Spatial and temporal variations of estuarine stratification and flushing time across the continental U.S.

Abstract

Estuarine circulation attributes such as stratification and flushing time significantly influence estuarine ecological processes. Stratification reflects how much vertical mixing occurs in an estuary, while flushing time can describe the exchange rate of pollutants between the estuary and ocean. A recently developed estuarine characterization framework used estuarine geophysical attributes and water exchange datasets to characterize estuarine circulation for 360 estuaries in the continental U.S. between 1950 and 2015. The estuaries were grouped into nine ecoregions according to the Marine Ecoregions of the World. In the Gulf of Mexico and along the East Coast, most estuaries were well-mixed (63–93%), with 3–5% strongly-stratified estuaries. Along the West Coast, strongly-stratified estuaries dominated (46–63%), with the exception of the Puget Trough basin and the southern CA ecoregion with 83% and 75% well-mixed estuaries. The stratification type of some estuaries varied seasonally. Generally, they were more stratified winter through spring, then mixed during the summer, with the exception of southern FL, which had a reverse pattern due to the positive correlation between the stratification parameter and freshwater inflow (97% estuaries with R² > 0.9). The flushing times of the 300 well-mixed and partially-stratified estuaries were estimated using Tidal Prism (TPM) and Freshwater Fraction Methods (FFM). Flushing time seasonal variation exhibited a negative correlation with freshwater inflow (R² > 0.8 for 50% of estuaries using TPM). Generally, estuarine flushing times were short in winter and long in summer (reversed in FL and a portion of the Gulf of Mexico). On the West Coast, estuaries tended to flush quickly compared with estuaries in other regions, even though they usually had low freshwater inflows, since other factors, e.g., the estuarine volume, affected the flushing time as well. To ensure appropriate interpretation of responses to change in nutrient loading, the significant intra- and interannual variations in stratification and flushing time need to be incorporated into management and assessment of estuaries.

Graphical Abstract

1. Introduction

1.1. Estuarine Circulation

Studies of the physics of estuarine circulation, stratification and flushing time, have clear biogeochemical significance, affecting nutrient and particle retention and the development of anoxic conditions. Estuaries are regions of transition from river to ocean. They are important ecological systems and function as efficient traps for nutrients, sediment, and pollutants. Within the estuary, water exchanges continuously between the freshwater from riverine discharge and denser saltwater from the ocean. This bidirectional flow, also termed the exchange flow, significantly influences estuarine sensitivity (degree of response) to nutrient loading (Geyer & MacCready 2014). The exchange process, triggered by flow density and tidal current or lateral frictions, is referred to as the estuarine circulation. Generally, the different water densities of freshwater inputs near the estuarine surface and marine inputs near the estuarine bottom result in vertical stratification within the estuary.

Estuarine stratification can be observed directly through vertical salinity distributions. It reflects the process of vertical mixing of water in estuaries (Hansen & Rattray 1966; Geyer 1993; Li et al. 2018). It also reflects whether the mixing process is dominated by riverine or tidal inputs. Flushing time is a critical transport time scale in estuarine circulation, measuring the time interval necessary for the freshwater volume retained in the mixing zone to be replaced within the estuary, along with concentrations of other substances in the estuarine water mass (Manoj 2012; Haddout et al. 2020). Thus, both stratification and flushing time potentially indicate estuarine sensitivity to the input of nutrients, sediment, and organic matter into estuaries. This sensitivity will be affected by the increasing frequency of extreme climate events which will also influence the delivery of nutrients, estuarine physical-chemical properties and ecosystem structure and function (Wetz & Yoskowitz 2013; Navas-Parejo et al. 2020).

1.2. Methods of Estuarine Characterization

Analytical theories and simple numerical techniques exploring the attributes of estuarine circulation have been well-developed in the past century (MacCready & Geyer 2010). Several factors affect stratification, including tidal action, wind, river discharge and geomorphologic characteristics (Scully et al. 2005; Du et al. 2018; Valle-Levinson et al. 2009). Several classic criteria have been developed for estuarine classification, including the empirical classification scheme based on vertical salinity profiles from observations (Pritchard 1955), the empirical Flow Ratio Scheme (Simmons 1955) and the classic stratification-circulation diagram established by Hansen & Rattray (1966). Based on the stratification-circulation diagram, numerous stratification criteria have been proposed (Fisher et al. 1972; Prandle 1985; Scott 1993; Guha & Lawrence 2013).

Flushing time, an important water transport time scale, is an integrative parameter, describing the general exchange characteristics of a waterbody without identifying the underlying physical processes or their spatial distribution (Haddout et al. 2020). The water transport time scale for estuaries has been computed by means of both an Eulerian and a Lagrangian approach (Cucco et al. 2009). Flushing time used here is focused on the concept of the water transit time, as opposed to water residence time as described in Cucco et al (2009), that corresponds to the time it takes for any water particles of the sample to leave an estuary through its outlet. Several simplified and fundamental theories have been developed to help estimate flushing time, including the empirical Flux Rate-River Discharge diagram, the tidal prism method (TPM; Ketchum & Rawn 1951) and steady-state freshwater fraction method (FFM; Officer & Kester 1991; Fischer et al. 1979). These methods assume the estuary as a steady-state and well-mixed system with simple geometry. They have been further refined as the segmented tidal prism method and the adjusted tidal prism method by considering the ebb return factor or incomplete mixing factor (Dyer & Taylor 1973; Sanford et al. 1992; Guo & Lordi 2000).

At the next level of complexity are box model approaches for estimating residence time, the time to remove a given fraction of a conservative constituent from the modeled portion of an estuary. Miller and McPherson (1991) applied a single layer case of the box model approach of Officer (1980) to estimate tidal dispersion and then estimate residence times by simulation, thereby allowing the steady-state assumption to be relaxed. Hagy et al. (2000) extended this approach with a mixed one-layer to two-layer box model approach, allowing residence time to be estimated as a function of both flow and point of origin. However, these approaches have more intensive data requirements than the simpler TPM and FFM approaches. With the development of numerical hydrodynamic modeling, more comprehensive studies have been conducted to simulate the estuarine circulation in fine spatial and temporal resolution, by taking into consideration the complexity of the three-dimensional geometry and hydrodynamic processes of an estuary, as well as other influencing factors such as wind, precipitation and temperature. One downside of the numerical modeling approach is that it requires advanced technical skills and significant computational resources, which may limit its application across large temporal and spatial scales, and also may have high data requirements.

1.3. Research Goals

The methods to define estuarine circulation described above have been broadly applied to estuaries across the world. However, in most research, applications were focused on a single estuary or several estuaries in a certain region, such as estuaries in Rhode Island (Abdelrhman 2007), Georgia estuaries (Alber & Sheldon 1999), and estuaries in the Gulf of Mexico (Solis & Powell 1999, Murrell & Caffrey 2005). Comprehensive assessments have been conducted across the continental United States (U.S.), but that work was conducted with incomplete spatial and temporal coverage and did not consider the temporal variation of estuarine circulations in detail (Engle et al. 2007; Bricker et al. 2008; Detenbeck et al. 2019). Due to the lack of continuous data and uniform methods, little work has been done to develop a simplified and practical framework to estimate the estuarine stratification and flushing time across the large spatial and temporal coverage in the continental U.S..

