The modeling of the system’s substance flows and stocks can be attempted in different ways. Three are identified here:
1. accounting: keeping track of flows and stocks afterwards by registering them, thus enabling policy makers to spot trends, and to evaluate the effects of certain changes including policy measures;
2. static modeling: specifying the steady-state relations between stocks and flows (for example the Leontief I–O models).
3. dynamic modeling: including time as a modeling parameter, thereby making it pos- sible to predict future situations.
There is no ‘best’ choice: each type of modeling is useful, each has different functions for supporting environmental policy, and each has different data requirements.
Accounting
Thefirst way to ‘model’ the system is to treat it as an accounting system. The input for such a system consists of data regarding the size of the system’s flows and stocks of goods and materials, that can be obtained from trade and production statistics, and if necessary also data regarding the content of specific substances in those goods and materials. Emissions and environmentalflux or concentration monitoring can be used for the environmentalflows. A combination of these data together with application of
Mining and extraction
Production
Waste treatment
Usage 64 967 3 065
26 159 67
2 031 50 261
26 963 125 047
87 267
9 291
48 828
58 959 3 133
26 116
FOREIGN COUNTRIES ENVIRONMENT
1 102 162 26
12 054 3 99
Figure 9.1 A substance life cycle for copper in the Netherlands, 1990 (kT Cu/year)
the mass balancing principle then must lead to the desired overview of flows and stocks.
The accounting overview may also serve as an identification system for missing or inac- curate data. Missing amounts can be estimated by applying the mass balance principle. In this way, inflows and outflows are balanced for every node as well as for the system as a whole, unless accumulation within the system can be proved. This technique is most com- monly used in materials flow studies, and can be viewed as a form of descriptive statistics (for example, Ayres et al. 1988; Olsthoorn 1993; Fleckseder 1992; Kleijn and van der Voet 1998; Palm and Östlund 1996; Tukker et al. 1996, 1997; Hansen and Lassen 2000). There are, however, some examples of case studies that specifically address societal stocks (Bergbäck and Lohm 1997; Bergbäck, Johansson and Molander 2000) and these are used as an indicator for possible environmental problems in the future.
Static Modeling
In the case of static modeling, the process network is translated into a set of linear equa- tions describing theflows and accumulations as dependent on one another. Emission factors and distribution factors over the various outputs for the economic processes and partition coefficients for the environmental compartments can be used as such variables.
A limited amount of accounting data is required as well for a solution of the set of equations, but the modeling outcome is determined largely by the distribution pattern.
The description of the system as such a matrix equation opens up possibilities for various types of analysis: the existence of solutions, the solution space and the robust- ness of the solution can be studied by means of standard algebraic techniques, as is shown by Baueret al. (1997) and by Heijungs (1994, 1997a) for the related product life cycle assessment.
Static Modeling and Origins Analysis
For a pollutants policy, insight into the origins of pollution problems is essential. The origins of one specific problematical flow can be traced at several levels (van der Voet et al. 1995c; Gleiß et al. 1998). Three levels may be distinguished:
1. direct causes, derived directly from the nodes balance (for example, one of the direct causes of the cadmium soil load is atmospheric deposition);
2. the economic sectors, or environmental policy target groups, directly responsible for the problem, identified by following the path back from node to node to the point of emission (for example, waste incineration is one of the economic sectors responsible for the cadmium soil load);
3. ultimate origins, found by following the path back to the system boundaries (for example, the import of zinc ore is one of the ultimate origins of the cadmium soil load).
With the origins analysis, a specific problematicflow can be traced back and it can be estab- lished which fraction comes from which process. The ultimate origins are the most difficult to trace, mainly because of the looped processes that occur within the system, and are the main concern of the modeled origins analysis. The origins analysis is made for a specific year. The set of equations, when solved, must therefore lead to an overview that is identical
to the ‘bookkeeping’ overview for the same year. The account thus serves as a check, but could also be used to derive formulae. For the origins analysis, the set of equations is used in reverse: the specific problemflow is expressed in terms of thefixed variables. From this it follows that, for this purpose, all system inflows and nothing but the system inflows must be appointed as thefixed variables. All otherflows are then dependent, either directly or indi- rectly, on the inflows. In some cases, this may run contrary to our perception of causality, but it is a necessary condition for a successful origins analysis.
Steady-state Modeling: the Effectiveness of Abatement Measures
The overview as obtained by accounting will rarely describe an equilibrium situation. In the economy as well as in the environment some stocks are building up while others decrease. Disequilibrium implies that the magnitude offlows and stocks, even with a con- stant management regime, is sure to change. Steady-state modeling aims at calculating the equilibrium situation belonging to a (hypothetical) substance management regime. It is not a prediction of a future situation. The result of steady-state modeling may instead be regarded as a caricature of the present management regime, not blurred by the buffering of stocks. It is therefore most suitable for comparisons between management regimes. In Chapter 30, a steady-state model is applied to the case of heavy metals to assess whether the present regime is sustainable. A comparison is made between the present management regime and a number of others, containing different sets of abatement measures. Static and steady-state models have been proposed by Anderberg et al. (1993) and applied for example by Schrøder (1995), Baccini and Bader (1996), Boelens and Olsthoorn (1998), van der Voet et al. (2000b) and also, for purely environmental flows, by Jager and Visser (1994).
Technically, steady-state modeling is roughly equivalent to comparative static model- ing in economics, as well as to the type of modeling as used in environmental fate models (Mackay and Clark, 1991). The set of equations also contains distribution coefficients but the bookkeeping overview is not duplicated, since mass balance of flows is enforced at every node of the system and accumulation is ruled out. The outcome, within its limita- tions, is rather more robust than that of more sophisticated dynamic models, because many uncertainties are excluded.
Dynamic Modeling
For a dynamic model, additional information is needed with regard to the time dimension of the variables: the life span of applications in the economy, the half-life of compounds, the retention time in environmental compartments and so forth.
Calculations can be made not only on the ‘intrinsic’ effectiveness of packages of meas- ures, but also on their anticipated effects in a specific year in the future, and on the time it takes for such measures to become effective. A dynamic model is therefore most suitable for scenario analysis, provided that the required data are available or can be estimated with adequate accuracy.
The main difference between static and dynamic SFA models lies in the inclusion of stocks in society (Ford 1999): substances accumulated in stocks of materials and prod- ucts in households or in the built environment. Some studies are dedicated to the analy- sis of accumulated stocks of metals and other persistent toxics in the societal system (Gilbert and Feenstra 1992; Bergbäck and Lohm 1997; Baccini and Bader 1996; Fraanje
and Verkuijlen 1996; also Lohm et al. 1997; Kleijn, Huele and van der Voet 2000). Such build-ups can serve as an ‘early warning’ signal for future emissions: one day, the stocks may become obsolete or recognizably dangerous (as has happened with asbestos, CFCs, PCBs and mercury in chlor-alkali cells). Then the stocks may be discarded and end up as waste and emissions. In some cases, this delay between inflow and outflow can be very long indeed. Bergbäck and Lohm (1997) also draw attention to stocks of products no longer in use, but not discarded yet: old radios or computers in basements or attics, out- of-use pipes still in the soil, old stocks of chemicals no longer produced, such as lead paint or pesticides and suchlike. They conclude that such ‘hibernating stocks’ could be very large. In order to estimate future emissions, which is a crucial issue if environmental policy