets available from NOAA that extend over at least 75 years.  In each case the trend is extrapolated to 2100.  Additionally, the likely local relative sea levels corresponding to 1 meter and 1.8 meter global sea level rises for the 21st century are shown.

Music is by Mechett and licensed under Creative Commons

The likely local relative sea levels are calculated by by assuming that the global anthropogenic sea level rise would be distributed evenly over the planet.  This assumption may not be entirely accurate but it is a good first approximation. Here is how the calculation is done.

Let

• GSLR (20th century) be the 2oth century global sea level rise
• LSLR (20th century) be a local 20th century sea level rise
• GSLR(21st century) be the projected 21st global sea level rise
• LSLR(21st century) be the projected local 21st century sea level rise

Then
LSLR(21st century) = LSLR (20th century) – GSLR (20th century) + GSLR(21st century)

Say the 2oth century global sea level rise was 18cm and the projected 21st century global sea level rise is 100cm.   And say the local 20th century sea level rise was 18cm at location A, 30cm at location B, and -10cm at location C.  Then the local projected 21st century sea level rises would be

Location A
Projected rise = 100cm = 18cm – 18cm + 100cm

Location B
Projected rise = 112cm = 30cm – 18cm + 100cm

Location C
Projected rise = 72cm = -10cm – 18cm + 100cm

Comparison of Arizona Nuclear and Solar Energy

Let’s compare and contrast solar energy and nuclear energy in Arizona. There is only one nuclear power plant in the state, the Palo Verde Nuclear Generating Station in Tonopah. There are several solar energy sites, so we will pick the Aqua Caliente Solar Project because it won the Renewable Energy World Solar Project of the Year category in their 2012 Excellence in Renewable Energy Awards.

Palo Verde Nuclear Generating Station

This nuclear plant consists of three reactors with with a total nameplate capacity of 3,937 MW. If these reactors ran for 24 hours day for 365 days a year they would yield 34,500 GWh (gigawatt hours) per year. The actual output is about 31,300 GWh per year (2010). This means they have a capacity factor of about 90%. Averaged over time Palo Verde yields 3,543 MW.

Palo Verde became operational in 1988 and is currently approved to operate until 2047, giving a lifetime of nearly 60 years.

Palo Verde’s construction cost was $5.9 billion in 1988 ($11.86 billion in 2015 dollars). Its operating costs for fuel and maintenance were about 1.33 cents per kWh in 2004 (1.67 cents in 2015 dollars.)

Based on an average power yield of 3,543 W and a cost of $11.86 billion (in 2015 dollars), the construction cost per watt for Palo Verde was $3.34 per Watt (in 2015 dollars).

Agua Caliente Solar Project

This 9.7 square kilometer solar energy farm has a nameplate capacity of 290 MW peak.  Its first year of full operation was 2014. If it were able to produce its nameplate capacity of 290 MW continuously for one year the energy output would be 2540 GWh. The energy output was 741 GWh in 2014, which means a capacity factor of 29%, an excellent result for solar energy. Averaged over time, this solar farm yields 84.6 MW.

Construction cost for Aqua Caliente was $1.8 billion.

Based on an average yield of 84 MW and a construction cost of $1.8 billion, the construction cost per watt for Aqua Caliente was $21.43 per Watt.

Comparison

The cost per kilowatt hour of energy for either of these sources is combination of the construction cost and the operation, fuel and maintenance cost.  The longer the facilities are in operation the lower the fraction of construction cost per kilowatt hour.

The operation, fuel and maintenance cost for the Palo Verde Nuclear plant were about 1.33 cents per kWh in 2004 (1.67 cents in 2015 dollars.)  The great advantage of the Agua Caliente solar farm is that its fuel cost is zero, and we will assume for the sake of argument that its other operation and maintenance costs are also zero.

The following chart shows various costs per kilowatt hour for each of the facilities for various lifetimes.

