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Impacts of sea-level rise on estuarine circulation: An idealized estuary and San Francisco Bay
Impacts of sea-level rise on estuarine circulation: An idealized and San Francisco Bay Vivien P. Chua, Ming Xu PII: DOI: Reference:
S0924-7963(14)00141-9 doi: 10.1016/j.jmarsys.2014.05.012 MARSYS 2552
To appear in:
Journal of Marine Systems
Received date: Revised date: Accepted date:
10 March 2014 29 April 2014 7 May 2014
Please cite this article as: Chua, Vivien P., Xu, Ming, Impacts of sea-level rise on estuarine circulation: An idealized and San Francisco Bay, Journal of Marine Systems (2014), doi: 10.1016/j.jmarsys.2014.05.012
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IMPACTS OF SEA-LEVEL RISE ON ESTUARINE
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CIRCULATION: AN IDEALIZED ESTUARY AND SAN
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FRANCISCO BAY
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Vivien P. Chua1* and Ming Xu2
1*,2
National University of Singapore
Department of Civil and Environmental Engineering 1 Engineering Drive 2, Singapore 1*
[email protected], (65) 90018140
ACCEPTED MANUSCRIPT ABSTRACT Estuaries lie at the interface of land and sea, and are particularly vulnerable to sea-level rise due
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to climate change that might lead to intrusion of salt water further upstream and affect circulation
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patterns. Climate change is also likely to have a major impact on hydrological cycles and consequently lead to changes in freshwater inflows into estuaries. An idealized estuary model is
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employed to investigate the effects of sea-level rise and freshwater inflows on estuarine
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circulation. Rising sea levels result in a stronger longitudinal salinity gradient an increase in the strength of the gravitational circulation
, higher longitudinal dispersion
and enhanced salinity intrusion. Under low-flow conditions, the effects of sea
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coefficients
, indicating
level rise on salinity intrusion are largest because sea-level rise has a greater impact due to
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weaker vertical stratification. Strong flows increase the strength of the gravitational circulation, resulting in higher vertical stratification, which leads to the nonlinear feedback between vertical
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mixing and stratification. The effect of sea-level rise on salinity intrusion is reduced owing to the suppression of mixing by stratification. Supporting three-dimensional simulations from northern San Francisco Bay are presented. The intrusion length scale
is used as a substitute for
regulating inflows to ensure that sufficient fresh water is available to flush the Bay. Following a set of standards explicitly stated in the 1994 Bay-Delta Accord, a series of simulations are performed and we find that with sea-level rise stronger inflows are required to maintain
at the
proposed locations.
Keywords: Estuaries; freshwater inflows; numerical modeling; salinity intrusion; sea-level rise
ACCEPTED MANUSCRIPT 1
INTRODUCTION
Rising waters as a result of climate change will likely reshape the world's coastlines and may
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lead to significant impacts on estuarine areas. Global warming leads to sea-level rise due to the
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melting of ice caps and thermal expansion of oceans (Gornitz et al., 1982; Wigley and Raper, 1987; Root 1989; Vermeer and Rahmstorf, 2009). Global warming is also likely to have a major
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impact on hydrological cycles and consequently lead to a change in freshwater inflows into
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estuaries (Rapaire and Prieur, 1992; Statham, 2012). Sea-level rise projections by the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) range
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from 0.18 to 0.81 m by 2100 with respect to the base year 1990. A significant acceleration of 0.013 ± 0.006 mm/year2 was reported over the 20th century, and sea levels rose at a rate of 1.7 ±
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0.2 mm/year and since 1961 at a rate of 1.9 ± 0.4 mm/year (Church and White, 2006). Recent altimeter observations indicate an increase in the rate of sea-level rise during the past decade to
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3.2 mm/year, well above previous estimates of 1.5 – 2 mm/yr (Carton et al., 2005). Tidal gauge and satellite data reveal that sea-level rise is not geographically uniform, and spatial variability in the rates of sea-level rise is expected due to non-uniform changes in temperature, salinity and ocean circulation.
For estuarine areas, sea-level rise leads to an increase in the salinity of surface and ground water through salt water intrusion. Rising sea levels result in a landward shift of the estuarine salinity field, threatening freshwater supplies upstream (Williams, 1987; Hull and Titus, 1986). Studies have found that sea-level rise results in higher salinities upstream and also affects tidal currents in estuaries (Hong and Shen, 2012; Chua, 2012). Intrusion of salt water and changes in circulation patterns may have serious consequences for marine ecosystems that are unable to tolerate high salinity (Schallenberg et al., 2003; Short and Neckles, 1999). We are particularly
ACCEPTED MANUSCRIPT interested in the effects of sea-level rise on physical processes such as estuarine circulation, stratification and vertical exchanges, which would play an important role on regulating
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biological phenomena and aquatic habitats.
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Numerical models have been employed to investigate the effects of sea-level rise on salinity and tidal ranges in estuarine environments. Hong and Shen (2012) found the salt content, salinity
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intrusion length and stratification in Chesapeake Bay will increase subject to seasonal and inter-
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annual variability as sea level rises. They also quantified the impact of sea-level rise on circulation and transport in the Bay by simulating the transport of passive tracers. With a
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combination of numerical modeling and statistical techniques, Hilton et al. (2008) demonstrated an increase in bay-averaged salinity of 0.5 psu as sea level rises 0.2 m in Chesapeake Bay.
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Singha et al. (1997) found a positive sea level trend in the Hooghly Estuary, and that there exists a substantial increase in the amplitude and velocities of the tidal wave due to sea-level rise.
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Zhong et al. (2008) noted that sea-level rise will change the resonance characteristics of Chesapeake Bay and suggested that the tidal range will increase by 15 – 20% with a sea-level rise of 1.0 m.
In this paper, an idealized estuary model is employed to investigate the effects of sea-level rise and freshwater inflows on estuarine circulation. The simulations are performed with an idealized model to remove the influence of irregular coastlines, lateral variation in depth and presence of bathymetric features, so that the effects of sea-level rise and freshwater inflows on estuarine circulation are isolated. Variability of freshwater inflows is difficult to predict due to the huge range of uncertainty in inflows that are expected with climate change. Hence, our simulations are performed for a wide range of inflow conditions. Insights on the physical characteristic of estuaries gleaned through idealized simulations may be incorporated to improve our
ACCEPTED MANUSCRIPT understanding of estuaries with realistic coastlines and bathymetry. Supporting three-dimensional simulations from northern San Francisco Bay are presented. In the
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San Francisco Bay-Delta system which provides freshwater supplies to Southern California and
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the Central Valley, and for local domestic, industrial and agricultural use, salt water intrusion upstream will result in water intakes that might draw on salty water during dry periods. Coastal
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aquifers recharged by freshwater upstream are also likely to become saline as salt water is
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pushed upstream (Werner and Simmons 2009; Oude Essink 1999; Bobba 2002; Sherif and Singh 1999; Meisler et al. 1984). The availability of freshwater in San Francisco Bay interacts with
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other factors, including changes to the local hydrology due to climate change (Miller et al. 2003; Dettinger et al. 2004; Knowles and Cayan 2002; Knowles and Cayan 2004), and changes in
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demand due to population growth and urbanization. The combination of these factors is likely to compound water stress in coastal areas. An unstructured-grid SUNTANS model is applied to
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perform three-dimensional simulations of flow in San Francisco Bay, and a series of simulations are performed to investigate the effects of sea-level rise and freshwater inflows on estuarine circulation.
The remainder of the paper is structured as follows. Section 2 describes the hydrodynamic model. Section 3 presents the results of our idealized simulations. Section 4 describes three-dimensional simulations in San Francisco Bay. Section 5 provides conclusions. 2
HYDRODYNAMIC MODEL
The climate change simulations are performed with the SUNTANS hydrodynamic model (Fringer et al., 2006). The governing equations are the three-dimensional, Reynolds-averaged Navier-Stokes equations under the Boussinesq approximation and hydrostatic assumption: ,
(1)
ACCEPTED MANUSCRIPT ,
(2)
subject to incompressibility,
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,
and
and
,
and
are the Cartesian velocity
directions. The horizontal and vertical eddy viscosities are given by
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components in the ,
and
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velocity vector is
, the free-surface height is , the
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where the horizontal gradient operator is
(3)
, respectively. The vertical momentum equation is not present because
is
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solved using Eq. (3). The baroclinic head is given by
(4)
,
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is the constant reference density and the total density is given by
term is given by
using
,, where
is the angular velocity of the Earth and
. The Coriolis is the latitude.
is computed with a linear equation of state in terms of the salinity
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The density perturbation
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where
, where
and
are reference states and
psu-1.
The free-surface evolves according to the depth-averaged continuity equation:
where
.
(5)
is the water depth.
The effects of temperature on stratification are neglected in our estuarine simulations. The transport for salinity neglects horizontal diffusion and is given by , where
(6)
is the vertical turbulent eddy diffusivity. These equations are solved using the methods
described in Fringer et al. (2006), in which the free-surface height, vertical diffusion of
ACCEPTED MANUSCRIPT momentum and vertical scalar advection are advanced implicitly with the theta-method, and all other terms are advanced with the second-order Adams-Bashforth method. For advection of
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momentum, the Eulerian-Lagrangian method (ELM) is employed.
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The scalar concentrations defined at cell centers of staggered grids are interpolated to their cell faces using the method described in Casulli and Zanolli (2005). The scheme is monotonicity-
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preserving and uses a combination of first-order upwinding and a higher-order antidiffusive flux
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via the TVD (Total Variation Diminishing) constraint (Harten and Lax, 1984). The Superbee limiter (Roe 1984) produces the best results and is chosen for our simulations (Gross et al., 1999).
