Issues of Model Structure in a Geocomputational

When working either in a geocomputational mode or in complex modeling situations, it is unlikely that the scientist or professional will be working with just a single tool. It is likely instead that several different tools are used. The way these are configured and pass data may have important influences on the outcome. In Chapter 6 and subsequently, we have seen how in coastal oil spill modeling there are, in fact, three models that cascade. Initially there is the hydrodynamic model that from bathymetric, shoreline, and tidal data calculates the tidal current over the study area using finite element method (FEM). In the next stage, these tidal currents together with other data, such as wind and the properties of the particular type of oil, are used in the oil spill trajectory model.

The trajectory model is a routing model requiring only arithmetic calculation and, therefore, is carried out on a grid. However, this requires a reinterpolation of the tidal current from a triangular network to a grid. As we have noted above, not only is there algorithm choice for reinterpolation, but that there is likely to be some level of corruption of the output data from the hydrodynamic modeling as it is transformed to a grid by the chosen interpolation algorithm. Experiments by Li (2001) have shown that errors in the bathymetry and tidal data will be propagated and amplified through the hydrodynamic modeling and affect the computed currents.

Interpolation of those currents to a grid further degrades the data by increasing the amount of variance by about 10%. This is then propagated through the next stage of modeling. These are inbuilt operational errors that are a function of overall model structure. Because different components or modules within the overall modeling environment work in very different ways such that they cannot be fully integrated but remain instead tightly coupled, then resampling or reinterpolation becomes necessary. Both model designers and model users, however, should be more aware of and try to limit the effects.

Another aspect of model structure that is hard to guard against is inadvertent misuse. While blunders, such as typographic errors in setting parameters, are sure to occur from time to time and will normally manifest themselves in nonintuitive outputs, there are subtle mistakes that result in believable but wrong outputs. In hydrodynamic modeling, for example, the forced tidal movement at the open boundary requires a minimum number of iterations in order for its effect to be properly calculated throughout the study area. For a large network with many thousands of elements in the triangular mesh, this may take many iterations at each time step. The model usually requests of the modeler the number of iterations that should be carried out; too many can be time consuming for a model with many thousands of time steps, but too few can give false results. Figure 9.8(a/b) shows the results of hydrodynamic modeling for an adequate number of iterations at 0 h and at 2 h. The tide is initially coming in and then starts to turn on the eastern side of the study area. In Figure 9.8(c/d), the exact same modeling has been given an
insufficient number of iterations at each time step to give the correct answer.

After 2 h, the tide continues to flow in and has not turned. The result of this error on the oil spill trajectory modeling can be seen in Figure 9.9. This can be compared for half-hourly intervals against Figure 9.1(a/f), which uses the correctly simulated tidal currents. With an insufficient number of iterations, the oil spill ends up in quite a different place and may adversely affect decision making.

In agent-based modeling there is a different, but by no means less complex set of issues in assessing the validity and usefulness of the results. In Chapter 5, we identified how agent-based models could have many thousands of agents all programmed with microlevel behaviors in order to study the macro patterns that emerge over time from these behaviors (Figure 5.15). Aspects for consideration include the stability or robustness of the emergent patterns, possible equifinality of emergent patterns from different initial states, boundary conditions and parameter values, different emergent patterns depending on parameter values, nonlinear responses to parameter change, and the propagation of error.

In order to illustrate a nonlinear response to incremental changes in a parameter, Figure 9.10 shows emergent patterns after 200 iterations of the Schelling three-population model implemented as cellular automata (CA). Only one parameter has been changed—minimum neighborhood tolerance—that has been incrementally increased by 10%. Each final state at 200 iterations has been quantified using a global Index of Contagion (O’Neill et al., 1988), as implemented in FRAGSTATS (http://www.umass.edu/landeco/), which measures the level of aggregation (0% for random patterns, 100% where a single class occupies the whole area). As illustrated in Figure 9.10, between a parameter value of 20% and 30% is a tipping point after which a high level of clustering quickly replaces randomness. As the parameter is further increased, so there is a nonlinear return to randomness. Such a sensitivity analysis (see the next section: Issues of Calibration) is the usual approach to exploring the robustness of the solution spaces, but in models where there are many parameters, the task can quickly become intractable. Li et al. (2008) have proposed the use of agent-based services to carry out such sensitivity analysis and model calibration of multiagent models; in other words, using the power of agents to overcome the complexity of using agents. The same approach can be used to explore all parameter spaces in n-dimensions to discover all possible emergent patterns of interest.