sign in sign up
<<
Home , Admiralty Inlet, Puget Sound region, Saratoga Passage, Skagit Bay, South Puget Sound, Swinomish Channel

Estuarine, Coastal and Shelf Science 93 (2011) 305e319

Contents lists available at ScienceDirect

Estuarine, Coastal and Shelf Science

journal homepage: www.elsevier.com/locate/ecss

Tidally averaged circulation in sub-basins: Comparison of historical data, analytical model, and numerical model

Tarang Khangaonkar a,*, Zhaoqing Yang a, Taeyun Kim a, Mindy Roberts b a Pacific Northwest National Laboratory, Marine Sciences Division, 1100 Dexter Avenue North, Suite 400, , WA 98109, USA b State Department of Ecology, PO Box 47600, Olympia, WA 98504-7600, USA article info abstract

Article history: Through extensive field data collection and analysis efforts conducted since the 1950s, researchers have Received 25 September 2010 established an understanding of the characteristic features of circulation in Puget Sound. The pattern Accepted 25 April 2011 ranges from the classic fjordal behavior in some basins, with shallow brackish outflow and compensating Available online 10 May 2011 inflow immediately below, to the typical two-layer flow observed in many partially mixed estuaries with saline inflow at depth. An attempt at reproducing this behavior by fitting an analytical formulation to Keywords: past data is presented, followed by the application of a three-dimensional circulation and transport modeling numerical model. The analytical treatment helped identify key physical processes and parameters, but fjords fi fi partially mixed estuaries quickly recon rmed that response is complex and would require site-speci c parameterization to analytical solution include effects of sills and interconnected basins. The numerical model of Puget Sound, developed using 3-D hydrodynamic model unstructured-grid finite volume method, allowed resolution of the sub-basin geometric features, unstructured grid including presence of major islands, and site-specific strong advective vertical mixing created by Puget Sound bathymetry and multiple sills. The model was calibrated using available recent short-term oceanographic FVCOM time series data sets from different parts of the Puget Sound basin. The results are compared against 1) recent velocity and salinity data collected in Puget Sound from 2006 and 2) a composite data set from previously analyzed historical records, mostly from the 1970s. The results highlight the ability of the model to reproduce velocity and salinity profile characteristics, their variations among Puget Sound sub- basins, and tidally averaged circulation. Sensitivity of residual circulation to variations in freshwater inflow and resulting salinity gradient in fjordal sub-basins of Puget Sound is examined. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Fraser River in Canadian waters, and substantial regional runoff help create stratified two-layer conditions where the tidally Puget Sound, the , and Georgia Strait, averaged circulation consists of outflow mixed brackish water in recently defined as the Salish Sea, compose a large and complex the surface layer and inflow of saline water through the lower estuarine system in the Pacific Northwest portion of the United layers. States (U.S.) and adjacent Canadian waters. Pacific tides propagate Much of our present understanding of tidally averaged circula- from the west into the system via the Strait of Juan de Fuca tion in Puget Sound is based on analysis and interpretation of around the , north into Canadian waters through considerable data collected since the 1950s and insights gained the Georgia Strait. Propagation of tides into Puget Sound occurs from the application of a physical scale model of Puget Sound at the primarily through (see Fig. 1(a)). This is a glacially (Rattray and Lincoln, 1955). The historical carved fjordal estuarine system with many narrow long and records of moored current meter and salinity profile observations relatively deep interconnected basins. The freshwater discharged are extensive and date back to 1930. Cox et al. (1981) tabulated by 19 gaged rivers including those in Puget Sound, the inflows to known current observations, including periods of intensive moni- the Strait of Juan de Fuca, the freshwater discharge from the toring from 1951 to 1956 and in the 1970s and 1980s. Ebbesmeyer et al. (1984) and Cox et al. (1984) provided a synthesis and inter- pretation of these current measurements in Puget Sound. Using this information, Ebbesmeyer and Barnes (1980) developed a concep- * Corresponding author. Pacific Northwest National Laboratory, Marine Sciences Division, 1100 Dexter Avenue North, Suite 400, Seattle, WA 98109, USA. tual model of Puget Sound which describes circulation in the main E-mail address: [email protected] (T. Khangaonkar). basin of Puget Sound as that in a fjord with deep sills (landward sill

0272-7714/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ecss.2011.04.016 306 T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319

Fig. 1. (a) Oceanographic regions of Puget Sound and the Northwest Straits (Salish sea) including the inner sub-basinsdHood Canal, Whidbey Basin, Central Basin, and South Sound. (b) Intermediate scale FVCOM grid along with composite current and salinity profile stations from Cokelet et al. (1990). zone at and a seaward sill zone at Admiralty Inlet) branched system, consisting of seven, two-layered boxes (Box Model defining a large basin, outflow through the surface layers, and of Puget Sound) was developed by Babson et al. (2006) based on the inflow at depth. Analysis of long-term current meter records by work by Li et al. (1999). The basin characteristics, such as depth of Cannon (1983) showed a departure from the classic fjordal signa- zero flow to determine the thickness of boxes representing specific tures seen in and to one where depth basins, were adopted from the composite information of Puget Sound of zero flow (where tidally averaged velocity crosses zero between developed by Cokelet et al. (1990). A key simplification in these and outgoing surface layer and inflowing deeper layer) was deeper in prior Puget Sound box models, including those by Friebertshauser the water column in the main basindabout 25% of depth, lower and Duxbury (1972) and Hamilton et al. (1985),isthefixed and than conventional fjords (10e15%) in the main basin. The depth of constant surface and bottom layer depth in each basin. Only a limited peak inflow varied from near 50e75% of depthddeeper than classic number of hydrodynamic modeling studies exist that cover the entire fjords, but higher in the water column than typical shallow estu- Puget Sound, including a laterally averaged, vertical two-dimensional aries. This behavior may be recognized as a transition between model used to study density intrusion into Puget Sound (Lavelle et al., a fjord and partially mixed estuary and is a characteristic feature of 1991), and a three-dimensional (3-D), structured grid model devel- Puget Sound circulation. oped using Princeton Ocean Model (POM) code to study the vari- Nutrient pollution is considered a potential threat to the ecolog- ability of currents with a focus on complexities of the triple junction ical health of Puget Sound. There is considerable interest in under- site at the confluence of Admiralty Inlet, and the standing the hydrodynamics and the effect of nutrient loads entering Main (or Central) Basin of Puget Sound (Nairn and Kawase, 2002). Puget Sound and, given climate change and sea-level rise possibili- Water quality in Puget Sound, as indicated by conventional ties, how this balance may be altered in the future. This concern is not parameters such as dissolved oxygen, nutrients (nitrate þ -nitriteeni new. Recognizing that pollutant build-up problems and climatic trogen (NO3 þ NO2) and phosphateephosphorus (PO4)), algae, and changes are longstanding and require long-term application of fecal coliform bacteria, is generally considered to be good. However, models, Cokelet et al. (1990) developed a numerical model consisting there are several specific locations where water quality appears of a branched system of two-layered reaches separated by exchange reduced due to low dissolved oxygen and fecal coliform bacteria zones to calculate refluxing, salinity concentrations time series, and contamination. The areas with lowest dissolved oxygen levels include annual volume transports in nine sub-basins of Puget Sound. The southern Hood Canal, , Penn Cove, , technique used estimates of annual freshwater runoff and composite , Possession Sound, Saratoga Passage, and Sinclair Inlet. profiles of long-term mean currents and salinity profiles from historic Historical observations of primary production suggest that phyto- measurements in nine reaches to specify conservative mass trans- plankton growth in Puget Sound is closely coupled to the circulation ports for the Strait of Juan de Fuca and Puget Sound domain. A similar characteristics. This was demonstrated through the early work by T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319 307

