Howard T. Odum*
After reviewing the concepts of energy hierarchy and scale, emergy terms are
defined including transformity, emergy storage, empower, mass emergy, empower
density, work and emdollars. Emergy is related to spatial centers and to pulsing
with time. Evaluations include macroeconomics of states and nations and the
economic-environmental interface of microeconomics. Emergy indices are used to
evaluate alternatives for primary energy sources, environmental impacts, and
international exchange. Maximizing empower is a policy criterion for selecting
alternatives that maximize production and use of real wealth. Systems diagrams
help clarify emergy evaluation for some of the many different ways and scales
the human mind aggregates and simplifies the networks of society and
environment. An example is included of emergy evaluation in a lawsuit.
In this chapter let's look at the basic energetics of systems to show how the
work of nature and society can be evaluated on a common basis so as to select
alternatives which succeed. Systems diagrams are used to clarify the
simplifications that humans need in their window of attention.
The structures and storages that operate our world of humanity and
environment are sustained against the depreciation of the second law by
productive inputs for replacement and maintenance. Maximizing the products and
services for growth and support appears to be a design principle of self
organization as given by Alfred Lotka as the maximum power principle. Pathways
in Figure 1 illustrate the flows and conservation of energy. The storage is
represented with a tank symbol. The heat sink symbol represents the dispersal of
available energy from processes and storages according to the second law. The
feedback from right to left interacts as a multiplier increasing energy intake.
This autocatalytic loop is one of the designs that prevail because they
reinforce power intake and efficient use.
Figure 1. Energy transformation, storage, and feedback reinforcement found
in units self organized for maximum performance. Energy systems symbols (3).
Self organization develops a network of energy transformations in a series.
With Figure 2 we put our window of attention on a typical network of energy
transforming components like the one discussed in Figure 1. From left to right
the total quantity of energy decreases, but the quality increases (in the sense
of more energy transformations required in the making). Since energy flows are
converging at each step to make fewer flows of energy at the next, it is an
energy hierarchy. Energy decreases from left to right, but the transformed
energy increases its ability to reinforce other units of the system. Since all
known processes can be arranged with each other in series network like that in
Figure 2, the energy hierarchy appears to be a universal law. Examples are the
energy chains in organisms, ecosystems, economies, earth processes, and the
Work is defined here as the available energy degraded in an energy
transformation. Since many joules of available energy on the left are required
to make the successive transformations to form a few joules of available energy
on the right, it is quite invalid to use joules of one kind of energy as
equivalent to joules of another for purposes of evaluating contributions (1, 6).
However, we can express each kind of available energy in units of one kind of
Figure 2. Systems window-view of a network of mutually necessary, energy
transformation running on the same source.
Emergy (spelled with an "m") evaluates the work previously done to make a
product or service. Emergy is a measure of energy used in the past and thus is
different from a measure of energy now. The unit of emergy (past available
energy use) is the emjoule to distinguish it from joules used for available
energy remaining now. Scienceman describes emergy as energy memory (Odum, 4, 6,
10; Scienceman, 9, 10). A book summary of emergy concepts and accounting is
available (6), and elementary introductions and examples are included in our new
text on Florida (7). Definitions are summarized in Table 1.
Table 1. Emergy and Related Definitions(6)
Available Energy = Potential energy capable of doing work and being degraded
in the process (Units: kilocalories, joules, BTUs, etc.)
Useful Energy = Available energy used to increase system production and
efficiency (units: available joules, kilocalories, etc.)
Power = Useful energy flow per unit time (units: joules per time)
Emergy = Available energy of one kind previously required directly and
indirectly to make a product or service (units: emjoules, emkilocalories, etc.)
Empower = Emergy flow per unit time (units: emjoules per unit time)
Work = An energy transformation process which results in a change in
concentration or form of energy.
