TWO-DIMENSIONAL HYDRODYNAMIC MODELING OF BARNSTABLE HARBOR AND GREAT MARSH, BARNSTABLE, MA

TWO-DIMENSIONAL HYDRODYNAMIC MODELING OF BARNSTABLE HARBOR AND GREAT MARSH, BARNSTABLE, MA by Jon D. Wood John S. Ramsey Sean W. Kelley Prepared for: The Town of Barnstable, MA Final Report December 1999 Applied Coastal Research and Engineering, Inc. 766 Falmouth Road, Building A, Unit 1C Mashpee, MA 02649

TABLE OF CONTENTS Section Page 1. Introduction... 1 2. Description of Barnstable Harbor/Great Marsh System....3 2.1 Harbor/Marsh Field Data.. 4 2.2 Tidal Harmonic Analysis... 6 3. Numerical Model Development 10 3.1 Numerical Model Description.... 11 3.2 Grid Generation and Boundary Conditions....12 3.3 Calibration Procedure..13 3.4 Model Verification.17 3.5 Wetting/Drying Processes 19 4. Flushing Characteristics.......23 5. Conclusions....26 6. References.. 28 i

LIST OF FIGURES Figure Page 1. Mosaic of Massachusetts topographic maps of Barnstable Harbor and Great Marsh (portions of the Dennis, Hyannis, and Sandwich quadrangles). The Harbor inlet is shown to the east. Locations of tide gauges used in this study are indicated by numbered points: 1) Cape Cod Bay, 2) Mussel Point, 3) West Barnstable Harbor, 4) mouth of Scorton Creek, and 5) upper Scorton Creek. 2 2. Tidal elevation observations for Cape Cod Bay, Mussel Point, and western Harbor locations 5 3. Tidal elevation curves for mouth of Scorton Creek, upper Scorton Creek, and upper Bridge Creek 5 4. Bathymetry data represented on 3-foot contours. Dark blue areas are deep water, green represents salt marsh, and aqua areas represent intertidal flats. Elevations are relative to NGVD 1929. The tides range from approximately +7 feet to approximately 4 feet, meaning at low tide areas above 4 feet are dry and at high tide areas below +7 feet are submerged. Blue areas are submerged a majority of the time. 7 5. Example of tidal distortion in upper Scorton Creek. The solid line is the Scorton Creek tide; the dashed line represents the tide in Cape Cod Bay. Tidal distortion within this estuary shows up as a reduction in the tidal range as well as a delay in the times of high and/or low water. In addition, the ebb tide has a longer duration, representative of the slow draining marsh and intertidal flats, and a more rapid flood tide phase. The brief flood tide means the tidal currents are stronger (faster) on the flood phase than on the ebb phase.. 9 6. Finite element grid of Barnstable Harbor and Great Marsh RMA2 model, showing (A) computational mesh, and (B) divisions of mesh material types used to compute flushing volumes and vary bottom friction factors... 14 7. Example output from RMA2 hydrodynamic model of Barnstable Harbor during ebb tide. Color contours are of velocity magnitude (red is greatest velocity). Vectors indicate flow direction and relative velocity magnitude (scaled by the arrow lengths.16 8. Comparison of the model output to the observed field data for the model calibration runs. Errors are greatest in the creek regions, where significant tidal distortion was observed.20 9. Verification model run compared to measured data. Error analysis is presented in Table 4 21 10. Map of water depths through Barnstable Harbor and Great Marsh during high tide conditions in Cape Cod Bay (upper plot, water surface elevation is 7.75 ft NGVD) and low tide conditions (lower plot, water surface elevation is -5.0 feet NGVD).. 22 ii

LIST OF TABLES Table Page 1. Tidal Constituents for Barnstable Harbor System computed using tide gauge data from August-September 1992.6 2. M 2 Phase Delays Barnstable Harbor System August-September 1992 (Delay in minutes relative to Cape Cod) Bay....8 3. Percentages of Tidal versus Non-Tidal Energy Barnstable Harbor August- September 1992... 10 4. Manning's roughness coefficients input to RMA-2 model of Barnstable Harbor. Material type divisions are shown in Figure 6(B).17 5. Comparison of Tidal Constituents from calibrated RMA2 model and measured tidal data during same time period (August to September 1992). Error between measured and computed tidal constituents also is provided..18 6. Mean embayment volume, average tidal prism, and residence times for the Barnstable Harbor system and selected sub-embayments 25 iii

