Case Study: Analysis and Forecasting of Salinity in Apalachicola Bay, Florida, Using Box-Jenkins ARIMA Models

The Apalachicola Bay is one of the most productive estuaries in Florida. Variations of salinity directly influence the productivity of the aquatic habitats. Physical conditions that affect the salinity include tidal elevations, wind and current velocities, precipitation, and the discharge of the Apalachicola River. In the present paper, cross-correlation techniques, autoregressive integrated moving average (ARIMA), and dynamic regression transfer models using the Box-Jenkins methodology are employed to analyze the time series data. The rational distributed lag transfer functions between hourly variations of tidal water levels and salinity allow forecasting of short-term fluctuations in the salinity, whereas multivariate correlation analyses of daily salinity with river discharge, wind stresses, water levels and currents, and precipitation shed light on the important control variables. Several conclusions with regard to the hydrodynamics and water quality of the bay can be drawn from identification of auto- and cross correlations and the appropriate ARIMA models. Fluctuations of tidal water levels result only in short-term periodic variations in salinity, with a linear transfer function that has a lag-two as the highest coefficient. The cross-correlation analysis shows that the Apalachicola River, being the major fresh-water source of the bay, strongly affects the currents and salinity in the bay area over the long term. Though regional precipitation controls the amount of fresh-water inflow, either through river discharge or groundwater seepage, its effect on the daily variations in salinity is statistically insignificant. In contrast, the effect of daily wind stress is significant. Salinity is positively correlated with western currents in the bay because most of the oceanic flow enters the bay from the east. A lag between the daily discharge and salinity indicates that up to a week is required for the peak of the inflow fresh water to flush through the exit of the bay.