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Tuesday, January 7, 2014

Limits on the Growth of Wind and Solar Power, Part II -- Rare Earth Elements

Here’s a bit of trivia for you.   There is about one ton of neodymium in every large wind turbine.
Neodymium is element number 60 on the periodic table with an atomic weight of 144, and it is one of the "rare earth" group of elements.

And there is literally a ton of neodymium in every wind turbine, from Denmark to Kodiak Island.   Published estimates vary, but between 500 pounds to 2000 pounds of neodymium are needed for every megawatt of wind power.  The USGS estimates that the United States will need 380 metric tonnes of neodymium annually to provide 20% of our electrical power by 2030.  My calculations show that we need more -- a minimum of 3100 metric tonnes of neodymium per year.   The availability of so much neodymium is in doubt, and may limit the growth of wind power in the United States.

Neodymium has unique magnetic properties which make it the most efficient material for the generators inside the turbines.  It is considered essential for the construction of new turbines.  Attempts to find adequate substitute materials have been unsuccessful.  Other essential elements in wind turbine generators include praseodymium, dysprosium, and terbium.  Without these elements, we cannot build wind turbine generators without serious deterioration in efficiency and cost. 

A study completed in 2012 by MIT concluded that meeting the climate goal of 450 ppm CO2 will require a 7-fold increase in use of Neodymium, and a 26-fold increase in use of dysprosium over the next 25 years.

Solar cells have similar requirements in exotic elements.  Tellurium, indium, gallium, germanium, and palladium are each essential to some kind of solar photovoltaic cell.   Rare elements are particularly essential in high-efficiency solar cells.

The question is whether a sufficient supply of these elements exists to allow renewable energy to significantly replace fossil fuels, or whether availability of exotic elements places a limit on the growth of renewable energy.  

Let’s take a look.

Rare-Earth Elements
Rare-earth elements (REE) are heavy elements found in low concentrations in the earth’s crust.  The elements carry improbable names, reminiscent of the name of some tropical disease, or something from bad science fiction.  But some of the most important elements in today’s technology include Dysprosium, Terbium, Praseodymium, Yttrium, Ytterbium, Lutetium, Gadolinium, and Neodymium.  Rare-earth elements, and their unique properties probably inspired the fictional element “Unobtainium” in James Cameron’s film “Avatar”.
Uses of Rare Earth Elements
Rare-earths elements were discovered fairly late in the history of chemistry, and are displayed like a footnote at the bottom of the periodic table, in the rows labeled Lanthanides and Actinides.  The rows of elements are shown disconnected and without context, like the state of Alaska on a typical map of the United States.  According to the logic of the periodic table, the table should be expanded horizontally, and the rare earths should be inserted, forming another step in the table, representing another shell of electrons in the structure of the atom.  Lanthanides should be inserted between Barium and Hafnium, and the Actinides should be placed immediately below.  The electrical properties of these elements make them uniquely valuable in various electrical applications, especially in environmentally important technologies.  Non-technical literature often incorrectly includes other scarce and strategic elements as “rare earths”, in particular, tellurium, indium, and lithium.

 Some of these technologies are as follows:
Wind Turbines (Neodymium, Praseodymium, Dysprosium, Terbium)
Solar panels (Indium, Tellurium, Gallium, Germanium, Palladium)
Hybrid cars (Lanthanum, Neodymium, Praseodymium, Dysprosium, Terbium)
Exhaust catalysts (Cerium, Lanthanum)
Compact fluorescent lights (Yttrium, Europium, Terbium)
LEDs (Yttrium, Europium, Terbium)

Rare earth elements are also used in consumer electronics of all kinds, medical applications, high-tech electronics, water treatment, nuclear reactor control, pigments, fertilizer, coatings, ceramics, glass, superalloys, petroleum catalysts, industrial and coal-plant pollution scrubbers, etc.

Geologic Occurrence and Mining
Rare earth elements might be better described as “dispersed earth elements”.   Because of their complex chemical properties, REEs do not occur in minerals with simple, distinct composition.  Instead, REEs occur as complex minerals showing a range of composition involving different REEs.  REEs occur in low concentrations, and separation of individual REEs is difficult. 

The great majority of rare-earth production is as a by-product of mining for another commodity.  This means that the cost of rare earth elements is generally subsidized by the principal mining product, and expansion of rare earth production volumes is difficult.

Most of the world’s rare earth element production and nearly all of the heavy REE (actinide) production comes from a single iron mine in Inner Mongolia.  In 2010, China cut its export quotas of REE, and declared an intention to reserve its production of REE for internal use.  The supply disruption caused extreme volatility in the price of REEs, and prompted the resumption of REE mining in other parts of the world.   Although REE are present in many parts of the world, there are only a handful of mines producing rare earth elements.  Mount Weld in Australia, and Mountain Pass in California are among the mines re-opened in the last two years. 

Production of rare earth elements as a by-product of other activity provides a substantial subsidy in the price of rare-earth elements.  The volume of production is a function of the production of the primary ore; this creates a barrier to expanding supply as a result of market demand.

Environmental Issues
Rare-earth elements generally occur with thorium and other radioactive or toxic elements.  Processing the ore requires finely grinding the ore, and chemical treatments to separate the rare-earth elements from the tailings.  Tailings are generally toxic and an environmental problem. 

The Mountain Pass mine in California has a rare earth oxide ore grade of 8.9% by weight, which is about 4% by volume.  Neodymium is about one-eighth of the total REE production.  The Mount Weld mine is one of the richest deposits of rare earth elements on earth, about 15.4% by weight.  Neodymium and Praseodymium comprise about one-quarter of the rare earth oxides.  For a sense of scale, in order to mine enough neodymium from these very rich mines, it will require generating about 10 to 90 metric tons of toxic, radioactive mining tailings for each large wind turbine.  (To be fair, other valuable elements are extracted with the neodymium.)

In the past, ore from the United States was sent to China for processing (also called beneficiation), and ore from Australia (as of my last information) is still being sent to Malaysia for processing.  The refined rare-earth metals are returned to the host country, and the toxic waste remains in China and Malaysia.  We have literally exported the environmental damage associated with our “green” energy.

Neodymium Supply and Demand for Wind Power
A USGS paper published in 2011 concluded that the United States would need 380 metric tonnes of Neodymium annually to meet a “market goal” of producing 20% of the country’s electricity from wind power by the year 2030.   Working from data from the US Energy Information Agency, I calculate a much larger number, requiring over 3100 metric tonnes of neodymium annually to meet this goal.  I have not yet resolved the source of the difference in the estimates.

My calculation of Neodymium demand for wind generation
         4,047,765 Gigawatt-Hours  --  US Net Electrical Generation (2012).
809,553  Gigawatt-Hours – 20% of annual electrical generation.
      27.2 % -- Current average wind capacity factor (efficiency: power generated/capacity).
339,608  Megawatts – Required capacity to provide 20% of US electrical generation.
  59, 075 Megawatts – Current installed wind generation capacity.
            280, 533 Megawatts – New capacity required to meet 20% goal.
             15,585 Megawatts – New-build capacity required annually, given 18 years from 2012 to 2030.
               3,117 Tonnes – Neodymium needed annually, at 200 kg Nd per megawatt.

The Mountain Pass Mine in California was the world’s principal source of rare earth elements 1970s though 1990s.  Mountain Pass recently re-opened after being closed for a decade due to competition from China.  

It is currently the United States' only domestic supply of rare earth elements.   Production targets announced by the company would suggest that neodymium production could reach 2000 to 2500 metric tonnes per year.  If the nation’s entire supply of neodymium were dedicated to wind power, production from Mountain Pass and another source might meet the demand.  However, neodymium is also a critical element in other technologies with growing demand – mobile telephones, computer screens, anti-lock brakes, glare-free mirrors, hybrid and electric cars, medical devices, and military technologies. 


