Contrasting Seasonal and Fortnightly Variations in the Circulation of a ...

Estuaries and Coasts DOI 10.1007/s12237-012-9548-1

Contrasting Seasonal and Fortnightly Variations in the Circulation of a Seasonally Inverse Estuary, Elkhorn Slough, California Nicholas J. Nidzieko · Stephen G. Monismith

Received: 23 March 2012 / Revised: 23 July 2012 / Accepted: 28 July 2012 © Coastal and Estuarine Research Federation 2012

Abstract Three and a half years of hydrographic, velocity, and meteorological observations are used to examine the dynamics of upper Elkhorn Slough, a seasonally inverse, shallow, mesotidal estuary in central California. The long-term observations revealed that residual circulation in Elkhorn Slough is seasonally variable, with classic estuarine circulation in the winter and inverse estuarine circulation in the summer. The strength of this exchange flow varied both within years and between years, driven by the annual cycle of dry summers and wet winters. Subtidal circulation is a combination of both tidal and density-driven mechanisms. The subtidal magnitude and reversal of the exchange flows is controlled primarily by the density gradient despite the significant tidal energy. As the density gradient weakens, the underlying tidal processes generate vertically sheared exchange flows with the same sign as that expected for an inverse density gradient. The inverse density gradient may then further strengthen this inverse circulation. These data were collected as part of the Land/Ocean Biogeochemical Observatory and demonstrate the utility of long-term in situ measurements in a coastal system, as consideration of such

N. Nidzieko (B) Horn Point Laboratory, University of Maryland Center for Environmental Science, 2020 Horns Point Road, Cambridge, MD 21613, USA e-mail: [email protected] S. Monismith Environmental Fluid Mechanics Laboratory, Stanford University, 450 Serra Mall, Stanford, CA, USA

a wide range of forcing conditions would not have been possible with a less comprehensive data set. Keywords Low-inflow estuary · Inverse estuary · Negative estuary · Hypersalinity · Residual circulation · Elkhorn Slough, California

Introduction Elkhorn Slough is a seasonally inverse, shallow, mesotidal estuary in central California (Fig. 1a). From January 2005 to June 2008, we observed that subtidal circulation (tidally averaged velocity) in upper Elkhorn Slough varied seasonally, in concert with the reversal of the along-estuary density gradient (Fig. 2). Wet winters produced subtidal circulation in the main channel that was seaward at the surface and landward near the bed– the same as expected for classic estuarine circulation (e.g., Pritchard 1952). In the summer, evaporation exceeded precipitation and inflows. The negative water balance lead to the formation of hypersalinity and then an inverse estuary with subtidal circulation that was the opposite of winter. Flows were seaward and landward, near the bed and surface, respectively–an inverse estuarine circulation (Stommel 1961; Nunes Vaz et al. 1990; Hearn 1998; Largier 2010). The direction and magnitude of the depth-averaged flow in the channel and over the shoals also changed seasonally. Observations of these density transitions are few (Largier et al. 1997), and we know of no detailed observations of subtidal circulation throughout such a range of conditions. Field studies of estuarine dynamics are typically limited from weeks to a few months, and the extended duration of our observations allows insight into the momentum

Estuaries and Coasts

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Fig. 1 a Map of Elkhorn Slough and vicinity. Locations of LOBO moorings with (black diamond) and without (white diamond) ADCPs. Meteorological data were obtained from Moss Landing Marine Laboratories, indicated with arrow. b Bathymetry of

upper Elkhorn Slough showing location of LOBO mooring L02 (white circle) and lateral shoal deployment (white square). c Cross-section at L02, including position of moorings. Crosssection is depicted looking west, i.e., from Kirby Park

balance and circulation over a broad range of fortnightly tidal and seasonal hydrographic conditions. The purpose of this paper is to examine how the dynamics vary over such a multidimensional parameter space. In the following section, we provide a short overview of the relevant physics. In “Field Site and Methods” we describe in detail the field site, data collection, and analysis methods. An Appendix gives specific attention to difficulties encountered with long-term observational data quality in the estuarine environment. Observations of the circulation reversal in response to changing hydrography are presented in “Seasonal Changes in Estuarine Exchange Flows”. These observations are presented in a tidal phase-averaged framework in “Tidal Phase-Averaged Dynamics”. Utilizing the long data set, these tidal-

phase averages are binned based on spring-neap and hydrographic conditions in order to assess tidal and seasonal variability, respectively. Finally, the observations are aggregated as subtidal quantities in “Subtidal Momentum Balance”. While there is a pronounced spring-neap modulation in subtidal circulation, the modal velocities varied most significantly with the axial density gradient, as the spring-neap tidal modulation also affected the magnitude of the density gradient.

The Tidally Averaged Momentum Balance Any mechanism that alters the cross-sectional structure of axial currents asymmetrically with respect to

Estuaries and Coasts Fig. 2 Hourly hydrographic, velocity, and meteorological observations from Elkhorn Slough. a Daily precipitation (black bars) and cumulative rain year totals (shaded gray). b salinity, temperature and density at LOBO mooring L02. c Stratification at L02. d Subfortnightly filtered depth-averaged velocity (blue) and vertical shear (red) in the main channel and on shoal (green). Subfortnightly filtered mid-water column vertical velocity (thick purple). Subfortnightly filtered along-channel density gradient at L02 (shaded). e Hourly water level, relative to MLLW. f Along-channel (285◦ ) wind velocity component, from MLML roof-top station