Recent improvements in the quality of fine-scale topobathymetry (Thatcher et al. 2016; Love et al. 2020) and freshwater discharge estimates (McKay et al. 2012; Miller et al. 2018) have allowed us to develop a more comprehensive assessment of estuarine circulation and estuarine sensitivity to nutrient loading. The goal of this research is to evaluate the estuarine circulation attributes for all estuaries in the continental U.S.. In this process, the simple and practical framework established here will provide an easy way for public use of the estuarine characterization, which will help coastal managers make better informed decisions about estuarine water quality, as well as providing the basis for comparison of systems across the continental U.S.. It will potentially contribute to assessing estuarine vulnerability to nutrient inputs, which will be helpful in the development of estuarine management strategies and predicting estuarine recovery following nutrient load reductions.

2. Methods

2.1. Framework

The analytical framework for estimating stratification parameters and flushing time is presented in Figure 1. Estuarine physical attributes, e.g. estuarine volume, area, average depth and width of the estuarine outlets, were acquired based on the estuarine boundary and bathymetry. Based on estuarine morphometry and data on water exchanges (tides, tidal prism volume and freshwater inflow), estuarine stratification was described through different schemes. The selection of the schemes depended on several factors, including method accuracy and the availability of tidal current and salinity data. Then, for estuaries with different stratification types, appropriate methods were chosen to estimate the estuarine flushing times.

Figure 1.

The framework for deriving stratification parameters and flushing time for estuaries in the continental U.S.. Choice of methods is determined both by available data and the underlying assumptions of different methods. Φ is the stratification parameter.

Ultimately, time series analysis was used to explore the temporal variation of flushing time and Generalized Additive Models (GAMs) were applied to analyze the correlation between freshwater inflow and flushing time. We chose GAMs since it is more flexible and can uncover the hidden relationships among variables, even if they are not linear (Hastie & Tibshirani 1987). GAMs were implemented with the mgcv library in R.

2.2. Data

The data sources used in this work are listed in Table 1.

Table 1.

Data Sources for Calculation of Estuarine Stratification Parameters and Flushing Times.

Data Category	Source	Dataset	Resolution or Scale
Estuarine Boundary	U.S. EPA	Estuary Data Mapper	varies, average 1:70,000
	The Pacific Marine and Estuarine Fish Habitat Partnership (PMEP)	West Coast USA Current and Historical Estuary Extent	1:20,000,000 ~ 1:5,000
Other Shapefiles	The Nature Conservancy (Spalding et al. 2007)	Marine Ecoregions of the World (MEOW)	NA
	USGS and U.S. EPA	National Hydrography Dataset Plus (NHDPlus) Version 2	1:100,000
Digital Elevation Models (DEMs)	USGS’s CoNED Applications Project	USGS Coastal National Elevation Database (CoNED, Thatcher et al. 2016)	~1 meter
	NOAA’s National Centers for Environmental Information (NCEI)	NOAA Continuously Updated Digital Elevation Model (CUDEM)	~1 meter
		NOAA Coastal Elevation Model (CEM)	10 meters
		NOAA Coastal Relief Model (CRM)	90 meters (resampled to 30 meters)
	NOAA Office for Coastal Management	NOAA Lidar Datasets	1–10 meters
Freshwater Inflow	USGS Water Data for the Nation	USGS NWIS (1950–2018)	Daily
	USGS’s WMA - Earth System Processes Division	USGS Monthly Flow Estimates Database (1950–2018)	Monthly
Precipitation	PRISM Climate group in Oregon State University	monthly PRISM datasets (1950–2018)	Monthly
Tide	Center for Operational Oceanographic Products and Services, NOAA	NOAA Tide Predictions (1950–2018)	Daily
Tidal Current		NOAA Current Predictions (2017–2018)	Daily
Longshore Current	The Global High Frequency Radar National Network Production (Roarty et al. 2012)	High Frequency Radar National Network Production (2012–2019)	Monthly, ~ 6 Kilometers
Ocean Salinity	NOAA’s National Centers for Environmental Information (NCEI)	NOAA World Ocean Atlas (WOA) Version 2 2013 data (2005–2012)	Monthly
Estuarine Salinity		Global Temperature and Salinity Profile Programme (GTSPP, 1990 – 2018)	Hourly
	U.S. EPA	EPA National Aquatic Resource Surveys (NCA:1999 & 2006; NCCA: 2010 & 2015)	hourly or daily

2.2.1. Estuarine Boundaries

A total of 517 estuaries were identified by combining estuaries from the Estuary Data Mapper (EDM) database and the West Coast Estuary database from the Pacific Marine and Estuarine Fish Habitat Partnership (PMEP, https://www.pacificfishhabitat.org/). We excluded 157 estuaries in the West Coastal region because they are seasonally-closed or have DEM elevations higher than the Local Mean Sea Level. Those estuaries were considered as having no, or limited, surface water exchange between the fresh and salt water, which made it difficult to estimate the surface exchanges. We targeted and analyzed 360 estuaries, including 321 from EDM and 39 from the PMEP database. Estuaries were spatially grouped into the nine marine ecoregions defined by a global classification system – the Marine Ecoregions of the World (MEOW, Figure 2, Spalding et al. 2007).

Figure 2.

Estuaries and ecoregion boundaries (based on Marine Ecoregions of the World scheme (Spalding et al. 2007) across the continental U.S. Numbers within ecoregions refer to the number of estuaries contained within.

2.2.2. Elevation

Estuarine topography was acquired from available coastal merged Digital Elevation Models (DEMs) with the finest available spatial resolution (1–30m; Table 1). For some estuaries, only the DEMs from the Coastal Relief Model (90 meters, CRM) were available and were resampled to 30 meters. If the DEM grids were contiguous to the estuarine water bodies and their elevation values were lower than the estuarine highest observed tide, they were assumed to be part of the estuarine flood plain and were included in the estuarine DEM. All the DEM data were transformed into the NAD83/Albers Equal-Area Conic Projection before analysis. The other estuarine morphologic attributes were derived from estuarine boundaries and DEMs, including the average depth, area, estuarine volume (via Surface Volume function in ArcGIS 3D Analyst) and the width of their outlets.

2.2.3. Freshwater Inflow

The terminal non-tidal streamlines of river discharge linked to estuaries and their associated USGS gaging stations were identified based on the National Hydrography Dataset Plus (NHDPlus) Version 2 (McKay et al. 2012). Daily observed river discharges from 1950 to 2018 were downloaded from the USGS National Water Information System (USGS NWIS). Monthly discharges were calculated only when the daily data coverage within a month was ≥ 90%. If there were no USGS stations associated with the terminal streamlines or USGS data were only available for a portion of the time period, the monthly streamflow supplements were obtained from the monthly Flow Estimates Database for 1950 to 2015 (Miller et al. 2018). If discharge gaps still existed after the data matchup process above, those gaps were filled by referring to the closest upstream reach if the existing discharge showed strong correlation with its closest streamline. However, for some streamlines without either USGS observed data or estimated monthly discharge, their discharge values were estimated based on the ratio of their Divergence-routed Cumulative Drainage Area (DivDASqKM in NHDPlus Version 2) to the DivDASqKM of the closest streamlines with discharge data.

For the 35 estuaries with estuarine area exceeding watershed drainage area, direct precipitation to the estuarine surface was added to the freshwater inflow. Monthly total precipitation over estuarine surfaces from 1950 to 2015 were obtained from the PRISM Spatial Climate Datasets (Daly et al. 2000). For systems with lesser estuarine: watershed area ratios, we assumed precipitation also contributes to the total freshwater inflow, but it comprises a relatively small part compared to the river discharge, especially after accounting for potential evaporation, and was ignored.