Given the price volatility of neodymium, and environmental barriers to establishing new mines, I think it is unlikely that industry will establish significant sources of new supply in a timely fashion.  The lack of new supply will lead to shortages and limits on the growth of wind power by 2030.

Critical Elements for Photovotaic Solar Panels
Photovoltaic solar panels come in three varieties: silicon-based cells, polycrystalline thin-film devices, and multi-junction devices.   Silicon based solar cells are the most common but least efficient, representing 90% of the current market.  High efficiency solar cells are thin-film and multi-junction devices. 
Polycrystalline thin-film devices are made of layers of either cadmium-tellurium (CdTe) or copper-indium-gallium-selinide (CIGS).  Tellurium and indium are the critical elements.  Multi-junction devices utilize a different suite of exotic elements, including gallium, indium, and germanium.

Ninety percent of commercial tellurium is a by-product of copper production.  Tellurium is a trace element; 500 tons of copper must be processed to yield one pound of tellurium; a ratio of 1,000,000:1 (unverified reference in Wikipedia).  The primary process to recover tellurium is electrolysis, used on high-grade ores.  As the copper industry increasing utilizes lower-grade ores, solvent-based processes are preferred.  Unfortunately for tellurium supply, solvent-based extraction is less suited for recovery of tellurium.  Although incremental gains might be achieved by increasing the efficiency of the electrolysis process, in general, increasing the supply of tellurium will require a proportional increase in the supply of copper.   And a two-fold, three-fold, or ten-fold increase in copper production, in timely fashion to replace fossil fuels, is unlikely.

Indium, the critical component in CIGS solar cells, is similarly co-produced and derived from zinc mining.  In all, the exotic elements required for high-efficiency solar photovoltaic devices (tellurium, indium, gallium, and germanium) are of limited supply, and will ultimately constrain the growth of high-efficiency solar cells. 

Pricing
The price of rare earth elements is volatile, due to rapid changes and uncertainties in supply and demand.  In May, 2010, the price of Neodymium was $42/kg.   During a time of increasing demand for wind turbines and hybrid cars, China indicated that it would set limits on REE exports, to retain sufficient supply for its own needs.  By May, 2011, the price of Nd rose to $284/kg, a nearly 700% rise.   By 2013, the market had settled to the range of $75 to $105/kg, a 65% drop from the earlier peak.  Similar price volatility exists for other rare elements.  A continuous price history is available on the internet, but is held by copyright.  The following chart was constructed by interpolation of data points in the public domain.



Tellurium prices rose from $30/kg in 2000 to $360/kg in 2011.  Following the bankruptcy of several solar cell manufacturers in 2012, tellurium dropped to the current price of $90/kg.  As with the rare earth elements, price uncertainty will be a barrier to investment to increase supply. 

Under conditions of such price volatility, it is very difficult for mining companies to make firm capital commitments for billion-dollar projects to expand supply. 

Conclusion

Renewable wind and solar energy are growing rapidly, as a result of dedicated efforts to reduce our dependence on fossil fuels.   However, electrical generation from wind and high-efficiency solar panels is dependent on a number of exotic elements, notably neodymium, tellurium and indium.   Expanding the supply of these elements is problematic, due to co-production with other minerals, environmental impacts and permitting delays, costs of establishing new mines, and volatile and uncertain pricing for the products.  

Part I of this post, "Limits on the Growth of Wind and Solar Power, Part I -- Area"
can be found here:
http://dougrobbins.blogspot.com/2013/12/limits-on-growth-of-wind-and-solar.html

---
References and notes:
China controls 93 percent of all RE production, and 99 percent of certain elements (dysprosium & terbium).   No new articles since June 2011.

Neodymium is necessary for wind turbines and electric motors in hybrid cars.  China produces over 98% of world REE production.
A single 3.5 MW wind turbine contains 600 kg (>1300 pounds) of rare earth elements; a hybrid car contains about 5 kg of REE.

MIT Elisa Alonso  REE supply and demand study.

Evaluating Rare Earth Element Availability: A Case with Revolutionary Demand from Clean Technologies ,  Alonso et.al, Environ. Sci. Technol., 2012, 46 (6), pp 3406–3414
Meeting the climate goal of 450 ppm CO2 will require 700% increased consumption of Neodymium, and 2600% increased consumption of dysprosium, over the next 25 years.

Rare Earth prices
2013 Nd prices ranged from $74/kg to $105/kg, current price (1/3/14) of $90/kg.
2013 Dy prices dropped from $780/kg to $605/kg.

17 elelments.   Two mines outside China are planned for start-up in 2012: Mountain Pass, Molycorp, California, and Mount Weld, Lynas, Australia.  [Mountain Pass re-opened April 2011.]
China sharply reduced REE export quotas, briefly embargoed exports of REE to Japan in 2010, in response to a territorial dispute.
Hybrid  car contains about 5 pounds of REE in its magnets and battery electrodes.  Other uses include earbud speakers and phosphor laptop displays.
Every Megawatt of wind power requires about a half-ton of REE.  Projections of growth of wind power call for 10,000 MW of new turbines, but “there just isn’t the supply” ( Keith Delaney, the executive director of the Rare Earth Industry and Technology Association).

May 2010:  Nd $19/pound  =  $41.80/kg
May 2011:  Nd $129/pound  =  $283.80/kg
2011, US gets 92% of REE from China; only US mine, (Molycorp, Mountain Pass, CA, closed 2002) re-opened April 2011.  The mine suffered waste-water leaks from 1984 to 1998.
List of REE and uses.
Chart showing REE composition at Mountain Pass. Nd is about 1/8 of total REE production. 

China cut export quotas 35% in 2010; established limits on pollutants and emissions in tailings from REE mining in Oct, 2010.

China owns 50% of known REE deposits, but produces 98% of REE production.
Summary of Alonso MIT study, 2600% increase in demand for dysprosium;  700% increase in demand for neodymium in 25 years.

Good Infographic, much information.    Pricing 2008 – 2011 for dysprosium, europium, terbium oxides; all show huge price increases.
Reserves; China 50%; CIS 17%; US 12%.  Total world reserves REE oxides 114 million tons, USGS.
2010 production: 133,000 tonnes; expected 2015 production 210,000 tonnes.

Several web-pages of textbook type information.  
Typical hybrid car contains 28 kg REE.  [Note difference from MIT study.]
Green technologies:  exhaust catalysts (Ce, La),  Wind Turbines (Nd, Pr, Dy, Tb).
Compact Fluorescent lights, LEDs (Y, Eu, Tb).
Also Consumer electronics of all kinds, Medical applications, high-tech electronics, water treatment, nuclear reactor control, pigments, fertilizer, coatings, ceramics, glass, superalloys, petroleum catalysts, industrial and coal-plant pollution scrubbers, etc.
More than 200 minerals contain essential or significant REE. 
REE occur in alkaline intrusive igneous complexes, i.e. low-calcium granitoid rocks and pegmatites.
Other commercial sources are apatite and loparite Russia, REE-bearing clays (LongNan clay, Jiangxi Province),

Monazite is a rare-earth phosphate.  Occurs in pegmatites and placer deposits (density 4.6 to 5.7).  Often contains Thorium, and is radioactive.
Placers are found in India, Australia, Brazil, Sri Lanka, Malaysia, Nigeria, Florida and N.Carolina;  pegmatites in Wyoming, New Mexico, Virginia, Colorado, Maine, N. Carolina; Bolivia, Madagasgar, Norway, Austria, Switzerland, Brazil, and Finland.