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The quadratic drag law is applied at the bottom boundary to compute the bottom stress with
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is the horizontal velocity vector in the first grid cell above the bed,
where
is the location of
above the bed and
is its magnitude
is computed from the bottom roughness parameter z0,
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and the drag coefficient
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where
(7)
,
(8)
,
at a distance of one-half the bottom-most vertical grid spacing
is the von Karman’s constant. The roughness coefficient is set to
m, a value typical for most real estuaries (Ludwick, 1975; Li et al., 2004). The horizontal turbulent mixing of momentum is determined with a constant eddy viscosity, while the horizontal turbulent mixing of scalars is ignored. The horizontal and vertical background eddy viscosities are set to the background vertical eddy diffusivity is set to
m2/s and
m2/s, respectively, and m2/s. These background values are
required to allow turbulence to grow due to production in the turbulence model. The MellorYamada level 2.5 (MY2.5) model (Mellor and Yamada, 1982), with stability functions modified by Galperin et al. (1988) is used to compute the vertical eddy viscosity and eddy diffusivity.
ACCEPTED MANUSCRIPT Details of implementation of the turbulence model in SUNTANS are described in Wang et al. (2011). A comparison of turbulence closure schemes for estuarine modeling show that
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differences between the k ‒ kl (Mellor-Yamada Level 2.5), k ‒ ε and k ‒ ω schemes are
IDEALIZED ESTUARY
3.1
Model Setup
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3
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relatively minor (Warner et al., 2004; Wang et al., 2011).
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The model domain includes a rectangular channel estuary attached to a shallow coastal ocean (Fig. 1). The estuary has length 500 km and width 5 km, and the ocean boundary extends to 200
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km east of the mouth of the estuary. The estuary has a constant depth of 10 m. The depth of the coastal ocean varies from 10 m at the mouth of the estuary to 50 m at the ocean boundary. The
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dimensions of the idealized estuary have been chosen to be close to that of San Francisco Bay. The finite volume grid is unstructured in the horizontal and structured in the vertical. The
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unstructured grid for the domain was generated using SMS (Environmental Modeling Systems, Inc.). The average resolution of the grid, based on triangular edge lengths, is 1 km, and the grid edge lengths gradually become larger east of the mouth of the estuary. The decrease in grid resolution in the coastal ocean reduces computational time, and the gradual transition in grid edge lengths prevents numerical errors associated with abrupt transitions in grid size. The grid has 20 vertical structured z-levels, and the vertical resolution is 0.5 m. The simulation is initialized with a flat free surface and a quiescent velocity field. The ocean salinity is assumed to be 32 psu. The salinity field in the estuary is initialized with increasing salinities from the “river” end at 0 psu to the mouth at 32 psu. The open boundaries are located at the ocean boundary and at the “river” end. The model is tidally forced along the ocean boundary with the idealized M2 tidal constituent. The “river” end is forced with constant freshwater
ACCEPTED MANUSCRIPT inflows. The idealized forcing of tides at the ocean boundary and constant freshwater inflows at the “river” end allow the model to come to steady state. The cross-sectionally averaged velocities
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are imposed by dividing the inflow fluxes by the cross-sectional area of the “river” end. The
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cross-sectionally averaged velocity is given by
where
is the surface area of the boundary and
(9)
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,
is the constant freshwater flow rate.
is
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computed for each time step as the surface area changes with the tides. A 200 day simulation is
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performed with a time step size of 120 s. The simulation is performed using 4 processors on a quad core Intel Xeon machine for a total of 144000 time steps. The Coriolis parameter is to simulate a coastal current that would prevent the formation of a bulge
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of freshwater at the estuary mouth.
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specified as
Our simulations are performed with freshwater inflows Q ranging from 1000 to 10000 m3/s and ranging from 0.00 to 0.81 m. The forcing parameters are chosen to simulate
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sea-level rise
conditions ranging from well-mixed to stratified estuaries. The mean sea-level heights are determined from the IPCC Fourth Assessment Report (AR4) based on the higher emission A1F1 scenario. The upper limit (95-percentile) was selected for the five sea-level rise scenarios, namely: 0.00 m (year 1990), 0.10 m (year 2020), 0.27 m (year 2050), 0.56 m (year 2080), 0.81 m (year 2100). The idealized tides are forced relative to the different mean sea-level heights. The sea-level heights are given by (10) where
is the mean sea-level height,
m is the amplitude of the constituent,
frequency of the constituent and t is time. 3.2
Estuarine Circulation and Salinity Intrusion
is the
ACCEPTED MANUSCRIPT The model is run to steady state for different values of sea-level rise
and freshwater inflows
. Fig. 2 presents the vertical profiles of the steady state, tidally-averaged along-channel salinity
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for the runs over the parameter space. The x-axis refers to the distance from the river head
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(landward) and the y-axis refers to the water depth.
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The changes in estuarine circulation depicted in Fig. 2 are investigated quantitatively from the
is the cross-sectional area, is the salinity,
is the river flow, and
(11)
is the longitudinal
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where
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cross-sectionally and tidally averaged salt transport equation (Fischer et al. 1979):
dispersion coefficient. By assuming a balance between the longitudinal pressure gradient arising
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from the longitudinal salinity gradient and turbulent shear stresses arising primarily from bottom-
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generated turbulence, Hansen and Rattray (1965) demonstrate that the magnitude of the
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baroclinically-induced gravitational circulation is proportional to the longitudinal salinity gradient. By taking the balance between friction and pressure gradient terms in the Navier-Stokes equation, a velocity scale for the exchange flow is represented with
where
is the coefficient of salt expansion,
(12)
is the water depth, and
is the vertical eddy
diffusivity. An approximation for the exchange flow (MacCready and Geyer, 2010) is given as (13)
At steady state, the salt balance is given by (14)
ACCEPTED MANUSCRIPT The longitudinal dispersion coefficient
is obtained from the salt balance equation. The
estuarine properties such as gravitational circulation velocity
are computed for runs over the parameter space. The longitudinal salinity gradient
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coefficient
and longitudinal dispersion
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is calculated with a linear fit to the tidally- and cross-sectionally averaged salinity over
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roughly one tidal excursion (10 km). The longitudinal salinity gradient approaches zero when salinity approaches zero towards the upstream end of the estuary.
and
are not calculated in
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locations where the longitudinal salinity gradient is less than 0.05 psu per km.
coefficient , respectively.
are highly variable with distance from the mouth of the
is maximum at the mouth of the estuary and minimum at roughly
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estuary. For all inflows,
and
and longitudinal dispersion
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Figs. 3 and 4 show the gravitational circulation velocity
is observed at roughly 200 km from
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100 km from the mouth of the estuary. Another peak for
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the mouth of the estuary. An opposite trend is observed for , where the minimum values are found at the mouth of the estuary and at roughly 200 km from the mouth and the maximum values are found at roughly 100 km from the mouth. The huge variability makes it difficult for comparison across different runs and the effective values for
and
are computed by
averaging over the longitudinal length of the estuary domain. The effective values are tabulated in Table 1. Increased inflows compress the salinity gradient, and lead to a stronger longitudinal salinity gradient
, which in turn drives a stronger gravitational circulation
horizontal salinity gradient
An increased
also corresponds to larger longitudinal dispersion . Rising
sea levels result in a stronger baroclinic pressure gradient which is proportional to the water depth. The longitudinal salinity gradient arises from the baroclinic pressure gradient, indicating
ACCEPTED MANUSCRIPT an increase in the strength of the gravitational circulation
and larger longitudinal dispersion
. In addition, sea-level rise reduces the impact of bottom-generated turbulence, which leads to and larger longitudinal
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less vertical mixing, and results in stronger gravitational circulation
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dispersion .
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The length scale L is a measure of salinity intrusion and is defined as the distance (in km) measured along the longitudinal axis from the mouth of the estuary to the location where the
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bottom salinity is 2 psu. The length scale L is also commonly refered to as
. The power-law
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dependence of L on inflows has been found from classical estuarine theories by Hansen and Rattray (1965) and constructued successfully from data for many estuaries (Bowen and Geyer,
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2003; Monismith et al., 2002). We proceed to find a similar power-law dependence of L on sea-
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level rise as presented in Fig. 5. A regression analysis is performed of the form m is the average depth over the transect and
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, where
is the sea-level rise. The
coefficients for the least-squares fit obtained at the 95% confidence level are tabulated in Table 2. Our results show reduced salinity intrusion accompanies strong inflows due to compression of the salinity field. L increases with sea-level rise, and the rate of increase is fastest for estuaries with low freshwater inflows. Under low-flow conditions, the exponent
is the largest, since sea-
level rise has a greater effect on salinity intrusion due to weaker vertical stratification. For high inflows, the exponent
is the smallest and reduced approximately by a factor of 2. Stronger
inflows increase the strength of gravitational circulation, which acts to create higher vertical stratification leading to the nonlinear feedback between vertical mixing and stratification. The effect of sea-level rise on salinity intrusion is reduced, owing to the suppression of mixing by stratification.
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APPLICATION TO SAN FRANCISCO BAY
The idealized simulations performed in the previous section provide a first-order approximation
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on the effects of sea-level rise and freshwater inflows on estuarine circulation. Further
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understanding requires that we employ realistic simulations of complex estuaries. In this section, we will describe the scenario simulations performed on a calibrated and validated model of San
Model Setup
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4.1
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Francisco Bay.