1.  $0.0133 per kilowatt hour in 2004.  Converted to 2015 dollars.
2. 2013 energy output.
3. $5.9 million construction cost in 1988 dollars.  Converted to 2015 dollars.
4. 2014 energy output
5. $1.8 billion construction cost in 2014.
6. (GWh/year) x (number of years) x (1,000,000)
7. (Construction cost) / (kilowatt hours produced over lifetime)
8. (Construction cost per kWh) + (operating cost per kWh)

Two blocks of data are highlighted in yellow.  These are the most likely lifetime scenarios for each of the power generating plants.  The Palo Verde nuclear plant has had its license extended to 60 years.  Aqua Caliente solar farm is made from First Solar CdTe modules that have a 10 year material and workmanship warranty and a  warranty of 80% of the nominal output power rating during twenty-five (25) years.  It is reasonable to hope that it will last 40 years

There is one more thing to be considered.  We have assumed so far that the yearly output of each of these power generating stations it the same year after year.  That is not entirely correct.  Historically, the Palo Verde nuclear plant has increased its capacity factor through time as operations have become more efficient.  Whether that trend will continue is unknown.

Solar modules tend to slowly degrade with time.  The First Solar CdTe modules that are used at Aqua Caliente will likely decay at about 0.5% per year. The chart above gives a best case estimate for Agua Caliente and does not compensate for this degradation.

Based on the highlighted sections of the above chart, Aqua Caliente Solar Farm will likely cost about 2.5 times more per kilowatt hour than the Palo Verde Nuclear Plant over the course of their lifetimes.

One more point.  Aqua Caliente requires 9.7 square kilometers to generate an average of 84.6 MW.  Palo Verde Nuclear Plant generates and average of 3,543 MW.  So it would take 41 Agua Calientes to equal the power of Palo Verde.  That would require about 400 square kilometers.

Energy is the lifeblood of civilization.  The pursuit of energy abundance is the pursuit of healthier and more fulfilling lifestyle for greater numbers of people.  I present this data to help inform the choices that need to be made in that pursuit.

How much photovoltaics to provide 100 kilowatt hours per person per day?

Suppose you wanted to power the world at the level that each human being can enjoy the same level of energy abundance as the average American. And suppose we wanted to do it all with photovoltaic solar energy. What would it take?

There are an average of 250 kilowatt hours consumed per person per day in the United states. Maybe that seems like a lot to you because you occasionally look at your home electric bill and see less than 1000 kilowatt hours used in a entire month for a home that houses four people. That 1000 kilowatt hours for four people in a month works out to only about eight kilowatt hours per person per day. But that electric bill is a very poor indicator of how much energy is actually expended for your benefit. That is why claims that some energy source will power X number of homes is incredibly misleading.

Here is the reality.  According to Lawrence Livermore National Laboratory the United States consumes 98.3 quads of energy every year.

That works out to about 250 kilowatt hours per person per day

(98.3 quads/year) x (2.933 x 10¹¹ kw-hr/quad) / (year / 365 days) / (3.2 x 10⁶ people) = 247 kilowatt hours/person/day

Fortunately, this daunting amount of energy is also somewhat misleading.  Look at the right side of the graph from Lawrence Livermore.  Notice that the two final energy outputs on the right side of the graph are “Energy Services” and “Rejected Energy.”  “Energy Services” is energy that actually does some useful work.  “Rejected Energy” is energy that is lost, mostly in form of waste heat.  For example, if you burn a lump of coal in a steam generator and get a kilowatt of energy out in the form of electricity, but lose two kilowatts in the form of heat to the atmosphere, then you got one kilowatt hour of Energy Service but two kilowatt hours of Rejected Energy.  As you can see from the graph, only 40% of the energy that is input comes out the the system as Energy Services (38.9 quads / 98.3 quads).

One of the big advantages of solar photovoltaics is that you don’t lose 60% of your energy to heat.  Electric cars put far more of their stored electric energy into useful work (Energy Services) and far less into “Rejected Energy” than do blazing hot internal combustion engines.

