## 1. Introduction

Spatial and temporal variability of salinity is the major factor for determining the distribution of estuarine biota and habitat. The salinity regime in estuaries is controlled by a number of factors such as river discharge, coastal runoff, local precipitationāevaporation, winds, and water exchange with the ocean (dominantly due to astronomic tides). Understanding the roles these external forcing mechanisms play in controlling the salinity in an estuary is important for maintaining the ecological health of the coastal region, planning ecological restoration projects, and planning and management of coastal regions including development, conservation, and protection of estuarine biological resources. Numerical models and conceptual theoretical depictions of estuarine circulation, tools commonly applied to estuarine studies, must be developed in concert with observational data analysis. Unfortunately, it is not often that observations are collected with both adequate spatial and temporal coverage to achieve a full understanding of the estuarine structure. For example, in Apalachicola Bay in the northeastern Gulf of Mexico (Fig. 1) time series of water properties have been collected routinely for over a decade, but in few locations. It is readily apparent from the observational time series that the salinity is very nonstationary in that its variability changes considerably over time. This variability in salinity is of particular importance to certain sessile estuarine organisms. In this work, statistical methods are developed to quantify the response of the salinity variability from multivariate observational time series. The methods are applied to data collected from Apalachicola Bay, an estuary subject to large climate signals and potential artificial water diversions, to determine how the estuary responds to changes in the external forcing, demonstrating new techniques for effectively utilizing data from a long-duration, but spatially sparse, estuarine observing system.

Apalachicola Bay is a multiple-inlet estuary formed by a series of barrier islands at the mouth of the Apalachicola River. This river is the final leg of the ApalachicolaāChattahoocheeāFlint (ACF) River system, draining approximately 50 000 km^{2} of western Georgia, eastern Alabama, and north Florida, and is the largest freshwater source to the Gulf of Mexico east of Mobile Bay. Apalachicola Bay supports 90% of Floridaās oyster harvest, approximately 10% of the total oyster harvest of the United States, and serves as major breeding ground and nursery habitat for blue crab, shrimp, and finfish (Florida Department of Natural Resources 1992). The geographic region encompassing the ACF watershed exhibits marked precipitation variability at seasonal, interannual, and interdecadal time scales, leading to extended low- and high-flow regimes (Morey et al. 2009). The haline properties within the bay are particularly important to the oyster population, as extended high salinity can enhance mortality through predation and disease such as the protozoan parasite dermo (Perkinsus marinus; La Peyre et al. 2009), whereas extreme low salinities can retard recruitment and growth. Thus, salinity varying between low (i.e., 5) and higher values (i.e., optimally up to 28, but tolerable up to 40) may be optimal for maintaining healthy oyster populations in an estuary (Livingston et al. 2000; La Peyre et al. 2009).

Active management of the ACF system for irrigation, consumption, and hydroelectric power generation has been the subject of legal actions between the three states encompassing the watershed. A primary issue has been Georgiaās plan to divert some of the flow to reservoirs used to supply water to the Atlanta region, a plan that prompted numerous lawsuits concerning the availability of sufficient flow for electricity generation and for maintaining water quality in the Apalachicola River and the Apalachciola Bay estuarine system (Congressional Research Service 2008). To better understand the potential consequences of water management strategies on Apalachicola Bay, it is important to first characterize the variability of the system and how the estuary responds to this variability.

The purpose of this study is to develop and apply statistical analysis tools to hydrographic time series to gain understanding of the variability within the bay, physical mechanisms controlling the variability, and how the variability is linked to fluctuations of the freshwater input to the estuary. The datasets, collected within the Apalachicola National Estuarine Research Reserve (ANERR), are analyzed from 1993 through 2005. During this time period, the region experienced prolonged periods of both unusually wet conditions and drought conditions producing periods of extreme high and low flow for the Apalachicola River. The methodology for this project has been designed to consider changes in the hydrographic properties of the bay and the variability of these physical variables during different river flow regimes.

Some previous investigations have provided a valuable background setting for this study. Niu et al. (1998) performed statistical analyses on a portion of the ANERR dataset from two stations within the research reserve over a nearly 4-yr period. This work developed statistical models to explain how the salinity at the two stations varied as functions of other parameters (river discharge, winds, precipitation, and water level) at daily time scales. Further statistical models were developed to study the salinity variability in the bay by Sun and Koch (2001). Huang et al. (2002b) constructed a model of the bay to study its tidal hydrodynamics. Some effects of local winds on the daily salinity were examined with the numerical model by Huang et al. (2002a). This work showed the effects of varying eastāwest winds on the exchange of saline seawater with the estuary through the inlets. More modeling studies by Huang and Spaulding (2002) suggest residence times in Apalachicola Bay of between 3 and 10 days. Mortazavi et al. (2000, 2001) studied the nitrogen input to the Apalachicola Bay estuary and showed large seasonal variability relating to the annual cycle of the river discharge.

This paper presents results from several statistical models and newly developed analysis techniques to identify changes in the estuary that can be critical to local ecosystems. This study aims to fill knowledge gaps requiring new statistical techniques to more fully understand the response of the salinity variability to multiple forcing variables at different time scales. This work builds upon previous studies and has the advantage of a longer time series containing lengthy anomalously low-flow conditions that may yield insight into potential future conditions of the estuary under different climate or management scenarios. Among the new methods used to study the Apalachicola Bay for this project are the following: analyses of the climatology and variability of the estuarine and riverine systems, analysis of the link between the magnitude of the tidal variability and the river flow conditions, conditional sampling analysis to study the impact of different flow regimes on the duration of high-salinity events, and applications of multivariate regression and analysis of variance models to examine the variability of water properties and their dependence on other parameters at different time scales. It is anticipated that these analysis techniques can be applied to observations from other estuarine systems and are extendable to parameters other than salinity.