A three-dimensional, unstructured-grid SUNTANS model (Fringer et al. 2006) has been applied
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to perform simulations of San Francisco Bay. The model inputs include high resolution bathymetry from the NGDC database and an unstructured grid that enables refinement of the
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complex coastline (Fig. 6). The model is tidally forced at the open ocean boundary with the 8 major tidal constituents from observed water surface elevations at Point Reyes. Freshwater
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inflow estimates from the DAYFLOW program (CDWR 1986) are imposed as flow boundary conditions at the Delta boundary. The model is calibrated for the 45-day period of 1 January - 15 February 2005. The spring-neap tidal cycles and the mixed semi-diurnal and diurnal tidal ranges for sea surface elevations and currents are reproduced by the model. The salinity predictions are in good qualitative agreement with observation in terms of amplitude and phase, and the model is able to capture the periodic stratification of the estuary. Details of the implementation and validation are discussed in Chua and Fringer (2011). We use these simulations as the baseline and study the effects of sea-level rise and freshwater inflows on estuarine circulation. 4.2
Scenario Simulations
Over the past century, mean sea level at Golden Gate has risen by 0.22 m (Flick 2003) consistent with global average rates (Church et al. 2004). Based on global mean temperatures as projected
ACCEPTED MANUSCRIPT by the CCSM3 global climate model under the A2 greenhouse gas emissions scenario, 100-year projections of mean sea level at Golden Gate were produced by Cayan et al. (2008) using the
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method of Rahmstorf (2007). To study the impact of sea-level rise, we initialize the model with
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different mean sea-level heights based on values derived from the CCSM3-A2 global climate model.
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Four sea-level rise scenarios are studied, namely: 0.00 m (year 2000), 0.46 m (year 2050), 1.00
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m (year 2081) and 1.39 m (year 2099). The tides are then forced relative to the different mean sea-level heights, and we assume that the tidal constituents remain constant with sea-level rise
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(Cayan et al. 2008; Knowles 2010). Climate change impacts on hydrology are difficult to assess due to uncertainties in the projections of temperature and precipitation (Dettinger 2005; Maurer
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and Duffy 2005). However, it is likely that rising global temperatures will impact the Sacramento-San Joaquin watershed by reducing the snowpack, which would produce higher
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winter but reduced spring-summer flows (Miller et al. 2003; Dettinger et al. 2004; Knowles and Cayan 2002; Knowles and Cayan 2004). Rather than impose predicted inflows, we impose constant-in-time seasonally averaged inflows from the estimates of Knowles and Cayan (2004), namely: low inflow of 300 m3s−1 based on average summer conditions, a baseline average inflow of 800 m3s−1, and a high inflow of 2000 m3s−1 based on average winter conditions. Sea-level rise leads to an increase in the tidal prism of the Delta and flooding of Delta islands. The difficulties in modeling the inundation of low-lying Delta regions are circumvented by using a model with a false delta approximation (Fig. 6). The “false delta” consists of two rectangles sized to obtain the correct tidal behavior of the Delta as seen by the eastern boundary of the computational domain, while eliminating the need to resolve the highly complex channels and tributaries that make up the Delta. Making the assumption of “hard shorelines”, i.e. levees/dikes
ACCEPTED MANUSCRIPT are built to ensure the shoreline perimeter does not increase with rising sea levels, and eliminating the vulnerability of levee failures, the potential threat of shoreline retreat that could
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lead to an increase in the tidal prism of the Bay is not considered in our scenarios.
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In summary, we perform a total of twelve simulations in San Francisco Bay consisting of four different sea-level rise scenarios and three different freshwater inflow scenarios. All simulations
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are initialized with the same salinity field which is obtained from United States Geological
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Survey (USGS) synoptic observations collected on 11 Jan 2005. The ocean salinity is assumed to be fixed at 33.5 psu for all scenarios. The modeled salinity field is nearly tidally-periodic after 15
4.3
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days of spin-up time, and results are analyzed for the remaining 30 days. Estuarine Circulation and Salinity Intrusion
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The scenario simulations described in Section 4.2 are performed to investigate their influence on salinity intrusion and changes to the estuarine circulation in North San Francisco Bay. Fig. 7
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shows depth-averaged salinity fields that are averaged over simulation day 32 along a longitudinal transect extending from the Pacific Ocean and through North San Francisco Bay to the eastern boundary of the domain. The results show that sea-level rise leads to higher salinities due to intrusion of salinity further upstream into North Bay, while increased inflows freshen the Bay and push the salinity field downstream. A dip is observed at roughly 25 km from Golden Gate and is attributed to the constriction between Central Bay and San Pablo Bay. The interplay between rising sea levels and variable freshwater inflows is further illustrated with vertical profiles of tidally-averaged salinity along a transect in Carquinez Strait for the different scenarios. Similar results are obtained as in the idealized estuary case. Increased inflows cause the compression of isohalines that lead to higher horizontal salinity gradient and stronger
ACCEPTED MANUSCRIPT gravitational circulation. Rising sea levels increases the strength of the longitudinal salinity gradient and reduces vertical mixing, both of which results in stronger gravitational circulation.
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As field experiments by Monismith et al. (2002) in San Francisco Bay found that L is , we proceed to find a power-law
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proportional to inflows to the -1/7 power, i.e.
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dependence for L with sea-level rise. The dependence of L on sea-level rise in northern San Francisco Bay is investigated by performing a regression analysis of the form m is the average depth over the transect and
is the sea-level rise (Fig. 8).
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where
,
The coefficients for the least-squares fit are tabulated in Table 3. Our results verify that L
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increases with sea-level rise, and the rate of increase is fastest for estuaries with low freshwater inflows. A similar trend for the exponent is obtained as in the idealized models (Table 2), despite
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the bathymetric variability in northern San Francisco Bay. In the presence of low inflows, sealevel rise has a greater effect on salinity intrusion due to weaker vertical stratification. With
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strong inflows, the effect of sea-level rise is reduced as the strength of gravitational circulation and vertical stratification leads to the nonlinear feedback between vertical mixing and stratification. 4.5
Using
for regulating inflows
Direct measurements of inflows in San Francisco Bay cannot be made because of the complex geometry of the channels, which results in a high degree of uncertainty particularly at low flows. Therefore,
is used as a substitute for regulating inflows to ensure that sufficient fresh water is
available to flush the Bay. A set of standards for which explicitly states
was proposed in the 1994 Bay-Delta Accord,
maintained at Port Chicago, Chipps Island and Collinsville are
respectively 64, 74 and 81 km. The steady-state inflows required to maintain
at 64, 74 and 81
km are respectively 826 m3s−1, 352 m3s−1 and 194 m3s−1 (Sullivan and Richard 1994).
ACCEPTED MANUSCRIPT Fig. 10 shows the amount of freshwater inflows required to maintain
at the three locations for
the different sea-level rise scenarios. All three locations show that with rising sea levels, stronger at the proposed locations. Sea-level rise increases the strength
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inflows are required to maintain
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of the longitudinal salinity gradient and reduces the vertical mixing, both of which results in
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stronger gravitational circulation. This causes higher vertical stratification and greater salinity intrusion, hence requiring stronger inflows to maintain
at the downstream location of Port Chicago, since
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increase in inflows is required to maintain
at the proposed locations. The largest
this is the closest location amongst the three to the Pacific Ocean and most affected by sea-level
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rise. The increase in inflows required to maintain
due to a 1.39 m sea-level rise at Port Chicago,
Chipps Island and Collinsville are respectively 711 m3s−1, 456 m3s−1 and 308 m3s−1.
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CONCLUSION
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The effects of sea-level rise and freshwater inflows on estuarine circulation are investigated with
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an idealized estuary model and supported with three-dimensional simulations of San Francisco Bay. Increased inflows compress the salinity gradient, and lead to a stronger longitudinal salinity gradient, which in turn drives stronger gravitational circulation and larger longitudinal dispersion. Rising sea levels increase the strength of the longitudinal salinity gradient and reduces the impact of bottom-generated turbulence, both of which indicates an increase in the strength of the gravitational circulation and larger longitudinal dispersion. The power-law dependence of intrusion length scale L on sea-level rise is found using regression analysis. Under low-flow conditions, the exponent is the largest, since sea-level rise has a greater effect on salinity intrusion due to weaker vertical stratification. For high inflows, the exponent is reduced approximately by a factor of 2 due to the presence of strong gravitational circulation which results in nonlinear feedback between vertical mixing and stratification.
ACCEPTED MANUSCRIPT In San Francisco Bay, the intrusion length scale
is used as a substitute for regulating inflows
to ensure that sufficient fresh water is available to flush the Bay. A set of standards for
was
at Port Chicago, Chipps Island and Collinsville. A series of simulations
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required to maintain
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proposed in the 1994 Bay-Delta Accord, which explicitly states the amount of freshwater inflows
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are performed and we find that with sea-level rise stronger inflows are required to maintain the proposed locations. The largest increase in inflows is required to maintain
at
at the
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downstream location at Port Chicago, since this is the closest location amongst the three to the Pacific Ocean and most affected by sea-level rise.
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ACKNOWLEDGEMENTS The authors acknowledge the support of the National University of Singapore research grant
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(WBS R-302-000-021-133). MX acknowledge the support of the National University of Singapore PhD research scholarship. We also appreciate the discussions with Dr. Oliver Fringer.
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Pritchard, D. W., 1952. Salinity distribution and circulation in the Chesapeake Bay estuaries system. J. Mar. Res., 11, 106-123.
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Warner, J. C., Sherwood, C. R., Arango, H. G., and Signell, R. P., 2005. Performance of four turbulence closure models implemented using a generic length scale method. Ocean Modell. 8,
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1-113.
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Werner, A. D. and Simmons, C. T., 2009. Impact of sea-level rise on sea water intrusion in
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Wigley, T. M. L. and Raper, S. C. B., 1987. Thermal expansion of sea water associated with global warming. Nature, 330, 127 – 131.
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Williams, J., 1987. Meeting of the Estuarine and Brackish Water Science Association (EBSA). Office of Naval Research, London, UK.
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Zhong, L., Li, M., Foreman, M. G. G., 2008. Resonance and sea level variability in Chesapeake Bay. Cont. Shelf Res. 28, 2565-2573.
