Process-Based Statistical Models Predict Dynamic Estuarine Salinity DOI: http://dx.doi.org/10.5772/intechopen.89911

or (3) bias fishery-independent surveys that leads to over-inflated population abundance estimates [12]. Thus, the need to accurately predict the spatiotemporal dynamics of salinity is unprecedented. The specific goals of this study were to: (1) evaluate several statistical models to hindcast and forecast salinity in the second largest estuary and largest lagoonal estuary in the United States—Pamlico Sound, North Carolina, USA, and (2) assess salinity observations, predictions, and

Lagoon Environments Around the World - A Scientific Perspective

standard errors under five hydrologic scenarios characteristic of historic and future

strengths of applying numerical modeling tools to characterize morpho-

three-dimensional numerical models used for simulation and forecasting of

always refer to bottom salinity unless otherwise noted.

1.1 Statistical models to predict dynamic salinity

hydrodynamic processes in estuarine and coastal systems. Numerical methods can include a large variety of models and techniques, such as finite element, finite difference, finite volume, or Eularian-Lagrangian models (e.g., [17–19]). Complex,

dynamic estuarine salinity can require significant effort and computation time that is beyond the capabilities of many local management agencies. Local management agencies sometimes require a quick turnaround time for long-term simulations or short-term forecasts of estuarine salinity conditions, which could be produced using location-specific statistical models. Therefore, the goals of this study were to (1) develop and evaluate two types of statistical models of bottom salinity in PS, and (2) apply the best models to produce sound-wide retrospective maps of bottom salinity based on observational data. Bottom (as opposed to surface) salinity was chosen as the variable of interest because it characterizes habitats of mobile demersal species that are important members of benthic food webs, and that are the targets of valuable commercial and recreational fisheries. Hereafter, the term 'salinity' will

Producing retrospective salinity maps based on observational data does not require a statistical model based on hydrological mechanisms that affect salinity; it is possible to perform individual spatial interpolations for each time period of interest using an ordinary kriging model or a universal kriging model with a simple spatial trend. Predicting salinity under a hypothetical set of conditions, however, does require a model that can 'learn' about hydrological mechanisms based on retrospective data (e.g., [20, 21]). Thus, the more comprehensive goal of this study was to produce retrospective maps of salinity by developing a space-time statistical model in which the mean function represents the hydrological mechanisms that affect salinity, and a spatial covariance function makes up the difference between

To create such a model, we constructed explanatory variables that accounted for the effect of riverine freshwater inflow (FWI), distance to inlet sources of oceanic saltwater, and hurricane incidence on salinities at different locations in PS. We used

the observed salinity data and the mean function's salinity prediction.

Pamlico Sound (PS) is a relatively shallow estuary with a mean depth of 4 m and a maximum depth of 7 m. PS circulation is dominated by wind-driven currents and freshwater input [13, 14]. Seasonal cyclonic storms are also an important climatological component of the PS system. Since 1996, over three tropical storms or hurricanes have passed within 300 km of the North Carolina coast per year [10]. Given the important role that salinity plays in the abiotic and biotic system components of estuaries, and the likelihood that global climate change will increase the frequency of extreme weather events (e.g., floods, droughts, hurricanes—[9, 15, 16]), there is a critical need for models that can accurately forecast spatiotemporal variation in salinity (e.g., [17]). A recent review by Iglesias et al. [17] highlights the

climate changes.

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a forward-selection process to choose which of these variables to keep in the model. Standard errors based on the covariance function allowed for assessment of strengths and weaknesses of the representation of the hydrology in the mean function. Since an additional goal of this study was to provide a template for researchers to build process-based models of normally-distributed estuarine variables, we considered only models that could be fit using procedures in the SAS® software package, yet can be adopted to R-statistical software.

Other process-based models of PS salinity in the literature—all of which are differential-equation-based deterministic models—provided important insights into how different variables influenced spatiotemporal salinity variation in PS ([22, 23], and others). However, these models ultimately lacked the spatial resolution and/or coverage of the entire area of interest of this study, and none quantified uncertainty at every space-time prediction location. For example, Xu et al. [24] predicted surface and bottom salinity, and temperature at 30-second intervals over a spatial grid with varying cell size (200–800 m<sup>2</sup> ) in the Pamlico River Estuary (PRE), a PS tributary, using a customized extension of the Environmental Fluid Dynamics Code [25] to incorporate FWI from major tributary rivers, as well as tide and wind effects on circulation. Although this model incorporated environmental variation and produced salinity predictions suitable to assess long-term space-time trends, the PRE makes up only 18% of the area of PS. Predicting salinity across the entire PS using this model would require spatial domain expansion and reparameterization, and such extensions are not planned (J. Lin, NC State University, pers. comm. on behalf of Xu et al. [24]).

Though we are unaware of researchers that have constructed space-time statistical models of salinity in PS, there are examples of applying statistical models for spatial prediction of salinity in other estuaries. For example, Rathbun [26] used independent multiple linear regression models with spatially-correlated errors to predict salinity and dissolved oxygen (DO) in Charleston Harbor, SC over a twoweek time period in 1988 as a function of spatial coordinates and distance to the estuary mouth. Chehata et al. [27] performed three-dimensional spatial interpolation of salinity and DO measurements in Chesapeake Bay. Qiu and Wan [20] developed a salinity model based on time series analyses of salinity data for the Caloosahatchee River Estuary, Florida, USA. The structure of their model consisted of an autoregressive term representing the system persistence and an exogenous term accounting for physical drivers including freshwater inflow, rainfall, and tidal water surface elevation that cause salinity to vary. The model was calibrated and validated using up to 20 years of measured data collected they found that the time series model offers comparable or superior performance compared with its 3-D, numerical counterpart. This model has been used as a tool for water resources management projects relating to ecosystem restoration and water control in south Florida [20]. Similarly, Ross et al. [21] examined the response of salinity in the Delaware Estuary, USA to climatic variations using statistical models and long-term (1950-present) records of salinity from the U.S. Geological Survey and the Haskin Shellfish Research Laboratory. The statistical models included non-parametric terms and were robust against auto-correlated and heteroscedastic errors. After using the models to adjust for the influence of streamflow and seasonal effects on salinity, several locations in the estuary showed significant upward trends in salinity. Insignificant trends are found at locations that are normally upstream of the salt front. The models indicate a positive correlation between rising sea levels and increasing residual salinity, with salinity rising from 2.5 to 4.4 psu per meter of sealevel rise. The results suggest that continued sea-level rise in the future will cause salinity to increase regardless of any variation in fresh water influx [21]. Urquhart

et al. [28] present the results of multiple statistical models that predicted daily, gridded surface salinity at 1 km resolution across Chesapeake Bay, USA as a function of surface reflectance estimates of salinity from the NASA Moderate Resolution Imaging Spectroradiometer (MODIS), onboard the Aqua platform satellite. Eight statistical methods were tested, and sea surface salinity was accurately predicted via remote sensed products with an accuracy that was more than sufficient for many physical and ecological applications [28].

None of these previous studies, however, attempted to explicitly represent the hydrological processes by which fresh and saltwater mixing affects estuarine salinity. In this paper, we describe the development of candidate explanatory variables to represent mechanisms affecting PS salinity and how that development led to consideration of two fundamentally different mean functions. We then describe the forward selection process by which candidate variables were chosen to be retained in the models, and how candidate covariance functions were selected to pair with each mean function. Next, we examined maps of salinity observations, predictions, and standard errors under five hydrologic scenarios, analyzed these results, and provided overall implications of the findings.
