Dynamic Emergy Accounting

Dynamic Emergy Accounting Simulation of emergy and transformity, network analysis of emergy, case studies

Simulation of Emergy and Transformity In this lecture we show ways to add equations for EMERGY and transformity to simulation models calculate EMERGY per time (empower), EMERGY of storages, and transformities.

Simulation of Emergy and Transformity • Rate equations of simulation models are first calibrated in units of energy or matter because these quantities follow laws of matter and energy conservation: • Matter inflowing must equal that stored and outflowing, • Energy inflowing must equal that stored and outflowing.

Simulation of Emergy and Transformity EMERGY, however, is a tabulation of energy previously processed (used) in making the product and is not reduced by the drain pathways necessary for dispersal of energy and product matter according to the second energy law. EMERGY is a memory evaluation

Simulation of Emergy and Transformity • Notation: • Source energy is designated with S as the first letter • Storages of energy/matter are designated with a Q as the first letter • EMERGY flows and storages are designated with E as the first letter. ES is flow of EMERGY from the source; EQ is EMERGY in the storage. • Transformities are designated with Tr for the first letters. For example, TrQ is the transformity of stored quantity Q; TrS1 is the transformity of source energy

Simulation of Emergy and Transformity • EMERGY Flow on a Pathway • Given an energy flow and its transformity, you can multiply to obtain the EMERGY flow. For example, a block of wood containing 1 million joules (1 E6 J) of wood energy has a solar EMERGY content of 3 E10 solar emjoules obtained as follows: • (Energy)(solar transformity) = (Solar EMERGY) • (1 E6 J wood)(4,000 SeJ/J) = 4 E9 seJ

Simulation of Emergy and Transformity • EMERGY flow can also be evaluated from the flow of matter or dollars…. • If data are in grams (rather than energy), EMERGY is calculated by multiplying be the material’s specific emergy. • If data are for goods and services, expressed in dollars, EMERGY is calculated by multiplying by an EMERGY/currency ratio.

Simulation of Emergy and Transformity Where two independent pathways join, the EMERGY of both pathways are added (providing the sources of the two are independent and not from a closed loop feedback). EMERGY contributions add through a productive interaction.

Simulation of Emergy and Transformity When dynamic models are simulated, there are rate equations for the storage variables that may be calibrated in energy, mass, or monetary units, as may be appropriate for each.

Simulation of Emergy and Transformity the EMERGY of a storage is defined by three equations used to calculate EMERGY and a fourth equation to calculate transformity.

Simulation of Emergy and Transformity Equations for Storage in Simulation Programs • By definition the transformity of the storage at any time is the EMERGY of the storage divided by the energy stored. • TrQ = EQ /Q

Simulation of Emergy and Transformity Equations for Storage in Simulation Programs One of three EMERGY equations is used to tally the EMERGY depending on whether a storage is growing, constant, or decreasing: If dQ/dt > 0, then dEQ = Ein - Eout IFdQ/dt =0, then dEq = 0 If dQ/dt < 0, then dEQ = EQ- (TrQ*dq/dt)

Simulation of Emergy and Transformity • If storage is increasing (dQ/dT > 0). the equation for its EMERGY storage is the sum of the inflows of EMERGY minus the outflows of usable EMERGY, but the concurrent necessary depreciation is not subtracted. • The energy lost from availability in depreciation is a necessary part of the process of storing EMERGY. • By definition, EMERGY only includes a tally of the available energies contributing positively to its formation and all expressed in Joules of one kind of energy.

Simulation of Emergy and Transformity If storage is constant (dQ/dT = 0). When there is no change in storage or change in its nature, there is no change in EMERGY storage.

Simulation of Emergy and Transformity If storage is decreasing (dQ/dT < 0)… the loss in EMERGY is the loss of the energy times the transformity of the storage. The transformity of a stored quantity within the system is calculated on each iteration by dividing the EMERGY for that storage (EQ)by its energy storage (Q)

Simulation of Emergy and Transformity Notice that the accumulation of emergy levels off before the quantity stored reaches steady state.

Simulation of Emergy and Transformity During the last 5% of the growth in real world examples, the EMERGY input is not really adding new storage value because fluctuations of this magnitude are present from the smaller scale (sometimes called statistical noise). Therefore, programs are given a statement that stops adding new EMERGY when the growth is within 5% of the steady state.