Good description of why REE are “rare” – essentially dispersed, rarely concentrated in economic deposits.
Long, pedantic article.
REE occur in pegmatitic, and secondary deposits.  Hydrothermal deposits are possible near plutons, but long-distance hydrothermal transport is unlikely.
LongNan Jiangxi  -- Chinese Iron Mine
Relative abundances of REE in different mines.   Mountain Pass and Mount Weld have negligible dysprosium, Thulium, Holmium, but are enriched in neodymium.
Contains an article:  “How Green Is Green?”   R.E. Beauford, April 16, 2011, compares wind energy to coal-fired plants.   Largely a diatribe against coal-fired plants; good statistics on pollutants.   Disappointingly simplistic view of pure “clean” wind power.

USGS REE in Alaska.  Bokan mountain is one of few known deposits where Heavy REE can be commercially produced.   Bokan Mountain is a former uranium mine.  Granite host rock in rift setting.

USGS general report on REE in the United States, and world perspective.

USGS report on wind energy 2010 – 2030, and required resources (reported as average annual consumption), including REE.   380 metric tons of Neodymium required annually to meet a market goal of 20% wind energy by 2030.   [I question this number; it is much too low.   My calculation is 3100 metric tonnes per year.]

 July 2013 article.  More about China’s domination of REE production.   Australian mine now operating.

All of the world’s Heavy REE (including dysprosium come from Chinese sources, primarily the Bayan Obo iron mine in Inner Mongolia.

Rare earth prices
Trial subscription

Rare earth prices –trial subscription

Neodymium price elevated by 1400 percent 2010 to 2011.   Declined by 33 percent by Feb., 2012.

Penn State Energy Institue REE news; latest article 2011.

Environmental problems with Chinese REE mining.   “Baiyunebo in Inner Mongolia, where most of the world’s rare earth is mined, along with iron ore.”   REE tailings have ruined farmlands and aquifers.

Bokan Mountain report.   Concentrations of REE are measured in low tens to hundreds ppm.

interesting science blog

REE occurrences in the US

USGS studies gold-rush era mine tailing for REE.

Mountain pass project description

Molycorp Mountain Pass page
Graph of Mountain Pass production targets, and types of REE.

2011 Energy Department study reports supply challenges for five REE, (dysprosium, terbium, europium, neodymium, and yttrium) may affect clean energy technologies in coming years. 
Research for replacements is on-going.
Ditto, Energy Dept report, shortages until 2015.

More search for alternatives to REE

REE showed huge weekly changes:   47% for yttria, 35% for terbium.   Other increases in the range of 25%.
REE prices climb as China shuts illegal mines.

Weakening prices delays production from new mine in Australia.
REE prices are up recently, but significantly below a year ago.

Concerns about toxic waste from proposed REE mining in Malaysia, particularly thorium.    Examples of toxic residues in China.

Every megawatt of wind power requires 200 kg of neodymium.

Indium tin oxide is key element in solar panels.   Known indium reserves will satisfy only 20 years demand, and indium is expensive and subject to volatile pricing.   Half of the supply comes from China.
Zinc oxide is less efficient but available and cheaper.   Use of zinc oxide is still in the research realm, with application and integration methods not yet established.

Article date Nov 2011.   European Union study shows expected supply problems with REE critical to renewable energy and cleaner transport.    The study showed that five metals:  dysprosium, neodymium, tellurium, gallium, and indium, are at the highest risk of supply bottlenecks, due to high demand, concentration of supply and political risk.  Solar energy technologies will require 50% of the world supply of teluriumj, and 25% of the supply of indium. 

NERL Silicon based solar cells represent 90% of sales in 2011.   15 GW of Si-based Solar cells manufactured in 2011, 10x more than any other solar technology.
Polycrystalline thin-film devices
CdTe devices and CIGS (copper-indium-gallium-selenide) devices
Multijunction devices (gallium, indium, phosphorus, arsenic, germanium)

The US would need 400 t of tellurium for every gigawatt of solar energy (sic).
Total known world tellurium supply of 48,000 t would be hopelessly out of kilter if the world went solar.
General rule, 1 t of neodymium needed for one megawatt of wind power.
So far, attempts to use less neodymium have not worked.
Electric cars also require other REE.
Geologists seen as being in short supply!  Only 4000 world wide.

Talks hopefully about 100,000,000 electric cars in America by 2040, requiring 250 billion kWhrs. 
Equivalent of 30 1000-MW nukes, 75 combined cycle 800 MW gas plants or 250,000 1 MW turbines.
--Only 5% of electrical production in the US.

Knowledgeable article from power-hitter in metals industry.   Article is generally critical of analyses that show there is enough tellurium for solar power growth.
Market fundamentals for tellurium are an enigma.  No general agreement on size of global supply, rate of production, or locations of production.
90% of available tellurium is as a byproduct of copper.   Recovery of tellurium depends on the smelting process used.  The copper industry is actually moving away from processes that recover tellurium, in order to process lower-grade ores.
USGS estimate of global tellurium production in 2007 – 500 t. 
Maximum tellurium availability – 3200 t/year (calculation of author), most likely maximum 1600 t/yr, as calculated by NERL (1997).
USGS speculates that 1200 t/yr could be produced by separation from copper.

Tellurium is produced by “electro-winning” beneficiation process, from higher-grade ores.  As high-grade ores are exhausted, miners are shifting to a solvent-leaching process to treat lower-grade ores.  Solvent leaching “does not lend itself” to recovery of tellurium.

From Wikipedia:  One gigawatt of CdTe PV modules would require about 66 tonnes of Tellurium (at current efficiencies).
Installed electric generation in the US today is 1,100 GW – implied requirement would be 67,600 tonnes of tellurium, without considering capacity factor. (my conclusion)

Good discussion of the limited availability of dispersed elements, i.e. those that are mined only in association with another mineral.   Example Gallium.

The US would need 400 tons of Tellurium per Gigawatt of solar energy.

Typically, 500 tons of copper ore yields one pound of tellurium.  Year-end price 2000 was $14/lb, but by 2006 reached $100/lb.

US tellurium Price, production imports and exports.   Price per kg, rises from $82 in 2007 to $360 in 2011.

2013 price of tellurium has fallen from near $140/kg to current price of $90/kg (1/3/14).

Tellurium price volatility.   Tellurium traded as high as $350/kg in 2011, ranged from below $100 to over $300/kg in 2012.   March 2013 pricing at $100 - $140/kg, due to bankruptcy of solar power companies in 2012, reducing demand.

Very good site.    Nd,Pr, Dy, Tb are used in hybrid cars.


Each Toyota Prius contains about 1 kg of Nd, and the battery contains 10 to 15 kg lanthanum.

Rare earth based solar panels.

100,000 metric tons REE global production in 2012, source IHS Chemical.   Global growth expected to be 7.6 percent annually (doubling rate every 9 years).

Terbium, europium, and yttrium needed for fluorescent light bulbs.

Indium used in PV panels.   Research suggests possibility of replacing Indium with Zinc.

Projects being considered for development today are in the range of 0.2% to 12% Total Rare Earth Oxide ore grade.  Heavy REO enrichment is defined as HREO/TREO.   Heavy REO enrichment of proposed projects ranges from 0.6% to 55%. 

Mountain Pass mine – mostly LREE.   Rare earth oxides average about 8.9% of the ore by mass.  Ce, La, Nd, and Pr comprise about 99% of the REE output.
Mount Weld mine has one of the highest REE ore grades on the planet, about 15.4% by weight.   Nd and Pr are about 23.8% of oxides. 

The importance of Tellurium is still not recognized.   “Tellurium forms many compounds, but none that are commercially important.”

Despite doubling of supply due to improved extraction, the DOE expects a supply shortfall by 2025.

Cadmium – Tellurium PV panels have an efficiency rating of 11% to 13%, as compared to amorphous silicon panels, which have an efficiency of 7% - 9%.

CdTe PV panels represented about 8% of the solar PV panels installed in 2011.

CdTe PV panels are the cheapest on the market; CIGS (indium) are the most laboratory efficient panels.