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tidal phase contributes to subtidal circulation (Jay 1991; Monismith and Fong 1996). In the absence of density gradients, subtidal circulation is created by tidal currents interacting with bathymetry. Nonlinearities in the momentum and continuity equations (Zimmerman 1978; Ianniello 1979) include non-zero tidal-mean correlations between sea-surface height and velocity (i.e., Stokes velocity, Longuet-Higgins 1969), tidal-mean sea-surface gradients (balancing the Stokes velocity, see e.g., Uncles and Jordan 1980), and advective nonlinearities/asymmetries caused by spatially variable Eulerian tidal velocities (Zimmerman 1979). The magnitude and direction of these components are dependent on the length of the estuary and lateral variations in depth (Li and O’Donnell 2005). Axial density gradients can also produce subtidal exchange flow. In the classic example, a steady gravitational circulation is driven by an axial density gradient balanced by a vertical momentum flux (Pritchard 1956; Hansen and Rattray 1965). The notion of the steadiness of this circulation has eroded into a more

complex understanding of baroclinic subtidal circulation caused by several mechanisms that produce tidally symmetric momentum fluxes. The now classic example is strain-induced periodic stratification (Simpson et al. 1990): straining of an axial density gradient by vertically sheared ebb-tide currents leads to stratification and the suppression of vertical turbulent momentum flux, while flood-tide currents result in a destabilized water column and enhanced vertical mixing and momentum transport (Nunes Vaz et al. 1989; Stacey et al. 2001). For example, Burchard and Hetland (2010) found in a vertical onedimensional numerical study that tidal straining contributed approximately two-thirds of the time-averaged circulation compared to a one-third contribution from the steady baroclinic pressure gradient. The lateral transport of momentum has also been recognized as an important contributor of tidally asymmetric momentum fluxes. Lateral straining of the axial density gradient coupled to a lateral transport mechanism can suppress turbulence in the water column, resulting in an altered turbulent momentum flux (Scully


and Friedrichs 2007; Stacey et al. 2008). Likewise, lateral redistribution of along-channel momentum in the cross section with tidal-phase dependency can reinforce estuarine circulation (Lacy and Monismith 2001; Lerczak and Geyer 2004; Scully et al. 2009). In addition to vertically sheared exchange flows, cross-sectional bathymetric variability leads to laterally sheared exchange in frictional and/or wide estuaries (e.g., Valle-Levinson et al. 2009). Lateral asymmetries in depth shift vertical two-layer gravitational circulation horizontally, such that the baroclinic seaward-directed surface flow occurs over the shoals (Valle-Levinson et al. 2003). This is typically reinforced by barotropic flow in a short estuary, where depth-averaged subtidal currents tend to be landward in the channel and seaward over the shoal due primarily to depthdependent phase differences between velocity and seasurface height (Li and O’Donnell 2005). This has been observed in weakly stratified inverse or seasonally inverse estuaries, where weak along-channel density gradients increase the importance of barotropic phenomena (Winant and de Velasco 2003). In light of the observed seasonal changes in circulation in Elkhorn Slough (Fig. 2), we wish to quantify how the physics changes through the year, and so will consider how the relative contribution of the terms in the momentum balance vary. The analyses are based on the depth- and tidally averaged along-channel momentum balance (Stacey et al. 2010): ∂η ∂ g ∂ρ H ∂ 0 = −g − − [uu] H − [uv] H ∂x ρ0 ∂ x 2 ∂x ∂y ∂ u∗ |u∗ | τsurf ηu∗ |u∗ | − [uw] H − − − (1) ∂z H ρH H2 The variables are as follows: η is sea-surface elevation; g is gravity; u, v, and w are axial (along-channel), lateral (across-channel), and vertical velocities relative to an xyz-coordinate system, respectively, with x positive upstream and z positive above mean lower-low water (MLLW) H is total depth relative to the variable sea surface; ρ is density, with reference density ρ0 = 1,000 kg m−3 ; and the bottom stress τbed is represented as u∗ |u∗ | = τbed /ρ. Angle brackets indicate a tidal average, and the square brackets around the advective terms indicate an average over depth H. We assume that unsteadiness and Coriolis are negligible in this narrow, frictional estuary (Valle-Levinson 2008). The first term in Eq. 1 is the sea-surface setup, which balances the Stokes transport (Uncles and Jordan 1980). The second term is the depth-averaged baroclinic pressure gradient. The third through fifth terms are, respectively, axial, lateral, and vertical mo-

mentum advection. The sixth and seventh terms are the result of the depth-integration of vertical stress divergence; the former is the approximation of the bottom stress and the latter arises because the surface stress is applied to a tidally variable elevation that produces the correlation with η. Within Eq. 1, it is easy to measure or reasonably estimate a number of terms with the field observations, including both pressure gradients and the bottom and surface stresses. As described in the Appendix, the uncertainty in the velocity observations precludes calculating the advective acceleration terms. Winant and de Velasco (2003) estimated the axial advective term −u2 /L, where L is the distance to the head of the estuary, though subsequent studies have neglected this term based on scaling arguments (e.g., Lerczak and Geyer 2004; Scully et al. 2009). We consider this method and present several calculations in order to constrain the interpretation of our field measurements. The basic approach is to bin observations according to individual tidal cycle, starting from lower-low water (LLW), according to the spring-neap cycle and axial density gradient. Most of the terms have large tidal variance relative to the mean (tidal average), and so it is necessary to first consider the tidal dynamics prior to discussing the time-averaged results.

Field Site and Methods Elkhorn Slough is located in the center of the Monterey Bay coastline, in Moss Landing, California (Fig. 1a). The main channel extends 10 km inland, has a mean depth of 3.5 m relative to MLLW, and is ∼100 m wide. Narrow, lower-subtidal mudflats and wide, upper-intertidal salt marsh border the main channel (cf. Caffrey et al. 2002); the mean width of the estuary including the intertidal is ∼300 m. Tides in Elkhorn Slough are mixed, mainly semidiurnal, with a mean diurnal range of 1.63 m; the duration asymmetry in the rise and fall of the astronomical tide has a skewness of −0.1 (Nidzieko 2010), indicating shorter duration of falling water. Tidal currents in the main channel are O(50 − 100 cm s−1 ), with currents and water elevation close to quadrature. The tidal excursion distance along the main channel is O(5 km); the section of main channel immediately north of Parson’s Slough is roughly one tidal excursion from the estuary entrance, and so delineates Elkhorn Slough into upper and lower sections. The focus of this paper is upper Elkhorn Slough (Fig. 1b), where the flushing time is long enough for hypersalinity and an inverse estuary to form. The lower


