FREQUENCY RESPONSE OF A MARINE ECOSYSTEM 



29 



NO 



NONLINEAR MODELING 



AND FREQUENCY 



RESPONSE METHODS 



ESTIMATE 



NATURAL FREQUENCY 



AND DAMPING RATIO 



Fig. 4 Input— response spectral methodology for verifying linearity 

 of ecosystem response and estimating frequency response of 

 ecosystem. 



significant frequencies. If squared coherence is significant over a 

 broad band of frequencies, two more statistics can be calculated. 

 These are the amplitude ratio and phase as functions of frequency. 

 When plotted, these are the Bode frequency response plots described 

 previously (see Fig. 7). Rather than being generated from a mathe- 

 matical model, however, they are calculated directly from real data 

 measured in the field or the laboratory. If the input— response 

 transfer behaves linearly (i.e., if it has a significant squared coherence 

 and amplitude and phase plots resembling those of linear systems), 

 then a Laplacian transfer function model, the natural frequency 

 (cOn), and the damping ratio (f), all can be estimated graphically 

 (Brewer, 1974). Again, we should note that this whole process 

 (Fig. 4) represents a black-box approach in which only a qualitative 

 cause— effect hypothesis is necessary. We use it to evaluate the 

 linearity of the Narragansett Bay ecosystem. 



