2.9 Variable selection

2.5 Wind speed and direction

tion of salinity.

our models.

northing<sup>2</sup>

166

northingit ∗ easting<sup>2</sup>

2.8 Hurricanes

mean over all observations.

2.7 Spatial coordinates

using the categorical variable montht, where

Lagoon Environments Around the World - A Scientific Perspective

2.6 Evaporation and direct precipitation

A prevailing wind field that is north/northeast from March to August and south/southwest from September to February is the primary driver of currents in PS [39]. Thus, wind speed and direction were incorporated into the modeling process

montht <sup>¼</sup> 1 if <sup>t</sup> is in Sept

is used to examine the effects of seasonal wind patterns on the spatial distribu-

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

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

it, northingit,

it ∗ eastingit,

it are considered as explanatory variables.

Hatteras Inlet saltwater plume is reached. Thus, eastingit, easting<sup>2</sup>

it, and northing<sup>2</sup>

it, and the interactions northingit <sup>∗</sup> eastingit, northing<sup>2</sup>

it ∗ easting<sup>2</sup>

All coordinates are centered before they are squared or cubed by subtracting the

Hurricanes can rapidly introduce large volumes of freshwater to estuaries via riverine influx, push large volumes of saltwater in through inlets via storm surge,

0 if t is in June

Section 3 identifies 46 candidate explanatory variables for the process model mean function: 1wkFWII\_rit and 2moFWII\_rit (8), plus selected pair-wise interactions (explained below) (24); spatial coordinates, their powers, and specified interactions (9); closest\_inlet\_distit; montht; and hurricane variables inverse\_days\_surveyt , categoryt , and num\_stormst. For the time model, there were an additional 39 time period indicator variables. Some variables—in either model—may be redundant. There is overlap among the hurricane variables, and spatial coordinates may not be necessary if other variables explain more variability in salinity. The set of variables included in the final model(s) should balance goodness-of-fit with parsimony. We first describe the variable-selection process for the process model, then for the time model.