Winter et al. (1975). Subsequent studies and review of historic data vu vw þ ¼ 0; (1) show that although spring and summer blooms occur regularly, the vx vz potential for eutrophication impacts in the main basin is mitigated by the presence of strong residual circulation and water renewal from vu vu 1 vP v vu fl fi u þ w ¼ þ Km ; (2) freshwater discharges and in ow of water from the Paci c Ocean. vx vz r vx vz vz However, poorly flushed inner basins and shallow embayments, particularly in the southern end, show depleted surface nitrate P ¼ r$g$ðh zÞ: (3) concentrations during the summer and very low oxygen concentra- tions at depth (Harrison et al., 1994; Newton and Van Voorhis, 2002). Equations (1) and (2) are continuity and momentum equations in Therefore to correctly simulate nutrient, algae and dissolved oxygen the x direction, assuming that the longitudinal momentum diffu- balance for water quality management in Puget Sound, the ability to sion terms are small for long, narrow estuaries. Equation (3) is the reproduce observed characteristics of tidally averaged circulation hydrostatic pressure, where u(x,z) and w(x,z) are velocities (m/s) in including bottom water renewal and surface water flushing is the x and z directions, r is the density of water (kg/m3), h(x) is the essential. free-surface elevation (m), and Km(z) is the vertical eddy viscosity In this paper, we first present an analytical approach to describe coefficient (m2/s). For fjordal waters and partially mixed estuaries, tidally averaged current and salinity profiles in Puget Sound and the equation of state may be approximated by: examine whether inter-basin variability can be captured through r ¼ r $ð þ b$ Þ; variation in principle physical quantities, such as inflow, water 0 1 s (4) depth, and salinity gradient. We then present a numerical approach where s(x,z) is salinity in practical salinity units (ppt), and based on an advanced 3-D baroclinic model of Puget Sound, b z 7.7 10 4/ppt. including the Salish Sea reaches in U.S. and Canadian waters, that The salt balance is given by the steady state advectionediffusion was previously developed (Khangaonkar and Yang, 2011; Yang and balance: Khangaonkar, 2010). A computationally efficient, intermediate scale version of the model suitable for multi-year simulations was vs vs v vs u þ w ¼ Ks ; (5) adopted for this investigation and calibrated using data from 2006. vx vz vz vz Quantitative model skill analysis is also presented in the form of 2 error statistics at available representative stations around Puget where Ks(z) is the vertical eddy diffusion coefficient (m /s). Sound. A year-long application of the model was then used to Starting from the early work done by Pritchard (1952, 1954, generate tidally averaged current and salinity distributions and 1956), variations of these basic equations have been used by compared to composite current and salinity profiles developed by many researchers in the past to develop analytical solutions for Cokelet et al. (1990) from historical data. The comparison demon- coastal plain estuaries, well-mixed estuaries, partially mixed strates the ability of the model to reproduce tidally averaged estuaries, and highly stratified fjordal estuaries (e.g., Hansen and circulation patterns and the ability to simulate inter-basin vari- Rattray, 1965; Rattray, 1967; Jay and Smith, 1990a,b; MacCready, ability of mean currents and salinity profiles. The model was also 2004). used to evaluate the sensitivity of tidally averaged circulation, peak We seek a formulation that would allow consideration of depth- inflow, outflow, and surface-layer thickness to inflow and salinity dependent Km(z) for application to fjordal conditions of the type gradient in one of the sub-basins (Saratoga Passage) of Puget observed in Puget Sound with a varying degree of vertical shear and Sound. Saratoga Passage was selected for this analysis. This basin is mixing. Here, we introduce a non-dimensional depth variable influenced by discharge which is the largest freshwater z ¼ z=H,whereH is the water depth, and an exponential variation of discharge into Puget Sound. Km and Ks with depth, similar to the form used by Rattray (1967) is defined by:

z 2. Analytical formulation KmðzÞ¼Kmo$ea$ ; (6)

Prior analytical efforts to describe Puget Sound’s mean circula- ðzÞ¼d$ ðzÞ¼d$ $ a$z: tion using an analytical approach were conducted nearly four Ks Km Kmo e (7) decades ago by Winter (1973) and Winter et al. (1975). They applied For narrow fjordal estuaries with a uniform cross section, the ’ Rattray s (1967) general fjord circulation theory to the main basin of solutions for u(z) and s(z) are obtained by solving governing Puget Sound and found approximate agreement in current equations, assuming that the vertical velocity component w(x,z)is fl magnitudes but shallower depth of zero ow. To obtain a solution small and the longitudinal momentum term is negligible relative to in a closed form, we have adopted an analytical approach where the pressure gradient and the shear stress terms. The analytical a theoretical formulation previously used by Hansen and Rattray solution in closed form is proved below and the detailed derivation (1965), Dyer (1973), and MacCready (2004) for partially mixed is presented in Appendix A. estuaries based on a constant eddy viscosity assumption was The tidally averaged longitudinal velocity solution, also referred expanded to incorporate an exponential variation with depth to here as the “variable Km solution,” is expressed by: similar to the form used by Rattray (1967). Governing equations applicable to narrow, long fjordal estuaries ! az 2 C1 e $ðazþ1Þ U z z 2z 2 are the continuity and Reynolds momentum equations in a vertical uðzÞ¼ $ $e a þ þ þC3; (8) two-dimensional (xez) coordinate system, an equation of state Kmo a2 Kmo a a2 a3 relating salinity to density, and the hydrostatic assumption for pressure. Under steady-state conditions employing the Boussinesq where approximation, the simplified governing equations with the origin located near the mouth of the estuary, the x direction pointed vs toward the open ocean boundary, and the z axis being positive U ¼g$b$ $H3; upwards may be expressed as follows: vx 308 T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319 U 1 2 2 D a D ¼ þ ; u$Kmo $ð $e J1Þ a a2 a3 2 C1 ¼ ; C3 ea$ð1 aÞ J2 ea 1 ea$ð1 aÞ1 2 aa I ¼ ; I ¼ ; I ¼ ea$D ; 1 a 2 2 3 3 U$D$ a að Þ a a ¼ e C1 $e 1 a : 2$Kmo Kmo a2 I 2$I 2$I a$I þ I J ¼ 3 þ 2 þ 1 ; J ¼ 2 1; The variable Ks solution for the depth-varying component of 1 2 3 2 2 a a a a salinity is exhibited by:

Fig. 2. Comparison of predicted and observed velocity profiles at various stations in Puget Sound and the Straits (Data source: Cannon, 1983). T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319 309

Table 1 Variation in input parameter valuesdanalytical model of Puget Sound.

Basin name Physical properties Analytical model parameters Depth, Width, River inflow, Surface eddy viscosity Depth-penetration Salinity gradient, vs=vx, (ppt m 1) 3 1 2 1 H (m) W,(m) Qr,(m s ) Kmo, (m s ) factor, “a” Admiralty Inlet 100 5446 1.347 10 10 5 0.001 1.03 10 7 Shilshole Marina 200 5900 241 10 10 5 3.3 9.62 10 8 Puget Sound main basin 190 6177 289 10 10 5 6.0 3.13 10 7 Saratoga Passage 82 4166 475 10 10 5 17.0 4 10 5