Transformity = Emergy per unit available energy of one kind (units: emjoule
Solar Emergy = Solar energy required directly and indirectly to make a
product or service (units: solar emjoules)
Solar Empower = Solar emergy flow per unit time (units: solar emjoules per
Solar Transformity = Solar emergy per unit available energy (units: solar emjoules per joule)
There is a different kind of emergy for each kind of available energy. For
example: solar emergy is in units of solar emjoules, coal emergy in units of
coal emjoules, and electrical emergy in units of electrical emjoules. There is
no emergy in degraded energy (energy without availability to do work). Like
energy, emergy is measured in relation to a reference level. In most
applications we have expressed everything in units of solar emergy.
Aggregated view of the main energy hierarchy of the earth biosphere which starts
with 3 main energy sources
Figure 3 summarizes the energy hierarchy of the biosphere starting with the
abundant but dilute solar energy. The annual global emergy budget was calculated
as the sum of solar energy, tidal energy, and geological deep energy
contributing to surface transformations each expressed as solar emergy.
Transformities increase to the right as energy flows decrease. Information has
the highest transformities. The rate of use of fossil fuels emergy is now of the
same order of magnitude as the other planetary inputs. As the global climate and
other earth processes becomes coupled to this additional but temporary emergy
source, rains, winds, and waves may be developing higher transformities.
The rate of emergy flow is named empower with units: emjoules per time. Flows
of entirely different kind may be compared by expressing them all in empower
units of the same kind such as solar empower or electrical empower. For the
example in Figure 2b, which has only one independent source, the empower of all
the pathways is 1000 Type A emjoules per time.
The transformity is defined as the emergy (in emjoules) of one kind of
available energy required directly and indirectly (through all the pathways
required) to make one joule of energy of another type. Transformity is the ratio
of emergy to available energy. In
Figure 1 the transformity of the output is 10
type A emjoules per joule. With the units sej/J, transformity is not a
dimensionless ratio. Ten ways of calculating transformities were suggested (6,
p. 277). The most common way is to evaluate a system in which the item of
interest is a product.
In going from left to right through the energy hierarchy in Figure 2,
transformity increases greatly. Transformity measures the position of any energy
flow or storage in the universal energy hierarchy.
A familiar plot in many fields of science is the graph of turnover time
versus territory. Items of larger territory have longer turnover times.
Transformity also increases with scale. In our systems diagrams, items are
placed in their position according to their transformity. Scale of time, space,
and transformity increases from left to right.
The distribution of transformities is suggested with Figure 4, inverse to
energy flow. Energy of one kind is effectively used only when it interacts with
(amplifies) matching energy of lower or higher transformity. Thus there is an
appropriate position in the energy spectrum for efficient use of each kind of
In theory every item has a minimum transformity from the most efficient
formation possible consistent with operations at the optimal loading for maximum
empower. However, where a system is newly developed, is operating faster than
the rate for maximum empower, or is otherwise inefficient, the transformity may
be much higher than the thermodynamic minimum. Both transformities (a minimum
value and the observed larger values) are useful, one to compare potentials, the
other to evaluate current practices.
Figure 4. Distribution of transformities.
Self organization generates spatial centers as part of energy hierarchy. One
reason is that spatial concentration is a way of making transformed high quality
flows of less energy have a commensurate feedback effect outward to reinforce
the system. Examples are the information centers of cities, the water
convergence at the mouths of rivers, and the concentration of organic matter in
tree trunks. Concentrations are readily measured as areal empower density with
values ranging from less than 1 E11 sej/m2/yr in wilderness to 50,000 E11 sej/m2/yr
in city centers.
Flows and storages of matter carry available energy and emergy.
Transformations that concentrate matter require emergy inputs. For example,
emergy per mass of lead increases with lead concentration (8). For the practical
purpose of making emergy calculations, it is convenient to develop tables of
mass emergy (emergy per unit mass). McGrane (2) evaluated materials of the earth
cycles. Traditional biogeochemical cycles should be redrawn to reflect their
position in energy hierarchy according to their emergy/mass. Cycles of materials
converge to hierarchical centers and diverge again as they return to more dilute
environment. Emergy contribution of land can be evaluated from the erosion rate
times the transformity of the geologic substrate, which was formed at an earlier
Information including learned information and genetic information has energy
carriers (examples: paper, neurons, computer disk, sound waves), which can
disperse, depreciate, and develop error. Information has emergy according to the
emergy required to make and sustain it. Information is something which requires
less emergy to copy than to generate anew. Although copying is cheap,
maintaining information without error requires a population of duplicates and a
circular process of duplication, dispersal, reapplication, selection and
duplication again. Someone needs to rearrange the thousands of life cycle
diagrams of plants and animal life histories taught in biology courses in order
of the transformity of the stages and evaluate their emergy bases. Transformity
of extracted information (examples: a seed, code, or house plan) is higher than
the same information within the system it is operating (corresponding examples:
a plant, a computer, or a house). Values are large where information is widely
shared (examples: genetic plan of life, bible). Emergy of generating new
information from precursors can be huge, as in evolution.
