Increased abnormality in earth's weather pattern, as evidenced by tsunamis, numerous hurricanes and enhanced rainfall events, has renewed an interest to accurately model the water height in ecological systems. The water height in ecological systems is dependent on several spatial and temporal factors, such as the geographical location, shape and size of the water body, along with the effect of tides, wind, rainfall, etc. on that system. A mathematical model for predicting water height should judiciously incorporate these parameters into the model. An optimal approach is to utilize a modeling technique which can capture the effects of various causing parameters in a multi-scale formulation, where contributions from parameters that affect the water height at different rates are incorporated at different time scales in the model.

Dauphin Island in southern Alabama is at the tip of Mobile Bay, which is an estuary that is ecologically different from other areas that have been modeled. Over seven months of data, sampled hourly at the Dauphin Island, were available for this research. Included in the data were the water height, wind direction and magnitude and the amount of freshwater discharge into the Mobile Bay. The tidal component, estimated through harmonic analysis, was removed from the water height data, and the primary challenge was to explain the non-tidal component, hereby referred to as the residuals, as a function of wind and freshwater discharge into the Bay. The magnitude and directions of the wind data were transformed into two orthogonal components. Wavelets were employed to perform multi-scale decomposition on the time-series data for each of the variables. Wavelet approximations, which represent the core trend of the data, were then input into a dynamic partial least squares (PLS) model, which predicted the residuals for the water height. Comparison with conventional time-series based modeling approaches demonstrated superior performance by the wavelet-PLS model.