Acknowledgements Applied Coastal would like to thank Dr. Johan van der Molen and Dr. Orson van de Plassche for use of their research data in this study. Dr. van der Molen was contacted after we had read his book, Tides in a Salt-Marsh (Great Marshes, Barnstable, Cape Cod, USA, and became interested in collaborating on this program. These data were collected in 1990-1993 as part of the PIONIER project Coastal Records, funded by the Netherlands Organization for Scientific Research, supervised by Dr. Orson van de Plassche. Dr. van der Molen, through the project director, Dr. van de Plassche, kindly allowed Applied Coastal use of these data for this study, with the expressed understanding the Town would not give the data to third parties without formal approval from Drs. van der Molen and van de Plassche. This study would not have been as complete without the invaluable contribution these data made to the numerical model development. iv

1. Introduction The Barnstable Harbor and Great Marsh system are located along the northern shore of Cape Cod in Barnstable, Massachusetts (Figure 1). The system is bordered to the north by Sandy Neck barrier beach system and to the south by the Sandwich moraine. The western end of the system consists of large expanses of salt marsh that are flooded at high tide and go dry (with the exception of channels) during the lower portion of the tide cycle. The inlet to the east connects the Harbor to Cape Cod Bay, and is narrow and deep (approximately 45 feet at its deepest), with tidal flats emerging on both sides of this channel at low tide. The southeastern quadrant of the region is gradually sloping tide flats: dry at low tide and submerged at high water. The central Harbor system consists of isolated marsh islands and large regions of intertidal flats cut with meandering, sinuous channels. These channels are relatively narrow, and feature steep side slopes relative to surrounding flats. The system encompasses an area of approximately 8 square miles, about half the area belonging to the marsh, and is one of the largest estuarine systems on Cape Cod. In general, water quality studies of tidally influenced estuaries must include a thorough evaluation of the hydrodynamics of the estuarine system. Estuarine hydrodynamics control a variety of coastal processes including tidal flushing, pollutant dispersion, tidal currents, sedimentation, erosion, and water levels. Numerical models provide a cost-effective method for evaluating tidal hydrodynamics since they require limited data collection and may be utilized to numerically assess a range of management alternatives. Once the hydrodynamics of an estuary system are understood, computations regarding the related coastal processes become relatively straight-forward extensions to the hydrodynamic modeling. For example, the spread of pollutants may be analyzed from tidal current information developed by the numerical models. This study evaluated the hydrodynamic characteristics of this system for purposes of calculating system flushing rates for the entire system as well as local residence times for selected sub-embayments and creek systems. The study was performed by Applied Coastal Research and Engineering, Inc. (Applied Coastal) for the Town of Barnstable, Massachusetts. The purpose of the study is to evaluate flushing characteristics for selected areas to guide Town planning efforts within the system s watershed. To develop these characteristics, Applied Coastal developed a calibrated, twodimensional numerical model of the estuary. This model relied upon data collected by Dutch researchers during an earlier study of the system in 1991-1993 (Van der Molen, 1997). This study measured system geometry (marsh elevations, bathymetry) as well as measured tidal elevation variations at several strategic locations. These data were used to generate a computer model that represented key features of the estuary. The model was calibrated against the tidal measurements to assure the essential hydrodynamics were being simulated correctly. Once calibrated, the model was used to calculate the tidal prism (water volume transported into the system during a single flood tide) and system volume at various stages of the tide. These volume and tidal prism parameters are the primary input to the residence time and flushing rate equations. 1

6 1 4 2 3 5 Figure 1. Mosaic of Massachusetts topographic maps of Barnstable Harbor and Great Marsh (portions of the Dennis, Hyannis, and Sandwich quadrangles). The Harbor inlet is shown to the east. Locations of tide gauges used in this study are indicated by numbered points: 1) Cape Cod Bay, 2) Mussel Point, 3) West Barnstable Harbor, 4) mouth of Scorton Creek, and 5) Bridge Creek, and 6) upper Scorton Creek. 2