2.2.4. Tides

Predicted flood and ebb tide heights from the tidal stations closest to the estuarine outlets were obtained from the NOAA Tide Prediction database (Synolakis et al. 2007). For several large estuaries, if multiple tidal gaging stations were located within a single large estuary, the estuary was segmented into several parts based on either USGS delineation of sub-bays/sub-estuaries or the National Estuarine Data Atlas (OAD/SAB 1985) designating areas with similar tidal ranges (Detenbeck et al., 2009). If there were no NOAA tidal gaging stations within a given estuary, the nearest tidal gaging station was selected that had a similar aspect and “exposure” to winds. Tidal values were adjusted to match the tidal heights at the estuarine outlets. Since DEMs from different sources may have different vertical datums, the vertical datum of the tidal height for the certain estuary should be the same with its DEM. If it was not, using metadata on tidal gaging stations from NOAA’s Tides and Currents web site, the vertical datum of tide heights was converted to match that of the respective estuarine DEM. Based on the time series of the predicted daily tides acquired above, the monthly tidal prism volumes for estuaries were estimated.

To ensure the tide station selected would reasonably reflect the tidal condition near the outlet, the tidal height difference under the local Mean Sea Level (MSL) datum between the tidal station and the estuarine outlet were checked. If this difference was over 0.1 m, flood tides (or high tide, HT) and ebb tides (or low tides, LT) were adjusted. The tidal adjustment scheme varied along with the different vertical datum references for different estuaries (Figure 3, MSL as the vertical datum reference). Based on the adjustment scheme, the HT and LT of the estuarine outlet (point a in the Figure 3) would be adjusted from the HT′ and LT′ of the tidal stations, respectively (point a′). All of the correction factors, including MHW, MLW, MLLW, MHW’, MLW’ and MLLW’ under the MSL reference, were acquired through the NOAA’s online VDatum tool (https://vdatum.noaa.gov/vdatumweb/).

Figure 3.

The adjustment schemes of high tides and low tides from the tidal stations to the estuarine outlets. ΔH is the difference of Mean High Water between the tidal station and the estuarine outlet; ΔL is the difference of Mean Low Water between the tidal station and the estuarine outlet; ΔLL is the difference of Mean Lower Low Water between the tidal station and the estuarine outlet.

2.2.5. Tidal Prism Volume

In the tidal flushing process, during the flood tide stage, tidal water enters the estuaries and mixes with existing water in the estuary. When the tide falls, the water exits the estuaries as the ebb tide. The volume of the flushing tidal water in an estuary between high tide and low tide over a tidal cycle is named the tidal prism volume (V_tp). The “3D Surface Volume” tool under the ArcGIS 3D Analyst extension was applied to obtain the estuarine monthly V_tp. In this process, the maximum tidal volume and minimum tidal volume below the water surface were calculated from monthly mean high tide and low tide, respectively (Figure 4). The difference between them is the monthly average tidal prism volume.

Figure 4.

The method and variables used in the tidal prism volume calculation, using MSL as the vertical datum reference as an example.

2.2.6. Current

Tidal current occurs with the rise and fall of the tides, acting on the vertical and along-channel diffusivities to affect the vertical mixing of the estuary. The maximum flood current at the mouth of the estuary, also referred to as the amplitude of the depth-averaged tidal velocity, was incorporated into models to identify the estuarine stratification types (Ralston et al. 2008; Guha & Lawrence 2013). Existing tidal current stations were acquired from the NOAA Current Prediction database (Synolakis et al. 2007). The predicted daily current data with flood and ebb velocity (2017 and 2018) were selected if the closest station was located within 3500 meters to the corresponding estuarine outlet. Based on this dataset, the monthly maximum flood current was calculated.

The longshore current at the estuarine outlet was needed to calculate ebb return factors. By flushing the ebb tide discharge away before it returns to the embayment with the next flood tide, the longshore current will influence the rate of water exchange with the estuary. The monthly average amplitude of the longshore current (2012–2019) used in this research was obtained from the 6 km resolution version of the High-Frequency National Network database (Roarty et al. 2012).

2.2.7. Salinity

Ocean Salinity near the estuarine outlets was extracted from NOAA World Ocean Atlas (WOA) Version 2 2013 (from 2005 to 2012) (Wetz & Yoskowitz 2013). The grid nearest to the estuarine outlet was assigned to each estuary and the averaged ocean salinity from each grid was calculated. In addition, the time- and depth-averaged salinity of multiple monitoring stations within an estuary were obtained from different surveys. One of the main sources was the Global Temperature and Salinity Profile Programme (GTSPP, Sun et al. 2010), supplemented by data from EPA’s National Coastal Assessment (2015) and local organizations.

2.3. Stratification Scheme

Based on the water circulation in an estuary, estuarine stratification can be classified into three types: well-mixed, partially-stratified and strongly-stratified types. The complicated interaction between the river, the exchange flow, and the tides determines the estuarine stratification class (Guha & Lawrence 2013).

2.3.1. Froude Number Scheme

The Froude Number Scheme is a newly-developed and simple nondimensional scheme used to calculate the estuarine stratification parameter (Guha & Lawrence 2013, de Miranda et al. 2017). It is the first choice for our work. However, the tidal current velocity near the estuarine outlet is required for the Froude Number Scheme, which makes this scheme unavailable for some estuaries without available tidal current data. Therefore, other classic classification schemes must be applied, including the Flow Ratio Scheme and Salinity Scheme.

The Froude Number Scheme is a simple nondimensional scheme, which is developed by rewriting the classical underlying model that produces the stratification-circulation diagram (Hansen 1965; MacCready & Geyer 2010). This scheme requires the system to be represented as a tidally averaged estuary with rectangular geometry. It produces two nondimensional variables – the estuarine Froude number F_r and a Modified tidal Froude number ${\tilde{F}}_t$. Based on those parameters, the nondimensional salinity gradient at the estuary mouth ∑_x|0 and nondimensional stratification parameter $\Phi (\Phi =f(F_r,{\tilde{F}}_t,\sum _{x|0}))$ are computed, which can be used as a basis for the estuarine stratification scheme (Eq. 1). F_r and ${\tilde{F}}_t$ are nondimensional results calculated from $F_r=\overline{u}/C$ and ${\tilde{F}}_t=u_t/C$, where $\overline{u}$ is the cross-section-averaged river velocity, that can be calculated as the mean river flow rate divided by the cross-section area and u_t is the amplitude of the depth-averaged tidal velocity, equal to the maximum flood tide velocity. The coefficient C is defined as twice the speed of the fastest internal wave supported in an estuary (MacCready & Geyer 2010; Guha & Lawrence 2013).

$$\begin{gathered} {({\sum }_{x|0})}^3+C_1{F}_r^{2/3}{({\sum }_{x|0})}^2+\left(C_2{F}_r^{4/3}+C_1{\tilde{F}}_t^2{F}_r^{2/3}\right)*({\sum }_{x|0})=1 \\ \Phi =C_4{F}_r^{2/3}{({\sum }_{x|0})}^2+C_5{F}_r^{4/3}{\sum }_{x|0} \end{gathered}$$ (1)

where the coefficients, C₁, C₂, C₃, C₄ and C₅, are estimated based on the Schmidt number (S_c, Guha & Lawrence 2013, Table 2). We used the estimated value S_c ≈ 2.2 from Ralston et al. (2008).

Table 2.