## 2. Data

Daily river flow rates are obtained from the United States Geological Survey (USGS) National Water Information System for the Sumatra, Florida, gauge 02359170. This gauge is located 42 km upriver from the mouth, and data from this gauge are used as a proxy for the actual discharge rates. The portion of this river flow time series *Q _{S}* used for this study spans 1 January 1989ā31 December 2005. Data gaps (totaling 165 days for this portion of the data record) are filled based on the autocorrelation properties of the

*Q*time series and on the daily streamflow time series

_{S}*Q*from the Blountstown, Florida, gauge on the Apalachicola River (USGS station 02358700) 128 km upstream from the bay. Analysis of the river flow at Sumatra reveals that the

_{B}*Q*time series is highly correlated with

_{S}*Q*, so regression methods are used to fill gaps. The details of the regression methods for constructing a complete data record for

_{B}*Q*are given in appendix A.

_{S}Meteorological variables collected within the bay for this study include winds (speed and direction) and precipitation. These variables were collected every 30 min at a station on the St. George Island bridge causeway from 4 February 1993 to 10 April 2002 using a Handar automated weather data collection station operated by the Northwest Florida Water Management District.

Hydrographic parameters were collected as part of the ANERR water quality monitoring program at three stations within the bay. Data from Cat Point and Dry Bar are analyzed from 1 January 1993 to 31 December 2005 (Fig. 1). At these stations, the data have been collected from 0.3 m above the bottom (roughly 2-m depth). Data from two data loggers (near the top and bottom of the water column) are analyzed from the station in East Bay at 0.3 and 1.7 m above the bottom (depth at mean high water is 2.2 m). Data from this station are analyzed from 17 April 1995 (top datalogger) or 1 May 1995 (bottom datalogger) to 31 December 2005. The data were sampled at 30-min intervals by the YSI 6000, YSI 6600, YSI 6600EDS, and Hydrolab Datasonde 3 data loggers. Details of the sampling methods can be found in the metadata files archived at the National Estuarine Research Reserve System Centralized Data Management Office website (http://cdmo.baruch.sc.edu). Salinity is the primary parameter of interest to this study, and temperature data are also used for some of the analysis methods.

## 3. Climatology and variability of the Apalachicola River flow rate

Distributions of daily river flow rates for each calendar month are produced from the streamflow time series *Q _{S}* (Fig. 2a). High- and low-flow seasons can be identified by the monthly distributions as time periods when the monthly medians are either above or below the long-term median flow rate of 565 m

^{3}s

^{ā1}. The high-flow season lasts from January through April, peaking in March, with low flow typically existing from June through November, with lowest median values in October. Tails in the distributions are caused by extreme rainfall events, which may be either extratropical (during late fall through spring) or tropical (summer through early fall) in nature, over the watershed, or by droughts. The variability of the river flow, shown by the width of the distributions, also shows a similar annual signal, with maximum variability in March and minimum in October.

Distributions of Apalachicola River flow rates from daily observations at the Sumatra, FL, gauge during 1989ā2005 shown using boxplot diagrams. The boxes encompass the lower and upper quartiles (i.e., the 25th percentile to the 75th percentile) and the medians are indicated with the horizontal gray lines within each box. The lower and upper āwhiskersā extending from the boxes indicate 1.5 Ć the interquartile range, with values outside this range shown as gray ā+ā symbols. The dashed line shows the long-term median over the entire dataset (565 m^{3} s^{ā1}): (top) distributions by calendar months and (bottom) distributions by calendar years.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

Distributions of Apalachicola River flow rates from daily observations at the Sumatra, FL, gauge during 1989ā2005 shown using boxplot diagrams. The boxes encompass the lower and upper quartiles (i.e., the 25th percentile to the 75th percentile) and the medians are indicated with the horizontal gray lines within each box. The lower and upper āwhiskersā extending from the boxes indicate 1.5 Ć the interquartile range, with values outside this range shown as gray ā+ā symbols. The dashed line shows the long-term median over the entire dataset (565 m^{3} s^{ā1}): (top) distributions by calendar months and (bottom) distributions by calendar years.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

Distributions of Apalachicola River flow rates from daily observations at the Sumatra, FL, gauge during 1989ā2005 shown using boxplot diagrams. The boxes encompass the lower and upper quartiles (i.e., the 25th percentile to the 75th percentile) and the medians are indicated with the horizontal gray lines within each box. The lower and upper āwhiskersā extending from the boxes indicate 1.5 Ć the interquartile range, with values outside this range shown as gray ā+ā symbols. The dashed line shows the long-term median over the entire dataset (565 m^{3} s^{ā1}): (top) distributions by calendar months and (bottom) distributions by calendar years.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

Inspection of distributions of daily river flow created for each calendar year reveals marked interannual variability (Fig. 2, bottom). Morey et al. (2009) showed that precipitation variability over the ACF watershed was linked with the El NiĆ±oāSouthern Oscillation (ENSO), particularly evident during the late fall through early spring months, and manifesting similar interannual variability in the river flow. The monthly averaged river flow rate during March for all warm ENSO phases (from 1928 to 2007) is nearly 20% above average, and 13% below average during cold phases (Morey et al. 2009). This work also showed substantial variability at longer (decadal to interdecadal) time scales. There is some suggestion in the literature that this may be linked with other modes of climate variability, such as the Atlantic multidecadal oscillation (Enfield et al. 2001). A sustained period of anomalously low flow in the recent record is evident from 1999 through 2002.