( a 2azð z þ Þ U a C1 ð2aM þ 5M Þ U 0 z C1 e 2a 5 2az D2 ¼ $ 2 1 þ $ s ð Þ¼ $ e d$ 4 $ d$Kmo Kmo 4a4 2$Kmo Kmo Kmo 4a 2 Kmo ! ! z2 z 1 2 2 2 1 M3 þ 2M2 þ 2M1 þ 2 ð þ Þ þ þ þ ðaz þ 2ÞÞ aM2 2M1 a2 2a 4a2 8a3 a5 a2 2a 4a2 8a3 a5 ) z z ðaI þ I Þ I ea ðaz þ 1Þ ea þðC3 uÞ $ 2 1 þ 1D1: ðC3 uÞ $ D1 þ D2; (9) a2 a a2 a Salinity profiles are then computed using the definition: where sðzÞ¼s0ðzÞþs (where s0ðzÞ and s are the depth-dependent and depth-averaged components of s and the assumption that at the z seabed ð ¼1Þ, salinity may be assumed equal to ocean salinity e2a 1 e2a$ð1 2aÞ1 (i.e., sð1Þ¼s ). M ¼ ; M ¼ ; ocn 1 2a 2 4a2 Comparisons of measured currents in various parts of Puget Sound using varying magnitudes of the exponential decay coeffi- 2 cient “a” and Kmo values are shown in Fig. 2 and listed in Table 1. M ¼ e2a 1 2 þ 2 ; 3 2a 4a2 8a3 8a3 For calibration of the tidally averaged analytical model in Puget Sound, we have used previously published data collected from a 3$U 2$C1 different parts of Puget Sound as part of an effort to characterize D1 ¼ þ ; and d$Kmo Kmo,a4 Kmo$a3 temporal and spatial variability in circulation and large-scale dynamics of the estuarine system (Geyer and Cannon, 1982; Cannon, 1983). We selected four stations that highlight the

Fig. 3. (a) Tidal elevations at open boundaries: entrance of the Strait of Juan de Fuca (Black) and North End of the Strait of Georgia. (b) Basin-wide river inflowsdPuget Sound, the Strait of Juan de Fuca, and Georgia Strait. 310 T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319 different characteristics within Puget Sound (Fig. 1(a)). The velocity Further south in Puget Sound, the Shilshole and the Main Basin profile in Admiralty Inlet under the influence of mixing over the sites show that the shape of the residual current profile has entrance sill shows characteristics seen in coastal plain or changed. For the period of record, the peak inflow and zero flow a partially mixed estuary that is generally well described using (crossover) occurs at a much shallower depths in the Main Basin a near-constant description of the eddy viscosity coefficient, Kmo. and Shilshole sites relative to Admiralty Inlet. Fig. 2 shows that the As shown in Fig. 2, in Admiralty Inlet, the inflow at the bottom variable Km model works well over most of the region. In the 3 peaks approximately at three-fourths ( /4 ) of the water depth level. relatively exposed Puget Sound Main Basin location, it is likely that

Fig. 4. (a) Example of comparison between simulated and observed water surface elevation at Seattle station. (b) Example of comparison between simulated and observed currents in in the surface middle and bottom layers of the water column. T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319 311 wind mixing caused a reduction of the surface-layer outflow. This exercise was valuable in showing it is possible to aggregate Hence, the predicted solution is found to overestimate the outflow the effects of many dominant physical Puget Sound processes into currents. In the sheltered region of the Saratoga Passage, the a few parameters. The development of characteristic surface outflow surface layer appears to be intact, and the overall behavior, which is and shallow inflow in the upper half of the water column could be like a classic fjord, is matched well over the entire water column. created through the analytical formulation of Km, which increased The fit was achieved in two steps. After specifying physical prop- exponentially with depth. The depth of peak inflow and layer depth erties of the basin as input (H, W,andQr) and selection of a reasonable (or depth of zero flow) was controlled by the specified magnitude of but arbitrary value of surface eddy viscosity (Kmo ¼ 10 10 5), the “a,” and peak outflow or inflow was shown to be sensitive to depth-penetration factor “a” was adjusted so peak inflow depth components of exchange flow velocity UE (see Appendix A), which matched data. The depth-averaged salinity gradient ðvs=vxÞ was then includes depth H, Kmo, and the depth-averaged salinity gradient adjusted until a best match to velocity magnitudes was obtained. For vs=vx. If we assume that surface eddy viscosity (Kmo) within Puget a fixed “a” value and all other physical parameters remaining Sound may be set relatively uniform, the variation of circulation in unchanged, the ratio of vs=vx to Kmo controls exchange flow and sub-basins is controlled by 1) hydraulic features, such as sills and varies basin to basin, but is a constant in each basin. basin geometry, and 2) freshwater inflow. The combined effects

Fig. 5. (a) Simulated (line) and observed (circle) salinity profiles in February high-flow condition. (b) Salinity time series comparisons at Saratoga Passage, East Passage, and Hood Canal stations, respectively (Julian Day 1 ¼ January 1, 2006). 312 T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319

Table 2 Model calibration error statistics.

a) For water surface elevation (2006)

Station MAE (m) RMSE (m) RME (%) Correlation (R) Port Angeles 0.22 0.27 7.5 0.944 Friday Harbor 0.24 0.30 8.0 0.950 Cherry Point 0.30 0.36 8.6 0.953 Port Townsend 0.22 0.28 7.0 0.965 Seattle 0.26 0.31 7.2 0.976 Tacoma 0.27 0.33 7.6 0.977

Mean 0.25 0.31 7.65 0.961

b) For velocity

Station MAE (m/s) RMSE (m/s) Correlation (R)

Surface Middle Bottom Surface Middle Bottom Surface Middle Bottom 0.16 0.11 0.10 0.20 0.14 0.13 0.686 0.914 0.831 Dana Passage 0.26 0.26 0.26 0.30 0.30 0.31 0.919 0.943 0.913 Channel 0.26 0.33 0.30 0.32 0.37 0.34 0.754 0.555 0.466 Skagit Bay 0.30 0.21 0.18 0.38 0.29 0.22 0.652 0.798 0.795

Mean 0.23 0.28 0.769

c) For salinity

Station MAE (ppt) RMSE (ppt) Admiralty Inlet Entrance (ADM2) 0.60 0.85 Admiralty Inlet North (ADM1) 1.04 1.23 Admiralty Inlet South (ADM3) 0.81 0.97 Puget Sound main basin (PSB) 1.29 1.86 East Passage (EAP) 0.66 0.98 Gordon Point/Tacoma Narrows (GOR1) 0.67 0.93 Hood Canal (HCB003) 0.72 0.93 Saratoga Passage (SAR003) 0.63 1.10 (NSQ) 0.79 1.00 Dana Passage (DNA) 0.96 1.15

Mean 0.82 1.10

MAE ¼ mean absolute error; RMSE ¼ root mean square error.

of which are included in specified values of “a” and the resulting 3. Puget Soundd3-D circulation and transport numerical vs=vx, respectively. model It may be reasonable to assume that surface eddy coefficient Kmo, ratio of eddy viscosity to diffusivity d, and depth-penetration 3.1. Model setup factor “a” are likely governed by intrinsic geometric and hydraulic features of each basin for normal weather and wind conditions. A multiscale model of Puget Sound with a grid size capable of Once determined for each basin through parameter calibration or resolving small channels near river mouths to coastal open waters site-specific measurements, they may be expected to remain rela- was developed previously and has been applied on multiple tively constant. Salinity gradient, however, will vary seasonally and projects in connection with nearshore restoration actions for change with alterations to runoff and precipitation regimes with improving the water quality and ecological health of Puget Sound potential changes in climate. In the current analytical formulation, (Yang and Khangaonkar, 2010; Khangaonkar and Yang, 2011). The we have not attempted to relate vs=vx to inflow Qr. Therefore, Puget Sound model uses the finite volume coastal ocean model a direct application of the analytical solution to predict a response of current and salinity profile to changes in freshwater inflow is not possible. Without prior knowledge of these parameters, the exer- Table 3 cise at this point may be viewed as a sophisticated fitting of solution Compilation historical Puget Sound data (Cokelet et al., 1990). to the observed data in individual basins. As more data becomes Reach Years of observation available, there is potential for both practical applications and Velocity Salinity developing better understanding of circulation in fjord-like estu- Pillar Point 1975e1978 Primary salinity data was aries using this type of approach. New Dungeness 1964, 1978 obtained from the University In the absence of direct measurements, we turn to a 3-D numerical Point Jefferson 1972e1973, of Washington’s field program model with the ability to estimate eddy viscosity and eddy diffusivity 1975e1978 (1951e1956) coefficients internally through turbulence closure schemes and to East Passage 1943, 1977, e compute longitudinal and vertical salinity gradients in baroclinic 1982 1983 1947, 1977 mode for the entire domain. The reproduction of observed current Gordon Point 1945, 1977e1978 and salinity profiles (shape and magnitude) in Puget Sound using Devil’s Head 1945, 1978 a simple analytical formulation demonstrated here sets the standard Tala Point 1942, 1952, and performance expectations for the numerical model. The 1963, 1977e1978 Hazel Point 1942, 1978 numerical results may then be assimilated back into the analytical Saratoga Passage 1943, 1970, 1977 model for future development and application. T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319 313