List of parameters used in Froude Number scheme (Guha & Lawrence 2013)

Coefficients	Definition	Value used
C	$\sqrt{\text{g}\beta {\text{s}}_0\text{H}}$
g	Gravitational acceleration	9.81 m2/s
β	Constant	7.7 × 10−4 psu−1
C1	4.08Sc1/3	5.31
C2	3.57Sc2/3	6.04
C3	1.06×10−3 Sc−1/3	8.16×10−5
C4	5.43Sc1/3	7.06
C5	5.21Sc2/3	8.82

The estuarine stratification parameter is defined as Φ. A value of Φ = 0.1 defines the transition between well-mixed and partially-stratified types. A value of Φ = 1.0 defines the boundary between the partially-stratified and strongly-stratified types. Therefore, Φ < 0.1 indicates the estuary is well-mixed and Φ > 1 means the estuary is strongly-stratified.

2.3.2. Flow Ratio and Salinity schemes

Vertical stratification usually occurs when there is relatively large freshwater discharge into the estuary as compared to the tides. Based on empirical analysis, the Flow Ratio Scheme is introduced to indicate the predominant influence of the freshwater inflow or tidal movement on the vertical salinity stratification. In the Flow Ratio Scheme, the stratification parameter Φ is defined as the ratio of the freshwater inflow discharged into the estuary (QT₀) to the tidal prism volume (V_tp) during a tidal cycle (T₀, Eq. 2; Schultz & Simmons 1957). It applies the same thresholds of 0.1 and 1.0 to classify the estuarine stratification classes (Dyer 1997).

$$\Phi =Q{T}_0/V_{tp}$$ (2)

We can also apply the measured vertical salinity profile to classify estuaries, referred to as the Salinity Scheme in our framework. In this scheme, the Φ is the ratio of the time-averaged salinity difference between surface and bottom to the depth-averaged salinity (Hansen & Rattray 1966).

For the Salinity Scheme, the stratification parameter (Φ) is the ratio of the time-averaged salinity difference (ΔS = S_b − S_t) between surface and bottom to the depth-averaged salinity S (Eq. 3, Hansen & Rattray 1966). Ideally, a depth- and time-averaged salinity should be calculated over several tidal cycles. According to the classification diagram from Hansen & Rattray (1966), partially mixed estuaries have the Φ between 0.1 and approximately 1 with the salinity difference of 2–10 ppt between surface and bottom (Knudsen 1900). Strongly stratified estuaries have larger Φ and salinity differences, while well-mixed systems have Φ less than 0.1 and salinity difference below 2 ppt.

$$\Phi =\Delta S/S$$ (3)

However, the Flow Ratio Scheme is too simplistic in that it does not factor in the influence of estuarine geomorphology on the mixing process of freshwater and saltwater. On the other hand, with the Salinity Scheme it is hard to determine the transition thresholds between the partially-stratified and the well-mixed status or the partially to strongly-stratified status (de Miranda et al. 2017). Some estuaries may lack sufficient salinity data to apply the Salinity Scheme to classify their types. Therefore, in this work, the Salinity Scheme was applied only to estuaries with more than five salinity observations. Both Flow Ratio and Salinity schemes were compared to cross-check stratification results. If the results didn’t match, the Φ from Salinity Scheme was used to identify the stratification type of the estuary.

We estimated the estuarine monthly stratification parameters through the Froude Number Scheme from 2017 to 2018, or through the Flow Ratio Scheme from 1950 to 2015. For an estuary, if the well-mixed status occurred in 75% or more of all observations, we regarded it as well-mixed. However, it would be classified as strongly-stratified when the strongly-stratified observations reached 35% of the total or above. Estuaries that did not satisfy either condition were classified as partially-stratified.

2.4. Flushing Time Calculation

Simplified models were chosen for the flushing time calculation in the continental U.S. rather than hydrodynamic modelling approaches (Sanford et al. 1992; Sheldon & Alber 2006; Abdelrhman 2007). We applied different modeling methods with specific application assumptions and data requirements to estimate the estuarine flushing times according to their different stratification types. Three methods were selected in the framework: Tidal Prism Method (TPM), Freshwater Fraction Method (FFM), and Knudsen Salinity Balance Method (KSBM).

2.4.1. TPM and FFM

Tidal Prism Model (TPM) is a simple steady-state model based on the assumption that the systems are well-mixed and river flow is small compared with the tidal volume in the receiving body. In the Tidal Prism Model (TPM), the flushing time (T_tp) can be expressed as the ratio of the estuarine water volume (V_w) to its overall rate of renewal (R) during certain tidal periods (Ketchum & Rawn 1951). That is T_ft = V_w/R, the basis of the Tidal Prism Model (Figure 5).

Figure 5.

Model process of the Tidal Prism Model during one tidal period

In the tidal flushing process, some portion of water usually returns from the previous ebb tide, which does not contribute to the tidal flushing. To indicate the influence of this returning portion, the ebb return factor R₀ (0 < R₀ < 1) is introduced into the TPM equation (Sheldon & Alber 2006). Based on the physical theory of the ebb return and calculation methods for the ebb return factor (Sanford et al. 1992), a simplified method was presented by Abdelrhman (2007) to estimate the return flow factor using the estuarine volume (V), the amplitude of the longshore current and the averaged depth of the estuary. The revised TPM applied in this work is described in Eq. 4.

$$T_{ft}=\frac{V{T}_0}{\text{Q}+(1-R_0)V_{tp}}$$ (4)

Estuarine stratification type usually varies spatially and/or temporally. An estuary may be changed from a partially-mixed type to well-mixed type with variation of the freshwater discharge. Although application to well-mixed systems would be ideal, TPM is still applicable for partially-mixed systems (Sheldon & Alber 2006).

The Freshwater Fraction Method (FFM) is a widely used method, providing an estimate of the time required for freshwater inputs to replace the freshwater content in the estuary (Huang & Spaulding 2002). It was mainly used to calculate the flushing time of well-mixed or partially stratified estuaries. Generally, FFM is more suitable than TPM to be applied for partially stratified systems (Sheldon & Alber 2006). In this work, both TPM and FFM were used to calculate the flushing time for well-mixed and partially stratified estuaries and their results were compared.

In the Freshwater Fraction Method (FFM), the flushing time was determined by the ratio of the freshwater volume within the estuary to the freshwater inflow rate over a given period. To estimate the estuarine freshwater volume, the concept of freshwater fraction, f (0 < f < 1), was introduced in FFM as the difference ratio of the time- and depth-averaged estuarine salinity (S) over the available dates (1990–2018) to the salinity of seawater (S₀) at the mouth (de Miranda et al. 2017; Sheldon & Alber 2006).

$$f=\frac{S_0-S}{S_0}$$ (5)

$$T_{ft}=\frac{\sum (f{V}_0)}{Q}{T}_0$$ (6)

In this work, based on the monitored salinity values, we acquired the f across multiple monitoring points. To better reflect the spatial distribution of the freshwater fraction, Empirical Bayesian kriging (EBK) was used to interpolate f and generate 250m × 250m grids, describing the variation across the whole estuary (Samsonova et al. 2017). The EBK method was chosen in this process because it accounts for spatial pattern, which is introduced through the estimation of the underlying semivariogram. The semivariogram parameters in EBK were estimated using restricted maximum likelihood (REML), which reflects the spatial distribution of f with decreased trend seaward. Once the grid f was acquired, the estuarine freshwater volume could be estimated through ∑(fV₀). V₀ was the volume of each grid, calculated through the unit area (250m × 250m) multiplying the average depth of the grid derived from the estuarine Digital Elevation Model (DEM). Eq. 5 describes the Flushing Time calculation for the FFM. ArcGIS (^©ESRI) was used to execute the EBK. Through the Empirical Bayesian Kriging method, the freshwater fraction values were interpolated over the entire estuary and summarized as grids (250m × 250m).