ACCEPTED MANUSCRIPT LIST OF FIGURES Figure 1. Unstructured grid of idealized estuary model domain (a) and zoomed-in view of the
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mouth of the estuary (b).
ranging from 1000 to 10000 m3/s and sea-level rise
m (□),
ranging from 0.00 to 0.81 m. Legend:
m (Δ),
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Figure 4. Dispersion coefficients
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m (Δ),
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Figure 5. Dependence of length scale L on sea-level heights
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m (○).
m (+),
for runs with freshwater inflows Q ranging from 1000 to
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10000 m3/s and sea-level rise m (*),
for runs with freshwater inflows Q ranging
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Figure 3. Gravitational circulation velocity scale from 1000 to 10000 m3/s and sea-level rise
ranging from 0.00 to 0.81 m. The
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salinity contours are plotted every 5 psu interval.
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Figure 2. Vertical profiles of tidally-averaged along-channel salinity for freshwater inflows Q
inflows Q ranging from 1000 to 10000 m3/s and sea-level rise
m (□),
m (○). for runs with freshwater ranging from 0.00 to 0.81 m.
Legend: Q = 1000 m3/s (□), Q = 2500 m3/s (*), Q = 5000 m3/s (∆), Q = 7500 m3/s (+), Q = 10000 m3/s (○).
Figure 6. The San Francisco Bay model domain and bathymetry (a) Uunstructured grid of San Francisco Bay (b). Figure 7. Tidal and depth-averaged salinities from the Golden Gate along the longitudinal axis in North San Francisco Bay. Distances into the Bay are positive and those towards the ocean are negative. Legend: Freshwater inflows Q = 2000 m3s-1 (black), 800 m3s-1 (red), 300 m3s-1 (blue), and sea-level rise
= 0 m (‒ ‒ ), 0.46 m (‒ ‒ ), 1.00 m (‒ ∙) and 1.39 m (∙ ∙ ∙).
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(d) 1.39 m sea-level rise
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Figure 9. Dependence of length scale L on sea-level heights
simulations (with freshwater inflows Q ranging from 300 to 2000 m3/s and sea-level rise
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ranging from 0.00 to 1.39 m) in San Francisco Bay. Legend: Q = 300 m3/s (□), Q = 800 m3/s (*),
Figure 10. Inflows required to maintain
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Figure 7. Tidal and depth-averaged salinities from the Golden Gate along the longitudinal axis in North San Francisco Bay. Distances into the Bay are positive and those towards the ocean are negative. Legend: Freshwater inflows Q = 2000 m3s-1 (black), 800 m3s-1 (red), 300 m3s-1 (blue), and sea-level rise
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Figure 8. Vertical profiles of tidally-averaged salinity (psu) along a transect in Carquinez Strait for 2000 m3s-1, 800 m3s-1 and 300 m3s-1 freshwater inflows Q, and (a) 0 m (b) 0.46 m (c) 1.00 m (d) 1.39 m sea-level rise
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simulations (with freshwater inflows Q ranging from 300 to 2000 m3/s and sea-level rise ranging from 0.00 to 1.39 m) in San Francisco Bay. Legend: Q = 300 m3/s (□), Q = 800 m3/s (*), Q = 2000 m3/s (∆).
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Figure 10. Inflows required to maintain
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ACCEPTED MANUSCRIPT Table 1. Description of runs with freshwater inflows
ranging from 1000 to 10000 m3/s and
sea-level rise
ranging from 0.00 to 0.81 m. Effective values for gravitational circulation
velocity scale
and longitudinal dispersion coefficient
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are computed.
Run
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(m/s) 0.138 0.157 0.168 0.170 0.187 0.148 0.156 0.169 0.184 0.194 0.195 0.197 0.205 0.219 0.232 0.209 0.217 0.228 0.238 0.247 0.212 0.219 0.234 0.248 0.254
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(m) 0.00 0.10 0.27 0.56 0.81 0.00 0.10 0.27 0.56 0.81 0.00 0.10 0.27 0.56 0.81 0.00 0.10 0.27 0.56 0.81 0.00 0.10 0.27 0.56 0.81
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A1 A2 A3 A4 A5 B1 B2 B3 B4 B5 C1 C2 C3 C4 C5 D1 D2 D3 D4 D5 E1 E2 E3 E4 E5
(m3/s) 1000 1000 1000 1000 1000 2500 2500 2500 2500 2500 5000 5000 5000 5000 5000 7500 7500 7500 7500 7500 10000 10000 10000 10000 10000
(103 m2/s) 3.60 3.78 3.78 3.79 3.82 7.95 8.03 8.15 8.17 8.27 10.41 11.74 12.91 13.83 14.29 15.17 15.43 16.26 18.02 19.88 17.74 18.83 18.72 22.19 26.10
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0.19 0.23 0.24 1.70 2.16
3.2 2.9 2.8 2.0 1.8
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Confidence level (%) 95 95 95 95 95
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from 1000 to 10000 m3/s and sea-level rise
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2.88 15.61 14.40
1.31 0.59 0.58
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Inflows ( 300 800 2000
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Numerical simulations to investigate climate change impacts on estuarine circulation Rising sea levels lead to stronger and enhanced salinity intrusion With low inflows, effects of sea-level rise on salinity intrusion are largest Stronger inflows required with sea-level rise to maintain in San Francisco Bay
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S0924-7963(14)00141-9 doi: 10.1016/j.jmarsys.2014.05.012 MARSYS 2552
To appear in:
Journal of Marine Systems
Received date: Revised date: Accepted date:
10 March 2014 29 April 2014 7 May 2014
Please cite this article as: Chua, Vivien P., Xu, Ming, Impacts of sea-level rise on estuarine circulation: An idealized and San Francisco Bay, Journal of Marine Systems (2014), doi: 10.1016/j.jmarsys.2014.05.012
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IMPACTS OF SEA-LEVEL RISE ON ESTUARINE
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CIRCULATION: AN IDEALIZED ESTUARY AND SAN
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FRANCISCO BAY
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Vivien P. Chua1* and Ming Xu2
1*,2
National University of Singapore
Department of Civil and Environmental Engineering 1 Engineering Drive 2, Singapore 1*
[email protected], (65) 90018140
ACCEPTED MANUSCRIPT ABSTRACT Estuaries lie at the interface of land and sea, and are particularly vulnerable to sea-level rise due
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to climate change that might lead to intrusion of salt water further upstream and affect circulation
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patterns. Climate change is also likely to have a major impact on hydrological cycles and consequently lead to changes in freshwater inflows into estuaries. An idealized estuary model is
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employed to investigate the effects of sea-level rise and freshwater inflows on estuarine
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circulation. Rising sea levels result in a stronger longitudinal salinity gradient an increase in the strength of the gravitational circulation
, higher longitudinal dispersion
and enhanced salinity intrusion. Under low-flow conditions, the effects of sea
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coefficients
, indicating
level rise on salinity intrusion are largest because sea-level rise has a greater impact due to
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weaker vertical stratification. Strong flows increase the strength of the gravitational circulation, resulting in higher vertical stratification, which leads to the nonlinear feedback between vertical
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mixing and stratification. The effect of sea-level rise on salinity intrusion is reduced owing to the suppression of mixing by stratification. Supporting three-dimensional simulations from northern San Francisco Bay are presented. The intrusion length scale
is used as a substitute for
regulating inflows to ensure that sufficient fresh water is available to flush the Bay. Following a set of standards explicitly stated in the 1994 Bay-Delta Accord, a series of simulations are performed and we find that with sea-level rise stronger inflows are required to maintain
at the
proposed locations.
Keywords: Estuaries; freshwater inflows; numerical modeling; salinity intrusion; sea-level rise
ACCEPTED MANUSCRIPT 1
INTRODUCTION
Rising waters as a result of climate change will likely reshape the world's coastlines and may
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lead to significant impacts on estuarine areas. Global warming leads to sea-level rise due to the
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melting of ice caps and thermal expansion of oceans (Gornitz et al., 1982; Wigley and Raper, 1987; Root 1989; Vermeer and Rahmstorf, 2009). Global warming is also likely to have a major
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impact on hydrological cycles and consequently lead to a change in freshwater inflows into
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estuaries (Rapaire and Prieur, 1992; Statham, 2012). Sea-level rise projections by the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) range
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from 0.18 to 0.81 m by 2100 with respect to the base year 1990. A significant acceleration of 0.013 ± 0.006 mm/year2 was reported over the 20th century, and sea levels rose at a rate of 1.7 ±
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0.2 mm/year and since 1961 at a rate of 1.9 ± 0.4 mm/year (Church and White, 2006). Recent altimeter observations indicate an increase in the rate of sea-level rise during the past decade to
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3.2 mm/year, well above previous estimates of 1.5 – 2 mm/yr (Carton et al., 2005). Tidal gauge and satellite data reveal that sea-level rise is not geographically uniform, and spatial variability in the rates of sea-level rise is expected due to non-uniform changes in temperature, salinity and ocean circulation.
For estuarine areas, sea-level rise leads to an increase in the salinity of surface and ground water through salt water intrusion. Rising sea levels result in a landward shift of the estuarine salinity field, threatening freshwater supplies upstream (Williams, 1987; Hull and Titus, 1986). Studies have found that sea-level rise results in higher salinities upstream and also affects tidal currents in estuaries (Hong and Shen, 2012; Chua, 2012). Intrusion of salt water and changes in circulation patterns may have serious consequences for marine ecosystems that are unable to tolerate high salinity (Schallenberg et al., 2003; Short and Neckles, 1999). We are particularly
ACCEPTED MANUSCRIPT interested in the effects of sea-level rise on physical processes such as estuarine circulation, stratification and vertical exchanges, which would play an important role on regulating
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biological phenomena and aquatic habitats.