Germanium Is a by-product of zinc mining.
--
Rare-earth ore from the United States was formerly sent to China for beneficiation.  Lack of beneficiation alternatives contributed to the shutdown of Mt. Pass mine in California.
Dr. Susan Karl, USGS geologist , personal communication, 8/13/13
Australia still sends rare-earth ore to Malaysia for beneficiation
Dr. Susan Karl, USGS geologist, personal communication, 8/15/13
--
Tellurium Fact Sheet; UKERC, UK Energy Research Centre

USGS claim that only 380 metric tonnes of Nd per year are needed to reach 20% of electrical generation by 2030 needs a reality check ---
1)      Doesn’t make sense from supply point of view.  We know Nd supply is tight, but Mountain Pass will produce about 2300 tonnes of Nd per year.
2)      Other sources say that about 1 ton of Nd is needed in every wind turbine.  Surely we need more than 380 turbines per year to supply 20% of the US electrical demand.  Particularly when considering the capacity factor.  Assuming a 30% capacity factor, we would need a nameplate wind generation capacity of 60% of the US electrical demand, to produce 20% of our electricity.  

Good Neodymium fact sheet, lots of uses.   Associated pages on scientific properties of Nd and Nd oxide.

British Geological Survey REE report.  Contains forecast of supply and demand.

Good report on REE, contains market forecast from Brit Geol Survey,  and  Mountain Pass REE composition  from USGS report.
Rare earth prices have been artificially low since the 1990s, as the result of Chinese REE production [as a by-product of iron mining] exceeding demand.
Price table for REE from 2002 through 2011.

Rare Earth Elements—Critical Resources for High Technology


USGS REE fact sheet.    

Monday, December 23, 2013

Limits on the Growth of Wind and Solar Power -- Part I, Area

The scalability of solar photovoltaic and wind power is considered in this post.  Calculations performed by David MacKay (author, Sustainable Energy Without the Hot Air) show that solar and wind power would occupy extremely large physical areas to achieve meaningful replacement of fossil fuels. 

Replacing Fossil Fuels with Wind Power and Solar Power
Atmospheric CO2 is rising due to fossil fuel emissions.  If the science is correct (and I believe it is), it will result in serious problems due to climate change. 

The natural reaction to this knowledge is to try to replace fossil fuels with renewable energy.  Renewable energy – power from the sun, the wind and from growing plants – is a growing part of our energy supply.   Renewables are regarded as clean, of low impact to the environment, and most importantly, emit no carbon dioxide.  The use of renewables, together with conservation, have reduced CO2 emissions in some Western European nations, and slowed the growth of CO2 emissions in the United States.  Nevertheless, global CO2 emissions continue to rise due to expanding use of fossil fuels, relating to population growth and economic development. 

Environmental advocates propose large-scale investments in renewable energy, and governments have implemented subsidies and policies to encourage these investments.  It is a worthy goal, but before we make a wholesale commitment to building renewable energy infrastructure, we must ask whether it is possible and reasonable to replace fossil fuels with renewables. 

Several criteria must be met in order for renewable energy technologies to prevent climate change by replacing fossil fuels.  Renewable energy technologies must be efficient, scalable, timely, and reasonably certain to perform as expected.

This post and the next post will consider the scalability of wind and solar power; we will consider limits to the growth of solar and wind electrical generation. Part one discusses the physical footprint required for significant replacement of fossil fuels.  Part two will discuss the limited availability of key elements used in solar panels and wind turbines. 

Growth Rates of Wind and Solar Power
From 2005 to 2010, world electrical generation from wind power grew at an average annual rate of 27%.   Solar power grew at a faster pace, at the rate of 53%.   But these growth rates are on the basis of small numbers.   At the beginning of this period, wind power provided only 0.6% of world electrical generation, and the contribution of solar power was negligible.  By 2010, wind power provided 1.7% and solar power provided 0.2% of world electricity.  The current growth rates are remarkable; if we assume a 20% growth rate for wind power, wind would meet world demand by the year 2036.  If these growth rates could continue, renewables would soon eliminate CO2 emissions from electrical generation.  But there are limits to the growth of renewable energy. 

Sustainable Energy – Without the Hot Air
David MacKay has written an extraordinary book, Sustainable Energy – Without the Hot Air.  The book is available for free, in an electronic edition at this site:  http://withouthotair.com/

MacKay puts hard numbers to the question of renewable energy in Britain, as compared to energy demand.  MacKay is clearly an advocate of renewable energy.  However, his analysis reveals the low efficiencies and difficulty of replacing fossil fuels with renewables.

MacKay addresses the huge physical scale of generation facilities required to replace fossil fuels, given the known efficiencies of various kinds of sustainable energy. 

MacKay considers paving 5% of Britain with solar panels, to produce about 50 kWhr/day per capita.  The cost of power would be about 4-fold higher than today’s electrical rates.   The number of photovoltaic panels would require more than 100 times the total number of photovoltaic panels existing in the world (2008).   This installation would produce only slightly more than the energy required for heating, cooling, lighting and gadgets in the UK, or about 44% of the average per capita energy consumption in the UK.   The estimate does not include transformation and transmission losses, or implicit energy consumption in the form of imported goods, for which the energy of production is expended in another place.

MacKay also suggests covering the windiest 10% of Britain with wind turbines.  This would provide 20 kWhrs/day per capita, and require about twice the number of wind turbines in the entire world (2008).  This number of turbines would provide about one-half of the energy needed daily for automotive transportation.   MacKay gives further consideration to offshore wind, while noting that some existing offshore windfarms have had serious difficulties with mechanical lifetime due to corrorsion.  MacKay proposes covering one-third of the shallow water (<30 m) offshore Britain with wind turbines.  It is an area equivalent to putting a belt of wind turbines 4 kilometers wide around the entire coast of Britain.   These turbines would produce 16 kwh/day per capita, or less than half the energy required for automotive transportation in Britain.   Added to the onshore wind assumption, it would involve nearly four times the number of wind turbines in the entire world (2008). 

Energy Density
Let’s use the term Energy Density to indicate the energy produced per unit of surface area on the earth. 
Let’s compare the energy density for wind, solar and petroleum.    MacKay provides numbers for wind and solar power.   Wind power, in the windiest parts of Britain, amounts to about 2 watts/m2.  Solar power, after accounting for panel efficiency, latitude, clouds, time of day and darkness, achieves about 5 watts/m2.    By comparison, the energy density of new “shale-play” onshore oil and gas developments in the United States ranges from about 200 to 1100 watts/m2, assuming a 2.5 acre well pad and a 15 year well life.1

The energy density of wind and solar power is quite low compared to petroleum.  Replacing even a part of the energy provided by fossil fuels would require a physical footprint many times larger than the land currently occupied by petroleum infrastructure.

Area Required to Replace Fossil Fuels with Renewable Energy
The average Briton consumes about 125 kWhr/day of energy (MacKay).   If supplied entirely by wind power, this amount of energy would require a land area of 0.65 acres per capita, or 2.6 acres for a family of four.   The average American consumes about twice as much energy, 250 kWhr/day.   To supply an American with energy from wind power would require 1.3 acres, and more than 5 acres for a family of four.   Solar energy is somewhat more efficient in terms of energy density, but a Briton would still require a quarter acre of solar PV panels, and his family would require an acre.  An American family would require two acres of solar panels. 

Next, consider the area required to supply the full energy requirements of large population centers with solar or wind power.   The New York City metropolitan area contains nearly 20 million people, and covers 13,300 square miles, or 24% of the state of New York.   If we provided the energy requirements of the entire population with wind energy, it would require covering 74% of the state with wind turbines.2   If we assume the same solar efficiencies as Britain, we would cover 30% of New York State with solar panels, in order to provide all of the energy needed by the people of New York City.