However, FFM requires a sufficient spatial distribution of monitored salinity within the estuary to estimate an overall average. Since at least 10 salinity stations with non-zero value were required when using Empirical Bayesian Kriging method, we only applied FFM when at least 10 salinity stations were present within the estuary. According to the comparisons of the revised TPM and FFM from Sheldon & Alber (2006), those two methods theoretically should yield similar results at steady state conditions. We used both methods to estimate the flushing time for the well-mixed and partially-stratified estuaries and compared estimates across methods.

Seasonal flushing times were also calculated via the freshwater fraction method for estuaries selected to represent as many marine ecoregions as possible, with some modifications to correct for the fact that salinity is not at a steady state within the estuaries (Hagy et al. 2000). We adapted the method of Alber and Sheldon (1999). Daily total flows were estimated for each estuary by developing a quadratic equation to describe the relationship between monthly average daily flows at a reference station (generally the station with highest discharge to the estuary) and monthly average daily total flows, then applying that equation to the daily time series for the reference station. The following flow metrics were derived for the 2017–2018 time period: Qmin, Q25, Q50, Q75, and Qmax. At least ten stations with salinity observations taken at times corresponding to those characteristic flow values (or as close as possible) and distributed as evenly across the estuary as possible were used to estimate freshwater fraction at individual points. Freshwater fraction values were interpolated across the estuary for each Q value via Bayesian kriging. A polynomial relationship was developed between freshwater fraction at a reference station with frequent salinity observations and the system-wide freshwater volume, which was then used to generate a time series of freshwater volume estimates at approximately monthly intervals (subject to data availability). A series of moving averages were generated for each daily flow value, e.g., previous 2-day average, 3-day average, etc. The averaging time period that most closely corresponded to the associated flushing time estimate was selected so that the time scales would be consistent.

2.4.2. KSBM

For strongly stratified estuaries, the Knudsen Salt Balance method (KSBM, Dyer 1997) can be applied to estimate their flushing time. This method was developed from the Knudsen Hydrographical “theorem” based on the salt transport balance in stratified estuaries (Knudsen 1900). A key limitation of the KSBM is that both vertical salinity profiles and time series near the estuarine mouth are needed to estimate the flushing time. Because these data were rarely available, we did not use KSBM.

3. Results

3.1. Stratification

3.1.1. Stratification Types

Among 360 estuaries, 151 had available freshwater inflow and maximum flood tide velocity data to apply the Froude Number Scheme to calculate monthly estuarine Froude numbers F_r, and the Modified tidal Froude numbers ${\tilde{F}}_t$. Then the stratification parameter Φ could be evaluated and summarized across different ecoregions (Figure 6). Based on the Froude Number Scheme, 14 estuaries among 151 were strongly-stratified (red dots in Figure 6). In the Gulf of Mexico ecoregion, 18 of 21 estuaries were well-mixed. However, in Northern California and Virginian Ecoregions, only one estuary out of 15 was well-mixed. The others showed either partial or strong stratification. However, the Froude Number Scheme could be applied to only a limited number of estuaries in the West Coast, since many of them are small systems without available tidal current data near their outlets.

Figure 6.

Stratification types for estuaries in different marine ecoregions based on the Froude Number Scheme, plotted as combinations of ${\tilde{F}}_t$, the modified tidal Froude numbers, and F_r, the estuarine Froude number. Lines represent isoclines associated with different values for Φ, the stratification parameter. The green and red lines correspond with Φ = 0.1 and Φ = 1.0, the transitions between well-mixed (blue) and partially stratified systems (gold) and between partially-mixed (gold) and strongly stratified systems (red) respectively. The estuaries noted were classified as strongly-stratified, including: Merrimack River (MERR), Kennebec River Estuary (KENN), Susquehanna River (SUSQ), Winyah Bay (WINY), Sabine Lake (SABI), San Francisco Bay-Suisun Bay (SFRA4), Tillamook Bay (TILL), Columbia River (COLU), Quillayute River (QUIL).

The other 209 estuaries could be classified based on the Flow Ratio Scheme. Among them, 31 estuaries had ≥ five salinity observation records for which the monthly mean stratification parameters could be calculated from both the Flow Ratio Scheme and Salinity Scheme. Most of them (22 estuaries) showed the same results from these two schemes and only nine of them were classified differently by those two schemes (Table 3). Due to the limitation of the Flow Ratio Scheme, for those nine estuaries the classified result from the Salinity Scheme was chosen since it was directly based on salinity field observations.

Table 3.

Estuaries with different stratification results from the Flow Ratio Scheme and the Salinity Scheme methods.

Estuary name	Flow Ratio Scheme	Salinity Scheme
Great Bay (NJ)	well-mixed	Partial
New River (NC)	well-mixed	Partial
Lake Borgne (LA)	partial	well-mixed
Mississippi Bird’s foot (LA)	strong	Partial
Apalachicola Bay (FL)	well-mixed	Partial
Perdido Estuary (FL)	partial	Strong
The Thousand Islands (FL)	well-mixed	Partial
Mermentau River (LA)	partial	well-mixed
Suislaw River (OR)	partial	well-mixed

3.1.2. Spatial Distribution

Figure 7 displays the spatial distribution of estuarine stratification types across the continental U.S..

Figure 7.

The spatial distribution of estuarine stratification in the continental U.S. Pie charts display the proportion of estuaries in each marine ecoregion classified as well-mixed (blue), partially stratified (gold), and strongly stratified (red).

Most estuaries in the Gulf of Maine (93%) ecoregion were well-mixed. However, in the Pacific coastal region, especially in NCA and VCF ecoregions, estuaries tended to be strongly-stratified (46% in NCA, 63% in VCF) compared with estuaries in the East Coast and Gulf of Mexico with strongly-stratified estuaries equal or less than 5%. Even in southern California (SCB ecoregion), 13% of estuaries were strongly-stratified. In other ecoregions, including VGN, CRN and FLN in the Atlantic coastal region and Gulf of Mexico (GOM ecoregion), well-mixed estuaries were around 63% - 75% of the total. Among all 360 estuaries, 60 estuaries exhibited strong stratification, of which 50 were located at the Pacific coastal region. In PT where the Salish Sea is located, no estuaries showed strong stratification and most segments were well mixed.

Not only did stratification classifications vary spatially across the continental U.S., but they also varied by segment within a given estuary. Upper segments of the Delaware Bay and Narragansett Bay showed partial stratification and strong stratification, respectively, since rivers discharged freshwater directly into those segments, while the lower parts of those estuaries were generally well-mixed. However, for Aransas Bay and Galveston Bay, the more seaward segments tended to be more stratified than the upper segments. Most parts of the San Francisco Bay were partially-stratified, except its Don Edwards segment and Suisun Bay part, which were linked to the river discharge directly, and exhibited strong stratification during most of the year. Generally, our stratification results here were estimated at a large scale, with a single classification assigned to the full estuary. Therefore, the result didn’t indicate that every specific location within the estuary would have the same degree of stratification.

