As described in §3.1.1, ST practitioners define the boundaries of a problem or system using a model boundary chart. Building on the description of carbon bathtub dynamics given in §2.1.1, Table 4.2 shows the endogenous, exogenous and excluded variables in the physical analogue.
Table 4.2: Model-boundary chart for design of the T&P system. The endogenous and exogenous variables are considered in the T&P system. The excluded variables are not considered further in the model.
Endogenous Exogenous Excluded
atmospheric carbon stock terrestrial, geological and oceanic carbon stock rate of natural additions rate of natural removals rate of anthropogenic additions
desired atmospheric carbon level rate of anthropogenic removals carbon flux between terrestrial, geological and oceanic stocks heat storage in stocks
temperature difference between
stocks
insolation and radiative forcing feedback processes
The stock-and-flow representation of the T&P system shown in Figure 4.4 is made up of two stocks and three flows, as described in the model boundary chart in Table 4.2. Unlike the bathtub stock-and-flow model shown in Figure 3.6, the T&P system is closed; that is, the amount of carbon in the system observes conservation of mass. Terrestrial carbon can move to the atmospheric stock through the natural and anthropogenic additions, and atmospheric carbon can be returned to the terrestrial stock through the natural removals. As discussed in §2.1, there is no anthropogenic removals flow, as this flow is currently negligible, and will remain so in the foreseeable future.
natural additions anthropogenic additions natural removals terrestrial carbon stock atmospheric carbon stock
Figure 4.4: Stock-and-flow representation of the T&P system. Carbon (water) moves from the terrestrial carbon stock to the atmospheric carbon stock through the natural and anthropogenic additions flows, and is returned through the natural removals flow.
The stock-and-flow model in Figure 4.4 is shown as a diagrammatic represen- tation of the T&P system in Figure 4.5. Participants manipulate the pumps, which are connected to tubs of water using pipes. The pumps that represent the natural and anthropogenic additions transfer water from the tub that represents
terrestrial stock to the tub that represents the atmospheric stock. The pump that represents natural removals transfers water from the tub that represents the atmospheric stock to the tub that represents the terrestrial stock.
TERRESTRIAL CARBON STOCK ATMOSPHERIC CARBON STOCK ANTHROPOGENIC ADDITIONS PUMP NATURAL ADDITIONS PUMP NATURAL REMOVALS PUMP
Figure 4.5: Diagram of the T&P system. Participants manipulate pumps which change the state of the stocks. Coordination is required by team members to simulate the system.
In a stock-and-flow simulation model, the behaviour of the model is governed by relationships and formulae. In the T&P activity, the behaviour is governed by the relationships and instructions given to the participants. Unlike a simulation model, the instructions in the T&P activity can be ignored or readily modified by the participants as they experiment with the physical system.
Dynamical behaviour
The behaviour of the T&P system through the instructions follow a simple scaffolded structure, described further in §4.2. The two dynamical relationships of interest in the activity are the dynamic equilibrium of the natural carbon cycle, and then the anthropogenic perturbation to the natural carbon cycle as the anthropogenic additions pump speeds up.
In the dynamic equilibrium situation, the natural additions pump and natural removals pump must remain approximately equal. This behaviour is shown in Figures 4.6a and 4.6b. Small fluctuations occur naturally in the interaction of the participants pumping. Although not part of the formal T&P model, this fluctuation has been described by participants as analogous to seasonal variations due to biomass respiration.
In the anthropogenic perturbation behaviour, the anthropogenic additions pump speed that is called for in the activity instructions is shown in Figure 4.6c, and the resulting observed water level in Figure 4.6d. The y-axis values are not given, as they are relative to the speed of the pump. For example, in Figure 4.6a, the pump speed could be slow or fast, and as long as the average speed is the same, then the level will remain the same.
a)
pump speed
time
natural additions = natural removals
b)
observed water level
time small fluctuations natural level c) anthropogenic additions time pump speed d)
observed water level
time
natural level anthropogenic
perturbation
Figure 4.6: Expected behaviour over time graphs for physical simulation. According to the instructions, natural additions must be kept approximately equal to natural removals (a). The reality of the physical system means that small differences between the two natural pumps typically lead to an oscillating behaviour (b). The anthropogenic additions pump disrupts this balance (c), and increases the observed level of water (d).
The final instruction in the T&P activity is to explore (a) the “what-if” scenarios given the situation presented in Figure 4.6d and (b) the challenge of stopping the water level from rising. The group uses the T&P system to explore their strategies. With the constraint that the natural cycle pumps must be pumping on average at the same speed, the only solution is to reduce the anthropogenic additions pump speed to zero to maintain the observed water level.