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A Different Take on the Emergy Baseline –
Or Can There Really Be Any Such Thing
Marco Raugei
ABSTRACT
The phrase ‘emergy baseline’ refers to the total yearly environmental support to the geobiosphere in
terms of the emergy concept, and should include all three fundamental sources of exergy (i.e. sunlight,
tidal exergy and deep earth heat). Ever since its introduction, the emergy baseline has undergone a
continuous revision process, which, however, has so far focussed on the underlying equations and
resulting numerical values, without questioning the fundamental theoretical soundness of such
calculations. An alternative take on the issue is presented here, namely that it may be
epistemologically incorrect to seek a simple scalar baseline encompassing all three exergy sources.
Instead, a ‘baseline vector’ could be defined, where the three fundamental inputs of exergy to the
geobiosphere are kept separate at all times, not unlike the three independent axes of a Cartesian
space.
BACKGROUND
The phrase ‘emergy baseline’ is commonly meant to refer to the total yearly environmental
support to the geobiosphere in terms of solar emergy, including all three fundamental sources of
available energy (i.e. sunlight, tidal exergy and deep earth heat). Ever since its introduction by H.T.
Odum [1996], the modern emergy baseline has undergone a continuous revision process, which has not
failed to spark controversy [Campbell, 2000; Campbell et al., 2010; Brown and Ulgiati, 2010].
However, the debate so far has centred on the underlying equations and resulting numerical value of
the baseline. This paper does not intend to further discuss which may be the most accurate or reliable
sets of exergy and emergy numbers for the global flows driving the geobiosphere; instead, it aims to
perform a critical review of the fundamental theoretical and methodological premises underpinning the
approaches that have hitherto led to such ‘emergy baselines’ in the first place.
The basic premise of the very concept of a simple, scalar emergy baseline is of course that it is
somehow possible to combine a set of equations so as to compute solar transformity values for the two
non-solar fundamental inputs of exergy to the geobiosphere, namely tidal exergy and deep earth heat.
Figures 1 and 2 and the related equations illustrate the most commonly adopted approach to
calculating the emergy baseline, based on Emergy Folio #2 [Odum, 2000] and a recent paper by Brown
and Ulgiati [2010]. Other calculation approaches [Campbell, 2000; Campbell et al., 2010] mainly
differ in how the individual emergy contributions to the global biogeosphere are combined, but do not
question the fundamental axiom whereby “the solar emergy of tidal energy and deep earth heat were
estimated by the special procedure of setting two inputs making the same product as equivalent”
[Odum, 2000].
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Figure 1. Energy Systems Language diagram for the generation of the exergy of crustal heat.
Source: after Brown and Ulgiati [2010]
Eqn. 1a)
Sun · 1 + Tide · TrT + RadHeat · TrH = CrustHeat · TrH
Crustal heat (CrustHeat) is “the difference between total geothermal heat (TotGeothHeat) and the
deep core heat (DeepHeat)” [Brown and Ulgiati, 2010]. Given that crustal heat may itself be
decomposed into the sum of surface crustal heat (SurfCrustHeat), which is generated by sunlight and
tidal exergy, and heat generated by radioactive decay in the crust (RadHeat), Eqn. 1a may be re-written
as:
Eqn. 1b)
Sun · 1 + Tide · TrT = SurfCrustHeat · TrH
It is thus plain to see that Eqn. 1b is essentially the same as Eqn.1 in Emergy Folio #2 [Odum,
2000].
Eqn. 2)
Sun · 1 + Tide · TrT + RadHeat · TrH + DeepHeat · TrH =
= OcnGepot · TrT
Figure 2. Energy Systems Language diagram for the generation of ocean geopotential exergy.
Source: after Brown and Ulgiati [2010]
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Eqns. 1a and 2 form a system of two equations with two unknowns, which may be combined to
arrive at the numerical values of TrH and TrT.