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Numerical models have been employed to investigate the effects of sea-level rise on salinity and tidal ranges in estuarine environments. Hong and Shen (2012) found the salt content, salinity
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intrusion length and stratification in Chesapeake Bay will increase subject to seasonal and inter-
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annual variability as sea level rises. They also quantified the impact of sea-level rise on circulation and transport in the Bay by simulating the transport of passive tracers. With a
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combination of numerical modeling and statistical techniques, Hilton et al. (2008) demonstrated an increase in bay-averaged salinity of 0.5 psu as sea level rises 0.2 m in Chesapeake Bay.
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Singha et al. (1997) found a positive sea level trend in the Hooghly Estuary, and that there exists a substantial increase in the amplitude and velocities of the tidal wave due to sea-level rise.
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Zhong et al. (2008) noted that sea-level rise will change the resonance characteristics of Chesapeake Bay and suggested that the tidal range will increase by 15 – 20% with a sea-level rise of 1.0 m.
In this paper, an idealized estuary model is employed to investigate the effects of sea-level rise and freshwater inflows on estuarine circulation. The simulations are performed with an idealized model to remove the influence of irregular coastlines, lateral variation in depth and presence of bathymetric features, so that the effects of sea-level rise and freshwater inflows on estuarine circulation are isolated. Variability of freshwater inflows is difficult to predict due to the huge range of uncertainty in inflows that are expected with climate change. Hence, our simulations are performed for a wide range of inflow conditions. Insights on the physical characteristic of estuaries gleaned through idealized simulations may be incorporated to improve our
ACCEPTED MANUSCRIPT understanding of estuaries with realistic coastlines and bathymetry. Supporting three-dimensional simulations from northern San Francisco Bay are presented. In the
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San Francisco Bay-Delta system which provides freshwater supplies to Southern California and
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the Central Valley, and for local domestic, industrial and agricultural use, salt water intrusion upstream will result in water intakes that might draw on salty water during dry periods. Coastal
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aquifers recharged by freshwater upstream are also likely to become saline as salt water is
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pushed upstream (Werner and Simmons 2009; Oude Essink 1999; Bobba 2002; Sherif and Singh 1999; Meisler et al. 1984). The availability of freshwater in San Francisco Bay interacts with
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other factors, including changes to the local hydrology due to climate change (Miller et al. 2003; Dettinger et al. 2004; Knowles and Cayan 2002; Knowles and Cayan 2004), and changes in
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demand due to population growth and urbanization. The combination of these factors is likely to compound water stress in coastal areas. An unstructured-grid SUNTANS model is applied to
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perform three-dimensional simulations of flow in San Francisco Bay, and a series of simulations are performed to investigate the effects of sea-level rise and freshwater inflows on estuarine circulation.
The remainder of the paper is structured as follows. Section 2 describes the hydrodynamic model. Section 3 presents the results of our idealized simulations. Section 4 describes three-dimensional simulations in San Francisco Bay. Section 5 provides conclusions. 2
HYDRODYNAMIC MODEL
The climate change simulations are performed with the SUNTANS hydrodynamic model (Fringer et al., 2006). The governing equations are the three-dimensional, Reynolds-averaged Navier-Stokes equations under the Boussinesq approximation and hydrostatic assumption: ,
(1)
ACCEPTED MANUSCRIPT ,
(2)
subject to incompressibility,
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,
and
and
,
and
are the Cartesian velocity
directions. The horizontal and vertical eddy viscosities are given by
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components in the ,
and
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velocity vector is
, the free-surface height is , the
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where the horizontal gradient operator is
(3)
, respectively. The vertical momentum equation is not present because
is
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solved using Eq. (3). The baroclinic head is given by
(4)
,
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is the constant reference density and the total density is given by
term is given by
using
,, where
is the angular velocity of the Earth and
. The Coriolis is the latitude.
is computed with a linear equation of state in terms of the salinity
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The density perturbation
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where
, where
and
are reference states and
psu-1.
The free-surface evolves according to the depth-averaged continuity equation:
where
.
(5)
is the water depth.
The effects of temperature on stratification are neglected in our estuarine simulations. The transport for salinity neglects horizontal diffusion and is given by , where
(6)
is the vertical turbulent eddy diffusivity. These equations are solved using the methods
described in Fringer et al. (2006), in which the free-surface height, vertical diffusion of
ACCEPTED MANUSCRIPT momentum and vertical scalar advection are advanced implicitly with the theta-method, and all other terms are advanced with the second-order Adams-Bashforth method. For advection of
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momentum, the Eulerian-Lagrangian method (ELM) is employed.
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The scalar concentrations defined at cell centers of staggered grids are interpolated to their cell faces using the method described in Casulli and Zanolli (2005). The scheme is monotonicity-
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preserving and uses a combination of first-order upwinding and a higher-order antidiffusive flux
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via the TVD (Total Variation Diminishing) constraint (Harten and Lax, 1984). The Superbee limiter (Roe 1984) produces the best results and is chosen for our simulations (Gross et al., 1999).
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The quadratic drag law is applied at the bottom boundary to compute the bottom stress with
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is the horizontal velocity vector in the first grid cell above the bed,
where
is the location of
above the bed and
is its magnitude
is computed from the bottom roughness parameter z0,
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and the drag coefficient
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where
(7)
,
(8)
,
at a distance of one-half the bottom-most vertical grid spacing
is the von Karman’s constant. The roughness coefficient is set to
m, a value typical for most real estuaries (Ludwick, 1975; Li et al., 2004). The horizontal turbulent mixing of momentum is determined with a constant eddy viscosity, while the horizontal turbulent mixing of scalars is ignored. The horizontal and vertical background eddy viscosities are set to the background vertical eddy diffusivity is set to
m2/s and
m2/s, respectively, and m2/s. These background values are
required to allow turbulence to grow due to production in the turbulence model. The MellorYamada level 2.5 (MY2.5) model (Mellor and Yamada, 1982), with stability functions modified by Galperin et al. (1988) is used to compute the vertical eddy viscosity and eddy diffusivity.
ACCEPTED MANUSCRIPT Details of implementation of the turbulence model in SUNTANS are described in Wang et al. (2011). A comparison of turbulence closure schemes for estuarine modeling show that
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differences between the k ‒ kl (Mellor-Yamada Level 2.5), k ‒ ε and k ‒ ω schemes are
IDEALIZED ESTUARY
3.1
Model Setup
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3
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relatively minor (Warner et al., 2004; Wang et al., 2011).
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The model domain includes a rectangular channel estuary attached to a shallow coastal ocean (Fig. 1). The estuary has length 500 km and width 5 km, and the ocean boundary extends to 200
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km east of the mouth of the estuary. The estuary has a constant depth of 10 m. The depth of the coastal ocean varies from 10 m at the mouth of the estuary to 50 m at the ocean boundary. The
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dimensions of the idealized estuary have been chosen to be close to that of San Francisco Bay. The finite volume grid is unstructured in the horizontal and structured in the vertical. The
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unstructured grid for the domain was generated using SMS (Environmental Modeling Systems, Inc.). The average resolution of the grid, based on triangular edge lengths, is 1 km, and the grid edge lengths gradually become larger east of the mouth of the estuary. The decrease in grid resolution in the coastal ocean reduces computational time, and the gradual transition in grid edge lengths prevents numerical errors associated with abrupt transitions in grid size. The grid has 20 vertical structured z-levels, and the vertical resolution is 0.5 m. The simulation is initialized with a flat free surface and a quiescent velocity field. The ocean salinity is assumed to be 32 psu. The salinity field in the estuary is initialized with increasing salinities from the “river” end at 0 psu to the mouth at 32 psu. The open boundaries are located at the ocean boundary and at the “river” end. The model is tidally forced along the ocean boundary with the idealized M2 tidal constituent. The “river” end is forced with constant freshwater
ACCEPTED MANUSCRIPT inflows. The idealized forcing of tides at the ocean boundary and constant freshwater inflows at the “river” end allow the model to come to steady state. The cross-sectionally averaged velocities
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are imposed by dividing the inflow fluxes by the cross-sectional area of the “river” end. The
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cross-sectionally averaged velocity is given by
where
is the surface area of the boundary and
(9)
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,
is the constant freshwater flow rate.
is
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computed for each time step as the surface area changes with the tides. A 200 day simulation is
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performed with a time step size of 120 s. The simulation is performed using 4 processors on a quad core Intel Xeon machine for a total of 144000 time steps. The Coriolis parameter is to simulate a coastal current that would prevent the formation of a bulge
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of freshwater at the estuary mouth.
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specified as
Our simulations are performed with freshwater inflows Q ranging from 1000 to 10000 m3/s and ranging from 0.00 to 0.81 m. The forcing parameters are chosen to simulate
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sea-level rise
conditions ranging from well-mixed to stratified estuaries. The mean sea-level heights are determined from the IPCC Fourth Assessment Report (AR4) based on the higher emission A1F1 scenario. The upper limit (95-percentile) was selected for the five sea-level rise scenarios, namely: 0.00 m (year 1990), 0.10 m (year 2020), 0.27 m (year 2050), 0.56 m (year 2080), 0.81 m (year 2100). The idealized tides are forced relative to the different mean sea-level heights. The sea-level heights are given by (10) where
is the mean sea-level height,
m is the amplitude of the constituent,
frequency of the constituent and t is time. 3.2
Estuarine Circulation and Salinity Intrusion
is the
ACCEPTED MANUSCRIPT The model is run to steady state for different values of sea-level rise
and freshwater inflows
. Fig. 2 presents the vertical profiles of the steady state, tidally-averaged along-channel salinity
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for the runs over the parameter space. The x-axis refers to the distance from the river head
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(landward) and the y-axis refers to the water depth.