(FVCOM) developed at the University of Massachusetts (Chen et al., temperature, salinity, and density equations in an integral form. 2003). FVCOM is a 3-D hydrodynamic model that can simulate The model employs the Smagorinsky scheme for horizontal mixing tidally and density-driven, and meteorological forcing-induced (Smagorinsky, 1963) and the Mellor-Yamada level 2.5 turbulent circulation in an unstructured, finite element framework. The closure scheme for vertical mixing (Mellor and Yamada, 1982). The unstructured-grid model framework of FVCOM is well suited to model has been successfully applied to simulate hydrodynamics accommodate complex shoreline geometry, waterways, and islands and transport processes in many estuaries, coastal waters, and open in Puget Sound. FVCOM solves the 3-D momentum, continuity, oceans (Zheng et al., 2003; Chen and Rawson, 2005; Isobe and

Fig. 6. (a) Comparison of simulated Year 2006 average velocity profiles at various Puget Sound sub-basins with composite data from Cokelet et al. (1990). (b) Comparison of simulated Year 2006 average salinity profiles at various Puget Sound sub-basins with composite data from Cokelet et al. (1990). 314 T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319

Beardsley, 2006; Weisberg and Zheng, 2006; Zhao et al., 2006; Aoki flux, and 4) sensible heat flux. These meteorological parameters and Isobe, 2007; Chen et al., 2008; Yang and Khangaonkar, 2009; were obtained from North American Regional Reanalysis (NARR) Yang et al., 2010a,b; Khangaonkar and Yang, 2011) data generated by the National Oceanic and Atmospheric Admin- For this study, we developed an intermediate (coarser) scale istration (NOAA) National Center for Environmental Prediction version of the same domain with grid size varying from 350 m in (NCEP) and used to compute and specify net heat flux at the estuaries and bays to as large as 3000 m in open coastal waters (see surface. Wind stress within FVCOM is calculated based on the well- Fig. 1(b)). The grid extends north into Canadian waters up to known Large and Pond method (1981). In general, winds are mostly northern Strait of Georgia (south of the entrance to Johnstone Strait), southerly within Puget Sound with low speeds during summer and west to Neah Bay at the entrance to the Strait of Juan de Fuca. A (<5 m/s) and high during winter (as high as 15 m/s). Winds can sigma-stretched coordinate system was used in the vertical plane reach gale-force easterly speeds, 17e24 m/s or higher, in the Strait with 10 terrain-following sigma layers distributed using a power law of Juan de Fuca (Holbrook et al., 1980). Local winds are known to be function with exponent P_Sigma ¼ 1.5 with higher resolution near affected by topography and accurate simulation of wind effects the surface. This scale allows sufficient resolution of the various would require specification of wind field at 1e5 km resolution. In major river estuaries and sub-basins while allowing year-long this application, representative wind field was specified using simulations within 1e2 days of run times on a multiprocessor NARR prediction from a station near main basin of Puget Sound. cluster computer. The bathymetry was from a combined data set consisting of data from Puget Sound digital elevation model d (PSDEM) (Finlayson, 2005) and data provided by the Department of 3.2. Model calibration 2006 data Fisheries and Oceans Canada covering the Strait of Georgia. The fi model bathymetry within the Puget Sound portion of the model The primary calibration effort was associated with re ning and fi south of Admiralty Inlet was smoothed to minimize hydrostatic smoothing of bathymetry; averaging of speci ed boundary forcing fi inconsistency associated with the use of the sigma coordinate salinity and temperature pro les; and adjustment of bed friction fi system with steep bathymetric gradients. The associated slope- until a stable model operation and best t of predicted water surface limiting ratio dH/H ¼ 0.2 was specified within each grid element elevation (WSE), velocity, salinity, and temperature to observed data inside the following guidance provided by at selected stations in Puget Sound was achieved. There are six real- Mellor et al. (1994) and using site-specific experience from Foreman time tidal stations maintained by NOAA as part their Physical et al. (2009),whereH is the local depth at a node and dH is change in Oceanographic Real-Time Systems (PORTS) program throughout the depth to the nearest neighbor. Straits and Puget Sound. Velocity data are quite limited in Puget fi The model setup was conducted using Year 2006 as the basis Sound. Acoustic Doppler Current Pro ler (ADCP) data in South Puget since it was the most data-rich year for salinity, temperature, and Sound, Skagit Bay, and were used for model water quality information from Puget Sound. Tidal elevations were calibration (Yang and Khangaonkar, 2009). Monthly salinity and fi specified along the open boundaries using XTide (harmonic tide temperature pro les collected by the Washington State Department clock and tide predictor) predictions (Flater, 1996) at the Tatoosh Island station located at the entrance of the Strait of Juan de Fuca and the Campbell River station at the mouth of Johnstone Strait. Fig. 3(a) shows tidal elevations forcing input specified at the open boundaries. In this study, temperature and salinity profiles along the open boundaries were estimated based on monthly observa- tions conducted by the Department of Fisheries and Oceans Canada (near the open boundaries). In the entire model domain, initial temperature and salinity conditions were specified uniformly as 9 C and 31.5 ppt, respectively, and water surface and velocities were set to zero. To obtain the final initial condition for the Year 2006 model run, the model was spun up with Year 2005 forcing inputs. Sensitivity tests using constant tidal forcing and steady freshwater flows showed that dynamic steady state over most of the model domain with respect to velocity and salinity profile was achieved in 6e7 months of simulation confirming that 1-year-long simulation would be an adequate spin up period. The model includes 19 rivers that are incorporated with the resolution of estuarine distributary reaches. The Puget Sound region experienced a significant flood event in November 2006, which is reflected in the river discharge time series. In contrast, the Fraser River inflow on the Canadian side of the domain, which is significantly higher than the rest of the inflows into Puget Sound and the Straits, shows a very different seasonal distribution pat- terndhigh flow in the late spring and summer and low flow in the fall and winter. Fig. 3(b) shows a plot of basin-wide freshwater discharges grouped by their discharge basins. The Whidbey Basin consists of the three largest rivers, Skagit River, , and , in Puget Sound and accounts for almost Fig. 7. (a) Tidally averaged salinity gradient ðvs=vxÞ time history at Saratoga Passage 70% of the total freshwater flow into Puget Sound. station simulated by the numerical model of Puget Sound for Year 2006. (b) Tidally averaged velocity profiles at Saratoga Passage station predicted using the analytical Meteorological parameters for calculation of net heat flux in model for salinity gradient ðvs=vxÞ varying from 0.5 10 5 ppt/m to 7 10 5 ppt/m as FVCOM include: 1) downward and upward shortwave radiation, provided by the numerical model. (c) Tidally averaged (monthly) velocity profiles 2) downward and upward longwave radiation, 3) latent heat extracted from the numerical model directly for the Year 2006 simulation. T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319 315 of Ecology as part of their ambient monitoring program throughout Table 3 shows the years of observations at the respective stations, Puget Sound were also used. and the station locations are indicated in Fig. 1(b). Examples of time series comparisons for WSE, velocity, and A one-to-one comparison with model results corresponding to salinity at selected stations are shown in Figs. 4(a), (b), and 5(b), Year 2006 and Cokelet et al. (1990) data is not appropriate as this respectively, to illustrate the quality of match in phase and composite representation of Puget Sound circulation was con- magnitude. Error statistics at all stations analyzed are provided in structed with data from multiple years. However, the ability to Table 2aec and provide a quantitative assessment of the model’s reproduce the characteristic features using the Puget Sound ability to reproduce observed oceanographic parameters. Circulation and Transport Model is encouraging. Fig. 6(a) shows As shown in Table 2a, mean absolute errors (MAEs) and root mean a comparison of velocity profiles from 10 stations in Puget Sound square errors (RMSEs) for WSE of all the stations are 0.25 m and and the Strait of Juan de Fuca digitized from Cokelet et al. (1990) 0.31 m, respectively. Relative mean errors (RMEs), defined as the ratio and the model results from Year 2006 averaged at the respective of MAE to the mean of daily tidal ranges, were within 10%. Sensitivity station location for the entire year of simulation. The velocity data tests indicate that the main source of error is likely the error in collected over multiple years was not averaged at each depth and specified boundary elevations at the Georgia Strait boundary. hence is shown as many discrete points. Fig. 6(b) shows a compar- Velocity data available for model calibration in 2006 were ison of model results to salinity data also collected over multiple limited. The ADCP data were collected within narrow, long channels years but plotted after averaging at each depth. with dominant longitudinal characteristics. For simplicity, compar- The historical composite velocity profiles show spatial variation isons were made between the model results and observed data and differences that also are recognizable in the simulated results. along the major axis of tidal currents at the surface, middle, and As postulated previously and based on observed data, Saratoga bottom layers of the water column as shown in Fig. 4(b). The largest Passage in Whidbey Basin and Hazel Point in Hood Canal exhibit errors are in the surface layer, and smallest errors are in the bottom classical fjord behavior, and the model reproduces the shallow layer. Larger errors in the surface layer are likely due to limited brackish outflow layer with inflow high up in the water column. accuracy associated with the use of wind field specified using NARR The comparisons of velocity profiles at other stations show prediction from a representative station near main basin of Puget appropriate changes in characteristics with a reasonable agreement Sound. The overall MAE and RMSE for all four stations are 0.23 m/s among the trends and magnitudes. For example, the tidally aver- and 0.28 m/s, respectively, as shown in Table 2b. aged currents are nearly unidirectional in Colvos Passage (north) Salinity and temperature predictions inside Puget Sound are and East Passage (south), respectively. Despite limitations of setting sensitive to specified boundary temperature and salinity