Emergy evaluation has to adapt to the way systems are aggregated in the
window view of the mind's eye. Figure 5a, called a split, drawn with a branch,
has a product outflow divided into two flows of the same kind (same transformity)
dividing energy and the emergy by the same percentages. Splits add if
recombined. For example, a stream may split as it flows around an island,
recombining on the other side. Figure 5b shows co-products, drawn with separate
lines from the transformation unit. Both have the same empower, but their energy
flows are different so the output transformities are different. Examples are the
meat and wool from sheep production and limbs and leaves from forest production.
Dashed lines within the block in Figure 5b suggests the way the two outputs may
develop different transformities by arising from a different level in the energy
hierarchy. Care has to be exerted not to double count the same emergy if these
flows recombine. Figure 5c is a mixture with co-products and a split. To
evaluate a mix, the emergy of each input flow is traced separately to the place
where its last available energy is used up and the results added (11). The
numerical results are given in the figure legend.
Figure 5. Types of
(a) Splits; (b) co-products; (c) mix
of splits and co-products with flows from each source evaluated separately and
added: A = 100; B = 20 + 50; C = 80 + 50; D = 100 + 50; E = 20 + 10; F = 80 +40;
G = 50.
Apparently, all systems on all scales pulse (Figure 6). Gradual accumulation
of one storage is followed by a short period of frenzied consumer use and
development which disperses materials, setting up the next growth period. Pulses
cause oscillations in emergy, empower, and transformity. Inputs from pulses on
smaller scale than the window of interest look like noise and can be averaged as
if there was a steady state. The infrequent pulses from the larger scale than
the window of interest are catastrophic with high transformity and effect
(hurricanes, earthquakes, economic pulses, information storms, etc.).
Figure 6. Pulsing on many scales.
To include emergy in a simulation model, three emergy evaluation equations
are added for each state variable: one for periods of storage growth, one for
periods of unchanging storage, and one for periods of declining storage. (1) If
there is growth, emergy increases as the sum of the contributing inflows used
times their transformities minus any outflow to other use (but not minus
depreciation). Depreciation during growth is a necessary energy dispersal to the
transforming and storing process. (2) If the storage is unchanging the emergy is
constant. 3) If the storage is declining for whatever reason, emergy loss is the
loss of storage times its transformity. The expression for storage transformity
is the emergy accumulated divided by the energy accumulated. For the program
EXTEND, Odum and Petersen (5) programmed icon-objects that automatically
evaluate emergy when connected on computer screen and simulated.
Real wealth (food, clothes, houses, materials, water, jewelry, knowledge,
literature, art, etc.) is measured by its emergy. Money buys real wealth
according to market prices. By dividing the total emergy use of a country by its
gross economic product, an emergy/money ratio is obtained (Figure 7). The part
of the gross economic product due to an emergy contribution can be estimated as
the emergy value divided by the emergy/money ratio. The result is in emdollars
(abbreviated em$). The emergy/money ratios of two countries are required to
evaluate the real wealth benefits of their international trade and financial
Figure 7. Emergy overview of the macroeconomy of the United States.
Emergy/money ratio = [(45+35+8) E23 solar emjoules/yr] / [6.7 E12 $/yr] =
1.33 E12 sej/$.
Economic use of environmental resources involves free inputs from environment
and purchased inputs from the economy (Figure 8). Resource use is evaluated with
energy and transformities.
