30 DWYER, NIXON, OVIATT, PEREZ, AND SMAYDA 



RESULTS 



All time-series data were tested for stationarity (constant mean 

 and variance) and for long-term linear trends. No time series showed 

 a significant slope over its entire length. Phytoplankton cell 

 abundance, the most variable time series, was broken arbitrarily into 

 six segments, each 2.5 years long, and slope, mean, and variance were 

 calculated for each segment. Since there were no significant 

 differences among any of the three statistics, the phytoplankton was 

 judged to be stationary. The solar-radiation, temperature, and 

 ammonia data were judged to be stationary by inspection (Fig. 1), as 

 were the time series for ammonia and chlorophyll in microcosm 2 

 (Fig. 2). 



Variance spectra were computed for the four bay time series 

 (Fig. 5), as previously described, by modifying the Weisberg (1974) 

 computer programs and were plotted with the graphics program of 

 Kramer and Weisberg (1975). A 95% confidence interval, used in 

 testing peak-height significance, is shown around phytoplankton 

 spectral estimates [Fig. 5(d)] . The resolvable frequency bandwidth B 

 and the number of adjacent spectral estimates over which moving 

 averaging was done are given in the figure legend. 



Variance spectra for solar radiation, temperature, and ammonia 

 [Fig. 5(a), 5(b), and 5(c)] are similar in that they all show only one 

 peak centered at 1 cycle/year. The flat, low-variance portion of the 

 spectra at higher frequencies (up to 26 cycles/year) is an example of 

 "white noise" or of a random process having variance equally 

 distributed over all frequencies (or "colors"). White noise represents 

 measurement errors, spatial heterogeneities, or other random errors. 

 The errors are quite small for easily measured, relatively determinis- 

 tic variables like solar radiation, temperature, and ammonia. 



The variance spectrum for phytoplankton abundance [Fig. 5(d)] 

 shows many more peaks and a high-frequency background white- 

 noise spectrum (e.g., > 10 cycles/year) of higher amplitude than the 

 input data. In particular, spectral peaks centered at 1, 2, and 4 

 cycles/year all appear to have confidence intervals that do not 

 overlap those of the background white noise or of the "valleys" on 

 either side of the peaks. We have found no evidence to indicate that 

 these higher frequency peaks are an artifact of our method of 

 analysis. A tendency for spectral peaks to "leak" variance to adjacent 

 frequency bands was almost completely suppressed by use of a 10% 

 cosine taper window (Bendat and Piersol, 1971). We know of no 

 environmental inputs that might pulse the Narragansett Bay ecosys- 

 tem at 2 or 4 cycles/year. Other possible environmental inputs, river 