The dedication of such large areas of land to energy production is clearly absurd.   We need land for agriculture; we must preserve lands for nature.   Wind and solar power can make some contribution to reducing global CO2 emissions, particularly in places where they are most efficient.  But sooner or later, the growth of solar and wind energy will meet a limit in terms of the land area which can reasonably be dedicated to energy production. 

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1.  The energy density of an onshore oil or gas well assumes the performance of the shale-gas and shale-oil wells currently under development in the United States.   Wells in the Eagle Ford Shale are expected to produce an average ultimate recovery of 200,000 barrels of oil (SPE).  Wells in the Bakken shale are expected to produce 500,000 to 900,000 barrels (EERC).   Wells in the Marcellus shale are expected to produce an average recovery of 1 BCF gas, or 166,000 barrels equivalent (USGS).   The energy density calculation assumes a 2.5 acre well pad per well, which is the area required during drilling.   After the well is on production, much of the area of the drilling pad can be reclaimed for the producing life of the well.

2.  This is under the generous assumption of the best wind power productivity of Britain, which would not exist through most of New York State.  

References:
David MacKay, 2008, Sustainable Energy Without the Hot Air, http://withouthotair.com/

USGS technically recoverable reserves, Marcellus Shale
USGS Marcellus Per Well Recovery

Bakken Oil EUR per well

Eagle Ford Oil EUR per well
Swindell, G. S., 2012, Eagle Ford Shale, an Early Look at Ultimate Recovery, SPE.

Thursday, November 7, 2013

Carbon Isotopes in the Atmosphere -- Part II

Finding Niño -- Correlating CO2 Carbon Isotopes in the Atmosphere with the El Niño Cycle

Abstract:
Carbon dioxide released by fossil fuels has a lighter isotopic composition than CO2 in the atmosphere.   The distinctive signature of light carbon released from fossil fuels provides a tool for tracking the movement of carbon through the atmosphere.  That same distinctive signature can also be used to measure the exchange of carbon between the atmosphere and carbon reservoirs on the earth’s surface.

Carbon istotope ratios in the air have been measured at monitoring stations around the globe since 1977.  Despite superficial similarity to the bulk CO2 record, isotope records tells a different story, and give deeper insight into the workings of the earth’s carbon systems. 

Part I of this post discussed how we can measure the size of carbon reservoirs exchanging carbon with the atmosphere.  We defined the term "Carbonsphere" representing the sum of all reservoirs freely exchanging carbon with the atmosphere.   We estimated the size of the carbonsphere as 5200 gigatonnes, about seven times the carbon volume of the atmosphere, based on the dilution of light isotopes from fossil fuel emissions.   

In this post, we will examine fluctuations in atmospheric carbon isotopes, and show how these can be correlated to the El Niño/La Niña climate cycle.  A number of mathematical operations on the base carbon isotope data reveal a clear correlation to the El Niño cycle.
 d C13/C12 CO2 isotope fluctuations correlate with the El Niño/La Niña climate cycle.

The El Niño/La Niña cycle controls how the Pacific Ocean exchanges carbon with the atmosphere.  The mechanism is not clear.   Two hypotheses are considered.  First, ocean currents may move carbon from shallow water into the deep ocean during La Niña events.  Or second, ocean temperatures may cause selective absorption and release of carbon isotopes, favoring absorption of light isotopes in cool water, and heavy isotopes in warm water.  The isotope cycles represent the ocean "breathing" -- taking in light isotopes during the cool phase, and exhaling during the warm phase.  Isotope data from dissolved carbon dioxide in the Pacific Ocean would answer the question.

 Carbon isotope data should be monitored throughout the earth’s carbon reservoirs to recognize and quantify the movement of carbon, and to understand the destiny of carbon emitted by burning fossil fuels.
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Carbon Isotopes in the Atmosphere
As described in previous posts, the isotope ratio d C13/C12 is the standard expression of stable carbon isotopes.   The d C13/C12 formula allows recognition of small but meaningful changes in the ratios of carbon isotopes.    In this post, d C13/C12 will be referred to by the expression “del 13”.
Let’s begin by comparing the bulk CO2 record (the “Keeling Curve”) to the del 13 record. 
Figure 1 shows atmospheric CO2, as measured at monitoring stations located from the Arctic Ocean to the South Poel.   The chart shows increasing CO2 concentration in the atmosphere due to fossil fuel emissions.  The record shows a strong seasonal cyclicity resulting from plant growth in the northern hemisphere, as discussed in previous posts.  The chart is color-coded according to the latitude of the monitoring stations.  


Figure 2, location of CO2 and Carbon Isotope Monitoring Stations.

Figure 3 shows the isotopic ratio d C13/C12, otherwise known as “del 13”, in atmospheric CO2.
The del 13 record resembles the Keeling Curve.  There is a strong cyclity in the isotope record resulting from seasonal plant growth and decay in the Northern Hemisphere, as discussed in a previous post. 
In general , the isotope record is a mirror image of the bulk CO2 record.   The long-term bulk CO2 is increasing due to fossil fuel emissions, and the del 13 record is decreasing, reflecting the light isotopic composition of fossil fuels.  The del 13 ratio of fossil fuel emissions is about – 26, compared to the del 13 ratio of the atmosphere, at about – 7.5.   The seasonal cyclicity is likewise a mirror image.  As plants take up carbon in the summer, the concentration of atmospheric CO2 decreases, while the del 13 ratio increases, because the plants preferentially remove light isotopes from the atmosphere. 

Let’s begin the investigation of atmospheric carbon isotopes by removing the seasonal cycle.   For reference, we will first look at the bulk CO2 data, after filtering the seasonal cycles with a one-year rolling average, seen in Figure 4 below.


 Let’s compare the del 13 carbon isotope data, after removing the seasonal cycle with the same technique, shown in Figure 5.

 This is an amazing chart!    There are two surprises immediately apparent in the del 13 chart, in comparison to the bulk CO2 chart.   First, there is a wide separation between the curves on the del 13 chart, whereas the bulk CO2 curves are in a narrow band.   Second, the del 13 chart shows large waves moving through the data, whereas the bulk CO2 curves are smooth and nearly linear.   Let’s explore these two differences.
The del 13 chart shows a wide separation of curves by latitude.  The time required for equilibration between northern and southern hemisphere is much longer in the isotope data than in the bulk CO2 data.   The falling del 13 ratio at the South Pole lags the readings in Alaska by about eight years, while the rising bulk CO2 concentration at the South Pole lags the northernmost readings by only about two years.
Figure 6 shows the 2- year time lag required for the concentration of CO2 at the South Pole to equilibrate with the far northern hemisphere.  
Figure 7 shows the 8-year time lag required for the CO2 del 13 ratio at the South Pole to equilibrate with the far northern hemisphere.

What can account for the difference in the time required for equilibration between bulk carbon and carbon isotopes?   I suggest that light isotopes released in the northern hemisphere by fossil fuels have a long residency time in carbon reservoirs.    The difference in equilibration times shows exchange of carbon between the atmosphere and carbon reservoirs.  These reservoirs are not simply carbon sinks, but are actively exchanging carbon with the atmosphere.   Light carbon from fossil fuels is absorbed by carbon reservoirs near the point of emission; the bulk CO2 concentration of the atmosphere is maintained by the release of heavier carbon from the reservoir back to the atmosphere.

There is a second surprise in the del 13 chart, compared to what we see in the bulk CO2 data.  When we remove the seasonal cycle from the bulk CO2 data, the curves are very smooth, almost linear.   However, when we remove the seasonal cycle from the del 13 data, we see a series of large waves, observed at every monitoring station across the globe.  These are events which were not removed by the seasonal filter.  There are a few events which occurred only in the northern hemisphere, and a few which occurred only in the southern hemisphere. 