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The changes in estuarine circulation depicted in Fig. 2 are investigated quantitatively from the
is the cross-sectional area, is the salinity,
is the river flow, and
(11)
is the longitudinal
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where
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cross-sectionally and tidally averaged salt transport equation (Fischer et al. 1979):
dispersion coefficient. By assuming a balance between the longitudinal pressure gradient arising
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from the longitudinal salinity gradient and turbulent shear stresses arising primarily from bottom-
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generated turbulence, Hansen and Rattray (1965) demonstrate that the magnitude of the
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baroclinically-induced gravitational circulation is proportional to the longitudinal salinity gradient. By taking the balance between friction and pressure gradient terms in the Navier-Stokes equation, a velocity scale for the exchange flow is represented with
where
is the coefficient of salt expansion,
(12)
is the water depth, and
is the vertical eddy
diffusivity. An approximation for the exchange flow (MacCready and Geyer, 2010) is given as (13)
At steady state, the salt balance is given by (14)
ACCEPTED MANUSCRIPT The longitudinal dispersion coefficient
is obtained from the salt balance equation. The
estuarine properties such as gravitational circulation velocity
are computed for runs over the parameter space. The longitudinal salinity gradient
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coefficient
and longitudinal dispersion
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is calculated with a linear fit to the tidally- and cross-sectionally averaged salinity over
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roughly one tidal excursion (10 km). The longitudinal salinity gradient approaches zero when salinity approaches zero towards the upstream end of the estuary.
and
are not calculated in
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locations where the longitudinal salinity gradient is less than 0.05 psu per km.
coefficient , respectively.
are highly variable with distance from the mouth of the
is maximum at the mouth of the estuary and minimum at roughly
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estuary. For all inflows,
and
and longitudinal dispersion
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Figs. 3 and 4 show the gravitational circulation velocity
is observed at roughly 200 km from
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100 km from the mouth of the estuary. Another peak for
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the mouth of the estuary. An opposite trend is observed for , where the minimum values are found at the mouth of the estuary and at roughly 200 km from the mouth and the maximum values are found at roughly 100 km from the mouth. The huge variability makes it difficult for comparison across different runs and the effective values for
and
are computed by
averaging over the longitudinal length of the estuary domain. The effective values are tabulated in Table 1. Increased inflows compress the salinity gradient, and lead to a stronger longitudinal salinity gradient
, which in turn drives a stronger gravitational circulation
horizontal salinity gradient
An increased
also corresponds to larger longitudinal dispersion . Rising
sea levels result in a stronger baroclinic pressure gradient which is proportional to the water depth. The longitudinal salinity gradient arises from the baroclinic pressure gradient, indicating
ACCEPTED MANUSCRIPT an increase in the strength of the gravitational circulation
and larger longitudinal dispersion
. In addition, sea-level rise reduces the impact of bottom-generated turbulence, which leads to and larger longitudinal
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less vertical mixing, and results in stronger gravitational circulation
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dispersion .
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The length scale L is a measure of salinity intrusion and is defined as the distance (in km) measured along the longitudinal axis from the mouth of the estuary to the location where the
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bottom salinity is 2 psu. The length scale L is also commonly refered to as
. The power-law
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dependence of L on inflows has been found from classical estuarine theories by Hansen and Rattray (1965) and constructued successfully from data for many estuaries (Bowen and Geyer,
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2003; Monismith et al., 2002). We proceed to find a similar power-law dependence of L on sea-
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level rise as presented in Fig. 5. A regression analysis is performed of the form m is the average depth over the transect and
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, where
is the sea-level rise. The
coefficients for the least-squares fit obtained at the 95% confidence level are tabulated in Table 2. Our results show reduced salinity intrusion accompanies strong inflows due to compression of the salinity field. L increases with sea-level rise, and the rate of increase is fastest for estuaries with low freshwater inflows. Under low-flow conditions, the exponent
is the largest, since sea-
level rise has a greater effect on salinity intrusion due to weaker vertical stratification. For high inflows, the exponent
is the smallest and reduced approximately by a factor of 2. Stronger
inflows increase the strength of gravitational circulation, which acts to create higher vertical stratification leading to the nonlinear feedback between vertical mixing and stratification. The effect of sea-level rise on salinity intrusion is reduced, owing to the suppression of mixing by stratification.
ACCEPTED MANUSCRIPT 4
APPLICATION TO SAN FRANCISCO BAY
The idealized simulations performed in the previous section provide a first-order approximation
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on the effects of sea-level rise and freshwater inflows on estuarine circulation. Further
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understanding requires that we employ realistic simulations of complex estuaries. In this section, we will describe the scenario simulations performed on a calibrated and validated model of San
Model Setup
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4.1
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Francisco Bay.
A three-dimensional, unstructured-grid SUNTANS model (Fringer et al. 2006) has been applied
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to perform simulations of San Francisco Bay. The model inputs include high resolution bathymetry from the NGDC database and an unstructured grid that enables refinement of the
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complex coastline (Fig. 6). The model is tidally forced at the open ocean boundary with the 8 major tidal constituents from observed water surface elevations at Point Reyes. Freshwater
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inflow estimates from the DAYFLOW program (CDWR 1986) are imposed as flow boundary conditions at the Delta boundary. The model is calibrated for the 45-day period of 1 January - 15 February 2005. The spring-neap tidal cycles and the mixed semi-diurnal and diurnal tidal ranges for sea surface elevations and currents are reproduced by the model. The salinity predictions are in good qualitative agreement with observation in terms of amplitude and phase, and the model is able to capture the periodic stratification of the estuary. Details of the implementation and validation are discussed in Chua and Fringer (2011). We use these simulations as the baseline and study the effects of sea-level rise and freshwater inflows on estuarine circulation. 4.2
Scenario Simulations
Over the past century, mean sea level at Golden Gate has risen by 0.22 m (Flick 2003) consistent with global average rates (Church et al. 2004). Based on global mean temperatures as projected
ACCEPTED MANUSCRIPT by the CCSM3 global climate model under the A2 greenhouse gas emissions scenario, 100-year projections of mean sea level at Golden Gate were produced by Cayan et al. (2008) using the
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method of Rahmstorf (2007). To study the impact of sea-level rise, we initialize the model with
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different mean sea-level heights based on values derived from the CCSM3-A2 global climate model.
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Four sea-level rise scenarios are studied, namely: 0.00 m (year 2000), 0.46 m (year 2050), 1.00
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m (year 2081) and 1.39 m (year 2099). The tides are then forced relative to the different mean sea-level heights, and we assume that the tidal constituents remain constant with sea-level rise
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(Cayan et al. 2008; Knowles 2010). Climate change impacts on hydrology are difficult to assess due to uncertainties in the projections of temperature and precipitation (Dettinger 2005; Maurer
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and Duffy 2005). However, it is likely that rising global temperatures will impact the Sacramento-San Joaquin watershed by reducing the snowpack, which would produce higher
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winter but reduced spring-summer flows (Miller et al. 2003; Dettinger et al. 2004; Knowles and Cayan 2002; Knowles and Cayan 2004). Rather than impose predicted inflows, we impose constant-in-time seasonally averaged inflows from the estimates of Knowles and Cayan (2004), namely: low inflow of 300 m3s−1 based on average summer conditions, a baseline average inflow of 800 m3s−1, and a high inflow of 2000 m3s−1 based on average winter conditions. Sea-level rise leads to an increase in the tidal prism of the Delta and flooding of Delta islands. The difficulties in modeling the inundation of low-lying Delta regions are circumvented by using a model with a false delta approximation (Fig. 6). The “false delta” consists of two rectangles sized to obtain the correct tidal behavior of the Delta as seen by the eastern boundary of the computational domain, while eliminating the need to resolve the highly complex channels and tributaries that make up the Delta. Making the assumption of “hard shorelines”, i.e. levees/dikes
ACCEPTED MANUSCRIPT are built to ensure the shoreline perimeter does not increase with rising sea levels, and eliminating the vulnerability of levee failures, the potential threat of shoreline retreat that could
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lead to an increase in the tidal prism of the Bay is not considered in our scenarios.
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In summary, we perform a total of twelve simulations in San Francisco Bay consisting of four different sea-level rise scenarios and three different freshwater inflow scenarios. All simulations
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are initialized with the same salinity field which is obtained from United States Geological
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Survey (USGS) synoptic observations collected on 11 Jan 2005. The ocean salinity is assumed to be fixed at 33.5 psu for all scenarios. The modeled salinity field is nearly tidally-periodic after 15
4.3
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days of spin-up time, and results are analyzed for the remaining 30 days. Estuarine Circulation and Salinity Intrusion
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The scenario simulations described in Section 4.2 are performed to investigate their influence on salinity intrusion and changes to the estuarine circulation in North San Francisco Bay. Fig. 7
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shows depth-averaged salinity fields that are averaged over simulation day 32 along a longitudinal transect extending from the Pacific Ocean and through North San Francisco Bay to the eastern boundary of the domain. The results show that sea-level rise leads to higher salinities due to intrusion of salinity further upstream into North Bay, while increased inflows freshen the Bay and push the salinity field downstream. A dip is observed at roughly 25 km from Golden Gate and is attributed to the constriction between Central Bay and San Pablo Bay. The interplay between rising sea levels and variable freshwater inflows is further illustrated with vertical profiles of tidally-averaged salinity along a transect in Carquinez Strait for the different scenarios. Similar results are obtained as in the idealized estuary case. Increased inflows cause the compression of isohalines that lead to higher horizontal salinity gradient and stronger
ACCEPTED MANUSCRIPT gravitational circulation. Rising sea levels increases the strength of the longitudinal salinity gradient and reduces vertical mixing, both of which results in stronger gravitational circulation.
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As field experiments by Monismith et al. (2002) in San Francisco Bay found that L is , we proceed to find a power-law
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proportional to inflows to the -1/7 power, i.e.