slough is more marine in character with shorter flushing times. There is a significant spring-neap modulation in both tidal range and diurnal inequality, and consequently velocity magnitude in upper Elkhorn Slough varies with the spring-neap cycle. Root-mean-square tidal velocities ranged from 0.14 to 0.22 m s−1 between neap and spring tides, respectively; typical peak current magnitudes doubled from 0.25 to 0.5 m s−1 (not shown). On average, the velocity skew of the depth-averaged velocities was −0.66, reflecting a mean ebb-dominance in tidal currents (Nidzieko and Ralston 2011). Data Collection Hourly observations of hydrography and currents were obtained with the Land/Ocean Biogeochemical Observatory (LOBO; Fig. 1a, Johnson et al. 2007; Jannasch et al. 2008). Mooring L02, near Kirby Park, was located near 36◦ 50 27.2 N, 121◦ 44 51.7 W, 6.9 km alongchannel from the ocean with an elevation of −1.9 m MLLW; temperature and salinity were measured at 0.4 and 1.2 m depth at hourly intervals. This mooring was in place for the duration of the study, with the exception of the period from September 18 to October 5, 2006, when the buoy was removed for maintenance. Upon redeployment, the mooring was repositioned roughly 20 m northwestward of the given coordinates. Water column velocity measurements in the main channel were made using a bottom-mounted, upwardlooking, Teledyne RD Instruments 1,200-kHz acoustic Doppler current profiler (ADCP). The ADCP was configured to sample 0.25-m bins 45 times over 2 min, at which time ensemble-averaged water column data were stored. The exception to this was from February to June 2005 when 0.5 m vertical bins were used. The 2-min ensemble profiles were averaged into 10-min ensembles then subsampled to hourly intervals for comparison with LOBO hydrographic data. Two-minute ensembles had a standard deviation of 1.9 cm s−1 (PlanADCP v.2.02 Teledyne RD Instruments 2006); the hourly 10-min-averaged ensembles (n = 5 observations) used √ in the analyses have a standard error of s.d./ n = 0.85 cm s−1 . ADCPs were colocated with LOBO moorings L01 and L02 from February 2005 to June 2008. East–north velocities were rotated into axial (u) and lateral (v) coordinates based on tidal ellipse orientations derived for each sub-deployment (described in the Appendix). For each ensemble, the horizontal velocity profiles were extended to the surface and a near-bed reference location z0 assuming a log-linear relationship; vertical velocities were assumed to have zero velocity at z0 and a surface velocity equal to the rate of free surface

displacement. The extrapolation was generally over the upper 25 cm and lower meter of the water column. The extrapolated velocity profiles were adjusted to a nondimensional vertical coordinate z = z/H, where H is the total water column depth, over bins of z from 0.05 to 0.95 at intervals of 0.05. These adjusted profiles were used in the calculation of upper and lower water column velocities, as well as for modal analysis and interpolation across service data gaps. Subtidal velocities were computed as lunar day averages between times of LLW, described below, while subfortnightly time series were computed using a running mean over 14.75 days. Meteorological data were collected from a weather station located on the roof of Moss Landing Marine Laboratories (MLML), elevation 12.2 m (http:// weathernew.mlml.calstate.edu/). Deployment of an anemometer at L02 in 2007 found good agreement between that site and the MLML station. Analysis Methods Scalar along-channel gradients were computed using the transformation ∂ρ dρ ρ ≈ ≈− , ∂x dx ut

where the tidal excursion is estimated as − u t summed up between slack tides and ρ is the difference between slack tide values of density. This minimizes measurement errors due to fouling by relying on a single sensor for the calculation and the calculated gradient is effectively centered on the mooring location. This transformation assumes that the rate of change of the gradient is slower than the tidal frequency, a reasonable assumption in Elkhorn Slough except perhaps during intense storm events, which were infrequent. Comparisons of circulation and hydrographic structure are based on the sign of the density gradient and the spring-neap fortnightly tidal cycle. Using an alongchannel x-axis positive landward, horizontal density gradients that are negative (∂ρ/∂ x < 0) are referred to as classic, and we use the term inverse to denote ∂ρ/∂ x > 0 (Pritchard 1952). Hypersalinity refers to ∂ S/∂ x > 0 (Largier 2010). The fortnightly change in tidal asymmetry was used as a quantitative proxy for spring-neap tide ranges. Spring tides along this section of the California coast are characterized by a significant diurnal inequality that largely vanishes during neap tides. The phasing between the diurnal and semidiurnal constituents that produces the diurnal inequality results in an asymmetry in the duration of rising and falling water over a lunar day. This asymmetry can be quantified by computing


the daily skewness of the water level time derivative, γ0 (Nidzieko 2010). In Elkhorn Slough, large spring tides with a great diurnal inequality are negatively skewed, while neap tides are roughly symmetric and have little diurnal inequality and so have little to no skewness. The duration asymmetry (third moment of the time derivative) was normalized by the variance of the entire data set to the 3/2 power in order to preserve magnitude information (Nidzieko and Ralston 2011). Consequently, γ0 exceeds the range −1 to 1. Estimates of the shear velocity, u∗ , were made by fitting a log profile to the velocity profile as u∗ z ln (2) u(z) = κ z0 where κ = 0.4. Owing to the the near-surface velocity gradient reversal, the regression only included observations up to the first zero crossing of d2 u/dz2 ; 92 % of the hourly observations had an R2 fit of better than 0.95. A roughness scale of z0 = 0.01 m was assumed based on previous turbulence measurements near this site (Monismith et al. 2005). The barotropic pressure gradient was computed as a finite difference between L02 and L01 (with x = 6.9 km). As described in the Appendix, water level records were comprised of tidal harmonics and subtidal water level observations. Differencing the two water level records revealed uncorrectable nonlinear trends that were clearly associated with mooring placement and recovery, including discrete baseline shifts at times of mooring replacement and long-term trends indicating gradual settling of the mooring anchor into the soft substrate. While these small shifts have a negligible effect on the tidal dynamics, they were unsuitable for computing the subtidal difference between the two stations. Thus, our estimate of the barotropic pressure gradient is based solely on predicted tidal records from the two stations, including fortnightly and semiannual constituents. The observed water level difference between the two stations and the difference between the predicted tides only erred significantly for the largest spring tides, suggesting that there were increased nonlinearities during this period that the harmonic analysis was poorly suited to account for. We have high confidence in the estimated barotropic pressure gradient using the predicted water levels alone, however, because of the good linear relationship with the calculated shear velocity (R2 = 0.79). While there is uncertainty associated with fitting of u∗ from observations, we expect a general pressure gradient/friction balance for a shallow, mesotidal estuary, and the friction estimate provides an independent test for the quality of the barotropic pressure gradient estimate.