profiles. A the model boundary at Neah Bay in the Strait of Juan de Fuca, the review of the data from monthly profiles collected at the boundaries velocity profile characteristics that resemble partially mixed estu- showed that seasonal salinity and temperature variations were only aries with inflow of saline water from the coast, peaking at three- 3 notable in the upper 50 m of the water column and nearly constant fourths ( /4 ) depths, and outflow of combined Puget Sound and below throughout the year. Open boundary temperature and salinity Canadian freshwater discharges through the surface appear to be values were set constant at 7.4 C and 34 in the Strait of Juan de Fuca correctly reproduced. As seen in Fig. 6(b), a salinity simulation and 9.3 C and 30.6 in Georgia Strait. Although year-long time correctly converges to a stable solution of approximately 30e31 histories were not available, salinity and temperature profiles were throughout Puget Sound. This also illustrates the ability of the 10- collected on a monthly basis at 25 monitoring stations within Puget layer intermediate scale model to develop stratified Puget Sound Sound. In this study, we selected 11 stations representing the sub- conditions, including the sub-basins and inner passages. basins in Puget Sound for temperature and salinity profile compar- isons. Fig. 5(a) shows a comparison between simulated and observed 5. Results and discussion salinity profiles in February 2006 (high-flow condition). Table 2c shows that MAE and RMSE for salinity profiles at all stations were Despite mixing and recirculation induced by the sills and sub- 0.81 and 1.0 ppt respectively. basins, the tidally averaged salinity and current profiles in Puget In addition to salinity profiles in Fig. 5(a), a comparison of pre- Sound continue to retain many major fjord-like characteristics. As dicted and observed salinity is presented in the form of time series seen in the numerical model comparison to historical data and data from Saratoga Passage, Hood Canal, and East Passage sub- calibration using Year 2006 salinity profiles (Figs. 6 and 7), basins in Fig. 5(b). a distinct stratified upper layer, varying between 5 and 20 m in depth (z5e15% of the water depth), is maintained. Salinity varia- 4. Tidally averaged velocity profilesdcomparison with tion below this surface layer is uniform with <1 ppt variation and historical data determined primarily by the salinity of near-bed inflow waters from the Strait of Juan de Fuca near the mouth of Admiralty Inlet. In Capability of the Puget Sound hydrodynamic model of repro- pronounced fjordal sub-basins, such as Saratoga Passage and Hood ducing tidally averaged circulation is of importance as this drives the Canal, and inner reaches within , freshwater mean transport and residence times, thereby influencing overall inflow relative to basin size can be high. In these sub-basins, during water quality. This requires a comparison of low-passed, tidally periods of high runoff surface strong stratification with brackish averaged currents and salinity with model results. The available salinity of 20e30 is seen within the shallow upper layer. The ability current meter records from Year 2006 were from inner sub-basins to simulate this response, as seen in the profiles and time series not particularly well suited for evaluation of the tidally averaged comparisons, demonstrates the ability of the FVCOM with the transport in key locations such as Admiralty Inlet, Saratoga Passage, Mellor-Yamada level 2.5 turbulent closure scheme to simulate Main Basin, and Hood Canal. Therefore, we turned to historical fjordal estuaries such as Puget Sound. records of currents and salinity measurements. As mentioned in the Tidally averaged peak outflow velocities at the surface vary from Introduction, much of our understanding of circulation in Puget as <0.1 m/s in the inner basins, such as Hood Canal and parts of Sound is based on synthesis and interpretation of historical data South Puget Sound to 0.1e0.2 m/s in the Main and Whidbey Basins mostly from 1951 to 1956 and the 1970s and 1980s. Cokelet et al. to as high as z0.3 m/s in Strait of Juan de Fuca. Peak inflow (1990) used this information to develop composite vertical current velocities in fjordal basins of Hood Canal and Saratoga Passage are and salinity profiles in each reach from short-term measurements. small (0.03e0.05 m/s), distributed over a larger depth relative to 316 T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319 outflow, and occur at relatively stable depths varying between 5% (z34 ppt) sets up the near-bed salinity of the water that enters (Saratoga Passage) and 10e30% (Hood Canal) of water depth based Puget Sound at Admiralty Inlet. on location relative to the sill. The depth of peak inflow drops to z near mid-depth ( 50% water depth) in the Puget Sound main basin Acknowledgements at the Shilshole and Point Jefferson mooring locations. It is only in regions with high energy mixing in the Strait of Juan de Fuca and The development of this model of Puget Sound was partially fi Admiralty Inlet where pro les show characteristics matching those funded through a grant from the U.S. Environmental Protection fl z of partially mixed estuaries with in ow at 75% or greater depths Agency (EPA) and Washington State Department of Ecology. Partial z peaking at 0.20 m/s. funding also was received via a grant from the U.S. Department of Using the analytical approach in combination with numerical Energy as part of the Energy Efficiency and Renewable Energy fi model results recon rmed that river runoff is a key driver of the program. We would like to acknowledge Mr. Ben Cope of the EPA fi mean circulation, and the mixing and strati cation is dependent on and Ms. Karol Erickson for their encouragement and support. We mean circulation as opposed to tidal currents. Lumping of important also would like to acknowledge comments provided by reviewers physical estuarine processes into a few parameters allowed a closed- from the model development technical advisory team with repre- form analytical solution, and, with the help of depth-varying eddy sentatives from King , the University of Washington, and fi fi fi coef cients, it was possible to t observed data despite site-speci c other stakeholders. complexity. The solution presented is limited by the fact that depth- penetration parameter “a” must be externally specified along with the choice of Kmo. Yet, once the combination of Kmo and “a” is Appendix A. Analytical solution for mean circulation in fjord- determined as basin-specific parameters, the solution then is like estuaries primarily controlled by salinity gradient vs=vx, which, in turn, is most For a narrow fjordal estuary with a uniform cross section, the directly controlled by freshwater inflow Qr. To illustrate this further, daily average values of vs=vx at Saratoga Passage were extracted vertical velocity component w(x,z) is small, and the longitudinal from the Year 2006 model results and plotted as a function of Skagit momentum term is negligible relative to the pressure gradient and River inflow. The correlation between salinity gradient and river flow the shear stress terms (Dyer, 1973; MacCready, 2004) such that is evident and is shown in Fig. 7(a). Fig. 7(b) shows that for the basin- Equation (2) reduces to: specific values of eddy viscosity parameters (Kmo, “a”), the magni- 1 vP v vu tude of the tidally averaged current profile is directly proportional to 0 ¼ þ Km : (A1) r vx vz vz the salinity gradient (Equation (8)). This analytical model result is validated in Fig. 7(c), which shows monthly averaged velocity Seeking an exact solution in an integral form, as opposed to a power profiles at the same location extracted from the numerical model series approximation by Rattray (1967), we adopted the approach 6 simulation. The salinity gradient varied from 0.5 10 to used by MacCready (2004). In this approach, the velocity u(x,z) and 6 7 10 ppt/m, and the simulated tidally averaged outflow velocity salinity s(x,z) are split into depth-averaged (u and s) and depth- at the surface varied from 0 to 0.2 m/s. The depth of zero flow in the varying (u0 and s) parts, respectively, which is expressed as: analytical model is a constant determined by the choice of Kmo and 0 0 “a”. The numerical model result shows that in sheltered locations uðx; zÞ¼uðxÞþu ðx; zÞ and sðx; zÞ¼sðxÞþs ðx; zÞ: (A2) such as Whidbey Basin, which receives high amounts of freshwater, Using Equations (3) and (4) and assuming that ðvs0=vxÞðvs=vxÞ, the depth of upper layer may remain relatively stable (z8m in the pressure gradient may be written as: Saratoga Passage in 2006). 1 vP vh vs v vu ¼g þ g$b$ z ¼ KmðzÞ : (A3) r vx vx vx vz vz 6. Conclusion 0 If Km were to be assumed constant (Kmo) as in the case of coastal Tidally averaged circulation and transport processes in Puget plain estuaries or even partially mixed estuaries, eliminating the Sound were analyzed using a combination of analytical and pressure gradient terms between equations (A1) and (A3) and numerical models. An analytical solution was derived using an taking another derivative with z eliminates the x-dependent terms exponential form of the eddy viscosity coefficient and was shown and presents: to fit observed historical data in Puget Sound. Sensitivity tests with the analytical model highlighted the importance of freshwater v3u g$b vs ¼ $ : (A4) discharge to the surface waters of Puget Sound. Mixing and vz3 Kmo vx development of stable stratified layers in Puget Sound is deter- Similarly, if Ks were assumed constant (for simplicity, the eddy mined not by tidal currents, but by tidally averaged circulation and diffusivity is assumed to be a ratio of vertical eddy viscosity flushing. This was confirmed by the 3-D hydrodynamic model of Ks ¼ d$Kmo) per Pritchard (1954), for partially mixed systems, Puget Sound, the Straits of Juan de Fuca, and Georgia Strait (Salish Equation (5) may be reduced to: Sea) developed using the unstructured-grid coastal ocean modeling tool FVCOM. Composite salinity and velocity profiles from 2 0 0 vs v s a historical data set were used to validate the Puget Sound model’s u $ zðd$KmoÞ : (A5) vx v 2 ability to reproduce the tidally averaged structure of Puget Sound z circulation. The model results showed that surface salinity in Puget The development above culminating in Equations (A4) and Sound responds rapidly to freshwater discharge, but salinity at (A5) is identical to that presented in MacCready (2004),where depth is almost entirely determined by the salinity and exchange in a solution for (A4) and (A5) in the form of velocity and salinity the Strait of Juan de Fuca and Georgia Strait. The salinity gradient profiles through direct integration. Appropriate free-surface and between Canadian waters in Georgia Strait, which receives seabed boundary conditions are used, and there are net-flow considerable freshwater discharge (z30 ppt), and the saline Pacific and salt-flux balance considerations across the selected cross Ocean waters near the entrance to the Strait of Juan de Fuca section. T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319 317

