Another rather interesting approach is to change each of the parameters to a sine
or cosine function varying the mean value of the parameter, similar to what we have
done in the preceding section of this chapter. Each parameter is assigned its own
frequency and the model is run with all parameters and initial values varying in this
way. A spectral analysis can be performed on the variations in the main variable
with the hope of finding certain critical frequencies, leading you directly to the
parametrical culprits.
Generally though, big computer-based models create a demand for big computers as they are needed to sift through the parameter and initial value specification
problem. There is no easy way around this situation. The problem is actually larger
than the parameter problem discussed here. There are many sources of modeling
error. Gertner et al. [4] and Gertner and Guan [5] wisely advocate the use of Error
Budgets as a way of pinning down the critical areas of error sources. He and his
colleagues have developed the methods of breaking down the source of error in
several categories (Input Measurement, Sampling, Components of the model (sets
of equations), Grouping and Computational). They are able to isolate the sources of
variation in the main variable. With such information the model can be effectively
revised or the data collection effort intelligently redirected.
For very large spatial dynamic models with thousands of cells, the testing
problem is very great, seemingly impossibly large. But efficient testing algorithms
have been and are being developed.
1
In presenting your models and their results, you should always include the
variations in the main variables of interest with changes in the critical parameters.
This display reveals to the critical observer that you have a respect for the trouble
that can be caused by what is still unknown about the process you study. The best
thing that can happen to modelers is to have one of their models used to aid
important decision-making. No good decision maker will use a model that has
not been screened for its error potential.
2.6 Difference and Differential Equations
Let us more closely investigate how STELLA treats the equation we specify in our
models. If we set DT ¼ 1, then state variables are updated every full time period,
such as every year, month or week. In this case, we have a model of discrete time.
As DT is lowered, we still have a discrete time model, but more closely approach
the case of continuous time. The model of this section illustrates the differences
between the two cases.
1 For a review of this approach and the general strategy of developing, sensitivity testing and using
these large spatial models, see: http://ice.gis.uiuc.edu, generally and: http://ice.gis.uiuc.edu/
TortModel/tortoise.html, specifically for the error budgeting process.
2.6 Difference and Differential Equations
37
or cosine function varying the mean value of the parameter, similar to what we have
done in the preceding section of this chapter. Each parameter is assigned its own
frequency and the model is run with all parameters and initial values varying in this
way. A spectral analysis can be performed on the variations in the main variable
with the hope of finding certain critical frequencies, leading you directly to the
parametrical culprits.
Generally though, big computer-based models create a demand for big computers as they are needed to sift through the parameter and initial value specification
problem. There is no easy way around this situation. The problem is actually larger
than the parameter problem discussed here. There are many sources of modeling
error. Gertner et al. [4] and Gertner and Guan [5] wisely advocate the use of Error
Budgets as a way of pinning down the critical areas of error sources. He and his
colleagues have developed the methods of breaking down the source of error in
several categories (Input Measurement, Sampling, Components of the model (sets
of equations), Grouping and Computational). They are able to isolate the sources of
variation in the main variable. With such information the model can be effectively
revised or the data collection effort intelligently redirected.
For very large spatial dynamic models with thousands of cells, the testing
problem is very great, seemingly impossibly large. But efficient testing algorithms
have been and are being developed.
1
In presenting your models and their results, you should always include the
variations in the main variables of interest with changes in the critical parameters.
This display reveals to the critical observer that you have a respect for the trouble
that can be caused by what is still unknown about the process you study. The best
thing that can happen to modelers is to have one of their models used to aid
important decision-making. No good decision maker will use a model that has
not been screened for its error potential.
2.6 Difference and Differential Equations
Let us more closely investigate how STELLA treats the equation we specify in our
models. If we set DT ¼ 1, then state variables are updated every full time period,
such as every year, month or week. In this case, we have a model of discrete time.
As DT is lowered, we still have a discrete time model, but more closely approach
the case of continuous time. The model of this section illustrates the differences
between the two cases.
1 For a review of this approach and the general strategy of developing, sensitivity testing and using
these large spatial models, see: http://ice.gis.uiuc.edu, generally and: http://ice.gis.uiuc.edu/
TortModel/tortoise.html, specifically for the error budgeting process.
2.6 Difference and Differential Equations
37