Two fundamental assumptions are revealed when looking at Eqns. 1a and 2, though, namely that:
a) the solar transformities of (i) deep heat from the earth’s core (DeepHeat), (ii) heat from radioactive
decay in the crust (RadHeat), (iii) surface crustal heat (SurfCrustHeat), (iv) (total) crustal heat
(CrustHeat), and (v) total geothermal heat (TotGeothHeat) are all assumed to be equal;
b)the solar transformities of (vi) tidal exergy (Tide) and (vii) total ocean geopotential exergy
(OcnGeopot) are assumed to be equal.
Given that most, if not all, of the heat emanating from the earth’s core is widely understood to be
of radioactive origin, the assumption that Tr(DeepHeat) = Tr(RadHeat) = TrH may be maintained to
be true by definition. But we are still left with the following two assumptions that call for careful
consideration and discussion, in the light of the fundamental dictates of the emergy theory:
Eqn. 3)
Eqn. 4)
TrH = Tr(CrustHeat)
TrT = Tr(OcnGeopot)
BACK TO BASIC THEORY
If we go back to Eqn. 1a, we see that, in principle, we should have:
Eqn. 5)
Sun · 1 + Tide · TrT + RadHeat · TrH = CrustHeat · Tr(CrustHeat)
Since RadHeat is only one of the contributors to the formation of CrustHeat, according to the basic
emergy algebra:
Eqn. 6)
Tr(CrustHeat) = (Sun + Tide · TrT + RadHeat · TrH) / CrustHeat
The same reasoning holds for Eqn. 2, which leads to:
Eqn. 7)
Tr(OcnGeopot) = (Sun + Tide · TrT + RadHeat · TrH +
+ DeepHeat · TrH) / OcnGeopot
This is now a set of two equations with four unknowns, which is no longer solvable. A convenient
way out of this conundrum is of course to introduce the assumptions listed in Eqns. 3 and 4, which
essentially correspond to stating that if two exergy flows (RadHeat and CrustHeat, or Tide and
OcnGeopot) are indistinguishable at the point of use (an eminently user-side consideration), then their
transformity must also be the same. However, according to the theory, emergy is supposed to be the
“the available energy (exergy) of one kind that is used up in transformations directly and indirectly to
make a product or service” [Odum, 1996]; this being the case, two exergy flows which were clearly
produced by different processes (such as RadHeat vs. CrustHeat, or Tide vs. OcnGeopot) should not be
expected to have the same transformity, regardless of the ability to tell them apart at the point of use.
But there is an even more fundamental fault with the whole idea of calculating an ‘emergy
baseline’ as a simple scalar quantity. The very concept of ‘solar transformity’ relies on the premise that
it is possible to find a series of transformations that link back the formation of a product or service to
the amount of sunlight exergy that was ultimately at its origin. It is not coincidental that at the dawn of
the emergy theory the focus was placed only on sunlight as the sole input to the geobiosphere, as this
makes the calculations straightforward and sidesteps the whole baseline issue altogether. For instance,
if X Joules of solar exergy are required to drive the photosynthetic processes that lead to 1 J of plant
biomass, and then Y J of such plant biomass is required by a herbivore’s metabolism to produce 1 J of
living tissue, we may say that the herbivore’s solar transformity is X · Y seJ/J, of course. The
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fundamental point being made with this simple example is that, in first approximation, sunlight is the
ultimate exergy source underpinning those two transformations. If one instead considers tidal exergy or
heat from radioactive decay, the problem becomes fundamentally different. The origin of tidal exergy
(Tide) lies in the gravitational pull exerted by the earth-moon system, and that of ‘deep earth heat’
(intended as that part of total geothermal heat which is independent of sunlight and tides, i.e.
RadHeat+DeepHeat) lies in the radioactive decay of chemical elements which were originally formed
at the same time as (or even before) the solar system itself. Clearly, neither of these processes can be
said to have been ultimately driven by sunlight exergy. Thus, in essence, since the origins of tidal
exergy and ‘deep earth heat’ cannot be traced back to sunlight, it is arguably conceptually impossible
to compute solar transformities for them while staying true to the fundamental dictates of the emergy
theory.