Where data on labor and services are in money units, the average empower can
be estimated using the emergy/money ratio of the economy contributing the
services. However, allocating emergy according to an average does not evaluate
many services correctly. Some are not paid for. With a wide range of
transformities services do not correspond to money paid. However, evaluation can
be made using transformities of occupations, education, and experience.
Purchased inputs such as fuels, electricity, and critical materials have high
emergy values in addition to that in the services involved.
Useful emergy indices for comparing states and nations include: emergy use
per person, fraction of emergy that is electrical power, emergy self
sufficiency, net benefit from foreign exchange, ratio of economic emergy/free
emergy, and emergy signature (graph of emergy inputs versus transformity).
For economic use of resources (Figure 8), the net emergy ratio measures the
net benefit to the economy (emergy of the yield Y divided by the emergy of the
feedback F from the economy). Because of the high emergy of human services
required, net emergy contributions of some alternate energy sources such as
biomass ethanol and solar technology are small or negative.
Figure 8. Interface between environment and economic use.
Environmental impact (Figure 8) is measured by the emergy investment ratio
defined as the ratio of the emergy purchased from the economy divided by the
emergy from the local environment. Developed states have ratios of 7 or higher.
National parks and wilderness have ratios of 1 or less. Ratios higher than those
of the surrounding area do not compete economically because costs are higher
than alternative investments.
To form public policy for maximum benefit, select alternatives that maximize
useful empower. By restating Lotka's principle in empower units we recognize
that beneficial organization increases intake emergy (first priority) and its
efficient use (second priority) on all scales (not just maximizing levels with
more energy; not maximizing some levels at the expense of others).
The net emergy ratio of its best fuel sources determines a state's support
for other activity. Developed countries in recent years have had ratios between
3 and 12 times more emergy input than was used to get it.
In practical applications evaluation starts by defining a window and drawing
a systems diagram usually with energy language symbols. Important pathways are
identified and data are assembled for each line item. Energy flows and storages
are multiplied by transformities to get emergy values and divided by emergy/money
ratios to get emdollars. Table 2 is an emergy evaluation table used in a
A landowner destroyed 84 hectares of mangrove ecosystems and their water
exchange pattern in Lee County Florida. Environmental protection agencies
engaged him in a regulatory lawsuit in which the value of the mangroves was in
debate. The market value of the fish and mangrove wood was in the thousand
dollar range. Market evaluations are usually smaller than emdollar evaluations,
because economic values only cover the services involved,
The Florida State Environmental Protection lawyers asked for an emdollar
evaluation. The annual emergy previously harnessed by mangrove production was in
the million emdollar dollar range, just from a partial analysis in Table 2. In
mangroves that required 30 years to develop, the natural capital stored was 30
times greater. After two formal depositions, the landowner settled out of court.
Table 2. Annual Emergy Uses by 84 ha of Mangroves in Lee
Solar Energy Environment
1000 U.S Emdollars
a. (energy in J/yr)(solar transformity in sej/J)/(1.3 E12 sej/1997 U.S. $)
b. Direct environmental contributions
c. Direct environmental contribution plus its attracted economic inputs
assuming regional emergy investment ratio for Florida of 7/1.
d. Transformities from page 309 in Environmental Accounting
1. (0.5 m tide)(706 tides/yr)(1.02 E3 kg/m3)(9.8 m/sec2)(8.4 E5 m2 area) =
3.0 E12 J/yr
2 .Freshwater flow from inland:
(1.3 m3/m2/yr)(1 E6 g/m3)(5 J Gibbs En./g)(8.4 E5 m2) = 5.5 E12 J/yr
3. Rain used: (1.0 m3/m2/yr)(1 E6 g/m3)(5 J Gibbs En/g)(8.4 E5 m2) = 4.2 E12
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* Environmental Engineering Sciences, University of Florida, Gainesville, 32611. The extended explanation of Emergy Evaluation can be found
Odum, H.T. 1996. Environmental Accounting, Emergy and
Decision Making. John Wiley, NY, 370 pp.
This paper was presented at the International Workshop on Advances in Energy Studies: Energy
flows in ecology and economy, Porto Venere, Italy, May 27,1998.
See original at < http://www.enveng.ufl.edu/homepp/brown/syseco/default.htm >.