2.6 Evaporation and direct precipitation

Holding other factors constant, sound-wide salinity in time periods that experience more evaporation of water from the surface of PS would likely be higher than those in time periods that experienced less evaporation, but no evaporation data were available for the space-time domain of interest. Salinity in time periods for which there was more direct precipitation into S should be lower than those in lower-precipitation time periods, however precipitation data were only available at two weather stations on the edges of PS from which information about individual spatial locations within PS would be difficult to infer. Giese et al. [40] found that direct precipitation constitutes only 8% of mean PS freshwater input, thus the signal from riverine FWI should dominate in explaining salinity variability. Therefore, we did not include evaporation or direct precipitation variables in our models.

## 2.7 Spatial coordinates

Estuarine salinity varies over space such that functions of spatial coordinates might explain variability in salinity not accounted for by the other variables. Scatterplots of salinity versus easting and northing suggested that salinity is quadratic in the former and cubic in the latter. The quadratic function of easting can be explained by examining a west-to-east path through PS along the 35° 16<sup>0</sup> N parallel (A in Figure 1): salinity should initially increase, reach a maximum at the saltwater plume near Ocracoke and Hatteras Inlets, and decrease again on the other side of the plume in the waters on the western shore of Hatteras Island near Buxton, NC. The cubic function of northing is best described by examining a north-to-south path along longitude of 75° 42<sup>0</sup> W (B in Figure 1), where salinity should increase traveling south from Albemarle Sound, reach a local maximum near Oregon Inlet, decrease continuing past the saltwater inlet plume, and increase again as the Hatteras Inlet saltwater plume is reached. Thus, eastingit, easting<sup>2</sup> it, northingit, northing<sup>2</sup> it, and the interactions northingit <sup>∗</sup> eastingit, northing<sup>2</sup> it ∗ eastingit, northingit ∗ easting<sup>2</sup> it, and northing<sup>2</sup> it ∗ easting<sup>2</sup> it are considered as explanatory variables. All coordinates are centered before they are squared or cubed by subtracting the mean over all observations.

#### 2.8 Hurricanes

Hurricanes can rapidly introduce large volumes of freshwater to estuaries via riverine influx, push large volumes of saltwater in through inlets via storm surge, Process-Based Statistical Models Predict Dynamic Estuarine Salinity DOI: http://dx.doi.org/10.5772/intechopen.89911

and alter circulation patterns through abrupt changes in wind speed and direction [7, 10]. Hurricanes can also open new inlets to PS, which can alter current flow and increase saltwater intrusion [41]. The variable 1wkFWII\_rit should capture variability in salinity due to hurricane-produced FWI. Three additional variables may account for non-FWI-related variability in salinity due to hurricane passage. These variables are unique to a given time period t but are constant over all sites i within t. The continuous variable inverse\_days\_surveyt is the reciprocal of the number of days between the most recent hurricane and mt, except when there is no hurricane within the 61 days, and then it takes the value zero. The categorical variable categoryt equals the category of the most recent hurricane rated on the Stafford-Simpson scale (1, … , 5), but if no hurricane made landfall in the 61 days prior to mt, it takes the value zero. Finally, the discrete variable num\_stormst equals the number of hurricanes making landfall in NC in the 61 days prior to mt.