Simulation of Emergy and Transformity …without the 5% constraint, a simple storage with depreciation will accumulate emergy indefinitely .

Simulation of Emergy and Transformity Tilley (2000) suggested that the 5% constraint was not necessary as long as there was a Yield outflow…

Network Analysis of Emergy Using concepts of networks and input output analysis, emergy and transformity are calculated within “whole systems” taking into account transformation efficiencies and cycling…

Network Analysis of Emergy Definitions… Input/Output Analysis: Input/output analysis quantifies direct and indirect trophic effects for each component in a network. From this analysis, one can determine the full dependency of one compartment relative to all other compartments.

Network Analysis of Emergy Definitions… Trophic Status:The complexity of the structure of food webs can be simplified by mapping their trophic exchanges into a simple linear chain of composite trophic levels (Lindeman, 1942) by weighting and averaging the trophic position at which each compartment feeds.

Raymond Lindeman …the trophic-dynamic concept, by which organisms are classified according to how they obtain, use, and pass on energy to the next trophic level. As one follows the food chain of an ecosystem up through its trophic levels, the amount of available energy decreases dramatically with each step. Lindeman efficiencies …the efficiency of transformation from one trophic level to the next.

Network Analysis of Emergy Definitions… Cycling:A cycle is defined as a pathway in which material and energy travels through the food web to arrive at where it began (also known as an "arc").

Network Analysis of Emergy Cycling cont’d… System properties important in cycling include the number of cycles, whether cycles occur over short and fast pathways vs. long and slow pathways, and the percentage of material and energy that is recycled. Other measures include: 1) information about each arc, such as the amount of material and energy recycled through that arc and other pathways using that same arc (a "nexus"), and, 2) separation of cyclic and noncyclic pathways.

Network Analysis of Emergy Definitions… Ecosystem Indices: Ulanowicz (1986) has developed a suite of ecosystem level indices based on information theory. These indices characterize the state of a food web. They include total system throughput, ascendency, developmental capacity, overhead, and redundancy.

Network Analysis of Emergy Definitions… Total system throughputis simply the sum of all the flows that occur in that food web; it characterizes the overall activity of the ecosystem.

Network Analysis of Emergy Definitions… Ascendencyis a measure of the size and organization of flows and can be interpreted as the tightness of the constraints that channel trophic linkages. Higher values for ascendency represent a food web with more trophic specialists, increased cycling, and higher efficiency, while lower values for ascendency represent a more generalist-based food web, decreased cycling, and lower transfer efficiencies. The limit, or upper bound, to ascendency is the developmental capacity.

Network Analysis of Emergy Definitions… Developmental capacity is proportional to the variety of flows in a network, and is a surrogate for the complexity of an ecosystem. Developmental capacity minus ascendency equals overhead.

Network Analysis of Emergy Definitions… Overheadrepresents the amount of developmental capacity that does not appear as organized structure or constraints. That is, overhead represents all the ambiguities of connection and incoherencies of flow (i.e., disordered activity) that are available to be reorganized as an ecosystem develops.

Network Analysis of Emergy Definitions… Redundancyis that component of the overhead that reflects parallelisms in the internal pathways of trophic structure… Redundancy is believed to be an indicator of stress For example, a large number of redundant pathways present in a system may represent a system that is adapting to stress

Network Analysis of Emergy Energy systems diagram of a generic ecosystem.

Network Analysis of Emergy Energy, emergy and transformity in a typical food chain. The maximum empower principle predicts that feedback controls from a component (inferred from transformity) are commensurate with the emergy invested in supporting that component

Network Analysis of Emergy Diagram of bilateral and internal energy pathways compiled for each compartment within the input-output matrix.

Network Analysis of Emergy EXCEL Solver equations

Network Analysis of Emergy The “Legendary”, Brown/Herendeen Emergy puzzle

Energy flows Empower Transformities

X8 X6, X7 X2 X1 X3 X4, X5

3400 (+24%) 620 (+10%) 4800 (+60%) 12000 (+60%) 170 (-8%) There does not seem to be a pattern to the differences… Although the transformities are within reason… 2400 (-20% 4800 (+60%) 3400 (-47%) 620 (-42%) 4800 (-27%) 12000 (+220%) 170 (-34%) 2400 (-9% 4800 (+83%)

Network Analysis of Emergy

Network Analysis of Emergy Computed transformities for the Everglades ecosystem…

Dynamic Emergy Accounting