We seek a formulation that would allow consideration of depth- where a is a measure of the depth penetration of the circulation, dependent Km(z) for application to fjordal conditions of the type and d is the ratio of Ks/Km. Note that z varies from 0 to 1 and Ks observed in Puget Sound with a varying degree of vertical shear and and Km increase with depth. Substituting Equation (A7) into (A6) mixing. Eliminating the vh=vx term from Equation (A3) and taking expresses: the depth dependence of Km into consideration results in: ! v v2 v3 2 u u u 2 2 3 U ¼ Km$ a $ þ 2$a$ þ vs v Km vu vKm v u v u vz vz2 vz3 g$b$ ¼ $ þ 2$ $ þ Km$ : (A6) (A9) vx vz2 vz vz vz2 vz3 vs and U ¼g$b$ $H3: Here, we introduce a non-dimensional depth variable z ¼ z=H, vx where H is the water depth, and an exponential variation of Km The solution for u(z) is obtained by integrating Equation (A9) and Ks with depth similar to the form used by Rattray (1967) with respect to z subject to the conditions that vu=vz ¼ 0atz ¼ 0 defined by: (free-surface zero shear assumption) and u(z) ¼ 0atz ¼1 (zero velocity at the seabed). Also, the depth-averaged velocity, a$z Z KmðzÞ ¼ Kmo$e ; (A7) 0 Qr u ¼ ¼ uðzÞdz, where Qr is the freshwater river inflow H$W z 1 KsðzÞ¼d$KmðzÞ¼d$Kmo$ea$ ; (A8) and H and W are the water depth and width of an equivalent

Fig. A1. (a,b) Along channel velocity “u” and profiles computed using variable Km. Solutions are plotted against non-dimensional depth z. (a) shows velocity profiles for a partially mixed estuary using a small value of decay “a” (0.01) and typical values of Kmo ¼ 10 10 5. (b) shows velocity profile matching typical fjordal characteristics as in Rattray (1967) using a higher magnitude of eddy viscosity and depth-penetration factor. (c, d) Corresponding salinity solutions. 318 T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319