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dependence for L with sea-level rise. The dependence of L on sea-level rise in northern San Francisco Bay is investigated by performing a regression analysis of the form m is the average depth over the transect and
is the sea-level rise (Fig. 8).
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where
,
The coefficients for the least-squares fit are tabulated in Table 3. Our results verify that L
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increases with sea-level rise, and the rate of increase is fastest for estuaries with low freshwater inflows. A similar trend for the exponent is obtained as in the idealized models (Table 2), despite
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the bathymetric variability in northern San Francisco Bay. In the presence of low inflows, sealevel rise has a greater effect on salinity intrusion due to weaker vertical stratification. With
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strong inflows, the effect of sea-level rise is reduced as the strength of gravitational circulation and vertical stratification leads to the nonlinear feedback between vertical mixing and stratification. 4.5
Using
for regulating inflows
Direct measurements of inflows in San Francisco Bay cannot be made because of the complex geometry of the channels, which results in a high degree of uncertainty particularly at low flows. Therefore,
is used as a substitute for regulating inflows to ensure that sufficient fresh water is
available to flush the Bay. A set of standards for which explicitly states
was proposed in the 1994 Bay-Delta Accord,
maintained at Port Chicago, Chipps Island and Collinsville are
respectively 64, 74 and 81 km. The steady-state inflows required to maintain
at 64, 74 and 81
km are respectively 826 m3s−1, 352 m3s−1 and 194 m3s−1 (Sullivan and Richard 1994).
ACCEPTED MANUSCRIPT Fig. 10 shows the amount of freshwater inflows required to maintain
at the three locations for
the different sea-level rise scenarios. All three locations show that with rising sea levels, stronger at the proposed locations. Sea-level rise increases the strength
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inflows are required to maintain
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of the longitudinal salinity gradient and reduces the vertical mixing, both of which results in
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stronger gravitational circulation. This causes higher vertical stratification and greater salinity intrusion, hence requiring stronger inflows to maintain
at the downstream location of Port Chicago, since
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increase in inflows is required to maintain
at the proposed locations. The largest
this is the closest location amongst the three to the Pacific Ocean and most affected by sea-level
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rise. The increase in inflows required to maintain
due to a 1.39 m sea-level rise at Port Chicago,
Chipps Island and Collinsville are respectively 711 m3s−1, 456 m3s−1 and 308 m3s−1.
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CONCLUSION
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The effects of sea-level rise and freshwater inflows on estuarine circulation are investigated with
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an idealized estuary model and supported with three-dimensional simulations of San Francisco Bay. Increased inflows compress the salinity gradient, and lead to a stronger longitudinal salinity gradient, which in turn drives stronger gravitational circulation and larger longitudinal dispersion. Rising sea levels increase the strength of the longitudinal salinity gradient and reduces the impact of bottom-generated turbulence, both of which indicates an increase in the strength of the gravitational circulation and larger longitudinal dispersion. The power-law dependence of intrusion length scale L on sea-level rise is found using regression analysis. Under low-flow conditions, the exponent is the largest, since sea-level rise has a greater effect on salinity intrusion due to weaker vertical stratification. For high inflows, the exponent is reduced approximately by a factor of 2 due to the presence of strong gravitational circulation which results in nonlinear feedback between vertical mixing and stratification.
ACCEPTED MANUSCRIPT In San Francisco Bay, the intrusion length scale
is used as a substitute for regulating inflows
to ensure that sufficient fresh water is available to flush the Bay. A set of standards for
was
at Port Chicago, Chipps Island and Collinsville. A series of simulations
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required to maintain
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proposed in the 1994 Bay-Delta Accord, which explicitly states the amount of freshwater inflows
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are performed and we find that with sea-level rise stronger inflows are required to maintain the proposed locations. The largest increase in inflows is required to maintain
at
at the
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downstream location at Port Chicago, since this is the closest location amongst the three to the Pacific Ocean and most affected by sea-level rise.
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ACKNOWLEDGEMENTS The authors acknowledge the support of the National University of Singapore research grant
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(WBS R-302-000-021-133). MX acknowledge the support of the National University of Singapore PhD research scholarship. We also appreciate the discussions with Dr. Oliver Fringer.
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Gornitz, V., Lebedeff, S. and Hansen, J., 1982. Global sea level trend in the past century. Science.,
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Hansen, D. V., Rattray, M., 1965. Gravitational circulation in straits and estuaries. J. Mar. Res. 23, 104-122.
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Harleman, D. R. F. and Thatcher, M. L., 1974. Longitudinal dispersion and unsteady salinity intrusion in estuaries. La Houille Blanche 1-2, 25-33.
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Harten, A. and Lax, P. D., 1984. On a class of high resolution total-variation-stable, finitedifference schemes. SIAM J. Numer. Anal. 21, 1-23.
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Hetland, R. D. and Geyer, W. D., 2004. An idealized study of the structure of long, partially mixed estuaries. J. Phys. Oceano. 34, 2677-2691. Hilton, T. W., Najjar, R. G., Zhong, L., Li, M., 2008. Is there a signal of sea-level rise in Chesapeake Bay salinity. J. Geophys. Res. C09002, doi:10.1029/2007JC004247. Hong, B. and Shen, J., 2012. Responses of estuarine salinity and transport processes to potential future sea-level rise in the Chesapeake Bay. Est., Coast. Shelf Sci. 104-105. Hull, C. H. J., Titus, J. G., Lennon, G. P., Thatcher, M. L., Tortoriello, R. C., 1986. Greenhouse Effect, Sea Level Rise, and Salinity in the Delaware Estuary. U.S. Environmental Protection Agency, Washington, DC.
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Geophys. Res. 109, C03034, doi:10.1029/2003JC001991.
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Ludwick, J. C., 1975. Variations in boundary-drag coefficient in the tidal entrance to Chesapeake Bay, Virginia. Mar. Geol. 19, 19-28.
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Knowles, N. and Cayan, D. R., 2002. Potential effects of global warming on the Sacramento/San
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Joaquin watershed and the San Francisco estuary, Geophys. Res. Letters, 29, 1891 – 1895. Knowles, N. and Cayan, D. R., 2004. Elevational dependence of projected hydrologic changes in
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the San Francisco estuary and watershed, Clim. Change, 62, 319 – 336.
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Meisler, H., Leahy, P. P. and Knobel, L. L., 1984. Effect of eustatic sea-level changes on
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saltwater-freshwater in the Northern Atlantic Coastal Plain. Technical report, USGS, Reston,
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Virginia. USGS Water Supply Paper 2255. Mellor, G. L. and Yamada, T., 1982. Development of a turbulence closure model for geophysical fluid problem. Rev. Geophys. 20, 851-875. Miller, N. L., Bashford, K. E. and Strem, E. (2003). Potential impacts of climate change on California hydrology. J. Am. Water Resour. Assoc., 39, 771 – 784. Monismith, S. G., Burau, J. R., and Stacey, M. T., 1996. Stratification dynamics and gravitational circulation in northern San Francisco Bay. In San Francisco Bay: The ecosystem, 123-153, Hollibaugh, T., ed., AAAS Pacific Division, San Francisco, California. Monismith, S. G., Kimmerer, W., Burau, J. R., and Stacey, M. T., 2002. Structure and flowinduced variability of the subtidal salinity field in northern San Francisco Bay. J. Phys. Oceano. 32, 3003-3019.
ACCEPTED MANUSCRIPT Oude Essink, G. H. P., 1999. Impact of sea level rise in the Netherlands. In J. Bear, A.-D. Cheng, S. Sorek, D. Ouazar and I. Herrera (Eds.), Seawater Intrusion in Coastal Aquifers – Concepts,
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Methods and Practices, pp. 507 – 530. Dordrecht, The Netherlands: Kluwer Academic
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Park, K. and Kuo, A. Y., 1996. Effect of variation in vertical mixing on residual circulation in narrow, weakly nonlinear estuaries. In Buoyancy Effects on Coastal and Estuarine Dynamics,
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301-318, Aubrey, D. G. and Friedrichs, C. T., eds., AGU.
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Pritchard, D. W., 1952. Salinity distribution and circulation in the Chesapeake Bay estuaries system. J. Mar. Res., 11, 106-123.
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Pritchard, D.W., 1954. A study of the salt balance in a coastal plain estuary. J. Mar. Res., 13, 133-
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Simons, R. D., Monismith, S. G., Johnson, L. E., Winkler, G., and Saucier, F. J., 2006.
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Zooplankton retention in the estuarine transition zone of the St. Lawrence Estuary. Limnol. Oceano. 51, 2621-2631.
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Simpon, J. H., Brown, J., Matthews. J., and Allen, G., 1990. Tidal straining, density currents and
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beel in Dubri district of Assam and its impact on fish productivity. Environ. Ecol., 15(1), 202205.
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Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K. B., Tignor, M., Miller, H. L., 2007. IPCC, 2007: Summary for policymakers. In Climate Change 2007: The Physical
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Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, UK and New York, USA.
Stacey, M. T., Fram. J. P., and Chow, F. K., 2008. The role of tidally periodic density stratification in the creation of estuarine subtidal circulation. J. Geophys. Res. 113, 13 p. Statham, P. J., 2012. Nutrients in estuaries – An overview and the potential impacts of climate change. Scien. Tot. Environ., 434, 213 – 227. Thatcher, M.L, and Harleman, D.R.F., 1981. Long-term salinity calculation in Delaware Estuary. J. Envir. Engr. Div. 107, 11-27. Vermeer, M. and Rahmstorf, S., 2009. Global sea level linked to global temperature. Proc. Nation. Acad. Scien., 106, 21527-21532
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116, C02036, doi:10.1029/2010JC006135.