We estimated axial momentum advection following Winant and de Velasco (2003) as ∂/∂ x(uu) ≈ −u2 /L. Following Stacey et al. (2010), we estimated ∂/∂ y(uv) by assuming zero velocity at the bank. ∂/∂z(uw) was calculated directly from the ADCP data. Each of these terms was computed at z and then depth-averaged. The lateral and vertical advective terms were prone to errors as a result of horizontal ADCP placement (described in the Appendix) and can only be interpreted qualitatively. Empirical orthogonal functions (EOF; Emery and Thomson 2001) were extracted from the depthnormalized axial velocity profiles using a 2-year period from June 22, 2005 to September 25, 2007, as this was the period with the best data quality. In the analysis, we normalized each mode shape by its maximum absolute value, so that the modal structures span the range −1 to 1; the amplitude time series were multiplied by this normalizing value, so that they are amplitude time series with units of m s−1 in order to facilitate comparison between modes. Finally, because the tidally averaged momentum equation (Eq. 1) contains several terms with large tidal variance compared to the mean, it is necessary to include tidal-scale observations when considering subtidal dynamics. To examine such a large data set at multiple time scales, we first extracted lunar day observations between successive times of LLW according to discrete bins of the along-channel density gradient and diurnal inequality (quantified through skewness γ0 ). These observations, which cover the same time span as the EOF analysis, were tidal phase-averaged according to hour after LLW.

Seasonal Changes in Estuarine Exchange Flows Hydrography The Mediterranean climate cycle—warm, dry summers and cool, wet winters—dictated hydrographic conditions in Elkhorn Slough (Fig. 2a–c). Rainfall totals for rain years 2007 and 2008 (from October to September) were roughly half the 50-cm annual average for the Monterey Bay region (Renard 2006). Consequently, the winters of 2006–2007 and 2007–2008 had much higher minimum salinity than the previous two winters, and salinity in the slough returned to oceanic levels (S0 ≈ 33.5) much earlier in spring (Fig. 2b, blue trace). At the event scale, salinity responded rapidly to precipitation in the rainy season, whereas water temperature tended to follow the annual solar cycle and was


less susceptible to storm events. The upper slough was nearly fresh after the largest rainfall events and hypersaline in the dry season. Stratification (Fig. 2c) was weak during the dry season and varied in strength during the rainy season in response to precipitation events. Both salinity and temperature had regular spring-neap variability, with hypersalinity (S > 33.5) and temperature increasing during neap tides in summer. Elkhorn Slough is a classic estuary in the wet season and an inverse estuary late in the dry season (filled trace in Fig. 2d), with water density in upper Elkhorn Slough greater than Monterey Bay for most of the summer and autumn months. The transition from an inverse estuary to a classic estuary was fast, driven by the sudden influx of freshwater runoff and precipitation, whereas the transition to an inverse estuary was gradual. Hypersalinity formed over a time period of weeks; however, the effect on the density gradient was offset by increases in temperature. Cooling later in the summer lead to the strongest inverse estuarine conditions. The magnitude of the density gradient increased during neap tides when along-channel exchange due to tidal stirring was reduced. Although the strength of the inverse density gradient was weak relative to classic winter conditions (+0.5 kg m−3 km−1 compared to −3 kg m−3 km−1 ), the reversal is important because it could alter the consequences of vertical and lateral tidal straining of the axial density gradient.

sented in the next section). Mid-water column vertical velocities also showed a seasonal pattern, increasing in response to stronger buoyancy forcing. The velocity observations are generally consistent with expectations based on theory. The depth-averaged subtidal channel velocity was significantly muted during the summer months, the result of competing barotropic and baroclinic mechanisms, while shoal velocities were directed seaward during classic conditions and landward during inverse conditions. For barotropic flow in a short estuary, depth-averaged subtidal currents should be landward in the channel and seaward over the shoal (Li and O’Donnell 2005); this is roughly what we observed in classic conditions (∂ρ/∂ x < 0). This pattern was clearly affected, however, by the sign and strength of the density gradient. In classic conditions, the baroclinic seaward-directed surface flow should occur over the shoals (Valle-Levinson et al. 2003) and so for ∂ρ/∂ x < 0, baroclinicity should augment barotropic circulation; an inverse density gradient (∂ρ/∂ x > 0), by contrast, should compete with barotropic circulation (in the laterally sheared sense). To examine the interaction between these competing forces, we decomposed the time-varying spatial structure using empirical orthogonal functions and then binned and averaged the observations according to tidal and density conditions, as described in “Field Site and Methods”. Circulation Modes

Circulation Subtidal velocities at L02 varied inter-annually in response to changing hydrography (Fig. 2d). In the main channel, Eulerian subtidal flow was predominantly landward at all depths (only the depth-average is shown in Fig. 2d, blue line), but modulated in strength seasonally, with stronger currents coinciding with a stronger axial density gradient. This seasonality is also evident in the subtidal vertical shear (red trace in Fig. 2d). Vertical shear (computed here as a difference between the upper and lower halves of the water column) was strongest in the rainy season, with velocities directed seaward and landward in the upper and lower water column, respectively. These velocities reversed direction in the dry season, though the overall magnitude of this top–bottom residual shear was reduced. Additionally, subtidal depth-averaged velocity on the shoal also changed seasonally (green trace in Fig. 2d): it was landward in the dry season, seaward in the wet season, and was more sensitive to spring-neap fluctuations than the main channel (evident in the modal velocities pre-

There are two principal velocity modes in the xz plane of the main channel: the first mode describes a logarithmic velocity profile, the second mode describes a vertically sheared two-layer exchange flow (Fig. 3). The first vertical mode amplitude was dominated by the tidal signal (Fig. 4a) and contained 99.1 % of the total variance; the second vertical mode accounted for 0.7 % of the variance. Both fortnightly variability and seasonal shifts are evident in the tidally averaged trace (Fig. 4b). The seasonal reversals in both modes one and two are particularly clear when a subfortnightly filter is applied (Fig. 4c); the filtered first and second vertical modes accounted for 80 and 16 % of the subtidal variance, respectively. It is interesting to note that the mode one velocity changes direction seasonally, whereas the depth-averaged velocity trace in Fig. 2d reflects the competition between barotropic and baroclinic forcing and does not show as clear a reversal. There is a general coherence between the subtidal amplitude time series of the two modes: both modes one and two reverse direction seasonally around the same time, modulate at a quasi-fortnightly frequency,