## 4. Salinity variability and response to Apalachicola River discharge variability

### a. Climatology

Monthly distributions of salinity sampled every 30 min at the Cat Point show a seasonality similar to what one would infer from the Apalachicola River flow annual cycle (Fig. 3). The early spring salinity low corresponds to the seasonal high river discharge, and the October salinity high corresponds to the annual minimum river flow. A secondary salinity minimum in July is not obviously associated with any characteristic of the river flow climatology. At the Dry Bar station toward the west end of the bay, the March salinity minimum is still evident, but the annual salinity maximum shifts to June. The shift in the annual salinity maximum between the stations is likely due to the seasonal shift in dominant wind direction, from primarily southwesterly in the early summer to dominantly northeasterly in the fall. The influence of wind on the observed salinity is detailed further in section 5.

Distributions of salinity for each calendar month shown using ābox and whiskerā plots, as defined in Fig. 2, from 30-min observations from the (a) Cat Point, (b) Dry Bar, (c) surface and (d) bottom East Bay stations. (e) Distributions of the difference between the near-surface and bottom density calculated from the 30-min salinity and temperature observations at the East Bay station.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

Distributions of salinity for each calendar month shown using ābox and whiskerā plots, as defined in Fig. 2, from 30-min observations from the (a) Cat Point, (b) Dry Bar, (c) surface and (d) bottom East Bay stations. (e) Distributions of the difference between the near-surface and bottom density calculated from the 30-min salinity and temperature observations at the East Bay station.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

Distributions of salinity for each calendar month shown using ābox and whiskerā plots, as defined in Fig. 2, from 30-min observations from the (a) Cat Point, (b) Dry Bar, (c) surface and (d) bottom East Bay stations. (e) Distributions of the difference between the near-surface and bottom density calculated from the 30-min salinity and temperature observations at the East Bay station.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

At the much fresher East Bay location, the amplitude of the annual cycle is greater with a spring minimum and a fall maximum that can be seen in the monthly median values both near the surface and the bottom. Differences in the annual cycle observed near the surface and bottom in East Bay suggest that there may be some stratification, at least seasonally, at this location. Indeed, density differences between the bottom and surface measurements [calculated using the observed salinity and temperature time series with the (United Nations Educational Scientific and Cultural Organization) UNESCO (1983) equation of state] do suggest a seasonal cycle with typically destratified conditions during the spring and weak stratification during the late summer through midwinter (Fig. 3e). Weak vertical thermal gradients indicate that the seasonal density stratification is dominantly salinity controlled.

### b. Salinity response to the river flow rate

Inspection of the data strongly suggests a link between the salinity at the observation locations and the river flow rate, likely with a time lag. To determine whether there is a significant correlation, and at what lag, cross correlations are calculated between *Q _{S}* and the daily averaged salinity at the stations. Negative correlations are significant at the 99% confidence level at lags (river discharge leads the salinity response) of 1ā4 days for Cat Point and 2ā4 days at Dry Bar. At the top and bottom East Bay locations, negative correlations are significant with 1-day lag. Note that the cross-correlation functions have been computed after removal of the autocorrelation of each time series in order to accurately estimate confidence limits (e.g., Chatfield 1996).

To better understand the response of salinity in the bay to variations in the river flow, the salinity time series are conditionally sampled for each calendar month based on the river flow at Sumatra, *Q _{S}*. Low-flow and high-flow conditions for each month are defined by the 20th and 80th percentiles from the respective monthly distributions of daily flow rates. From the resulting histograms of the conditionally sampled salinity data, cumulative distribution functions (CDFs) can be computed (Fig. 4). The CDFs show

*P*(

*S*ā¤

*S*

_{0}), the probability that the salinity

*S*will be less than or equal to some value

*S*

_{0}(similarly, the probability of exceeding some value

*S*

_{0}āexceedanceāis given by subtracting the CDF value from 1.0).

CDFs of salinity at Cat Point and Dry Bar for various calendar months (thick gray curves) over the time period 1993ā2005. CDFs are also shown for the data conditionally sampled based on the river flow being below the 20th percentile value for each month (thin black curves) and above the 80th percentile values (dashed curves). The curves show the probability (ordinate) of the salinity being less than or equal to the values given along the abscissa.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

CDFs of salinity at Cat Point and Dry Bar for various calendar months (thick gray curves) over the time period 1993ā2005. CDFs are also shown for the data conditionally sampled based on the river flow being below the 20th percentile value for each month (thin black curves) and above the 80th percentile values (dashed curves). The curves show the probability (ordinate) of the salinity being less than or equal to the values given along the abscissa.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

CDFs of salinity at Cat Point and Dry Bar for various calendar months (thick gray curves) over the time period 1993ā2005. CDFs are also shown for the data conditionally sampled based on the river flow being below the 20th percentile value for each month (thin black curves) and above the 80th percentile values (dashed curves). The curves show the probability (ordinate) of the salinity being less than or equal to the values given along the abscissa.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

For each calendar month, the CDFs for low-flow conditions show a marked decrease (increase) in the probability of having low (high) salinity values at the measurement locations. For example, in May at Cat Point, the probability of the salinity remaining below 15 (practical salinity units are assumed throughout this paper) is approximately only 5% during low-flow conditions versus about 70% during high-flow conditions. Seasonal differences in the salinity and river flow distributions are particularly evident in the CDFs. For example, the probability of the salinity at Cat Point remaining below 15 when the river flow exceeds the 80th percentile in July is over 80%, but only 15% for the month of September.

The probabilities of extended high-salinity periods occurring during different Apalachicola River flow regimes can be estimated from the observational data. Here, a high-salinity event is defined by a daily averaged salinity exceeding 20, and remaining above that threshold for a period of time, although the methodology can be readily applied to recalculate the statistics for different salinity thresholds. The hypothesis is that the likelihood of extended periods of high salinity increases during extended low-flow conditions. For this analysis, gaps in the salinity time series are filled using the methodology explained in appendix B.