estuary of rectangular cross section. The tide-averaged longitudinal MacCready (2004) in combination with the constant Km cubic velocity solution, also referred to here as the “variable Km solu- velocity profile to develop the quintic profile for salinity. Following tion,” is expressed by: the treatment used by MacCready (2004), but with the exponen- tially varying Ks assumption of Equation (A8), the salt balance z C1 ea $ðaz þ 1Þ formulation may be written as: uðzÞ¼ $ Kmo a2 ! v vs0 2 ðzÞ ¼ a$ 0ðzÞ; U z z 2z 2 Ks u (A11) $e a þ þ þ C3; (A10) vz vz Kmo a a2 a3 where a ¼ H2$ðvs=vxÞ, u0 ¼½uðzÞu, and u(z) is taken from where Equation (A10). The integration of Equation (16) was completed using the boundary conditions that there is no salt exchange across the free-surface boundary, i.e., vs0=vz ¼ 0atz ¼ 0 and the depth 1 2 2 R D ¼ þ ; average of s0 ¼ 0, or ð 0 s0ðzÞdz ¼ 0Þ. The variable Ks solution for a a2 a3 1 the depth-varying component of salinity is formulated by: ( a a$ð Þ e 1 e 1 a 1 a 2 a 2azð z þ Þ U I ¼ ; I ¼ ; I ¼ e $D ; 0 C1 e 2a 5 2az 1 2 2 3 3 s ðzÞ¼ $ e a a a d$Kmo Kmo 4a4 2$Kmo ! ! 2 I3 2$I2 2$I1 a$I2 þ I1 1 z 2z 2 2 J1 ¼ þ þ ; J2 ¼ ; þ þ þ ðaz þ 2Þ a a2 a3 a2 a2 2a 4a2 8a3 a5 ) z z ea ðaz þ 1Þ ea ðC3 uÞ $ D1 þ D2 (A12) U 2 u$Kmo $ðD$ea J Þ a a 2 1 C1 ¼ ; ea$ð1 aÞ where J 2 aa e2a 1 e2a$ð1 2aÞ1 U$D$ea C eað1 aÞ M ¼ ; M ¼ ; C3 ¼ 1 $ : 1 2a 2 4a2 2$Kmo Kmo a2 2a 1 2 2 2 M3 ¼ e þ ; Note that in the Equation (A10) and subsequent developments 2a 4a2 8a3 8a3 (shown below), it is understood that u, and s are functions of (x, z), z a 3$U 2$C1 vs=vx and constants of integration with respect to , (C1, C2, and C3) D1 ¼ þ ; and d$ $ 4 $ 3 are applicable only for a specific location (xo). In the above equa- Kmo Kmo a Kmo a tions, the variation of Km in the vertical is governed by the value of a C1 ð2aM þ 5M Þ U the depth-penetration factor, a. D2 ¼ $ 2 1 þ $ d$ 4 $ Longitudinal velocity u(z) per equation (A10) is a function of Kmo Kmo 4a 2 Kmo physical parametersddepth-averaged velocity u ¼ Q =ðH$WÞ and r 1 M 2M 2M 2 depth-averaged longitudinal salinity gradient vs=vx. The solution 3 þ 2 þ 1 þ ðaM þ 2M Þ a2 2a 4a2 8a3 a5 2 1 also depends on model parameters eddy viscosity Km and depth- penetration coefficient “a”. For small magnitudes of a (jaj0.01), ðaI þI1Þ I þðC3 uÞ $ 2 þ 1D1: (A13) Km is nearly constant with respect to z, and the solution reduces to a2 a that provided by MacCready (2004). Fig. A1(a) shows the analytical solution of the longitudinal velocity per Equation (A10) using a small Salinity profiles are then computed using the definition: value of a ¼0.01. A corresponding constant Km solution for sðzÞ¼s0ðzÞþs and the assumption that, at the seabed ðz ¼1Þ, partially mixed estuaries is also plotted in terms of u and exchange salinity may be assumed equal to ocean salinity (i.e.,sð1Þ¼socn). b 3 flow velocity UE ¼ðg$ =KmÞðvs=vxÞðH =48Þ as presented by Typical profiles of salinity for a partially mixed estuary are shown in MacCready (2004, 2007). This is also recognized as the classic cubic Fig. A1(c). For a small value of the depth-penetration factor profile of Hansen and Rattray (1965). It is noted that exchange flow is (a ¼0.01), the solution reduces to the classic quintic profile related to U in the variable Km formulation. For typical conditions (Hansen and Rattray,1965; MacCready, 2004). Fig. A1(d) shows that encountered in partially mixed and deep, narrow estuaries, the ratio Equation (A13) may be used to generate the shallow brackish layer ðu=UEÞ1 results in a fixed-profile shape such that inflowing at the surface matching the classic fjordal circulation description current always occurs at a constant depth, z ¼ 0.75. This limits the (e.g., Rattray, 1967), using a higher magnitude of depth-penetration use of the constant Km solution to typical fjords, where peak inflow factor in the variable Km solution. may occur much higher in the water column. Fig. A1(b) shows aprofile that matches the classic fjordal circulation description (e.g., Rattray, 1967), where the main circulation is restricted to a strong References outflow in the upper layer with an inflow immediately below the pycnocline. This was obtained using a higher magnitude of depth- Aoki, K., Isobe, A., 2007. Application of finite volume coastal ocean model to penetration factor in the variable Km solutiondEquation (A10). hindcasting the wind-induced sea-level variation in Fukuoka Bay. Journal of Oceanography 63 (2), 333e339. Pritchard (1954, 1956) showed tidally averaged salt conserva- Babson, A.L., Kawase, M., MacCready, P., 2006. Seasonal and interannual variability tion for coastal and partially mixed estuaries is dominated by in the circulation of Puget Sound, Washington: a box model study. Atmosphere- e the balance between advective shear and vertical diffusion. This Ocean 44 (1), 29 45. Cannon, G.A., 1983. An overview of circulation in the Puget Sound estuarine system. formulation was used by Hansen and Rattray (1965) and NOAA Technical Memorandum ERL PMEL-48. T. Khangaonkar et al. / Estuarine, Coastal and Shelf Science 93 (2011) 305e319 319