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Fig. 3 EOF modes. a Vertical modes for along-channel velocity, normalized to maximum mode amplitude: first mode (black), second mode (dark gray), third mode (light gray). b The same modes scaled according to root-mean-square mode amplitude. c Horizontal modes for depth-averaged along-channel velocity, normalized to maximum mode amplitude. The channel observation is located at the origin, with the shoal observation at +y

and respond similarly to inter-annual variations in rainfall; however, a linearly regressed relationship between the two is weak (R2 = 0.23). We will use these first two vertical modes later in considering the response of

Fig. 4 a Time series of along-channel vertical mode amplitudes at L02: mode is indicated at right of trace. b Tidally averaged from (a). Horizontal axis is aligned with first mode (black); second (dark gray) and third (light gray) mode time series are shown at same scale, but offset by −2 and −4 cm/s, respectively, for presentation. c Subfortnight filtered from (a). The fortnightly variability in b has a similar variance to the seasonal signal in c. See Fig. 3 for mode shapes

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circulation to changing tidal and buoyancy forcing. The third vertical mode increased with greater buoyancy forcing, as changes in stratification result in additional velocity structure in the vertical not accounted for solely by the first two modes. We computed horizontal modes using depthaveraged velocities on the shoal and in the channel between April 5, 2007 and November 15, 2007. There are only two possible modes in this xy plane, owing to the limited spatial resolution (Fig. 3c). The first horizontal mode structure describes when the channel and shoal velocities are in the same direction, and this amplitude time series is predominantly tidal (Fig. 5a); the second horizontal mode describes when the two velocities are opposed. At the tidal time scale, horizontal mode two accounts for the different velocity phasing between the channel and shoal, as the larger role of friction to inertia on the shoal will cause the shoal velocity to slow before the channel. Additionally, horizontal mode two will increase in magnitude at any point when the lateral shear between the two stations deviates from that described by horizontal mode one. The subtidally filtered horizontal mode amplitude time series demonstrate the complex combination of tidal and buoyancy forcing in upper Elkhorn Slough (Fig. 5b–d). Both modes reverse in response to the


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Fig. 5 a Time series of along-channel horizontal (using the channel and shoal) mode amplitudes at L02: mode is indicated at right of trace. b Tidally averaged from (a). Horizontal axis is aligned with first mode (black); second (dark gray) mode time series is shown offset by −2 cm/s for presentation. c Subfortnight filtered from (a). d Time series of greater diurnal inequality, γ0 , and longitudinal density gradient, ∂ρ/∂ x, the metrics used to bin tidal and baroclinic forcing, respectively

changing axial density gradient, though the mode reversal lags by several weeks in the summer, similar to the delayed reversal of vertical mode one (Fig. 4c). Both horizontal modes have a monthly modulation in strength and direction, upon which more variable fortnightly modulations are superimposed. Both of the horizontal modes increase during neap tides (Fig. 5b). These is some sense that the monthly variability (i.e., the slower 27.3 day tropical modulation) affects the subfortnightly variability, but the true mechanism is unclear. Some of this variability is likely due to remote forcing from Monterey Bay (Breaker et al. 2008). The data set from the shoal is much shorter than the long-term record in the main channel, and only a few small rainfall events were recorded in late September and early October 2007 (Fig. 2a). The late September event, though small, was sufficient enough to temporarily reverse both mode directions. The change in mean current direction in response to this buoyancy input is evident in the raw velocity observations from

the shoal (Fig. 2d). Both of these precipitation events coincided with smaller, equinoctial tides; this reduced tidal forcing may have facilitated the quick response of circulation to the buoyancy input. Increased diurnal inequality and tidal range during the spring tides in the last week of October may have contributed to reducing the effect of this precipitation. Because the temporal coverage during which we can calculate the horizontal modes is less extensive than the vertical modes and the spatial resolution is limited with just two sites, we will focus the remainder of the analysis on the vertical modes.

Tidal Phase-Averaged Dynamics In order to isolate the roles of changing tidal and buoyancy forcing on circulation in upper Elkhorn Slough, we binned the hourly observations of each lunar day tidal cycle according to the axial density gradient and diurnal inequality, quantified as skewness γ0 . The daily observations within each bin were then tidal phaseaveraged. The number of tidal cycles in each density and skewness bin, as well as the bin divisions, are shown in Fig. 6. Effect of Tidal Range Larger spring tides are marked by a diurnal inequality, and the timing of higher high water at spring tide shifts slightly earlier in the tidal cycle relative to neap tides (compare the traces in Fig. 7a). The overall increase in tidal amplitude reduces the strength of the baroclinic pressure gradient from neap to spring tides (Fig. 7m). The increasing diurnal inequality produces intratidal variations, such that the first half of the tidal cycle (the first flood and ebb from LLW to ∼12 h after LLW) is different from the second half of the tidal cycle. On the first flood, the increase in tidal range has little effect on either the average elevation of lower high water (LHW) or vertical mode one velocity (Fig. 7c). The larger water level excursion from LLW to LHW is offset by a shift in rising water duration so that the overall flood velocity magnitude is largely unaffected. In contrast, mode one amplitude increases significantly in response to larger range during the second flood and ebb. Relative to neaps, the timing of spring peak flood occurs earlier and spring peak ebb shifts later in the tidal cycle as friction becomes more important (Fig. 7s). The velocity increase is partly due to nonlinear hypsometry over the upper intertidal (Boon and Byrne 1981), as the higher spring tides inundate a greater volume of intertidal marsh than do neap tides.