THE PROPOSED ALTERNATIVE
The realization that tidal exergy and deep earth heat cannot, by strict definition, have any solar
transformities, whatsoever, inevitably calls for a radically different approach to the whole issue of the
emergy baseline.
In principle, the first and possibly most obvious way to tackle this, from a conceptual viewpoint,
would be to simply take one step back and search for one common originator of all three fundamental
exergy flows that drive the geobiosphere as we know it. The usual emergy equations could then be
applied to the respective generating processes, in order to arrive at transformities for sunlight, tidal
exergy and radioactive heat that are fully consistent with the donor-side approach that characterizes
emergy theory. In practice, though, this would entail at least quantitatively analyzing, in terms of
exergy flows, the formation process of the solar system. But, apart from the sheer difficulty of
controlling the huge uncertainty in such calculations, it should also be noted that many radioactive
heavy metals (whose nuclei are heavier than Fe) which are found on earth today actually pre-date the
formation of the solar system, since they were released into cosmic space by previous supernova
explosions. The search for the ultimate common origin of sunlight and radioactive heat therefore
quickly turns into an almost infinite recursive process, which could arguably only find a proper closure
in the full emergy analysis of the entire universe. Theoretically fascinating though this may sound,
from a practical standpoint it is also clearly an essentially unachievable goal.
A second and more reasonable alternative for calculating the emergy baseline is instead proposed
here, which still takes into proper account all three fundamental global exergy inputs to the
geobiosphere, without violating any theoretical premise.
In essence, a ‘baseline vector’ may be defined, where the three fundamental and independent
inputs of exergy to the geobiosphere (Sun, Tide, and RadHeat+DeepHeat) are kept separate at all
times, not unlike the three axes of a Cartesian space:
baseline =
‹Sun, Tide, (RadHeat+DeepHeat)›
The correct units for the three components of such vector are thus, respectively, solar joules per
year (seJ/yr), tidal joules per year (teJ/yr) and radioactive heat joules per year (heJ/yr). It may also be
acceptable to adopt a shorthand “eJ/yr” for the vector as a whole, thereby just implying the appropriate
prefixes for the three individual components.
Clearly, we have:
Tr(Sun) = TrS
= ‹1, 0, 0› eJ/J
Tr(Tide) = TrT = ‹0, 1, 0› eJ/J
Tr(RadHeat) = Tr(DeepHeat) = TrH = ‹0, 0, 1› eJ/J
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Using for instance the recently revised values for the global exergy flows of Sun, Tide and
(RadHeat+DeepHeat) reported by Brown and Ulgiati [2010], one would get:
baseline =
‹ 3.59 E+24 , 1.17 E+20 , 1.63 E+20 › eJ/yr
It is then perfectly possible for one or more components of the newly defined transformity vectors
to be below unity. For instance, again according to Brown and Ulgiati [2010], the yearly total ocean
geopotential exergy flow (OcnGeopot) is 2.14E20 J/yr. Given that, according to Figure 2, all three
independent exergy inputs to the geobiosphere (Sun, Tide and RadHeat+DeepHeat) fully contribute to
the process that leads to OcnGeopot, we have:
Tr(OcnGeopot) = 1/(OcnGeopot) · baseline =
= 1 / (2.14 E+20) · ‹ 3.59 E+24 , 1.17 E+20 , 1.63 E+20 › =
= ‹ 1.68 E+04 , 0.547 , 0.762 › eJ/J
The interpretation for this is that, on average, during the generation of one joule of overall ocean
geopotential exergy, almost 17,000 J of sunlight are inflowing (and are thus accounted for as
contributing to the process), while the gravitational pull of the moon only adds about half a joule of
tidal exergy, and the radioactive decay processes occurring in the earth’s crust and core add an
additional 0.76 J of ‘deep earth heat’ (each along their respective linearly independent axes, having
units of SeJ/J, TeJ/J and HeJ/J).