3.1.3. Seasonal Variation

Stratification types shifted seasonally for some estuaries. For example, obvious seasonal stratification shifts were observed for 2017–2018 based on results from the Froude Number Scheme (Table 4). For most estuaries with shifts in stratification, the partially or strongly stratified periods tended to occur during winter to spring (Table 4). Estuaries were usually more stratified in winter and spring, and more mixed during the summer. However, estuaries in southern FL usually had the reverse pattern because the wet season occurs during summer, with a large amount of freshwater inflow discharging into the estuary and causing the significant vertical differences in salinity (Geyer 2010). Although seasonal differences in temperature may also have had an influence, there is more evidence of variations in discharge influencing temporal variation in stratification overall than wind and temperature. While temperature can have some influence, density differences due to salinity play a stronger role in estuary stratification (as evidenced in temperature-salinity diagrams) (Geyer 2010, Cloern et al. 2017).

Table 4.

Seasonal variation of estuarine stratification in different ecoregions for January 2017 through December 2018. Blue represents periods with well-mixed systems, gold represents periods of partial stratification, and red represents periods of strong stratification.

3.2. Flushing Time

We estimated the flushing times of the 300 well-mixed and partially-stratified estuaries from 1950 to 2015. For 94 of those 300 estuaries, we applied both TPM and FFM to estimated flushing times. For the others, only TPM could be applied. The results here showed the flushing time calculated from both of those two methods, as well as their spatial and temporal variations.

3.2.1. Empirical Bayesian Kriging

Figure 8 illustrates the interpolation results for some estuaries in different ecoregions. It shows the reasonable spatial distribution of f, as well as good agreement between the observed and interpolated f (r² = 0.43 − 1).

Figure 8.

Examples of the spatial distribution of the interpolated f in different estuaries (Note: In the SCB, the FFM method was not applied).

3.2.2. Spatial Distribution

For FFM, the results showed the reasonable spatial distribution, as well as good agreement between the observed and the interpolated f (Figure 8). The median flushing time of each estuary was used to explore the spatial distribution of the flushing time calculated via TPM and FFM (Figure 9a, b). Generally, whether the flushing time was calculated from TPM or FFM, estuaries along the West Coast usually flushed faster than the estuaries in other regions. More than 75% of estuaries had flushing times less than 30 days in the West Coast. In the GM and GOM ecoregions, around 55% and 65% of estuaries from the TPM showed fast flushing, with flushing time less than 30 days.

Figure 9.

The spatial distribution of flushing time (days) for estuaries of the continental U.S., based on: a) the tidal prism method (TPM), and b) the freshwater fraction method (FFM). The estuaries names noted in red in the figure had flushing time estimates larger than 300 days.

Generally, with significant variation of freshwater inflow in different hydrological years or seasons, estuaries had higher variation of flushing time estimates from the FFM compared to the results from the TPM, which means the FFM is more sensitive to inflow changes than TPM. Meanwhile, both of those two methods produced some abnormal results. Based on the FFM, 14 estuaries (n=6 CRN, n=4 VGN, n=2 GOM, n=1 SCB and NCA ecoregions) had very high estimated flushing times, with median value larger than 300 days, such as the Gardiner Bay in New York (352 days in the upper segment and 615 days in the lower segment), Pamlico Sound in North Carolina (647 days), Aransas Bay in Texas (294 days in the upper region and 307 days in the lower segment) (Figure 9(a)). However, according to the results of the TPM, only five estuaries had an extremely slow flushing rate (Figure 9(b)).

3.2.3. Seasonal & Annual Variation

To better display the seasonal and annual variations of flushing times, analysis of monthly and annual variation was focused on the estuaries with estimated flushing time less than 300 days (Figure 10a, b). The monthly median flushing time of estuaries in different ecoregions showed obvious different temporal patterns (Figure 10(a)). For TPM analyses, it was negatively correlated with the median freshwater inflow in each ecoregion. Well-mixed and partially-stratified estuaries generally had longer flushing times in the dry seasons than in the wet seasons.

Figure 10.

a) Monthly variation of median flushing time from TPM (green box plots, days) and median freshwater inflow (blue lines, m³/s), and b) annual variation of log normalized median flushing time (box plots) and log normalized median freshwater inflow (blue lines, m³/s) of estuaries within each marine ecoregion. The normalization of median flushing time and freshwater inflow represented the anomaly of their annual median value from the average. Distribution of median flushing times across estuaries in each ecoregion are shown in green box and whisker plots for the tidal prism method (TPM) and in red box and whisker plots for the freshwater fraction method (FFM) results. See Figure 1 for definition of ecoregion abbreviations.

In Figure 10(b), annual variation of median flushing times and median freshwater inflow from 1950 to 2015 were normalized by subtracting the average value to show their annual anomaly time series and then transformed using the log-modulus transformation (John & Draper 1980). Similarly, the variation of the annual flushing time and freshwater inflow also showed different trends that reflected the negative correlation between them. In the dry years, the estuarine flushing times were usually longer than in the wet years.

Sufficient data were available to calculate seasonal flushing times by the FFM method for only eight systems, distributed across seven of nine marine ecoregions (Figure 11). The Carolinean ecoregion was not represented due to challenges in applying this method to the complex flow pathways of the Albemarle-Pamlico system and lack of sufficient data for other systems in this ecoregion. Seasonal variation in flushing times was generally large, ranging from 5-fold to two orders of magnitude difference over 2017–2018 (Figure 11). In some cases, consistent patterns were observed across years, e.g., Charlotte Harbor and Tampa Bay, with gradually decreasing flushing times over the water year, while in other cases (San Francisco Bay), patterns varied between years. For Indian River Lagoon and San Francisco Bay, seasonal patterns were similar between TPM and FFM estimates, although the magnitude of flushing time predicted by FFM was much lower for San Francisco Bay (Appendix A).

Figure 11.

a) Seasonal flushing time by adjusted FFM method as days, and b) normalized to maximum flushing time per period of record.

4. Discussion

4.1. Influence of freshwater inflow

River discharge plays an important role in estuarine circulation. The stratification parameters of around 97% of estuaries showed significant positive correlations with the time series of freshwater inflows (R² > 0.9). Therefore, freshwater inflow could explain the seasonal and annual variations of estuarine stratification. During the wet seasons or wet years with large freshwater inflow, some estuaries tended to be more stratified, especially those estuaries with seasonal stratification shifts. According to the analysis framework (Figure 1), if the stratification parameter is always below 0.1 across all seasons, the estuaries are well-mixed throughout the year no matter how much freshwater inflow they receive. Although freshwater inflow significantly affects the estuarine stratification, it is not the only factor that determines the stratification type. Multiple factors contribute, including tide, wind, current, salinity, and estuarine morphology. For example, researchers found for both the Mobile Bay and the York River Estuary, wind plays an important role in governing the estuarine exchange flow, with different directions of winds having opposite influences (Scully et al. 2005). Baroclinity also has profound impacts for Mobile Bay, especially during periods of high stratification (Du et al. 2018). Bathymetry (also morphology) affects the stratification by inducing tidal residuals and affecting the water exchange process (Valle-Levinson et al. 2009).

Research in several different estuaries has demonstrated strong correlations between estuarine flushing time and freshwater inflow (Shaha et al. 2012; Ensign et al. 2004; Du et al. 2018). The correlation result through GAMs showed that the variation of flushing time for 151 out of 300 estuaries from TPM and 73 out of 94 estuaries from FFM could be mainly explained by freshwater inflow (negative correlation with R² > 0.8) (Figure 12). Thus, for most estuaries, a linear or nonlinear empirical model could be developed based on the relationship between freshwater inflow and flushing time. For some estuaries (97 out of 300 from TPM), tidal prism volume was the main factor influencing flushing time variation (negative correlation with R² > 0.8; Figure 12). For the remaining 52 estuaries, besides the freshwater inflow, tidal prism volume or other factors combined would significantly affect the flushing time, e.g., wind and topographic characteristics (Du et al. 2018; Dixon et al. 2014; Glorioso & Davies 1995).

