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].

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]

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) TrH = Tr(CrustHeat) Eqn. 4) 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

63 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

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

65 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 all- important 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 three- component 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.

REFERENCES

Brown and Ulgiati 2010. Updated evaluation of exergy and emergy driving the geobiosphere: A review and refinement of the emergy baseline. Ecological Modelling 221:2501-2508 Campbell D. E. 2000. A revised solar transformity for tidal energy received by the earth and dissipated globally: Implications for Emergy Analysis. pp. 255-263. In M.T. Brown, S. Brandt-Williams, D. Tilley, S. Ulgiati (eds.) Emergy Synthesis, Proceedings of the First Biennial Emergy Analysis Research Conference, The Center for Environmental Policy, Department of Environmental Engineering Sciences, Gainesville, FL. Campbell D., Bastianoni S., and Lu H., 2010. The Emergy Baseline for the Earth: Is it Arbitrary? Poster presented at the 6th Biennial Emergy Analysis and Research Conference, University of Florida, Gainesville, Fl. Odum H.T. 2000. Handbook of Emergy Evaluation Folio #2 - Emergy of Global Processes. The Center for Environmental Policy, Department of Environmental Engineering Sciences, Gainesville, FL. Odum, H.T. 1996. Environmental Accounting: Emergy and Environmental Decision Making John Wiley and Sons. New York.