Let’s make the assumption for now that every possible efficiency is applied, so that we only need to produce 40% of the 250 kilowatt hours per day per person, or 100 kilowatt hours per day per person.  Still a lot of energy, but more manageable than 250 kilowatt hours.

So, for 7 billion people we need 700 billion kilowatt hours per day (100 kilowatt hours per person x 7 billion people).  If we got all that energy from solar photovoltiacs, how much land would be required for solar arrays, how much would it cost?

Topaz Solar Farm

To get estimates of these values, we can look at some of the world’s biggest solar arrays.  Consider the Topaz Solar Farm in California.  It is one of the biggest and one of the newest in the world and in an area of very high solar insolation.  It is expected to generate 1,100 GWh of energy per year while occupying 25 km² with a cost of $2.5 billion.  Therefore it would generate the energy consumed by about 30,000 people at 100 kWh per person per day.

(1100 GWh/year)x(1×10⁶ kWh/GWh)x(year/365 days)/(100 kWh/person/day) = 30,136 people

From this it is clear that it would take about 6 million km² of solar photovoltaics of the Topaz Solar Farm density to generate all the energy consumed by 7 billion adequately powered people.

(7×10⁹ people) / (30,136 people/25 km²) = 5.8×10⁶ km²

Keeping in mind that the Topaz Solar Farm cost $2.5 billion and yields enough energy for 30,136 people, then the cost for 7 billion people would be about $580 trillion.

(7×10⁹ people) / (30,136 people/$2.5×10⁹) = $5.8×10¹⁴ .

For the sake of comparison the, the gross domestic product of the United States is about $17 trillion, or less that 3% of that $580 trillion.  The gross product of the entire world  is about $78 trillion, or about 13% of that $580 trillion.  So, if every penny or mark or yen, etc. of world product for about 7.5 years were dedicated to this project, it could be accomplished.

Some points to consider

What would be the consequences of covering 6 million square kilometers of land with PV?  This would be like completely covering an area the combined size of Arizona, Nevada, Colorado, Wyoming, Oregon, Idaho, Utah, Kansas, Minnesota, Nebraska, South Dakota, North Dakota, Missouri, Oklahoma, Washington, Georgia, Michigan, Iowa, Illinois, Wisconsin, Florida, Arkansas, Alabama, North Carolina, New York, Mississippi, Pennsylvania, Louisiana, Tennessee, Ohio, Virginia, Kentucky, Indiana, Maine, South Carolina, West Virginia, Maryland, Vermont, New Hampshire, Massachusetts, New Jersey, Hawaii, Connecticut, Puerto Rico, Delaware, Rhode Island with solar panels.  Of course, this would be spread out over the about 100 million square kilometers of land at latitudes lower than about 50 degrees.

This plan would also require a distribution system that could move energy from daytime areas to nighttime areas, or at least a few days of storage for every person on the planet.  Such a distribution system is not feasible at this time, and the massive amount of storage is prohibitively expensive.

Two days of storage would be 200 kilowatt hours of stored energy per person.  Probably the best mass storage option today (2015) is with Tesla’s Powerwall, which stores 7 kilowatt hours, costs $3,000, and weights 220 pounds.  So we would need about $90,000 and about 6,600 pounds of storage for each of the 7 billion people.  That adds another $630 trillion to the cost.

These calculations serve simply to give a feel for what could be done with solar photovoltaics and what the limitations might be.  I am not suggesting that the world should be powered solely with PV.  With other energy sources in the mix less money and land would need to be devoted to PV (but more to those other sources).  For example, if you did the same calculations for wind, then you would find that about twice as much area  (about 12 million square kilometers) would have to be covered by wind farms to get the same amount of energy.  But at least you can grow corn are graze cattle below the turbines in a wind farm.

I have led you to water.  It is up to you to drink up your own conclusions about the viability of using solar energy to bring the world up to a reasonable level of energy consumption.