Time Series Analysis of Salinity With Unequally Spaced Observations in Galveston Bay

Time series analysis was used to investigate the relationships between salinity in Galveston Bay and forcing variables such as freshwater inflow, wind and water level. The methodology included both spectral analysis and time domain modeling. The salinity data were unequally spaced so that conventional methods of time series analysis were inapplicable. The estimated spectrum is the convolution of the true spectrum with the spectral window function. The unequal spacing of the salinity data resulted in spurious features in the estimated spectra. The spectral window functions were inspected to identify the suspicious features in the estimated spectra. Another approach for spectral estimation, resulting in the Parzen spectra, was used to help in clarifying the spurious features in the spectra. Cross spectral analysis was performed between salinity and the forcing variables. For time domain modeling, continuous time state space models were used to represent the processes. The continuous time state equations were integrated over the intervals between observations to give the discrete time state equations corresponding to the observation points. The Kalman filter was developed for a variable time interval. The usefulness of the modeling technique was evaluated by numerical experiments with simulated data sets and an application to an equally spaced real data set. For salinity variations, the major time scales which can be resolved with the available data are the multi-year time scale and the annual time scale. Trinity gauged flow is the most dominant forcing variable affecting salinity. However there is a substantial spatial variation in the influence of Trinity gauged flow on salinity. In some parts of the estuary, other forcing variables appear to exert greater influence on salinity than Trinity gauged flow at the multi-year time scale and the annual time scale. Moreover, depending on the location in the estuary, Trinity gauged flow explains only 30% to 70% of the salinity variance. Wind has little influence on salinity at the major time scales in this study. The relationship between salinity and water level is inconclusive from this research and requires further investigation