STEP 9: SIMULATION OF THE ENERGETICS MODEL 



With the revolution in computer technology, it became more feasible for 

 the average researcher to simulate simultaneous solution of complex sets of 

 nonlinear differential equations such as one encounters in energetics models. 

 The two most popular simulation methods are: (1) the development of analogous 

 electrical circuits through the use of computer, and (2) numerical approxi- 

 mation using a digital computer. Each of these two methods has advantages and 

 disadvantages, but because digital computers are more frequently available to 

 the researcher, numerical approximation is the method more commonly employed. 

 A more detailed discussion of the simulation process is incorporated into the 

 "Results" section in Step 10. 



STEP 10: VALIDATION OF THE ENERGETICS MODEL 



There i§ no specific test to establish the validity of any large-scale 

 simulation model. Correlation analysis and other statistical methods have 

 been used by some researchers to compare similarities between the behavior of 

 the model and the behavior of the system itself as it functions in reality; 

 however, the results of these methods of analysis are inconclusive. 



Sensitivity analysis is helpful in validating large-scale simulation 

 models. Individual pathway coefficients are varied to test the system's sen- 

 sitivity of changes in the linkages. Sensitivity analysis is often helpful in 

 finding errors in the model design or construction when unexpected behavior 

 occurs. 



Other attempts at validating energetics simulation results are: (1) to 

 use historical data in the mode, simulating a period from the initial time to 

 the present, allowing simulation results to be compared with currently avail- 

 able empirical data; (2) in cases where the system being simulated is rela- 

 tively well understood, comparing the simulation results to known system 

 behavior can assist in the validation of a given energetics model. For 

 example, the researcher might be interested in changes in the simulation 

 results as different variables are changed to reflect the impact of hypothe- 

 tical future actions and events. 



RESULTS OF ENERGETICS MODELS 



INTRODUCTION TO HILLSBOROUGH COUNTY MODEL 



In illustrating the methodology for preparing an energetics simulation, 

 as was done previously in this report, a simple example was used. In this 

 section, a more complex model is considered, one that has been used to illus- 

 trate energy alternatives to public administrators. 



The earlier model (Figure 5), and the one prepared for this section 

 jre 9), s 

 'human" si 

 panded model . 



ine earner moaei ^i-igure b), ana tne one preparea to 

 (Figure 9), share the same structure incorporating "natural," "agricultural," 

 and "human" subsystems. The results discussed in this section are of this ex- 



293 