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Warner, J. C., Sherwood, C. R., Arango, H. G., and Signell, R. P., 2005. Performance of four turbulence closure models implemented using a generic length scale method. Ocean Modell. 8,
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1-113.
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Werner, A. D. and Simmons, C. T., 2009. Impact of sea-level rise on sea water intrusion in
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Wigley, T. M. L. and Raper, S. C. B., 1987. Thermal expansion of sea water associated with global warming. Nature, 330, 127 – 131.
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Williams, J., 1987. Meeting of the Estuarine and Brackish Water Science Association (EBSA). Office of Naval Research, London, UK.
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Zhong, L., Li, M., Foreman, M. G. G., 2008. Resonance and sea level variability in Chesapeake Bay. Cont. Shelf Res. 28, 2565-2573.
ACCEPTED MANUSCRIPT LIST OF FIGURES Figure 1. Unstructured grid of idealized estuary model domain (a) and zoomed-in view of the
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mouth of the estuary (b).
ranging from 1000 to 10000 m3/s and sea-level rise
m (□),
ranging from 0.00 to 0.81 m. Legend:
m (Δ),
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m (*),
Figure 4. Dispersion coefficients
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ranging from 0.00 to 0.81 m. Legend:
m (Δ),
m (+),
Figure 5. Dependence of length scale L on sea-level heights
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m (○).
m (+),
for runs with freshwater inflows Q ranging from 1000 to
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10000 m3/s and sea-level rise m (*),
for runs with freshwater inflows Q ranging
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Figure 3. Gravitational circulation velocity scale from 1000 to 10000 m3/s and sea-level rise
ranging from 0.00 to 0.81 m. The
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salinity contours are plotted every 5 psu interval.
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Figure 2. Vertical profiles of tidally-averaged along-channel salinity for freshwater inflows Q
inflows Q ranging from 1000 to 10000 m3/s and sea-level rise
m (□),
m (○). for runs with freshwater ranging from 0.00 to 0.81 m.
Legend: Q = 1000 m3/s (□), Q = 2500 m3/s (*), Q = 5000 m3/s (∆), Q = 7500 m3/s (+), Q = 10000 m3/s (○).
Figure 6. The San Francisco Bay model domain and bathymetry (a) Uunstructured grid of San Francisco Bay (b). Figure 7. Tidal and depth-averaged salinities from the Golden Gate along the longitudinal axis in North San Francisco Bay. Distances into the Bay are positive and those towards the ocean are negative. Legend: Freshwater inflows Q = 2000 m3s-1 (black), 800 m3s-1 (red), 300 m3s-1 (blue), and sea-level rise
= 0 m (‒ ‒ ), 0.46 m (‒ ‒ ), 1.00 m (‒ ∙) and 1.39 m (∙ ∙ ∙).
ACCEPTED MANUSCRIPT Figure 8. Vertical profiles of tidally-averaged salinity (psu) along a transect in Carquinez Strait for 2000 m3s-1, 800 m3s-1 and 300 m3s-1 freshwater inflows Q, and (a) 0 m (b) 0.46 m (c) 1.00 m .
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(d) 1.39 m sea-level rise
for climate change
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Figure 9. Dependence of length scale L on sea-level heights
simulations (with freshwater inflows Q ranging from 300 to 2000 m3/s and sea-level rise
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ranging from 0.00 to 1.39 m) in San Francisco Bay. Legend: Q = 300 m3/s (□), Q = 800 m3/s (*),
Figure 10. Inflows required to maintain
standards for the sea-level rise scenarios. Legend: Port
km (‒ ‒ , ○), Chipps Island
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Chicago
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Q = 2000 m3/s (∆).
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∙, *).
km (‒ ‒ , ◊) and Collinsville
km (∙ ∙
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-100
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600
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10
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0
(b)
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Figure 1. Unstructured grid of idealized estuary model domain (a) and zoomed-in view of the
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mouth of the estuary (b).
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Figure 2. Vertical profiles of tidally-averaged along-channel salinity for freshwater inflows Q ranging from 1000 to 10000 m3/s and sea-level rise
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0. 81 m
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salinity contours are plotted every 5 psu interval.
ranging from 0.00 to 0.81 m. The
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0.3
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(c) Q = 5000 m3/s 0.5
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(e) Q = 10000 m3/s
Ugc (m/s)
0.5 0.4 0.3 0.2 0.1
0 0
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Figure 3. Gravitational circulation velocity scale from 1000 to 10000 m3/s and sea-level rise m (□),
m (*),
m (Δ),
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for runs with freshwater inflows Q ranging ranging from 0.00 to 0.81 m. Legend: m (+),
m (○).
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x 10
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x 10
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K (m2/s)
5 4 3 2 1
0 0
100 200 300 400 Distance from mouth (km)
Figure 4. Dispersion coefficients 10000 m3/s and sea-level rise m (*),
500
for runs with freshwater inflows Q ranging from 1000 to ranging from 0.00 to 0.81 m. Legend:
m (Δ),
m (+),
m (○).
m (□),
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L (km)
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350
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250
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Figure 5. Dependence of length scale L on sea-level heights inflows Q ranging from 1000 to 10000 m3/s and sea-level rise
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(H0 + H) (m)
for runs with freshwater ranging from 0.00 to 0.81 m.
Legend: Q = 1000 m3/s (□), Q = 2500 m3/s (*), Q = 5000 m3/s (∆), Q = 7500 m3/s (+), Q = 10000 m3/s (○).
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Figure 6. The San Francisco Bay model domain and bathymetry (a) Unstructured grid of San Francisco Bay (b).
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Figure 7. Tidal and depth-averaged salinities from the Golden Gate along the longitudinal axis in North San Francisco Bay. Distances into the Bay are positive and those towards the ocean are negative. Legend: Freshwater inflows Q = 2000 m3s-1 (black), 800 m3s-1 (red), 300 m3s-1 (blue), and sea-level rise
= 0 m (‒ ‒ ), 0.46 m (‒ ‒ ), 1.00 m (‒ ∙) and 1.39 m (∙ ∙ ∙).
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1.00 m
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Sea-level rise
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Figure 8. Vertical profiles of tidally-averaged salinity (psu) along a transect in Carquinez Strait for 2000 m3s-1, 800 m3s-1 and 300 m3s-1 freshwater inflows Q, and (a) 0 m (b) 0.46 m (c) 1.00 m (d) 1.39 m sea-level rise
.
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80
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L (km)
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90
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12.6
13 13.4 (H0 + H) (m)
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Figure 9. Dependence of length scale L on sea-level heights
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14.2
for climate change
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simulations (with freshwater inflows Q ranging from 300 to 2000 m3/s and sea-level rise ranging from 0.00 to 1.39 m) in San Francisco Bay. Legend: Q = 300 m3/s (□), Q = 800 m3/s (*), Q = 2000 m3/s (∆).
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64 km
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Q (m3s-1)
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1000
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500
0.5
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0.0
∙, *).
81 km
H (m)
1.0
1.5
standards for the sea-level rise scenarios. Legend: Port
km (‒ ‒ , ○), Chipps Island
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Chicago
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Figure 10. Inflows required to maintain
74 km
km (‒ ‒ , ◊) and Collinsville
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ACCEPTED MANUSCRIPT Table 1. Description of runs with freshwater inflows
ranging from 1000 to 10000 m3/s and
sea-level rise
ranging from 0.00 to 0.81 m. Effective values for gravitational circulation
velocity scale
and longitudinal dispersion coefficient
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are computed.
Run
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(m/s) 0.138 0.157 0.168 0.170 0.187 0.148 0.156 0.169 0.184 0.194 0.195 0.197 0.205 0.219 0.232 0.209 0.217 0.228 0.238 0.247 0.212 0.219 0.234 0.248 0.254
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(m) 0.00 0.10 0.27 0.56 0.81 0.00 0.10 0.27 0.56 0.81 0.00 0.10 0.27 0.56 0.81 0.00 0.10 0.27 0.56 0.81 0.00 0.10 0.27 0.56 0.81
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D
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A1 A2 A3 A4 A5 B1 B2 B3 B4 B5 C1 C2 C3 C4 C5 D1 D2 D3 D4 D5 E1 E2 E3 E4 E5
(m3/s) 1000 1000 1000 1000 1000 2500 2500 2500 2500 2500 5000 5000 5000 5000 5000 7500 7500 7500 7500 7500 10000 10000 10000 10000 10000
(103 m2/s) 3.60 3.78 3.78 3.79 3.82 7.95 8.03 8.15 8.17 8.27 10.41 11.74 12.91 13.83 14.29 15.17 15.43 16.26 18.02 19.88 17.74 18.83 18.72 22.19 26.10
ACCEPTED MANUSCRIPT Table 2. Least-squares fit of the form
for the freshwater inflows
0.19 0.23 0.24 1.70 2.16
3.2 2.9 2.8 2.0 1.8
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Confidence level (%) 95 95 95 95 95
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n
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b
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Inflows ( 1000 2500 5000 7500 10000
ranging from 0.00 to 0.81 m.
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from 1000 to 10000 m3/s and sea-level rise
ranging
ACCEPTED MANUSCRIPT Table 3. Least-squares fit of the form Runs with freshwater inflows
for San Francisco Bay simulations.
ranging from 300 to 2000 m3/s and sea-level rise
m
2.88 15.61 14.40
1.31 0.59 0.58
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c
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Inflows ( 300 800 2000
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from 0.00 to 1.39 m. Confidence level (%) 95 95 95
ranging
ACCEPTED MANUSCRIPT Highlights
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Numerical simulations to investigate climate change impacts on estuarine circulation Rising sea levels lead to stronger and enhanced salinity intrusion With low inflows, effects of sea-level rise on salinity intrusion are largest Stronger inflows required with sea-level rise to maintain in San Francisco Bay
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