In the case of crustal heat (i.e. CrustHeat = TotGeothHeat – DeepHeat from the earth’s core),
according to Figure 1, only Sun, Tide and RadHeat contribute to its generation. Accordingly, one
should not apply the complete baseline, but only the part thereof that actually contributes to the
process. Leaving aside for the moment the issue of the remaining uncertainty on the exact
quantification of the three components of total geothermal heat, if one takes, for instance, RadHeat =
0.70 E+20 J/yr and CrustHeat = 5.6 E+20 J/yr (arithmetic means of the respective exergy value ranges
in Brown and Ulgiati [2010]), one gets:
Tr(CrustHeat) =
= 1 / (5.6 E+20) · ‹ 3.59 E+24 , 1.17 E+20 , 0.70 E+20 › =
= ‹ 6.4 E+03 , 0.21 , 0.13 › eJ/J
Surface crustal heat (defined as SurfCrustHeat = CrustHeat – RadHeat), being only generated by
Sun and Tide, will of course have a different transformity, in which the third component is zero:
Tr(SurfCrustHeat) =
= 1 / (5.6 E+20 – 0.7 E +20) · ‹ 3.59 E+24 , 1.17 E+20 , 0 › =
= ‹ 7.3 E+03 , 0.24 , 0 › eJ/J
Finally, if one is instead interested in total geothermal heat (TotGeothHeat = CrustHeat +
DeepHeat), one will revert to using the full baseline and get (adopting once again, for the sake of
simplicity, the arithmetic mean of the published exergy values in Brown and Ulgiati [2010]):
Tr(TotGeothHeat) =
= 1 / (7.3 E+20) · ‹ 3.59 E+24 , 1.17 E+20 , 1.63 E+20 › =
= ‹ 4.9 E+03 , 0.16 , 0.22 › eJ/J
It bears reiterating once again that the purpose of this paper is not to validate or even support any
particular author’s numerical estimates of the actual values of these global exergy flows (the choice to
employ the latest published estimates was just driven by the intention to avoid unnecessarily obsolete
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numbers). As a result, the resulting transformities computed here may or may not be numerically
accurate and reliable.
What instead is noteworthy is that, regardless of the uncertainties in the adopted numbers, from a
methodological point of view this new approach is, in all cases, perfectly consistent with the strictly
‘donor-side’ logic which fundamentally defines emergy theory, and it does not require any ‘ad hoc’
assumptions or “special procedure of setting two inputs making the same product as equivalent”. One
further clear advantage of defining the emergy baseline as a vector quantity is that it makes it much
more straightforward to correctly analyze those processes that draw from the three fundamental exergy
inputs to the geobiosphere in different proportions with respect to the global baseline.
CONCLUSIONS
A fundamentally new take on the issue of the ‘emergy baseline’ has been proposed and illustrated.
This new approach, based on vector algebra, completely sidesteps a number of previously inevitable
‘ad hoc’ assumptions that stretched the theory and left Emergy Synthesis somewhat lacking in the allimportant aspects of fundamental methodological rigour and integrity.
The downside is that adopting such new approach to emergy calculations would at once require a
complete overhaul of the entire body of existing case studies, since transformities and unit emergy
values (UEVs) for all products and services would have to be re-calculated and expressed as threecomponent vectors. Yet, this could possibly provide the only fully consistent and theoretically rigorous
way out of the lingering ‘baseline conundrum’.
ACKNOWLEDGEMENTS
The author gratefully acknowledges the inspiring exchange of ideas and viewpoints on the topic
that took place among the participants of the working group on ‘Emergy and LCA’, and specifically
the insightful comments made by Dr. Xin Ma, Prof. Sergio Ulgiati and Prof. Mark T. Brown.
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review and refinement of the emergy baseline. Ecological Modelling 221:2501-2508
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