First, the daily river flow time series at Sumatra *Q _{S}* is subsampled when the daily river flow falls below the 20th percentile (303 m

^{3}s

^{ā1}determined from the distribution of

*Q*). Each continuous segment of the subsampled time series is placed into one of three categories based on the length of the segment: 1ā5, 6ā10, and 11 or more days. Next, the salinity time series is searched for the condition

_{S}*S*ā„

*S*

_{0}1ā4 days after

*Q*falls below the 20th percentile (cross correlations between

_{S}*Q*and salinity at the stations are significant at 1

_{S}**ā**4-day lags). When this condition is satisfied, then the number of consecutive dates that the salinity remains above the threshold value (here,

*S*

_{0}= 20) is counted. The durations for the high-salinity events are grouped based on the length of time (

*t*) that the river flow rate remains below the 20th percentile. For each of these groups, the distribution of durations for

_{Q}*S*ā„

*S*

_{0}is calculated. Inverse CDFs (exceedance probabilities) are then computed from these distributions. Finally, the probability of the daily averaged salinity at a location (Dry Bar or Cat Point) remaining above the threshold

*S*

_{0}for at least

*t*

_{0}number of consecutive days following the river entering a low-flow period is estimated, and these probabilities are computed based on how long the river remains at low-flow conditions (Fig. 5).

Probability (ordinate) of the daily averaged salinity exceeding 20 at (top) Cat Point and (bottom) Dry Bar for at least *t*_{0} days (abscissa) when the river flow rate *Q _{S}* at the beginning of the high-salinity event remains below the 20th percentile (303 m

^{3}s

^{ā1}) for 5 days or less (thin black line), between 5 and 10 days (thick gray line), or greater than 10 days (dotted line).

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

Probability (ordinate) of the daily averaged salinity exceeding 20 at (top) Cat Point and (bottom) Dry Bar for at least *t*_{0} days (abscissa) when the river flow rate *Q _{S}* at the beginning of the high-salinity event remains below the 20th percentile (303 m

^{3}s

^{ā1}) for 5 days or less (thin black line), between 5 and 10 days (thick gray line), or greater than 10 days (dotted line).

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

Probability (ordinate) of the daily averaged salinity exceeding 20 at (top) Cat Point and (bottom) Dry Bar for at least *t*_{0} days (abscissa) when the river flow rate *Q _{S}* at the beginning of the high-salinity event remains below the 20th percentile (303 m

^{3}s

^{ā1}) for 5 days or less (thin black line), between 5 and 10 days (thick gray line), or greater than 10 days (dotted line).

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

These inverse CDFs indicate the probability that the salinity will exceed a threshold value and remain high for at least *t*_{0} days when the river flow rate falls below the 20th percentile and remains low for a certain length of time. For example, at Cat Point, the probability that the salinity will exceed 20 and remain high for at least 15 days if the river flow drops below the 20th percentile for 1ā5 days is approximately 26%, compared to 38% for low flow lasting 6ā10 days, and 53% for low flow lasting 11 or more days. At Dry Bar, a station with typically lower salinity, the durations of high-salinity events are not as long. The likelihoods for moderately extended high-salinity events at Dry Bar are also much less sensitive to the river flow state compared to Cat Point.

Looking at the tails of the inverse CDFs (Fig. 5), one can see that very long-duration high-salinity events only occur when the river is at low-flow conditions for extended periods. During these extended low-flow conditions, the bay will shift to a high-salinity regime because of its relatively short (3ā10 day) residence time influenced by tidal mixing with saline ocean water through the inlets (Huang and Spaulding 2002). With reduced freshwater flux, the bay is more likely to stay in this saline state for an extended period potentially affecting the local biota.

### c. Tidal variability

Typical of many estuaries, the salinity field in Apalachicola Bay is characterized by large gradients that can form a salinity front. Salinity advection by horizontal tidal motions in the presence of the salinity gradient is expected to produce oscillations in the salinity time series with tidal periods. Changes in the river discharge, as well as from wind forcing whose effects will be discussed later, can affect the position and magnitude of the large salinity gradients within the bay. The magnitude of the salinity variability due to tides at a fixed location will vary based on the presence or absence of the large salinity gradient.

Near the mouth of the Apalachicola River, tidal motion is oscillatory along the channel, with salinity increasing at a fixed point in the channel during a flood tide and decreasing during ebb (Huang et al. 2003). Outside of the river, tidal motions in this multiple inlet estuary are complex. A modeling study by Huang et al. (2002b) shows that during high tide, flow in the sound is generally to the west, and at low tide, strong eastward currents are found in the eastern part of the bay. Water enters and leaves the bay through the passes during the flood and ebb phases of the tidal cycle. The tidal cycle is at times clearly evident in the high sampling frequency (30 min) salinity time series. Examination of a portion (October 2003) of the 30-min salinity data from Cat Point (Fig. 6a) suggests that there is a link between the subtidal salinity variability and the amplitude of the tidal fluctuations in salinity. Here, lower-amplitude tidal variations tend to occur during high-salinity periods, which would suggest the salinity front has retreated toward the river (to the west of Cat Point) as salty water intrudes into the bay.

(a) 30-min salinity data from Cat Point. (b) 29-day-averaged salinity at Cat Point (black) and intraday salinity range (gray) averaged over the same 29-day periods for a 4-yr segment of the 13-yr record.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

(a) 30-min salinity data from Cat Point. (b) 29-day-averaged salinity at Cat Point (black) and intraday salinity range (gray) averaged over the same 29-day periods for a 4-yr segment of the 13-yr record.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

(a) 30-min salinity data from Cat Point. (b) 29-day-averaged salinity at Cat Point (black) and intraday salinity range (gray) averaged over the same 29-day periods for a 4-yr segment of the 13-yr record.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

Tides in Apalachicola Bay are mixed diurnal and semidiurnal, so the intraday salinity range is a useful proxy for the salinity tidal variability. Because of small salinity gradients in East Bay, salinity tidal variability here is small [the average intraday salinity range over the 11-yr salinity time series at the East Bay surface (bottom) station is 3.3 (3.1)]. The average (standard deviation) intraday salinity ranges at the Dry Bar and Cat Point stations over their 13-yr records are much larger at 8.9 (4.4) and 7.6 (4.3), respectively. Average intraday tidal ranges during spring (neap) tides are 9.3 (9.0) at Dry Bar and 7.9 (7.4) at Cat Point, so the contribution of the spring/neap cycle on the intraday salinity range is small.