There is a remarkable paradox in the del 13 chart.   The paradox lies in the different responses of the atmosphere to perturbations of the carbon isotope ratio.   Following a perturbation in del 13 as a result of fossil fuel emissions in the northern hemisphere, nearly a decade is required for the air at the South Pole to reach to the same level of isotopic composition.   But the waves moving through the del 13 chart occur nearly simultaneously at every monitoring station on earth!   Although the del 13 values do not equilibrate to the same value, this signal is felt around the world with a lag of less than six months.   I would speculate that this indicates two carbon reservoirs; one on land, and the other in the ocean.   The land system locks up carbon in forests and soils, accounting for the long residency time, while the ocean system more readily propagates changes around the globe. 

On that hunch, I plotted measurements of the El Niño – La Niña cycle on the del 13 plot.   Figure 8 shows an apparent correlation of strong El Nino events to periods of rapidly falling del 13. 
Figure 8.  Atmospheric carbon isotopes and El Niño events.

To clarify the wave-like signal in the data, I took the average of all curves, and a linear regression through the average curve.  
Figure 9.   Atmospheric CO2 del 13 ratios, with average curve and linear regression.

I then subtracted the linear fit from the data, to produce a chart of the residual values after removing the linear trend.
Figure 10.  Chart of Residual del 13, after subtraction of linear trend.
We can compare the residual chart with the El Nino events.  El Nino events tend to correspond to negative slopes on the residual chart. 
Figure 11.  Chart of Residual del 13, with El Niño events.

If we recall Part I of this post on carbon isotopes, a relative increase in del 13 corresponds to a larger carbonsphere; relative decreases in del 13 correspond to a smaller carbonsphere.   It is the slope of the residual function that is significant, rather than the peaks and valleys.   Changes in slope indicate a change in conditions.  A positive slope indicates an expanding carbonsphere – fossil fuel emissions are being diluted into a larger volume of carbon reservoirs.  A negative slope indicates a shrinking carbonsphere – fossil fuel emissions are being diluted into a smaller volume of carbon reservoirs. 
So, to complete the transformation of the del 13 data, we now take the derivative, or instantaneous slope of the residual curve.   On this chart, positive values will indicate an expanding carbonsphere, and negative values will indicate a shrinking carbonsphere. 
Figure 12.   Derivative of Residual del 13 data; all curves.

The initial chart is rather noisy.   A better signal to noise ratio can be obtained by taking the average of all curves, to produce the following curve.  Positive values indicate an expanding carbonsphere (the light isotope is being diluted into a larger volume), and negative values indicate a shrinking carbonsphere (the light isotope is being diluted into a smaller volume). 
Figure 13.  Derivative of residual del 13 data, from average of all curves.

La Nina/El Nino
El Niño is an oceanic phenomenon, involving anomalously warm surface waters in the Pacific Ocean.  The warm waters develop off the western coast of South America, and extend westward across the equatorial Pacific Ocean.  El Niño events have profound meteorological impact, and influence weather around the globe.   The opposite of the El Niño event is termed La Niña, and involves anomalously cool Pacific waters.
Figure 14.  Pacific Ocean Temperature Anomalies, showing El Niño and La Niña events;(from  NASA).
                  http://www.elnino.noaa.gov/lanina.html

The National Oceanographic and Atmospheric Administration keeps a record of the strength of the El Nino – La Nina cycle, and expresses that record as the Oceanic Nino Index (ONI).    The data are a time series of three-month average sea surface temperature anomalies.    For the purposes of this blog post, I have reversed the sign of the ONI values, making La Nina events positive, and El Nino events negative.
Figure 15.  Here is the chart of the Oceanic Nino Index (polarity reversed).  

We can superimpose the chart of the Oceanic Niño Index, and the slope of the residual del 13 measurements.   Despite some noise, there is a clear and perceptible correlation between the curves.  

Figure 16.   Averaged derivative of residual del 13 data, and Oceanic Niño Index (from NOAA).
The ONI curve does not match the isotope data, in terms of the timing of events.  There is a brief lag between the ONI curve (representing surface temperature anomalies, and the del 13 data indicating isotopic changes in the atmosphere.  I added a six month lag to the ONI curve, in order to make a better match to the observed isotope data. 
Figure 17.  Average derivative of the residual del 13 data, and ONI curve with a 6 month lag.
We’ve performed a number of transformations of the atmospheric CO2 carbon isotope data, in order to reach the curve that corresponds to the Oceanic Niño Index. 
Figure 18.   Here is a summary slide indicating the transformations. 

The meaning of the correlation is not clear at this time, but it is clearly a significant phenomenon for global climate study.  I can advance two hypotheses. 

Deep Current Hypothesis
My first thought was that La Niña conditions indicated currents which displaced waters of the shallow Pacific Ocean into deeper water.  When La Niña conditions prevail, carbon which is enriched in light isotopes due to fossil fuels is transported and sequestered in the deep ocean.  The shallow water would be replaced by deeper waters, which still carry pre-industrial del 13 ratios (of about -6.5, based on ice core data).   Such a current would expand the Carbonsphere (as discussed in the previous post) and dilute light isotopes from fossil fuels into a larger volume of carbon reservoirs.   El Niño conditions would be stagnant, allowing heat to build up in shallow waters, and light isotopes from fossil fuels to accumulate.  El Niño would shrink the Carbonsphere, relative to La Niña.

CO2 Solubility and Isotope Differentiation Hypothesis
My daughter suggested a different hypothesis to me; one that is more probably correct.  She suggested that temperature changes in the shallow ocean should change the solubility of CO2, and the rate of exchange with the atmosphere.  An extension of that thought is that changes in the temperature of the water may differentiate the carbon isotopes being exchanged with the atmosphere.   Thus, during La Niña events, with cold Pacific water, light isotopes may be better absorbed by the water, raising the del 13 of the atmosphere.   During La Niño events with warm Pacific water, heavy isotopes may be better absorbed by the water, lowering the del 13 of the atmosphere.

NOAA is now conducting research and modeling on sea-air carbon exchange, with a focus on the Pacific Ocean, and the El Nino-La Nina cycle.  However, I have not seen data regarding isotope differentiation through that process.  Figure 19 shows one map from that study.
Figure 19.  Carbon Flux map from NOAA study.  The upper map shows carbon flux in absolute terms; the lower map shows relative variability from the normal pattern.  Positive values (reds) indicate less uptake of CO2 by the ocean from the atmosphere.  The year chosen is a strong La Nina year.  However, the published maps do not address the behavior of carbon isotopes as a function of temperature.  

Carbon isotope data in the waters of the tropical Pacific is needed to resolve the question.  If the current hypothesis is correct, the cool waters of La Niña would be have high, pre-industrial del 13 values of about -6.5 (from ice-core data).   If the isotope differentiation model is correct, La Niña waters would be enriched in light isotopes relative to the atmosphere, lower than -8.2.   This question of interpretation would seem to be easily resolved by additional data.   Physical solubility data and modeling would be helpful, but direct measurements of carbon isotopes in water would be definitive.   The isotope data must target chemical species related to aqueous carbon dioxide – carbonate, bicarbonate, and carbonic acid. 

Further, if the current hypothesis is correct, La Niña is transporting a measurable quantity of atmospheric carbon into the deep ocean.   From that information, the volume of water and quantity of heat carried by the current could also be calculated, providing key data in understanding the pace of global warming on earth.

Isotope data through all of earth’s carbon reservoirs would be helpful in understanding the movement of carbon through those systems, and the destiny of carbon emitted by burning fossil fuels.
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References:
Atmospheric CO2 Carbon Isotope Data:
Keeling, R.F. S.C. Piper, A.F. Bollenbacher, and S.J. Walker. 2010. Monthly atmospheric 13C/12C isotopic ratios for 11 SIO stations. In Trends: A Compendium of Data on Global Change. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A.