Figure 12.

Temporal variation in flushing time estimates for individual estuaries from: a) the tidal prism method (TPM), and b) freshwater fraction method (FFM) is explained mainly as a function of freshwater flow (blue) or tidal prism volume (red) or a combination of the two (black) through Generalized Additive Models (GAMs).

The influence of freshwater inflow on stratification and flushing time demonstrated the effects of droughts on coastal systems. With the decrease of freshwater inflow, the salinity, related density and the hypersaline conditions will be altered, as well as the estuarine stratification patterns and flushing rate. Reduced flushing rate could result in pollutant and nutrient buildups, which could cause an increase in the frequency and intensity of algal blooms (Lehman et al. 2017; Palmer & Montagna 2015). On the other hand, the reduced freshwater inflow could lower nutrient inputs (Wetz & Yoskowitz 2013; Gilbert et al. 2012), especially for regions with nutrient inputs dominated by non-point sources. The higher the slope relating flow and flushing time, the more sensitive the flushing time of the estuary was to changes in freshwater inflow. This phenomenon was more obvious for the results from FFM analysis of annual flushing time, consistent with the research from Ensign et al. (2004). Therefore, with a significant decrease in freshwater inflow, drought events would sharply increase flushing time, making the flushing rate significantly slower, which would threaten the ecological health of the estuary.

4.2. Comparison of TPM and FFM

Although TPM and FFM are different methods for calculating the flushing time, their consistent derivation shows they have much in common (Sheldon & Alber 2006). However, in practice, since different parameters and datasets are used in the two methods, their flushing time results usually show discrepancies. In addition, both of those methods have limitations. Calculations assume steady-state and well-mixed estuaries. Both TPM and FFM likely yield inaccurate results at the high end of flushing times (> 300 days) because the assumption of steady-state conditions is violated. By comparing the results from TPM and FFM in this work, we found that FFM was more sensitive to the freshwater inflow than TPM and tended to estimate longer annual flushing times during dry periods than wet periods. It is because FFM features freshwater inflow prominently in the equation.

For TPM, the incomplete flood mixing should affect the flushing time as well, but that effect has not been included in this work other than via ebb return factors due to the difficulties of its quantification. This limitation tends to underestimate the flushing time. In addition, the TPM method neglects the influence of gravitational circulation (Hagy et al. 2000), so it should be applied to estuaries generally with weak or nonexistent gravitational circulation, which are usually with little freshwater inflow (Sheldon & Alber 2006). With respect to data requirements, data for the TPM method are more readily available than FFM, particularly for examining intra-annual variability in flushing time. Overall, for estuaries with small freshwater inflow or during the dry seasons, TPM is more suitable for flushing time calculation. TPM is a better choice than FFM for high flushing time estuaries, which generally have less freshwater inflow comparing with tidal prism volume, because incomplete salinity records are more likely to generate nonrepresentative result. For example, for San Diego Bay which usually has inflow less than 10 m³/s, TPM would be more suitable and accurate to apply for flushing time estimation and also it would produce the more reasonable results than FFM (Table 5).

Table 5.

Flushing time compared with other research (Med: median; Min: minimum, Max: maximum)

Estuary Name	Ecoregion	TPM, days			FFM, days			Flushing Time Reference, days
		Med	Min	Max	Med	Min	Max	Value	Method	Reference
Altahama Sound	CRN	15	2	35	4	0	24	5.8	FFM	Alber & Sheldon (1999)
Cumberland Sound	CRN	55	19	67	37	2	752	72	FFM	Alber & Sheldon (1999)
Jekyll Sound	CRN	44	11	57	20	1	778	66.8	FFM	Alber & Sheldon (1999)
Ossabaw Sound	CRN	27	6	40	17	2	340	20.7	FFM	Alber & Sheldon (1999)
Savannah River	CRN	6	1	10	4	0	12	5.6	FFM	Alber & Sheldon (1999)
Charlotte Harbor	FLN	60	25	76	110	8	1978	130	FFM	Solis & Powell (1999)
Indian River	FLN	27	10	35	94	10	2630	10~114	TPV (no ebb return)	Kim (2003)
Blue Hill Bay	GM	163	128	183	71	14	1825	28	TPV (no ebb return)	Price et al. (2017)
Boston Harbor	GM	33	21	37	14	2	248	2~10	FFM & Dye experiment	Hilton et al. (1998)
Cobscook	GM	24	21	27	4	1	64	1~7	3D numerical model	Brooks et al. (1999)
Great Bay	GM	19	8	25	9	1	142	2.5~20	3D numerical model	Matso (2018)
Apalachicola Bay	GOM	26	6	61	11	2	58	3~10	FFM	Huang & Spaulding (2002)
Galveston Bay - Upper	GOM	64	7	303	26	2	871	40	FFM	Solis & Powell (1999)
Galveston Bay - Lower	GOM	55	6	181	26	2	864	40	FFM	Solis & Powell (1999)
Aransas Bay	GOM	174	21	277	294	5	7575	168	FFM	Lowery (1998)
Choctawhatchee Bay	GOM	95	12	286	44	5	168	43	FFM	Lowery (1998)
Mobile Bay	GOM	30	5	156	14	2	113	10~33	FFM	Du et al. (2018)
Pensacola Bay	GOM	79	13	296	34	5	214	25	FFM	Murrell & Caffrey (2005)
San Antonio Bay	GOM	92	7	221	85	3	1585	38	FFM	Lowery (1998)
San Diego Bay	SCB	103	29	117	3479	24	5716694	10~100	TPV	Chadwick & Largier (1999)
Coos Bay	VCF	23	4	40	3	0	43	2~48	FFM	O’Neill (2014)
Grays Harbor	VCF	12	4	23	2	0	16	0.5~5	Salinity estimates	Loehr & Collias (1981)
Willapa Bay	VCF	27	14	35	13	2	167	21~35	3D numerical model	Banas & Hickey (2005)
Albemarle Sound	VGN	163	48	308	221	46	1013	90	TPV (no ebb return)	Molina, J. R. (2002)
Pamlico Sound	VGN	115	58	133	647	48	7448	90	TPV (no ebb return)	Molina, J. R. (2002)
Raritan Bay	VGN	28	9	43	7	1	70	16~21	TPV	Ketchum & Rawn (1951)
Rehoboth Bay	VGN	30	26	33	92	19	457	174	TPV	Cerco & Seitzinger (1997)
Hudson River	VGN	34	10	87	36	8	412	10~70	FFM	Zhang et al. (2010)
Chesapeake Bay Mainstem-Lower	VGN	97	26	188	60	10	652	96~140	FFM (include the subbays)	Shen & Wang (2007)
Chesapeake Bay Mainstem-upper	VGN	107	23	300	21	4	232	96~140	FFM (include the subbays)	Shen & Wang (2007)
Barataria Bay	VGN	31	25	33	43	11	130	13~19	3D numerical model	Li et al. (2011)
New York Harbor - Upper	VGN	15	4	86	0	0	3	26~40	3D numerical model	Li et al. (2019)
New York Harbor - Lower	VGN	29	8	92	3	1	34	26~40	3D numerical model	Li et al. (2019)
Great South Bay	VGN	40	37	43	138	38	475	4~34	Lagrangian Particle Method	Yang (2015)
Narragansett	VGN	137	58	181	24	4	179	10~40	empirical model	Pilson (1985)
Long Island Sound	VGN	388	169	590	4	1	27	1~30	Dye Experiment	Vallino & Hopkinson (1998)
James River	VGN	73	22	124	56	9	1352	95	Dye Experiment	Shen & Lin (2006)
Newark Bay	VGN	20	6	47	3	1	25	8	Dye Experiment	Caplow et al. (2003)
York River	VGN	89	23	152	43	5	806	90	Dye Experiment	Shen & Haas (2004)