The salinity time series are analyzed to determine if the intraday salinity range is indeed correlated with the subtidal variations in salinity and river discharge. The mean salinity and intraday salinity ranges are computed for nonoverlapping 29-day periods (which encompasses two spring/neap tidal cycles). The Apalachicola River flow rate time series *Q _{S}* is also averaged over these 29-day periods, leading the salinity time series by 2 days. The correlations are computed between the 29-day-average intraday salinity range and 29-day-averaged salinity, and also with the river flow-rate time series. The correlation coefficients are computed for randomly selected data with sample size of one-half the length of the time series to increase confidence of the correlation coefficient estimate and to reduce impact of small autocorrelation in the 29-day-averaged time series.

At Cat Point, the intraday salinity range is negatively correlated with salinity averaged over 29-day periods with a correlation coefficient of *r* = ā0.62 (|*r*| = 0.2 is significant with 99% confidence; Fig. 6b shows a 4-yr segment of the time series to illustrate the negative correlation). There is a significant positive, but smaller, correlation (*r* = 0.47) between the river discharge and the intraday salinity range. That is, as the river discharge decreases, the mean salinity at Cat Point increases as the salinity gradient retreats, and there is less tidal variability in the salinity. Conversely, larger river flows result in a larger salinity gradient near the station, thus leading to large salinity variations corresponding to tidal movements. At the Dry Bar station in the western end of the bay, correlations between the intraday salinity range and the 29-day-average salinity and river flow are ā0.59 and 0.53, respectively.

## 5. Statistical models describing salinity variability

*Ļ*+

*Ī±*is the intercept for each of four seasons (

_{i}*i*= 1: DecemberāFebruary,

*i*= 2: MarchāMay,

*i*= 3: JuneāAugust,

*i*= 4: SeptemberāNovember). The regression coefficient for wind speed

*Ī²*was based on 45Ā° bins of wind direction (in the standard meteorological convention with bins given by {(

_{j}*j*ā 1) Ć 45Ā° to

*j*Ć 45Ā°,

*j*= 1, ā¦ , 8}) and

*Ī³*

_{1,i}and

*Ī³*

_{2,i}are coefficients that depend on the season. The set of salinity data

*S*is for season

_{ijk}*i*and corresponds to wind from direction

*j*(

*k*is just a temporal index). The subset of wind speeds is

*U*, and

*P*and

*Q*are precipitation and river flow (derived from

*Q*) selected based on the wind direction

_{S}*j*and season

*i*. A residual term is

*e*. The observational data time series are averaged to produce daily, weekly, and monthly averaged datasets for application of the model at these time scales. For each application of the model the parameters are estimated using the Statistical Analysis Software (SAS) statistical software package.

*S*is the set of salinity data based on the river flow falling within the

_{i}*i*th decile estimated from the distribution of

*Q*. Here

_{S}*Ļ*+

*Ī±*gives an estimate of the expected salinity when the river flow rate lies within the interval defined by the

_{i}*i*th decile (

*e*is a residual term with

_{ij}*j*being an index counter within the

*i*th group). This model is applied to weekly averaged salinity and river flow data for each of the stations.

### a. Salinity at the Cat Point station

Applied to daily data, the ANCOVA model (1) explains 61% of the variance at Cat Point. Although models with better fits can be obtained by considering additional parameters, this model has been developed to help in achieving a better understanding of the physical mechanisms affecting the salinity variability in the bay. One such possible addition is water level, such a used by Niu et al. (1998), but at subtidal frequencies, water level is correlated with the local wind, particularly at synoptic time scales (Cragg et al. 1983), and the variance of salinity explained by water level fluctuations is included primarily in the wind term in the models. The relatively low variance explained by this model stems in part to the inherent stochasticity of daily fluctuations in salinity, as the regression model only works well for deterministic predictors. It will be shown later that the model fit is improved with temporal averaging, as this reduces the stochasticity in the time series. The overall *f* tests and individual *t* tests show that all regression parameters are significant at the 0.05 significance level except for precipitation (not presented). Parameter estimates with the 95% confidence intervals are given in Tables 1 and 2 and Fig. 7. The river discharge rate has a strong effect on salinity, with the salinity response to the river flow rate strongest in seasons 1 (winter) and 4 (autumn).

Estimates of the parameter *Ī² _{j}* and their 95% confidence intervals for model (1) applied to daily averaged data at Cat Point. The ranges of the wind directional bins are also given. The results in this table are illustrated in Fig. 7a and are given to aid in interpretation of the graphical representation of the

*Ī²*parameter estimates in that figure. To indicate units for the parameter estimates, the abbreviation PSU is used here to indicate practical salinity units.

_{j}Parameter estimates for model (1) applied to daily averaged and 7-day-averaged data for Cat Point, Dry Bar, and East Bay (surface) stations, along with their 95% confidence intervals. Seasons are indicated as 1: DecemberāFebruary (DJF), and so forth. To indicate units for the parameter estimates, the abbreviation PSU is used here to indicate practical salinity units.