Global Emissions average isotope data
Boden, T.A., G. Marland, and R.J. Andres. 2013. Global, Regional, and National Fossil-Fuel CO2 Emissions. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A. doi 10.3334/CDIAC/00001_V2013

El Nino/La Nina Climate Cycle
Oceanic Nino Index

Carbon Flux Models -- NOAA

Previous posts om this site regarding atmospheric CO2:
2)  The Keeling Curve and Seasonal Carbon Cycles
3)   Seasonal Carbon Isotope Cycles
4)   Long-Term Trends in Atmospheric CO2
5)   Modeling Global CO2 Cycles
6)   The Keeling Curve Summary:  Seasonal CO2 cycles and Global CO2 Distribution
       http://dougrobbins.blogspot.com/2013/05/the-keeling-curve-seasonal-co2-cycles.html
7)   Carbon Isotopes in the Atmosphere, Part I -- How Big is the Carbonsphere?
       http://dougrobbins.blogspot.com/2013/11/how-big-is-carbonsphere.html      

Sunday, November 3, 2013

Carbon Isotopes in the Atmosphere, Part I -- How Big is the Carbonsphere?

How Big is the Carbonsphere?

The term “biosphere” is commonly used to describe all of the living creatures on earth; and the term hydrosphere is used to describe all of the water at the surface of the earth.   In the same sense,  I would like to propose a new term: “carbonsphere”, to describe the sum of carbon reservoirs freely exchanging carbon with the atmosphere.   For the purpose of modeling CO2 in the atmosphere, and understanding interactions of the atmosphere, biosphere and oceans, it is important to answer the question: “How big is the carbonsphere”?

Carbon released by burning fossil fuels is isotopically lighter and distinct from atmospheric carbon.   The distinct signature of fossil fuel emissions provide a tool for tracking the movement of carbon through the atmosphere and through reservoirs exchanging carbon with the atmosphere.  We can estimate the size of the carbonsphere, given the known volumes of fossil fuel emissions and the change in isotopic composition of the atmosphere.  The calculation makes a simplifying assumption, that there is no fractionation of isotopes during the exchanges with carbon reservoirs.  These estimates may prove useful in climate change research and modeling atmospheric CO2.
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Carbon isotopes provide an important tool for understanding the destiny of carbon emitted by burning fossil fuels.  The distinctly different isotope ratio shows us the movement of carbon in the atmosphere, oceans, the earth’s surface and biosphere.

Imagine a cup of strong coffee, and a large barrel of weak coffee.  We pour the cup into the barrel.  If we know the volume of the cup, the concentration of coffee in the cup, and the change in the concentration of coffee in the barrel, we can calculate the volume of the barrel.  The barrel may have hidden compartments and baffles, but the change from coffee in the cup will soon be seen throughout the barrel.  The simple dilution model allows us to calculate the size of the carbonsphere, based on the volume of fossil fuel emissions, the carbon isotope ratio of fossil fuels and carbon isotope measurements in the atmosphere.

Carbon isotopes on earth exist in a ratio of about  1% C13 and 99% C12.    A measure of the ratios was devised to easily represent small but meaningful differences in the isotopic composition of different materials.   The measure is d C13/12, usually called “del 13”.  This measure expresses the ratio of the stable isotopes carbon 13 and carbon 12, as compared to the C13/C12 ratio in a standard material. 

The calculation of del 13 and seasonal fluctuation of carbon isotopes are explained in my earlier blog post: http://dougrobbins.blogspot.com/2012/03/seasonal-carbon-isotope-cycles.html.

The atmosphere is constantly exchanging carbon with carbon reservoirs on land and in the ocean.   The most obvious carbon reservoirs are plants, which exchange carbon with the atmosphere through photosynthesis and decay in a seasonal cycle.   Other reservoirs include soils, plant detritus, dissolved CO2 in shallow ocean waters, etc.   These reservoirs are often called “carbon sinks”, but I prefer the term reservoirs, because the reservoirs do not simply receive carbon from the atmosphere, but also actively return carbon to the atmosphere. 

Fossil fuels have released a measurable amount of isotopically light carbon into the atmosphere. The light carbon is very useful as a tracer, showing how carbon disperses in the atmosphere and moves between the atmosphere and carbon reservoirs.   The isotopic composition of the atmosphere has changed as a result of fossil-fuel use, similar to what we have seen in bulk atmospheric CO2 in previous posts.   

Figure 1 shows the location of global monitoring stations.   The monitoring stations have been collecting bulk CO2 data since the 1950s, but only began recording carbon isotope data in the 1970s.   

 Figure 2, for reference, shows the bulk CO2 concentration, commonly called the "Keeling Curve".  We can compare the rising bulk CO2 curve to the falling carbon isotope curve shown below.

Figure 3 shows the carbon isotope record, color coded by monitoring station according to latitude, with cool colors representing the Northern Hemisphere, and warm colors in the Southern Hemisphere.    As with bulk CO2, the isotope data show a strong seasonal cyclicity resulting from plant growth and decomposition in the Northern Hemisphere.   The isotope data appear noisier than the bulk CO2 data.

The atmospheric carbon isotope data appears noisy in comparison to the graph of bulk atmospheric CO2 seen in previous posts.   We’ll simplify the problem by taking the annual global average del 13 in data available from CDIAC, the Carbon Dioxide Information Analysis Center (Andres, Boden, and Marland, 2009).   [In fact, much of the "noise" in the carbon isotope record is actually meaningful data.  We explore these variations in part 2 of this post, "CO2 Carbon Isotopes and the El  Nino Climate Cycle".

Figure 4 shows the global average isotope record, by year (R.J.Andres, T.A.Boden and G.Marland, 2009).  Andres, Boden and Marland (2012) also calculated the volume of global emissions by year and the average del 13 values of those emissions.   These data allow calculation of the expected change in atmospheric del 13, given the known annual volumes and isotope ratios of fossil-fuel emissions.  
Atmospheric del 13 declined from a value of – 7.6 in 1978 to – 8.2  in 2008, reflecting the influx of light CO2 from fossil fuels.  But the decline in del 13 is much less than would be expected if all of the fossil-fuel emissions stayed in the atmosphere.   The difference shows that light isotopes from fossil fuels are being diluted into a much larger volume of carbon.

We can use a dilution model to solve for how much carbon from fossil fuels remains in the atmosphere.   Using the known volume of fossil fuel emissions, and average del 13 ratio of those emissions, we can calculate, for each year, how much the del 13 ratio of the atmosphere should have changed.   A weighted average equation is used for the dilution model.

((Ve/Ve+Va)* d13e) +((Va/Ve+Va)* d13a )  = Vna* d13n

Where:
Ve = Volume of Emissions
Va = Volume of Atmosphere
Vna = New Volume of Atmosphere
d13e = d C13/C12 of Emissions
d13a = d C13/C12 of Atmosphere
d13na = New d C13/C12 of Atmosphere

If all of the carbon from fossil fuel emissions remained in the atmosphere, the del 13 ratio of the atmosphere would have declined to  – 12 by 2008.  If about 60% of fossil-fuel emissions remained in the atmosphere, the del 13 ratio would be about – 10.  But the dilution model shows a fit to the observed average atmospheric del 13 trend when only about 14% of fossil fuel emissions remain in the atmosphere, yielding a del 13 value of – 8.2 in 2008.  This value is in marked contrast to the data for bulk CO2 composition, which indicates that 60% of fossil-fuel emissions remain in the atmosphere over the time range of our observations.  

Carbon isotope data show that the picture is complicated.  Isotopes ratios show that the greater part of fossil-fuel emissions are exchanged with other earth systems, while bulk CO2 levels seem to show a much larger retention of fossil fuel emissions in the atmosphere.   The process involves exchange and displacement.  As fossil fuel emissions are absorbed by carbon reservoirs,  other carbon is displaced, and enters the atmosphere to maintain equilibrium.   The specific molecules released by fossil fuels exchange places with carbon in carbon reservoirs, and atmospheric CO2 continues to rise.
  
