2.1 Data and notation

We used bottom salinity values measured by the North Carolina Division of Marine Fisheries (NC DMF) Pamlico Sound Trawl Survey Program 195 (the survey) every June and September from 1987 to 2006. The survey is conducted only in June and September each year. Designed to assess species abundance at depths over 2 m, the survey uses a weighted stratified random sampling design. For each time period, coordinates of stations are randomly generated within each of seven water body strata, with more stations allocated to larger strata, for a total of 54 stations per time period. Hereafter, we denote with S the spatial domain that includes all points sampled within the seven strata mentioned over the entire 1987–2006 temporal domain. Figure 1 shows the geographic location of each sampling station in S. Salinity was measured using a YSI-85 multi-function meter at the beginning of each trawl and recorded along with depth and spatial reference coordinates. All spatial coordinates used in this analysis were converted from decimal degrees to northings and eastings in nautical miles (nmi) from a reference point (the origin in Figure 1) located southwest of S at 34.6°N, �77.1°W. Salinity is always reported using the Practical Salinity Scale.

US Geological Survey (USGS) gauge station per tributary (Figure 1): Neuse River (NR) station 02089500 in Kinston; Tar-Pamlico River (TPR) station 02083500 in Tarboro; Roanoke River (RR) station 02080500 in Roanoke Rapids; and Ahoskie Creek (AC) station 02053500 in Ahoskie, which gauges Chowan River inflow.

Pamlico Sound, NC and the Chowan, Roanoke, Pamlico, and Neuse Rivers. Green squares show the four river gauge stations used in this study. Purple dots indicate all P195 trawl survey sample stations for the 1987–2006 time domain. The pink star indicates the reference point from which northings and eastings were calculated. As referenced in Section 3.5, Parallel A is located at 35° 16<sup>0</sup> N latitude and meridian B is at 75° 42<sup>0</sup> W longitude.

downloaded from the USGS Water Resources website for the state of North

chosen was the furthest downstream gauge that recorded data over the entire

The creation of explanatory variables reflects the modeling context—the objectives, the geographical features of the spatial domain, and the space-time coverage and resolution of the data—but the general thought process can be modified by other researchers in a different context. We index the term it as any variable that varies in both space and time, and with t any variable that varies over time but is

Sixty-one days is the average freshwater residence time of the four major rivers

flowing into PS [30–32], accounting for the temporal lag between the upriver

Carolina (USGS 2009) and were converted to m<sup>3</sup>

Process-Based Statistical Models Predict Dynamic Estuarine Salinity

DOI: http://dx.doi.org/10.5772/intechopen.89911

2.2 Candidate explanatory variables

constant over S within a time period.

2.3 Freshwater influx indices

/s for every day during the time domain (7305 days) were

/s. For each river, the gauge

Discharge rates in ft3

Figure 1.

temporal domain.

163

The temporal domain contains T = 40 time periods, or month/year combinations, indexed by the subscript t, so that t ¼ 1, … , T. A time period is approximately 2.5 weeks long, the time it takes to sample all stations. Since locations of the 54 stations sampled in each time period differed slightly, and since some data were missing in each time period, let nt represent the number of sites in time period t. Site refers to a specific spatial location nested within a particular time period and is indexed using the subscript i where i ¼ 1, … , nt. The dataset included N ¼ 2100 total observations of salinity, where <sup>N</sup> <sup>¼</sup> <sup>P</sup><sup>T</sup> <sup>t</sup>¼<sup>1</sup>nt. Denoted with salit observed salinity at site i in time period t.

The fresh water influx (FWI) data represented watersheds of the Neuse, Pamlico, Roanoke, and Chowan rivers, which comprise 80% of the land draining into PS [29]. FWI observations were average daily river discharge rates collected by one
