Nonlinear aspects of sea surface temperature in Monterey Bay

Larry Breaker
Moss Landing Marine Laboratories


Nonlinear aspects of sea surface temperature (SST) in Monterey Bay are examined, based on an 85-year record of daily observations from Pacific Grove, California. Oceanic processes that affect the waters of Monterey Bay are described, processes that could contribute to nonlinearity in the record. Exploratory data analysis reveals that the record at Pacific Grove is non-Gaussian and, most likely, nonstationary. A more recent test for stationarity based on a power law approximation to the slope of the power spectrum indicates that the record is stationary for frequencies up to ~8 cycles per year (~45 days), but nonstationary at higher frequencies. To examine the record at Pacific Grove for nonlinear behavior, third-order statistics, including the skewness, statistical measures of asymmetry, the bicorrelation, and the bispectrum, were employed. The bicorrelation revealed maxima located approximately 365 days apart, reflecting a nonlinear contribution to the annual cycle. Based on a 365-day moving window, the running skewness is positive almost 80% of the time, reflecting the overall impact of warming influences. The asymmetry is positive approximately 75% of the time, consistent with the asymmetric shape of the mean annual cycle. Based on the skewness and asymmetry, nonlinearities in the record, when they occur, appear to be event-driven with time scales possibly as short as several days, to several years. In many cases, these events are related to warm water intrusions into the bay, and El Nino warming episodes.

The power spectrum indicates that the annual cycle is a dominant source of variability in the record and that there is a relatively strong semiannual component as well. To determine whether or not the annual and semiannual cycles are harmonically related, the bispectrum and bicoherence were calculated. The bispectrum is non-zero, providing a strong indication of nonlinearity in the record. The bicoherence indicates that the annual cycle is a major source of nonlinearity and further implies that the annual and semiannual cycles are harmonically related. Based on the wavelet power spectrum (WPS), the appearance of the semiannual cycle is transitory; however, pathways between the annual and semiannual cycles appear at certain times when nonlinear interaction between them could occur. Comparisons between the WPS and the running skewness suggest that there is a tendency for periods when pathways exist, to coincide with increased positive skewness, and, often, with El Nino warming episodes. The Hilbert-Huang transform, a relatively new tool for nonstationary and nonlinear spectral analysis, was used to further examine the origin of the semiannual cycle. The time-dependent Hilbert spectrum reveals large and erratic variations in frequency associated with semiannual cycle but far greater stability associated with the annual cycle. As a result, the time-integrated Hilbert spectrum does not indicate the presence of a semiannual cycle. The method of surrogates from the field of nonlinear dynamics was also employed to test the Hopkins record for nonlinearity. Differences between the data and the surrogates were found that were statistically significant, implying the existence of nonlinearity in the record. Using the method of surrogates together with a one-year moving window, El Niño warming episodes appear to be a likely source of nonlinearity, consistent with the other analyses that were performed. Finally, the influence of stochastic variability due to serial correlation in the data was examined by comparing standardized statistics for the observations and for simulations based on an autoregressive model whose properties were obtained from the observations. The magnitude of the variability for the simulations was found to be far less than that associated with the original data, and thus stochastic variability does not appear to be a factor that significantly affects the interpretation of our results.