2.5 Wind speed and direction

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 using the categorical variable montht, where

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

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

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

The results of eight separate ordinary least squares linear regression models of salinity make up the rows Table 1. The first five consist of an intercept and a single

and montht. The sixth and seventh contain an intercept plus, respectively, the sets of four short and long-term freshwater influx indices 1wkFWII\_rit f g ,r ¼ 1, … , 4 , and 2moFWII\_rit f g ,r ¼ 1, … , 4 . We treated the short and long-term sets of indices as groups assuming that if an index evaluated for one river is meaningful, then it is also meaningful for other rivers. We discuss the eighth row in Section 4.2.

Adjusted R2 is a modification of R<sup>2</sup> that penalizes the number of explanatory variables. While R2 increases as more variables are added to a model, adjusted R2 increases only if the added variable decreases the error sum of squares enough to

The model with the long-term freshwater influx indices had the largest adjusted R2 at 0.38, followed by the model with the distance from the nearest inlet (0.34), and the model with the short-term FWI indices (0.27). None of the other four models explained more than 5% of the variability in salinity. We chose the model with the long-term freshwater influx indices as the base upon which to build the

To this base model we added the variable closest\_inlet\_distit since the model containing this variable had the second-best performance, thus beginning a forward-selection process. Each time we added a variable or set of variables to the model, we kept it in the model if the new adjusted R<sup>2</sup> exceeded the old. Variables

, inverse\_days\_surveyt

, and num\_stormst. For the time model, there were an additional 39 time

,

, num\_stormst,

of hurricanes making landfall in NC in the 61 days prior to mt.

Process-Based Statistical Models Predict Dynamic Estuarine Salinity

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

2.9 Variable selection

categoryt

time model.

2.10 Process model

mean function.

167

explanatory variable: closest\_inlet\_distit, categoryt

offset the loss in error degrees of freedom.

$$mont h\_t = \begin{cases} 1 & \text{if } t \text{ is in } \mathbf{Set} \\ 0 & \text{if } t \text{ is in } \mathbf{June} \end{cases}$$

is used to examine the effects of seasonal wind patterns on the spatial distribution of salinity.
