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(Haygarth and Jarvis, 1999). The volume of the cost-cube is proportional to the total<br />

pollutant loss. If each combination of dimension and <strong>as</strong>pect is equally important in<br />

contributing to the observed pollutant loss, then the Cost-Cube is made up of 27<br />

equally sized cubes.<br />

MOBILISATION<br />

Contingent<br />

S olubilis able<br />

Detachment<br />

Internal<br />

External<br />

Recycled<br />

SOURCE<br />

Surface<br />

Preferential<br />

Through<br />

TRANSPORT<br />

Figure 1: Dimensions and <strong>as</strong>pects of the Cost-Cube model<br />

A control me<strong>as</strong>ure that reduces pollutant losses can be visualised <strong>as</strong> targeting one or<br />

more of the cubes, reducing their volume and hence the magnitude of total pollutant<br />

loss, i.e. the sum of all the cube volumes. For example, a me<strong>as</strong>ure that affects animal<br />

diet to reduce the quantity of pollutant excreted will reduce the volume of all cubes<br />

on the recycled-source <strong>as</strong>pect dimension. A me<strong>as</strong>ure that involved careful spreading<br />

of animal manure to minimise losses by surface run-off will reduce the volume of<br />

all cubes on the recycled-source and surface-transport <strong>as</strong>pect dimensions. A farm<br />

system can be represented by one or more Cost-Cubes, making explicit the total<br />

pollutant loss and the relative importance of the pollutant pathways.<br />

Data in the literature were used to characterise control me<strong>as</strong>ures by their costs and<br />

percentage efficiencies. Each me<strong>as</strong>ure w<strong>as</strong> <strong>as</strong>signed a target area on the Cost-<br />

Cube, using the dimension and <strong>as</strong>pect co-ordinate system, explicitly representing<br />

their mode of action in the me<strong>as</strong>ure centric framework. This information w<strong>as</strong> then<br />

used by a mathematical sub-model to calculate the best order of implementation<br />

of the me<strong>as</strong>ures with the objective of achieving maximum pollution reduction for<br />

minimum cost. Such a calculation of the ‘cost-curve’ <strong>as</strong>sumes that me<strong>as</strong>ure effects<br />

are multiplicative.<br />

Parameterisation<br />

The Cost-Cube model can be parameterised using the output from mechanistic<br />

models or by summarising empirical data and expert opinion. In our approach,<br />

experts were <strong>as</strong>ked, for example, to estimate the proportion of the total pollutant loss<br />

due to detachment or solubilisation processes of mobilisation. Careful and iterative<br />

questioning, together with group discussions and review, allowed us to define expert<br />

expectations of the relative importance of each <strong>as</strong>pect of the pollutant source,<br />

94

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