Let’s look at some of the isotope data, and then consider the size of the carbonsphere.

The volume of fossil fuel emssions is known, and about 60% of fossil fuel emissions appears to accumulate in the atmosphere.   [The percentage would be somewhat lower, if carbon from burning forests is included in the calculation.]  We can calculate the expected change in del 13 based on the volume of fossil fuel CO2 emissions, and compare this figure to the observed isotopic change in the global average del 13.  

Between 1979 and 2008, 194 Gigatonnes of carbon (=710 Gt CO2) was released to the atmosphere by burning fossil fuels and manufacturing cement.   The weighted average del 13 ratio of these emissions was -28.4, reflecting the very light isotopic composition of most fossil fuels.  The atmosphere in 1979 contained about 3 1/2 times that volume of carbon, 718 Gt (=2634 Gt CO2), with an average del 13 of -7.6.  

If we assume that 60% of the fossil fuel emissions remain in the atmosphere, and run a simple mixing calculation, we conclude that the del 13 ratio of the atmosphere should have declined to about -12, a change in del 13 of -4.4.   Instead, we see a decline of only -0.7, from the initial value of -7.6 in 1979 to a value of -8.3 in 2008.   Looking at the thirty-year history of carbon isotope observations, we can calculate that only about 14% of the carbon released by fossil-fuel emissions remains in the atmosphere, by matching the results of a mixing model to the observed decline in global del 13.   The rest of the fossil-fuel carbon is diluted into a much larger reservoir of carbon than the atmosphere. 

Figure 5 shows the expected change in del 13, based on varying models of fossil fuel emissions remaining in the atmosphere.   The isotope ratio shows that only 14% of fossil fuel emissions remain in the atmosphere.
I’m going to coin a term, and call the sum of all carbon reservoirs freely exchanging carbon with the atmosphere, within an annual time-frame, the Carbonsphere.  The Carbonsphere includes the atmosphere, all plants and animals on earth (including you), dissolved carbon in the shallow ocean, weathering surfaces on limestones, coral reefs, seashells and limestone precipitating directly in the ocean.   The Carbonsphere does not include limestone below the weathering surface or carbon in the deep oceans.  These do not participate in the annual exchange of carbon with the atmophere.

With the same data used above, we can solve the inverse problem: what is the volume of reservoirs exchanging carbon with the atmosphere?  It is a dilution problem, described by the coffee analogy in the introduction.  We know the volume of fossil fuel emissions, the isotopic composition of those emissions, and the isotopic change in the atmosphere.  We can find the volume of the carbonsphere by the dilution of fossil fuel emissions.  (Note, this calculation assumes negligible fractionation of carbon isotopes during exchange with carbon reservoirs.)

Figure 6 shows a set of models, assuming a range of sizes for the carbonsphere.    The best match shows a carbonsphere of about 5200 gigatonnes in 1977.  There is fluctuation in the isotopic composition of the atmosphere which does not match the model, which we will explore in the next blog post.   The initial model of 1500 Gt is about twice the carbon volume of the atmosphere.  Over time, for the past 40 years, a carbonsphere of about 5200 gigatonnes is required to quantitatively match the dilution of the global average isotopic composition of the atmosphere.  
Estimates for the size of carbon reservoirs are available from a variety of sources.   Estimates are generated by estimating the carbon inventory for the atmosphere, land vegetation, soil, plant detritus, ocean biomass, and carbon dissolved in surface waters of the ocean.  There is a considerable range in the estimates for individual reservoirs, but general agreement about the total.  
Here is a sampling of estimates, randomly selected from the Internet: 
Traeger, C., 2009                                             3555 Gt  
Falkowski, 2000                                               3390 Gt
World Ocean Review, 2013                              3797 Gt
Corrosion Doctors                                            3000 Gt
Wheeling Jesuit University                                  3675 Gt
US Climate Change Program                             4918 Gt
CDIAC (2012)                                                 3948 Gt                                                                
All of these estimates are less than the result (5200 Gt) produced by calculating dilution of del 13 from fossil fuel emissions. 

We can speculate about the discrepancy between the results of the dilution calculation, and those obtained by making a carbon inventory.   One possibility is that the atmosphere is not in equilibrium with the carbonsphere, i.e., that isotopically light carbon from fossil fuel emissions is tied up in reservoirs near the point of emission.  Thus, there is a transient effect, a lag before the equilibration of the emissions and the atmosphere.   We will see some evidence of this in the second part of this article.   Secondly, it may be that there is a greater dispersion of carbon in the ocean than estimated in the carbon inventory.  We will see some evidence of that, also, in the second part of this article.   But for the moment, the conclusion of this work is that the carbonsphere – the sum of all carbon reservoirs freely exchanging carbon with the atmosphere – is larger than previous estimates.

I should note that these data and calculations include only fossil-fuel emissions and making cement.   The emissions volumes and del 13 averages do not include carbon released through changes in land use, principally clearing forests for agriculture by burning.  Addition carbon from burning forests is also isotopically light.  If carbon from changes in land use is included in the calculations, we would see that an even smaller percentage of carbon emissions remain in the atmosphere, and the calculated size of the carbonsphere would be even larger.

Conclusions:
1)  Isotopically light CO2 released by burning fossil fuels provides a tool for tracking movements of carbon through the earth’s systems, and for calculating the size of carbon reservoirs exchanging carbon with the atmosphere.

2)  Carbon isotope ratios show that the percentage of carbon remaining in the atmosphere from fossil fuel emissions is about 14% of those emissions.  This is in marked contrast with estimates based on bulk atmospheric CO2, which indicate that 60% of fossil fuel emissions remain in the atmosphere.   The difference is due to the exchange of carbon between the atmosphere and carbon reservoirs on the earth’s surface.

3)  The Carbonsphere can be defined as the sum of all reservoirs freely exchanging carbon with the atmosphere.   The size of the Carbonsphere can be calculated, based on the observed dilution of the del 13 carbon ratio.   The calculated size of the carbonsphere is about 5200 gigatonnes.  This estimate is substantially larger than published estimates of the size of carbon reservoirs interacting with the atmosphere.   Sources of error might include disequilibrium of the atmosphere with carbon reservoirs near the source of fossil fuel emissions, resulting in an overestimate of the size of the reservoirs diluting the fossil fuel emissions.

This study could be improved by incorporating data for emissions relating to land use.    
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References:
Annual  Isotope Global Average:
Andres, R.J. T.A. Boden, and G. Marland. 2009.  Monthly
Fossil-Fuel CO2 Emissions: Mass of Emissions Gridded by One Degree
Latitude by One Degree Longitude.  Carbon Dioxide Information Analysis
Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak
Ridge, Tenn., U.S.A.  doi: 10.3334/CDIAC/ffe.MonthlyIsomass.2009

Global Emissions average isotope data:
Andres, R.J., Boden, T.A, and Marland, G., 2012

Previous posts om this site regarding atmospheric CO2:
2)  The Keeling Curve and Seasonal Carbon Cycles
3)   Seasonal Carbon Isotope Cycles
4)   Long-Term Trends in Atmospheric CO2
5)   Modeling Global CO2 Cycles
6)   The Keeling Curve Summary:  Seasonal CO2 cycles and Global CO2 Distribution
       http://dougrobbins.blogspot.com/2013/05/the-keeling-curve-seasonal-co2-cycles.html
8)   Carbon Isotopes in the Atmosphere, Part II
       Finding Niño -- Correlation CO2 Carbon Isotopes in the Atmosphere with the El Niño Cycle
        http://dougrobbins.blogspot.com/2013/11/carbon-isotopes-in-atmosphere-part-ii.html