1. Emergy & Complex Systems Day 2, Lecture 4…. Dynamic Emergy Accounting Simulation of emergy and transformity, network analysis of emergy, case studies

2. Emergy & Complex Systems Day 2, Lecture 4…. 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

3. Emergy & Complex Systems Day 2, Lecture 4…. 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

4. Emergy & Complex Systems Day 2, Lecture 4…. 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

5. Emergy & Complex Systems Day 2, Lecture 4…. 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. E S is flow of EMERGY from the source; E Q is EMERGY in the storage. Transformities are designated with Tr for the first letters. For example, Tr Q is the transformity of stored quantity Q; Tr S1 is the transformity of source energy Simulation of Emergy and Transformity

6. Emergy & Complex Systems Day 2, Lecture 4…. 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

7. Emergy & Complex Systems Day 2, Lecture 4…. 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

8. Emergy & Complex Systems Day 2, Lecture 4…. (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 Where two independent pathways join, the EMERGY of both pathways are added

9. Emergy & Complex Systems Day 2, Lecture 4…. 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

10. Emergy & Complex Systems Day 2, Lecture 4…. 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

11. Emergy & Complex Systems Day 2, Lecture 4…. By definition the transformity of the storage at any time is the EMERGY of the storage divided by the energy stored. Tr Q = E Q / Q Equations for Storage in Simulation Programs Simulation of Emergy and Transformity

12. Emergy & Complex Systems Day 2, Lecture 4…. One of three EMERGY equations is used to tally the EMERGY depending on whether a storage is growing, constant, or decreasing: Equations for Storage in Simulation Programs If dQ/dt > 0, then dEQ = E in - E out IFdQ/dt =0, then dEq = 0 If dQ/dt < 0, then dEQ = E Q - (Tr Q *dq/dt) Simulation of Emergy and Transformity

13. Emergy & Complex Systems Day 2, Lecture 4…. 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

14. Emergy & Complex Systems Day 2, Lecture 4…. 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

15. Emergy & Complex Systems Day 2, Lecture 4…. 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 (E Q )by its energy storage (Q) Simulation of Emergy and Transformity

16. Emergy & Complex Systems Day 2, Lecture 4…. Notice that the accumulation of emergy levels off before the quantity stored reaches steady state. Simulation of Emergy and Transformity

17. Emergy & Complex Systems Day 2, Lecture 4…. 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). Simulation of Emergy and Transformity Therefore, programs are given a statement that stops adding new EMERGY when the growth is within 5% of the steady state.

18. Emergy & Complex Systems Day 2, Lecture 4…. Simulation of Emergy and Transformity …without the 5% constraint, a simple storage with depreciation will accumulate emergy indefinitely.

19. Emergy & Complex Systems Day 2, Lecture 4…. Simulation of Emergy and Transformity Tilley (2000) suggested that the 5% constraint was not necessary as long as there was a Yield outflow…

20. Emergy & Complex Systems Day 2, Lecture 4…. 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…

21. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy 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. Definitions…

22. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy 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. Definitions…

23. Emergy & Complex Systems Day 2, Lecture 4…. 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.

24. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy 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"). Definitions…

25. Emergy & Complex Systems Day 2, Lecture 4…. 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 Cycling cont’d…

26. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy 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. Definitions…

27. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy Total system throughput is simply the sum of all the flows that occur in that food web; it characterizes the overall activity of the ecosystem. Definitions…

28. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy Ascendency is 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. Definitions…

29. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy 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. Definitions…

30. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy Overhead represents 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. Definitions…

31. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy Redundancy is that component of the overhead that reflects parallelisms in the internal pathways of trophic structure… Definitions… 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

32. Emergy & Complex Systems Day 2, Lecture 4…. Energy systems diagram of a generic ecosystem. Network Analysis of Emergy

33. Emergy & Complex Systems Day 2, Lecture 4…. 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

34. Emergy & Complex Systems Day 2, Lecture 4…. Diagram of bilateral and internal energy pathways compiled for each compartment within the input-output matrix. Network Analysis of Emergy

35. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy EXCEL Solver equations

36. Emergy & Complex Systems Day 2, Lecture 4…. The “Legendary”, Brown/Herendeen Emergy puzzle Network Analysis of Emergy

37. Emergy & Complex Systems Day 2, Lecture 4…. Energy flows Empower Transformities

38. Emergy & Complex Systems Day 2, Lecture 4…. X2 X3 X8 X4, X5 X6, X7 X1

39. Emergy & Complex Systems Day 2, Lecture 4…. 3400 (+24%) 620 (+10%) 4800 (+60%) 12000 (+60%) 170 (-8%) 4800 (+60%) 2400 (-20% 3400 (-47%) 620 (-42%) 4800 (-27%) 12000 (+220%) 170 (-34%) 4800 (+83%) 2400 (-9% There does not seem to be a pattern to the differences… Although the transformities are within reason… There does not seem to be a pattern to the differences… Although the transformities are within reason…

40. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy

41. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy

42. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy

43. Emergy & Complex Systems Day 2, Lecture 4…. Network Analysis of Emergy Computed transformities for the Everglades ecosystem…