Parameter *Ī² _{j}* for (1) applied to (top) Cat Point, (middle) Dry Bar, and (bottom) East Bay surface salinity data. The numbers outside the circle indicate the increase in salinity (PSU) per 1 m s

^{ā1}of wind speed for winds blowing from the directions indicated by the numbers inside the circle (defined in Table 1). Zeros indicate no statistically significant effect of wind speed on salinity for wind blowing from the indicated direction. (left) Coefficients for the statistical model applied to daily averaged data, (middle) 7-day-averaged data, and (right) monthly averaged data.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

Parameter *Ī² _{j}* for (1) applied to (top) Cat Point, (middle) Dry Bar, and (bottom) East Bay surface salinity data. The numbers outside the circle indicate the increase in salinity (PSU) per 1 m s

^{ā1}of wind speed for winds blowing from the directions indicated by the numbers inside the circle (defined in Table 1). Zeros indicate no statistically significant effect of wind speed on salinity for wind blowing from the indicated direction. (left) Coefficients for the statistical model applied to daily averaged data, (middle) 7-day-averaged data, and (right) monthly averaged data.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

Parameter *Ī² _{j}* for (1) applied to (top) Cat Point, (middle) Dry Bar, and (bottom) East Bay surface salinity data. The numbers outside the circle indicate the increase in salinity (PSU) per 1 m s

^{ā1}of wind speed for winds blowing from the directions indicated by the numbers inside the circle (defined in Table 1). Zeros indicate no statistically significant effect of wind speed on salinity for wind blowing from the indicated direction. (left) Coefficients for the statistical model applied to daily averaged data, (middle) 7-day-averaged data, and (right) monthly averaged data.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

This model allows the data to show which wind directions are most influential on salinity, as opposed to analyzing the response to only the eastāwest and northāsouth wind directions, which is a common practice. The parameter values *Ī² _{j}* are given in table form (Table 1) but can more easily be interpreted in a graphical representation (Fig. 7). This shows that at daily time scales the salinity response to the wind speed is asymmetrical and strongest for winds blowing from the east-southeast and from the west. For example, for easterly winds blowing from between 90Ā° and 135Ā° (directional bin 3), daily salinity at Cat Point is expected to increase by nearly 0.7 for each 1 m s

^{ā1}of wind speed. Conversely, for wind blowing from the west, the salinity is expected to decrease by about 0.5 for each 1 m s

^{ā1}of wind speed. This result is consistent with the expected wind-driven salinity advection, with higher-salinity water east of the station and lower-salinity west of the station toward the river mouth. Note that since Dry Bar is located west of the river mouth, a nearly opposite salinity response to the wind is expected and will be shown later. This wind-driven salinity advection mechanism can explain the shift in the annual salinity maximum between Cat Point and Dry Bar introduced in section 4 (Fig. 3) due to the annual shift in wind direction.

When applied to 7-day-averaged data at Cat Point, model (1) explains 72% of the salinity variance. Individual *t* tests indicate that all parameters are significant but precipitation is only significant during season 1 (DecemberāFebruary). It is possible that this relation may really be due to the fact that the river flow is positively correlated to the local precipitation over the bay in this season (local precipitation during these months is typically due to large-scale synoptic weather patterns, which cause precipitation over most of the watershed), and that the riverās contribution to the salinity variability really dominates. The relationship between the Apalachicola River discharge rate and precipitation has also been suggested by Sun and Koch (2001). Indeed, when precipitation is removed from the model, it still explains 72% of the variance. Hence, it can be concluded that local precipitation does not have any real effect on salinity at weekly time scales.

Model parameters for (1) applied to weekly averaged data at Cat Point are given in Table 2, except for *Ī² _{j}*, which is shown only graphically (Fig. 7). Salinity increases due to winds with an easterly component are more significant at weekly time scales than daily time scales.

To gain a better understanding of how the salinity at Cat Point responds to different states of the Apalachicola River flow rate, the ANOVA model (2) is applied to 7-day-average salinity data and the *Q _{S}* time series (Fig. 8). Naturally, there is a decreasing trend in the salinity with deciles encompassing higher river flow rates. However, significant differences in the expected salinity can be seen when the river moves between certain states, such as from the third to second decile, which can occur with relatively small changes in the river flow rate. This indicates that threshold river flow rates may exist for maintaining certain critical salinity values within the bay.

Estimates, and 95% confidence intervals, of the expected 7-day-averaged salinity at (top) Cat Point, (middle) Dry Bar, and (bottom) East Bay surface stations based on 7-day averages of the river flow rate *Q _{s}* (by decile of the flow rate distribution) computed from the model in (2). The range of the river flow rate (m

^{3}s

^{ā1}) is shown for each decile along the abscissa.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

Estimates, and 95% confidence intervals, of the expected 7-day-averaged salinity at (top) Cat Point, (middle) Dry Bar, and (bottom) East Bay surface stations based on 7-day averages of the river flow rate *Q _{s}* (by decile of the flow rate distribution) computed from the model in (2). The range of the river flow rate (m

^{3}s

^{ā1}) is shown for each decile along the abscissa.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

Estimates, and 95% confidence intervals, of the expected 7-day-averaged salinity at (top) Cat Point, (middle) Dry Bar, and (bottom) East Bay surface stations based on 7-day averages of the river flow rate *Q _{s}* (by decile of the flow rate distribution) computed from the model in (2). The range of the river flow rate (m

^{3}s

^{ā1}) is shown for each decile along the abscissa.

Citation: Journal of Atmospheric and Oceanic Technology 29, 4; 10.1175/JTECH-D-11-00136.1

### b. Salinity at the Dry Bar station

At Dry Bar, for daily averaged data, model (1) (parameters given in Table 2) explains 59% of the variance in daily salinity. The individual *t* tests show that all regression effects are significant, including precipitation. However, as for the application of the model to weekly averaged data at Cat Point, individual *t* tests reveal that precipitation is only significant during the DecemberāFebruary season when local precipitation is correlated with the river flow. Again, removing precipitation from the model does not affect its fit to the observed salinity, indicating that local precipitation, apart from its influence on the river discharge, does not have any significant impact on the salinity.