sal for the larger spring tides) during the second half of ebb (hours 19–21). Effect of Density Gradient The most striking difference between the two density conditions in Fig. 7 (compare the left and right panels to contrast classic and inverse) is the increased prevalence of tidal straining in winter, evident in mode two velocities (e.g., compare blue traces panels e and f). Stronger buoyancy forcing in winter (panels m and n) leads to a reduction in friction during late ebb (panels s and t). This is well-captured by the Simpson number (panels g and h), Si ≡

Fig. 6 Number of tidal cycles contributing to tidal phaseaveraged observations in Fig. 7 through Fig. 10. Tick marks show bins used; end bins are inclusive of all observations beyond the bin division (e.g., the last bin for γ0 includes all observations < −1.25). Gridded numbers indicate total lunar-day tidal observations corresponding to each bin division of density gradient and diurnal inequality. Histogram along horizontal axis shows distribution of observations according to density gradient only; histogram along vertical axis shows distribution of observations according to tidal asymmetry only. Using observations from June 22, 2005 to September 25, 2007, there were a total of 769 25-h lunar day segments

g

/ρ0 |∂ρ /∂ x |H 2 u2∗

(3)

which increased consistently above unity only during the small ebb in classic conditions (Fig. 7g). There is little evidence of inverse tidal straining (stratification and negative mode two forming on flood instead of ebb) as the axial density gradient was significantly weaker. Similar to the classical density conditions, inverse mode two occurred during late ebb, counter to the expectation that inverse tidal straining should be destabilizing on ebb and accompanied by a near-zero mode two. Low Si during this phase of the tide, however, suggests that this is not a density-driven mechanism. Momentum Balance

There is a pattern of classic tidal straining evident in the mode two velocity when ∂ρ/∂ x < 0, with positive mode two and negative mode one during ebbs indicating increased shear relative to positive mode one and a weakly negative mode two during flood. (If the shear on flood and ebb were identical, then both modes one and two would have to be symmetrical about zero over the tidal cycle.) The tendency for tidal straining to occur during the first flood and ebb is generally independent of tidal range. The decrease in density gradient from neap to spring is compensated for by an increased small ebb (from LHW to higher low water) velocity during neap tides. The diminished diurnal influence during neap tides results in more regular tides with little diurnal inequality; this allows the first ebb to actually be of increased magnitude relative to velocities at the same phase of a spring tide. The most notable feature of the mode two velocities during the second ebb is their initial increase due to tidal straining (Fig. 7e, hours 18–21) followed by a subsequent reduction (and rever-

In the momentum equation, barotropic pressure gradient and friction changed the most significantly on a fortnightly scale (Fig. 7k,s). There was a reduction in baroclinic pressure gradient from neap to spring associated with stronger vertical mixing. As with velocities, barotropic pressure gradient, advection, and friction increased significantly during the second flood and ebb as the diurnal inequality increased. There was a systematic pattern in the sum of the calculated momentum terms, with a small residual required to account primarily for the imbalance between barotropic pressure gradient and friction during the second ebb (Fig. 7o). The magnitude of this residual increased from neap to spring tides and was negative late in the second ebb during the largest spring tides. While there is an unquantifiable error associated with our estimation of the pressure gradient, we interpret the reduced and negative mode two during late ebb to be an advective redistribution of momentum within the cross-section. A component of the late-ebb reduction is


(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)

(t)

Fig. 7 Tidal phase-averaged observations, showing variations associated with changes in diurnal inequality, as measured via skewness, γ1 . Contrasting along-channel density gradients are shown: (left panels) classic estuary, ∂ρ/∂ x < 1 kg m−3 km−1 , (right panels) 0 < ∂ρ/∂ x kg m−3 km−1 . Skewness binned into −1.75 to −1.25 (long dash), −1.25 to −0.75 (medium dash), −0.75 to −0.25 (short dash), and −0.25 to 0.25 (dotted). Shaded en-

velopes drawn around first and last bins show standard deviation in observations. The traces shown are: a, b tide height, c, d mode 1 velocity amplitude e, f mode 2 velocity amplitude, g, h Si number, Eq. 3, i, j unsteadiness, k, l barotropic pressure gradient, m, n baroclinic pressure gradient, o, p lateral advection, q, r lateral tidal stress, s, t surface stress, and u, v bottom stress


(a)

tive term estimates is similar (Fig. 8b) to the residual. Thus, it is likely that an advective redistribution of momentum contributes to the momentum balance at this location. Lateral velocities due to curvature are likely the cause of the lateral momentum advection.

Subtidal Momentum Balance

(b)

Fig. 8 Tidal phase-averaged momentum balance, for observations within ∂ρ/∂ x > 0 and −0.75 < γ0 < 0.25

certainly due to vertical mixing; however, the phasing occurs after max ebb and the advective terms are large enough to suggest that they play a role as well. In Fig. 8a, tidal-phase averaging all of the observations produces a residual term similar to the bin-specific residuals in Fig. 7. The residual accounts primarily for the imbalance between barotropic pressure gradient and friction, though the magnitude of these calculations is uncertain as the absolute pressure gradient offset may not be exact. Nevertheless, the sum of our advec-

(a)

(b)

In the preceding section, we presented tidal phaseaveraged observations, binned according to density and tidal conditions. All of these binned observations can be aggregated into a matrix representing the different tidal and density conditions by tidally averaging the phase-averaged traces. Modes one and two modulate with both density and tidal forcing (Fig. 9); the reversal is evident along the density axis, while the magnitude of circulation modulates with tidal forcing. Because of the seasonal change in circulation, the tidal modulations are averaged out when not separated according to density bins, as shown in the histograms along the vertical axes in Fig. 9. The strongest mode two circulation occurs for neap tides and classic conditions. Stronger tidal forcing reduces the magnitude of mode two circulation, even for strong buoyancy forcing (Fig. 9b). This same general pattern holds for mode one, Si (Fig. 9d) indicates that only neap tides and negative density gradients have circulation that is dominated by buoyancy. This implies that the observed reversal in estuarine circulation is not density-driven, but rather it is the absence of buoyancy forcing that allows the inverse circulation to occur. This modulation of buoyancy forcing is evident in the momentum equation (Fig. 10). Barotropic pressure

(c)

(d)

Fig. 9 Tidally averaged mode velocities: a mode 1, b mode 2, and c mode 3. d Tidally averaged Si number, Eq. 3. Negative values are shown in blue, with a diagonal line