Chen, C., Liu, H., Beardsley, R.C., 2003. An unstructured, finite-volume, three- Large, W.G., Pond, S., 1981. Open ocean momentum flux measurements in moderate dimensional, primitive equation ocean model: application to coastal ocean and to strong winds. Journal of Physical Oceanography 11 (3), 324e336. estuaries. Journal of Atmospheric and Oceanic Technology 20, 159e186. Lavelle, J.W., Cokelet, E.D., Cannon, G.A., 1991. A model study of density intrusions Chen, C., Rawson,M., 2005. Anecosystem managementmodelsystem fortheSatilla River into and circulation within a deep, Silled Estuary: Puget Sound. Journal of Estuary, Georgia. In: Oceans, 2005 Proceedings of MTS/IEEE, vol. 1, pp. 622e632. Geophysical Research-Oceans 96 (C9), 16779e16800. Chen, C., Xue, P., Ding, P., Beardsley, R.C., Xu, Q., Mao, X., Gao, G., Qi, J., Li, C., Lin, H., Li, M., Gargett, A., Denman, K., 1999. Seasonal and interannual variability of estu- Cowles, G., Shi, M., 2008. Physical mechanisms for the offshore detachment of arine circulation in a box model of the Strait of Georgia and Juan de Fuca Strait. the Chanjiang diluted water in the East China Sea. Journal of Geophysical Atmosphere-Ocean 37 (1), 1e19. Research 113 (C02002). doi:10.1029/2006JC003994. MacCready, P., 2004. Toward a unified theory of tidally-averaged estuarine salinity Cokelet, E.D., Stewart, R.J., Ebbesmeyer, C.C., 1990. The Annual Mean Transport in structure. Estuaries 27 (4), 561e570. Puget Sound. NOAA Technical Memorandum ERL PMEL-92. Pacific Marine MacCready, P., 2007. Estuarine adjustment. Journal of Physical Oceanography 37, Environmental Laboratory, Seattle, Washington. 2133e2145. Cox, J.M., Ebbesmeyer, C.C., Coomes, C.A., Hinchey, L.R., Helseth, J.M., Cannon, G.A., Mellor, G.L., Ezer, T., Oey, L.-Y., 1994. The pressure gradient conundrum of sigma Barnes, C.A., 1981. Index to observations of currents in Puget Sound, Wash- coordinate ocean models. Journal of Atmospheric and Oceanic Technology 11 ington from 1908 to 1980. NOAA Technical Memorandum, OMPA-5, pp. 51. (4), 1126e1134. Cox, J.M., Ebbesmeyer, C.C., Coomes, C.A., Helseth, J.M., Hinchey, L.R., Cannon, G.A., Mellor, G.L., Yamada, T., 1982. Development of a turbulence closure model for Barnes, C.A., 1984. Synthesis of current measurements of Puget Sound, Wash- geophysical fluid problems. Reviews of Geophysics 20 (4), 851e875. ington. Index of Current Measurements Made in Puget Sound from 1908e1980 Nairn, B.J., Kawase, M., 2002. Comparison of observed circulation patterns and with Daily and Record Averages for Selected Measurements, vol. I. NOAA numerical model predictions in Puget Sound, WA. In: Droscher, T. (Ed.), Technical Memorandum, NOS OMS 3, pp. 38. Proceedings 2001 Puget Sound Research Conference. Puget Sound Water Dyer, K.R., 1973. Estuaries: A Physical Introduction. John Wiley, New York, N.Y., pp. 140. Quality Action Team, Olympia, Washington, p. 9. Ebbesmeyer, C.C., Barnes, C.A.,1980. Control of a fjord basin’s dynamics by tidal mixing Newton, J.A., Van Voorhis, K., 2002. Seasonal Patterns and Controlling Factors of in embracing sill zones. Estuarine and Coastal Marine Science 11, 311e330. Primary Production in Puget Sound’s Central Basin and Possession Sound. Ebbesmeyer, C.C., Coomes, C.A., Cox, J.M., Helseth, J.M., Hinchey, L.R., Cannon, Publication # 02-03-059, Washington State Department of Ecology, Lacey. G.A., Barnes, C.A., 1984. Synthesis of current measurements in Puget Sound, Pritchard, D.W., 1952. Estuarine hydrography. In: Landsberg, H.E. (Ed.), Advances in Washington. Circulation in Puget Sound: An Interpretation Based on Geophysics, vol. 1. Academic Press, New York, N.Y., pp. 243e280. Historical Records of Currents, vol. 3. NOAA Technical Memorandum. NOS Pritchard, D.W., 1954. A study of the salt balance in a coastal plain estuary. Journal OMS 5, pp. 73. of Marine Research 13 (1), 133e144. Finlayson, D.P., 2005. Combined Bathymetry and Topography of the Puget Lowland, Pritchard, D.W., 1956. The dynamic structure of a coastal plain estuary. Journal of Washington State. University of Washington. Available from: http://www. Marine Research 15 (1), 33e42. ocean.washington.edu/data/pugetsound/. Rattray Jr., M., Lincoln, J.H., 1955. Operating characteristics of an oceanographic Flater, D., 1996. A brief introduction to XTide. Linux Journal 32, 51e57. model of Puget Sound. Transactions, American Geophysical Union 36 (2). Foreman, M.G.G., Czajko, P., Stucchi, D.J., Guo, M., 2009. A finite volume model simu- Rattray Jr., M., 1967. Some aspects of the dynamics of circulation in fjords. In: lation for the Broughton Archipelago, Canada. Ocean Modelling 30 (1), 29e47. Lauff, G.H. (Ed.), Estuaries, vol. 83. America Association for the Advancement of Friebertshauser, M.A., Duxbury, A.C., 1972. A water budget study of Puget Sound and Science Publication, pp. 52e62. its subregions. Limnology and Oceanography 17 (2), 237e247. Smagorinsky, J., 1963. General circulation experiments with the primitive equations. Geyer, W.R., Cannon, G.A., 1982. Sill processes related to deep water renewal in I. The basic experiment. Monthly Weather Review 91 (3), 99e164. a fjord. Journal of Geophysical Research 87 (C10), 7985e7996. Weisberg, R.H., Zheng, L.Y., 2006. Circulation of Tampa Bay driven by buoyancy, Hamilton, P., Gunn, J.T., Cannon, G.A., June 1985. A box model of Puget Sound. tides, and winds, as simulated using a finite volume coastal ocean model. Estuarine, Coastal and Shelf Science 20 (6), 673e692. Journal of Geophysical Research 111 (C01005). doi:10.1029/2005JC003067. Hansen, D.V., Rattray, M., 1965. Gravitational circulation in straits and estuaries. Winter, D.F., 1973. A similarity solution for steady-state gravitational circulation in Journal of Marine Research 2, 104e122. fjords. Estuarine and Coastal Marine Science 1, 387e400. Harrison, P.J., Mackas, D.L., Frost, B.W., MacDonald, R.W., Crecelius, E.A., 1994. An Winter, D.F., Banse, K., Anderson, G.C., 1975. The dynamics of phytoplankton blooms assessment of nutrients, plankton, and some pollutants in the water column of in Puget Sound, a fjord in the northwestern United States. Marine Biology 29, Juan de Fuca Strait, Strait of Georgia and Puget Sound, and their transboundary 139e176. transport. In: Wilson, R.C.H., Beamish, R.J., Airkens, F., Bell, J. (Eds.), Review of Yang, Z., Khangaonkar, T., 2009. Modeling tidal circulation and stratification in the Marine Environment and Biota of Strait of Georgia, Puget Sound, and Juan Skagit River estuary using an unstructured grid ocean model. Ocean Modelling de Fuca Strait: Proceedings of the BC/Washington Symposium on the Marine 28 (1e3), 34e49. Environment, Jan 13 and 14, 1994. Can Tech Rep Fish Aquat Sci, pp. 138e172. Yang, Z., Khangaonkar, T., 2010. Multi-scale modeling of Puget Sound using an Holbrook, J.R., Muench, R.D., Kachel, D.G., Wright, C., 1980. Circulation in the Strait unstructured-grid coastal ocean model: from tide flats to estuaries and coastal of Juan de Fuca: recent oceanographic observations in the Eastern Basin. NOAA waters. Ocean Dynamics 60 (6), 1621e1637. Technical Report ERL 412-PMEL 33. Yang, Z., Khangaonkar, T., Calvi, M., Nelson, K., 2010a. Simulation of cumulative Isobe, A., Beardsley, R.C., 2006. An estimate of the cross-frontal transport at the effects of nearshore restoration projects on estuarine hydrodynamics. Ecolog- shelf break of the East China Sea with the finite volume coastal ocean model. ical Modelling 221 (7), 969e977. Journal of Geophysical Research 111 (C03012). doi:10.1029/2005JC003290. Yang, Z., Sobocinski, K., Heatwole, D., Khangaonkar, T., Thom, R., Fuller, R., 2010b. Jay, D.A., Smith, J.D., 1990a. Residual circulation in shallow estuaries. 1: Highly Hydrodynamic and ecological assessment of nearshore restoration: a modeling stratified, narrow estuaries. Journal of Geophysical Research 95, 711e731. study. Ecological Modelling 221 (7), 1043e1053. Jay, D.A., Smith, J.D., 1990b. Residual circulation in shallow estuaries. 2: Weakly Zhao, L., Chen, C., Cowles, G., 2006. Tidal flushing and eddy shedding in Mount stratified and partially mixed, narrow estuaries. Journal of Geophysical Hope Bay and Narragansett Bay: an application of FVCOM. Journal of Research 95, 733e748. Geophysical Research 111 (C10015). doi:10.1029/2005JC003135. Khangaonkar, T., Yang, Z., 2011. A high resolution hydrodynamic model of Puget Zheng, L., Chen, C., Liu, H., 2003. A modeling study of the Satilla river Estuary, Sound to support nearshore restoration feasibility analysis and design. Georgia. Part I: flooding/drying process and water exchange over the salt Ecological Restoration 29 (1e2), 173e184. marsheestuaryeshelf complex. Estuaries 26 (3), 651e669.