Salinity decreases with increasing wind speed for winds blowing from the east-northeast and increases for winds blowing from the west, which is opposite to Cat Point (Fig. 7) and expected since Dry Bar is located west of the Apalachicola River mouth.

For 7-day-averaged data, the model explains 72.7% of the salinity variance at Dry Bar. As before, all parameters are statistically significant based on the *t* tests except precipitation, which is only significant during seasons 1 and 4 (Table 2). In this case, the parameter is positive for season 4, which is physically implausible (indicates that salinity increases with increasing precipitation) and is possibly an artifact of correlation between wind direction and precipitation. Furthermore, without precipitation included in the model, 72.5% of the variance of the weekly averaged salinity is still explained. This indicates that local precipitation plays a minor role in governing the salinity response at weekly time scales. The significance of precipitation during the winter season is likely due to the fact that precipitation during this season is associated with large-scale synoptic weather systems that affect the entire watershed, thus being correlated with river discharge, as opposed to the late spring through early fall months when precipitation is more commonly associated with localized convection (Morey et al. 2009). The salinity response to wind direction is stronger for the weekly averaged data than at daily time scales (Fig. 7).

Applying (3) to monthly averaged data at Dry Bar, the model explains 85% of the monthly salinity variability. Overall, the wind effect is significant, but wind speed does not have a significant impact on salinity for wind directions generally from the east and southeast (Fig. 7).

### c. Salinity at the East Bay station

At the East Bay location, model (1) applied to daily averaged data explains 61% of the variance of the salinity from the near-surface observations. The effects of precipitation are not significantly different from zero, but wind effects and river discharge rate do have statistically significant impacts on the salinity (Table 2). Winds blowing from the east and northeast are most strongly associated with increases in salinity, whereas winds from the west-southwest lead to weakly lower salinity values at the station (Fig. 7).

At weekly time scales, model (1) explains 71% of the salinity variance and the effects of winds on the salinity are quite similar to the results for daily time scales (Fig. 7). As is the case with the model applied to weekly data for the other stations, precipitation parameters show significance (for season 4), but again this likely stems from a correlation between precipitation and other more dominant factors (such as river flow and wind direction). River discharge has a strong impact on the salinity, especially during season 1 (Table 2).

Model (3) applied to monthly averaged data for the East Bay surface location explains 86% of the variance in monthly averaged salinity. Although wind speed is statistically significant for winds out of the northeast (Fig. 7), eliminating wind from the model altogether shows that the river discharge rate alone still explains 69% of the variance at the monthly time scale. The salinity at the East Bay station tends to be more sensitive to variations in the discharge rate of the Apalachicola River than at other stations, particularly during low-flow conditions.

## 6. Discussion and conclusions

A number of analysis techniques have been developed in this work for application to the long time series of observations in Apalachicola Bay, which has been the focus of a number of previous studies. Interest in this bay is due in part to its ecological importance, its establishment as a National Estuarine Research Reserve promoting scientific investigation and data availability, and also because of its role in riparian rights issues. Some of these works have focused on statistical descriptions of the water properties (e.g., Niu et al. 1998; Sun and Koch, 2001), and others using hydrodynamic models (e.g., Huang and Spaulding 2002; Huang et al. 2002a,b; Wang et al. 2008; Huang 2010). This study has focused on developing and applying statistical analysis tools to the available set of observations in Apalachicola Bay to build upon the earlier studies and has been chosen specifically to gain a better understanding of the physical mechanisms controlling the salinity variability. An important outcome of this work is the demonstration that relatively simple and computationally inexpensive statistical techniques can provide highly significant predictions of salinity, particularly at weekly and longer time scales, at given locations in an estuary. These techniques may be more readily applied for management decisions than running complex and expensive hydrodynamic models. The statistical techniques have been applied in this work primarily to understand the variability of salinity, but can also be potentially adapted for application to other water quality variables, or derived quantities such as stratification.

The results of the analyses show physical mechanisms responsible for controlling the salinity variability, and quantify the sensitivity of the bayās salinity regime to relatively small changes in the river flow. At the most basic level, salinity variability at the analyzed stations is dominated by the variability of the Apalachicola River discharge with local winds playing an important role as well. The statistical models show only that the salinity variability is related to the wind speed for certain wind directions, but an understanding of the circulation dynamics in shallow microtidal estuaries such as this one allows one to interpret the statistical model results as a manifestation of locally wind-driven transport of buoyant low-salinity water formed by the river discharge. Outside of East Bay, there is one dominant freshwater source, Apalachicola River. As a multiple inlet estuary, higher-salinity water enters through the passes by tidal and wind-forced intrusions. Thus, salinity gradients are directed from the river mouth toward the passes. When the wind blows from the direction of the river mouth toward a station, the statistical models show that the salinity decreases as the wind speed increases. This is consistent with the conceptual physical model of wind-driven transport of the low-salinity water from near the river toward the stations. At East Bay, it is more difficult to deduce the structure of the salinity field without obtaining additional data, such as from synoptic surveys or larger observational arrays, due to additional unmeasured freshwater runoff through Tateās Hell Swamp. However, wind-driven transport and pooling of the low-salinity water supplied via the swamp and the Apalachicola River within East Bay are still the likely controlling mechanisms for the salinity variability here, and its understanding would benefit from a more comprehensive observational and dynamical modeling study.

Although it might seem reasonable to expect that local precipitation may play a role in freshening of this shallow estuary, its impact on salinity is either generally so small, or significant only infrequently, that it does not show significance at daily time scales in the statistical models. At longer time scales, some tests for statistical significance are satisfied for precipitationās effects on the salinity variability, but further inspection suggests that this is due to seasonal correlation between precipitation and river discharge. During the late fall through early spring months, local precipitation generally is associated with large-scale atmospheric synoptic systems that generate rainfall over much of the watershed as they pass. Thus, during this time, precipitation variability at longer time scales is correlated with the river discharge rate. During the warm months, local precipitation occurs as part of local convective activity and is not representative of precipitation patterns over the entire watershed, and therefore is not correlated with the river discharge rate. This idea of local precipitation and river discharge showing positive correlation only during certain seasons has been shown by Morey et al. (2009).