In addition, the FFM method requires either a large number of salinity profiles to characterize the freshwater fraction over space and time or a sufficient number to interpolate values across the estuary. The EBK method requires a minimum of 10 coincident salinity profiles, and the temporal interpolation method of Albers and Sheldon (1999) requires that at least one of these stations be sampled across a range of flow values. It is possible that more estuaries could be characterized using segmented box models. Segmented box models can use salinity time series sampled across a range of flow values whether measurements at different stations are coincident or not. However, the segmented box model approach requires that salinity profiles be appropriately spaced (Sheldon & Alber 2002). Therefore, for those estuaries with sufficient salinity records in different inflow conditions, FFM would be a better choice, especially for partially-stratified estuaries. Since the FFM has the advantage of incorporating gravitational circulation, analyses for the estuaries with considerable freshwater inflow or during the wet seasons should include FFM in flushing time calculations.

4.3. Comparison with previous research

Flushing time estimates from this work were compared with the results from other research (Table 5). All of the FFM flushing time ranges except for New York Harbor bounded the estimated average or median values from the literature, and three-quarters of TPM estimates met the same criteria (Figure 13). However, when comparing the median value with their averaged value, some differences were observed. There are several reasons to cause those differences. The first one would be the method. For example, the Tidal Prism Method (TPM) used in most previous research does not consider the ebb return effect and thus, their flushing times would always be underestimated, sometimes considerably.

Figure 13.

a) Comparison of median literature flushing times with TPM flushing time range, and b) with FFM flushing time range.

In addition, we have demonstrated the significant spatial and temporal variation in stratification status and flushing time. Spatially, the estuary delineation is a key factor. In this work, we generally divided the sub bays from the main estuaries. For example, the Chesapeake Bay had 29 sub bays in total linking to its mainstem. Based on the recent improvements in coastal Digital Elevation Models (DEMs), most of the estuary DEMs used in this work have resolutions equal to or less than 30-meters. The finer resolution improved the accuracy of estimates of estuarine volume and tidal prism volume used in estimates of flushing time.

The data sets compiled for those years allowed us to analyze the estuarine stratification and flushing time over a long period. The analysis above has shown that flushing time is influenced significantly by freshwater inflow and the data also have a similar range of variation from month to month. For some estuaries, the flushing time can vary by orders of magnitude. Therefore, the time period chosen for assessment by previous researchers would also greatly affect the reported estimated flushing times.

4.4. Limitations

Drivers besides flow variability (e.g., wind and along-estuary topographic variations) influence the estuarine stratification and flushing time but have not been considered in this work. Previous studies have addressed their impacts on the mixing rate, stratification types, and the flushing process (Du et al. 2018; Dixon et al. 2014; Glorioso & Davies 1995). For example, in some estuarine systems (e.g., Neuse River Estuary and Chesapeake Bay), wind may significantly affect the estuarine mixing process, strengthening or reducing the stratification according to its landward or seaward direction and strength (Dixon et al. 2014; Kang & Xia 2022; Valle-Levinson et al. 1998; Xia et al. 2011).

The variation of the along-estuary topography also was not reflected in our work, since our work was conducted over a large spatial scale and the estuary was treated as the whole system. In the framework here, only the average depth of the estuary is used in the stratification scheme and flushing time method. Also, since the Flow Ratio Scheme doesn’t consider estuarine topography, its results need to be verified through other schemes (e.g., Froude Number Scheme and Salinity Scheme). For instance, results of the Flow Ratio Scheme showed some shallow systems in the West Coast are strongly-stratified with short flushing time. However, these shallow systems should have limited stratification (Gleason et al. 2011) and long flushing times due to the limited saltwater exchange. Thus, in the future application of these results, the specific topographic situation may need to be considered and empirical verification may be needed.

In addition, the temporal estuarine circulation is forced by various factors. Beyond the freshwater inflow and tides, the salinity and the spring-neap tidal cycle also play important roles in the variation of the estuarine circulation (Cho et al. 2020; Li et al. 2018). In FFM, the mean freshwater fraction was calculated based on the salinity averaged over all available dates in each station. Therefore, the temporal variations of annual flushing time from FFM haven’t taken the seasonal fluctuation of salinity into consideration.

4.5. Applications

While the methods summarized here are not novel, the comprehensive compilation of datasets allows an unprecedented comparison of stratification regimes and flushing times across space and time in the continuous United States. In comparisons of nutrient susceptibility across individual estuaries, stratification status and flushing times are often reported as static numbers (Bricker et al. 2008, Engle et al. 2007), while in reality stratification and flushing rates vary considerably over time. Likewise, “report cards” issued to track status of individual estuaries include discussion of trends in nutrient loading and response but rarely include information on changes in retention time whose influence can be at least as great as interannual variations in loading (Conservancy of Southwest Florida 2017, SFEP 2019, TBEP 2021, UMCES 2020). To ensure appropriate interpretation of responses to change in nutrient loading, the intra- and interannual variation in stratification and flushing time need to be incorporated into management and assessment of estuaries. For example, prediction of intermittent occurrences of stratification can be paired with information on the frequency of hypoxic events (Codiga 2020).

5. Conclusion

In conclusion, a framework for estuarine characterization was established. It provided a simple and practical way for managers to explore estuarine circulation through multiple stratification schemes and flushing time calculation methods. With the recent improvements in the quality of fine-scale topobathymetry and freshwater discharge estimates, this framework was applied to assess estuaries across the continental U.S. over large spatial scales and long-term periods, which provides a general overview of the spatial and temporal variations of estuarine circulations in the whole U.S..

We also demonstrated the effect of freshwater inflow on estuarine circulation. It showed the opposite influences on stratification and flushing times. Generally, freshwater discharge prominently and positively correlates to the seasonal variation of the estuarine stratification. On the other hand, its reduction would lead to an increase of the estuarine flushing time. Also, this increasing rate would be significantly higher with the reduced freshwater inflow. This result implies for estuarine managers that specific attention should be paid for some estuaries that are strongly-stratified across seasons and other estuaries under dry seasons. Those systems are potentially more vulnerable to nutrient inputs, especially during drought events.

Although other factors have not been included in the methods used here, this work provided a valuable evaluation of the estuarine circulation for numerous estuaries in the continental U.S., as well as their large-scale spatial and temporal comparisons. All the datasets and results here are integrated into the EDM database (www.epa.gov/edm; Detenbeck et al. 2009) that make it accessible for public use. Based on these data, we can further develop indices of estuarine vulnerability to nutrient inputs and extreme climate events.

Highlights.

• Methods for estimating estuarine stratification and flushing time were established.

• We applied these across the U.S. and over a long-term period (1950–2015).

• Freshwater inputs accounted for most of the variation in both parameters.

Data Availability

Data used in this work will be available at U.S. EPA’s ScienceHub: [INSERT SCIENCEHUB LINK WHEN AVAILABLE]. Supporting data will also be available for download via U.S. EPA Estuary Data Mapper virtual portal (www.epa.gov/edm; Detenbeck et al. 2009).