(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

gradient reflects the spring-neap modulation in tidal forcing. While baroclinic pressure gradient clearly shows the seasonal component, weaker buoyancy forcing with spring tides is evident within each density bin as baroclinic pressure gradient was strongest for neap tides. The friction term (Fig. 10f) subtidally balances both the barotropic and baroclinic pressure gradients,

Fig. 10

Tidally averaged momentum balance. Density gradient and diurnal inequality bins are the same as in Fig. 6. The shaded quadrant value is the result of tidally averaging the phaseaveraged binned quantities. The bar graphs along the horizontal axes are the tidally averaged observations without any binning for diurnal inequality and the bar graphs along the vertical axes show tidally averaged results without any density gradient binning; the bar graphs are shaded using the same color bar as within the fully binned quadrant results. Terms in the tidally averaged momentum equation are: (a) barotropic pressure gradient, (b) baroclinic pressure gradient, (c) along-channel advection, (d) lateral tidal stress plus lateral advection, (e) surface stress, and (f) bottom stress, (g) unsteadiness, and (h) minus the sum of (a–g). Negative values are shown in blue, with a diagonal line

and largely mirrors Si in Fig. 9d. Surface stress was small and negative, consistent with the predominant wind stress blowing from the northwest, seaward down the channel. Time-averaged unsteadiness was zero and is not shown. The measurement residual (the sum of panels a through d in Fig. 10e) increased primarily with spring tides but also changed magnitude as a function of density gradient, becoming negative during neap tides when buoyancy is most important. The residual is leading order with the other terms and suggests that one or more of the advective terms may contribute to closing the momentum balance. These are estimated in panels f through h. All of the estimated advective terms modulated with the spring-neap cycle. Both lateral and vertical advection modulate across both the density and tidal axes, though we do not have enough confidence in these estimations to make conclusive statements. Additionally, the estimate of axial advection cannot reverse, as seems to be required by the calculated residual. Figure 9 suggests that lateral advection in late ebb could provide the necessary momentum redistribution; however, the uncertainties described in the Appendix preclude presenting this data in more than a qualitative fashion. The central issue in our observations is: what is the mechanism responsible for the observed reversal in estuarine circulation? In the property–property plots in Fig. 11, tidally averaged quantities from Figs. 9 and 10 are shown. Despite the expectation that circulation would modulate tidally (i.e., through the spring-neap cycle), modal velocities were most coherent with the baroclinic pressure gradient (Fig. 11c) rather than the barotropic pressure gradient (Fig. 11a). This dependence on density is evident in Fig. 11b, where neap tides appear to have a bimodal distribution: for weak tidal forcing (γ0 near zero), circulation may be either nonexistent or maximum, depending on the strength


(a)

(b)

(c)

(d)

Fig. 11 Scatter plots of tidally averaged terms. Black symbols are mode one, grey/red symbols are mode 2; Open symbols denote times of inverse density gradient. (a) Barotropic pressure gradient; (b) skewness as spring-neap proxy; (c) baroclinic pressure gradient; and (d) Si number. R2 = 0.5 and 0.64 for linear regression of modes one and two, respectively, in panel c

of the density gradient. The regressions between mode velocities and density in Fig. 11c suggest that modal velocities may reverse prior to the formation of an inverse density gradient. Thus, it appears that as density gradients weaken, the underlying barotropic mechanisms begin to dominate, generating a two-layer circulation (Ianniello 1979). Stronger inverse density gradients appear to reinforce this barotropic circulation.

Conclusions Three and a half years of hydrographic, velocity, and atmospheric data collected as part of the Land/ Ocean Biogeochemical Observatory in Elkhorn Slough demonstrate the utility of long-term in situ measurements in a coastal system. These long-term observations revealed that residual circulation in Elkhorn Slough is seasonally variable, with classic estuarine circulation in the winter and inverse estuarine circulation in the summer. The strength of this exchange flow varies both within years and between years, driven by the annual cycle of dry summers and wet winters. Subtidal circulation in upper Elkhorn Slough is a combination of both tidal and density-driven mechanisms. The depth-averaged subtidal flows are landward

in the channel and seaward over the shoals during the winter when Elkhorn Slough is a classical estuary with fresher water at its head; in the summer, there is a negative water balance, hypersalinity forms, followed by the creation of an inverse estuary as the density gradient reverses sign. The time-varying structure of these flows was quantified using empirical orthogonal functions; the results of which indicate that both laterally and vertically sheared exchange flows occur at this location. The subtidal magnitude and reversal of the exchange flows is controlled primarily by the density gradient, despite the significant tidal energy. As the density gradient weakens, the underlying tidal processes generate vertically sheared exchange flows with the same sign as that expected for an inverse density gradient. More detailed observations are required in the cross-section to understand how the horizontally sheared exchange flows respond, however, as theory predicts that laterally sheared subtidal flow should still have a circulation pattern that is similar to classical density forcing, yet mode one appeared to reverse in concert with mode two. Another possible reason for the strong relationship between circulation and density may be related to the fact that axial dispersion is not specifically accounted for in these analyses. Axial exchange facilitated by lateral trapping within the marsh increases for larger tidal excursions (Okubo 1973; MacVean and Stacey 2011), such that horizontal gradients weaken during spring tides. In contrast to a partially stratified estuary where enhanced mixing reduces circulation and enhances gradients, it is possible for stronger mixing to both reduce subtidal circulation while also reducing the density gradient in weakly stratified estuaries. Acknowledgements This work was carried out as part of the Land Ocean Biogeochemical Observatory program supported by NSF through grant ECS-0308070 to the Monterey Bay Aquarium Research Institute and Stanford University. Additional support was provided by Stanford University’s Woods Institute for the Environment through its Environmental Ventures Program and Woods Hole Oceanographic Institution through USGS/WHOI Postdoctoral Scholar funds. We thank Ken Johnson for many discussions about Elkhorn Slough. Special thanks to Kristen Davis, Sarah Giddings, Jim Hench, Johanna Rosman, and Alyson Santoro for diving support in cold water with no visibility. Additional boat support was provided by Joe Needoba, Cary Troy, and Gang Zhou. We are indebted to Moss Landing Marine Laboratories Small Boat and Diving Operations; in particular, John Douglas, Scott Hansen, and Diana Steller. Luke Beatman provided the weather data collected from the MLML meteorological station. Bathymetry data used in Fig. 1 and the upper slough volume calculations were provided by Pat Iampietro and Rikk Kvitek at CSU Monterey Bay. We greatly appreciate the constructive comments of John Largier in the review of the manuscript.