Further analysis methods are applied to determine how the likelihood of high-salinity events and the duration of such events change with different river flow regimes. CDFs for salinity during each calendar month and subsampled based on the river flow rate in either the lowest or highest 20th percentile for each monthly distribution clearly show very large differences in the likelihood of high-salinity conditions. Inspection of the data has also shown that long-duration, high-salinity events are much more likely to occur during extended low-flow conditions, and large changes in the likelihood of long-duration, high-salinity events due to relatively modest changes in the duration of low-flow conditions are striking (particularly at the Cat Point station east of the river mouth).

Finally, this project has explored for the first time the high-frequency variability of salinity within the bay due to semidiurnal tides, and has shown a link between the magnitude of this variability and the flow rate of the river. Results show that during periods of high (low) river flow, the magnitude of the semidiurnal cycle in salinity at the Cat Point and Dry Bar stations increases (decreases). Physically, this is likely due to changes in the horizontal salinity gradients within the bay. It is plausible that during times of low river discharge, the salinity front retreats toward the mouth of the river and does not extend to the locations of the observation stations. Thus, this region of large salinity gradients may not pass over the observation location during the semidiurnal tidal excursions from its equilibrium location. If this physical interpretation of the analysis is correct, then it is possible that in other regions of the bay (presumably closer to the river mouth), the amplitude of the semidiurnal salinity oscillations might actually increase during times of low river discharge. The salinity range owing to the tides is as much as 6 at Cat Point during high-flow periods. These extreme rapid salinity fluctuations may have implications for the health of sessile organisms such as oysters.

The analyses and interpretations have suggested some possible circulation and salinity field patterns for the bay, but it is difficult to accurately determine characteristics of the field variables from time series at only three locations. A better description of the circulation and hydrography of the bay is desirable in order to better understand the dynamical roles the different external forcing mechanisms play in governing the salinity variability. A series of quasi-synoptic observations to understand the three-dimensional salinity gradients and the structure of the salinity fronts would be instructive. Perhaps most importantly, a highly realistic three-dimensional thermodynamic high-resolution model of the bay, coupled to the estuarine system and shelf waters, would be a very useful tool for future studies, as well as for monitoring and forecasting the circulation and water quality within Apalachicola Bay.

## Acknowledgments

This project was supported by the Florida Department of Environmental Protection (FDEP) under Contract OGC044. The authors wish to thank Lee Edmiston of FDEP and Graham Lewis of the Northwest Florida Water Management District for their advice. Observational data were supplied by the Apalachicola National Estuarine Research Reserve. The authors thank two anonymous reviewers for their thorough and helpful comments.

## APPENDIX A

### Method for Filling Gaps in the River Flow Data

The data gaps in the daily streamflow data from Sumatra (*Q _{S}*) are filled based on a weighting of results from three models.

- Backward regression:
- Forward regression:
- Regression on
*Q*(river flow at Blountstown):_{B}

*y*(

*t*) is the river flow at Sumatra (

*Q*) at time

_{S}*t*and

*x*is river flow at Blountstown (

*Q*). Here

_{B}*y*(

*t*ā 1) and

*x*(

*t*ā 1) are the values of river flow at Sumatra and Blountstown for the previous day, called lag values. Similarly,

*y*(

*t*+ 1) and

*x*(

*t*+ 1) are the values of river flow at Sumatra and Blountstown for the next day, called lead values. Regression parameters

*Ī±*and

_{i}*Ī²*are different for each model and are shown in Table A1. In (A1), the river flow at Sumatra is regressed backward in time on the flow at Blountstown and at Sumatra. In (A2), the river flow at Sumatra is regressed forward in time on the flow at Sumatra and backward on the flow at Blountstown. In (A3), the flow at Sumatra is determined by regressing on the flow at Blountstown. Note in all these models the only terms retained are those whose coefficients are determined to be significant based on individual

_{i}*t*statistics. The retention of the lead term (

*t*+ 1) in (A3) is interesting because Blountstown is upstream from Sumatra so one would expect only lag terms to be significant. However, this term may be due to a 1-day lag in regional rainfall runoff into the river that would affect both Sumatra and Blountstown.

*N*missing days, then weights for the mixed model in (A1) with backward regression are

*Q*) are

_{B}*C*is

*y*

_{1,2,3}are flow predictions obtained from (A1), (A2), and (A3), respectively.

## APPENDIX B

### Method for Filling Gaps in the Salinity Data Records

Although only approximately 3.4% of the salinity record is missing during the period 1993ā2005, gaps in salinity data complicate the analysis of duration of high-salinity events (presented in section 4b). Thus, gaps are filled to complete a record of daily-averaged salinity based on a combination of statistical models that give the best fit to the data.

*S*is used for filling the gaps:

*i*th season [DecemberāFebruary (DJF), MarchāMay (MAM), JuneāAugust (JJA), SeptemberāNovember (SON)] and wind from a given compass direction

*j*[(

*j*ā 1) Ć 45Ā° to

*j*Ć 45Ā°,

*j*= 1, ā¦ , 8]. Here

*R*is the residual,

*Ī±*is the intercept (for each season),

*Ī²*is the slope (for each wind direction), and

*Q*is the river flow lagged by 3 days. The covariance structure of the residual [

*R*(

_{ij}*t*)] is approximated with a second-order autoregression model:

*É*(

*t*) is an independent identically distributed random variable from a normal distribution. With properly determined parameters, the models explain ~87% and 81% of the variability in daily salinity at Cat Point and Dry Bar, respectively.

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