Appendix: Long-Term Mooring Considerations Several issues arose with the data quality of the longterm observations that are discussed here. The foremost problem with this extended observational effort was the gradual failure of the pressure sensors. Through comparison against the water level observations at the National Ocean Service Monterey, CA tide gauge (9413450), it was evident that both the ADCP pressure gauge and the L02 pressure gauge began to experience a degradation in response time that made these data unsuitable for tidal-time scale computations (such as Stokes drift). The ADCP pressure gauge, in particular, failed completely during the final, thirteenth deployment. This was particularly problematic because ADCP depth was essential for both removing bad bins above the surface and referencing the ADCP to small depth differences between deployments. In order to ensure that the degradation of the pressure signal throughout the observational period did not affect the analyses, we utilized the following procedure. First, tidal harmonics were computed from pressure observations (converted to depth) from the first 293 days of the observations, from January 11 to November 1, 2005; this harmonic analysis included extraction of 25 compound tide constituents that were required to capture the nonlinear tidal distortion in addition to the standard 68 astronomical constituents (Pawlowicz et al. 2002). Ultimately, a synthetic, predicted tidal signal could account for 99.1 % of the true record; the most significant tidal errors occurred during the large solstitial spring tides and a small amount of uncertainty may be associated with diurnal wind effects. The predicted tidal signal (excluding the fortnightly

Table 1 ADCP deployments at L02 in Elkhorn Slough

L02 (Kirby Park) Deployment

Duration

Start

All times are PST (UTC - 8). Dir refers to the up-channel direction determined from the orientation of the M2 ellipse The final line is the average of all of the previous lines

and semiannual constituents) was added to a subtidal water level record derived from the pressure sensor; we assumed that the gradual degradation of the pressure sensor response did not affect the ability to resolve subtidal water levels. This synthetic tide plus observed subtidal setup was used as the water level record for all subsequent analyses, including removal of bad bins above the surface. For each ADCP deployment, the relative vertical datum of the ADCP was determined by first finding the surface return based on acoustic signal strength. The average depth determined by the surface return was compared to the average depth from the same period in the quasi-synthetic water level record in order to account for subtidal water level changes. Another issue with the quality of the long-term data set was the issue of biofouling of the conductivity and temperature sensors. Hydrography data from the LOBO moorings were visually de-spiked and detrended based on service logs kept by Monterey Bay Aquarium Research Institute personnel (i.e., spikes and baseline shifts attributable to mooring servicing were assumed to be bad, and were removed or corrected, respectively). Finally, battery constraints and biofouling required periodic recovery and redeployment of ADCPs at 2to 4-month intervals. Servicing involved recovery of the ADCP by divers, on-site cleaning and battery installation, followed by redeployment; this process took 1 h. The short data gaps due to servicing were interpolated using a velocity record synthesized from tidal harmonics to create continuous velocity records at each nondimensional vertical coordinate. This regular servicing procedure resulted in slight differences in the horizontal placement of the ADCP. The ADCP was

Stop

M2 ellipse

Depth

(h)

Amp (m/s)

Dir (deg)

(m)

7 29 21 26 6 8 18 10 5 5 1 25 15

Feb Apr Jun Aug Jan Mar May Aug Oct Feb Jun Sep Jan

2005 2005 2005 2005 2006 2006 2006 2006 2006 2007 2007 2007 2008

16:58 12:48 15:18 14:19 15:35 12:04 11:02 14:29 15:06 15:34 10:52 12:53 12:46

29 21 26 6 8 16 10 5 5 1 25 15 6

Apr Jun Aug Jan Mar May Aug Oct Feb Jun Sep Jan Jun

2005 2005 2005 2006 2006 2006 2006 2006 2007 2007 2007 2008 2008

11:08 13:36 12:08 14:47 11:35 10:42 13:00 12:33 12:52 09:46 11:46 11:43 03:15

1938.2 1272.8 1580.8 3192.5 1460.0 1654.6 2018.0 1342.1 2949.8 2778.2 2784.9 2686.8 3422.5

0.221 0.227 0.238 0.222 0.204 0.217 0.225 0.241 0.229 0.224 0.238 0.219 0.206

285.0 284.2 285.4 285.4 284.4 284.8 285.6 288.3 281.6 287.8 289.9 283.4 291.8

3.10 3.04 3.07 3.30 3.29 3.25 3.30 3.32 3.16 3.15 2.90 3.20 2.74

7

Feb

2005

16:58

6

Jun

2008

3:15

2914.6

0.224

286.1

2.78


connected to the base of the LOBO mooring with stainless-steel wire rope, and so was always a constant distance from the mooring base, but varied slightly in later placement as conditions permitted. The interdeployment difference was on the order of meters in the lateral and order of tens of meters in the axial directions, as the entire LOBO mooring was redeployed on October 5, 2006. The similarity in axial parameters across all deployments (Table 1) indicates that discrepancies between locations were negligible with regard to along-channel-directed velocities. Error velocity variance changed, however, between deployments. The changes in error velocity were discrete and associated with individual deployments, and not any discernible fortnightly, seasonal, or hydrographic pattern. Further inspection revealed that the lateral velocity structure changed significantly between individual deployments; for most of the deployments, near-surface velocities during ebb were directed north–northeast, towards the outer bank of the broad bend around Kirby Park (Fig. 1b). During several deployments, however, nearsurface velocities were directed south–southwestward. This reversal in near-surface direction was observed to occur between two successive large ebb tides, separated by a redeployment of the ADCP; we surmise that wake structures caused during the large spring ebb tide affected the measurements. These errors significantly impacted the lateral and vertical velocities. The magnitude of both tidal velocities and the reversing axial subtidal circulation, however, is sufficiently large to have been unaffected by this relocation. Nevertheless, only qualitative results can be derived from this data set. Situations where data are of questionable quality are noted in the text.

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