This report consists of three main parts: Description of the data collected by Dutch researchers (Van der Molen, 1997), principally a harmonic analysis of the tide data at various locations throughout the estuary during the observational period of 1992. Description of the model development and calibration procedures, including error analysis relative to the collected field observations. Discussion of the results including flushing rates for the entire system as well as selected estuary sub-embayments. 2. Description of Barnstable Harbor/Great Marsh System The Barnstable Harbor system possesses a variety of physical features: deep channels, shallow intertidal flats, and vegetated salt marsh plains. The inlet to the system is open to Cape Cod Bay; a deep (of order 30-45 feet), steeply-sloped channel cuts through expansive intertidal flats. The inlet is bordered to the west by the tip of Sandy Neck barrier beach system, and to the east by shallow intertidal flats. A large flood tidal shoal exists just within the inlet that serves to split the entrance channel. This channel continues along the southern edge of the Harbor, feeding western areas of the system: the Millway, Scorton Creek, and the salt marsh. The west harbor areas are relatively shallow, much of which can go dry at low tide, and possess sparse peat islands. The western end of the system is dominated by the Great Marsh, an elevated plain of vegetated peat deposits through which are cut numerous smaller creeks (e.g., Scorton Creek, Bridge Creek, Spring Creek, and Brickyard Creek). These narrow creeks provide the primary pathways allowing marsh flooding and draining. Circulation in Barnstable Harbor is driven by tidal elevation changes in Cape Cod Bay. Tidal ranges in Cape Cod Bay are large, approximately 8-9 feet during neap tides and about 13 feet during the spring tide phase. Cape Cod Bay tides are dominated by the lunar semi-diurnal, or M 2, tide, which varies on a precise 12.42 hour period. The relatively large tide range, combined with the large spatial extent of the system, will combine to produce a large tidal prism, the volume of water flowing through the inlet every tide cycle. As a result of this large tidal prism, corresponding flow is expected to have relatively high velocities, especially within the channels and major creeks. The extensive intertidal flats, long sinuous channels, and salt marsh regions within the Barnstable Harbor system have a significant influence on the tidal wave, and can be considered the primary physical features affecting the hydrodynamic behavior within the estuary. These features will tend to slow down the entering tidal wave, as well as store, or trap temporarily, water inside the system, releasing the water back to the system on an ebb, or falling, tide. The result typically is a prolonged, but weak ebb tide followed by a briefer, but more intense flood tide. The slowing of the tide, as well as the store-and-release characteristics of the tidal flats and marsh, results in a distortion of the tide within the estuary. This distortion of the tidal wave entering from Cape Cod Bay increases as it propagates through the system. Tidal distortion results from frictional mechanisms in the shallow waters, narrow channels, and salt marsh. The effect of tidal distortion (known as tidal attenuation) is a reduction in overall tide range, as well as a phase delay in the time of high and low tides relative to the offshore tide. Distortion typically increases as the 3

tide progresses further into the estuary. Significant attenuation of the tide can affect flushing rates, or residence times, within estuaries; hence, accurate simulation of the frictional mechanisms that distort tides in estuaries is critical to evaluating a system s flushing characteristics. 2.1 Harbor/Marsh Field Data For this study, Applied Coastal utilized an extensive data set collected in 1991-1993 during a study by Dr. Johan van der Molen, Vrije University of Amsterdam, The Netherlands (van der Molen, 1997). These data were collected as part of the PIONIER project Coastal Records, funded by the Netherlands Organization for Scientific Research, supervised by Dr. Orson van de Plassche. The study aimed to recreate tidal hydrodynamics in this salt marsh system to study variations of historic mean high water contained in salt marsh peat deposits. Dr. van der Molen, through the project director, Dr. van de Plassche, kindly allowed Applied Coastal use of these data for this study, with the expressed understanding the Town would not give the data to third parties without formal approval from Drs. van der Molen and van de Plassche. The data used for this study consisted of tidal elevation observations at six (6) locations within the estuary (Figure 1), obtained during August and September, 1992, as well as bathymetric and topographic survey elevation measurements throughout the system. The tide data were corrected for variations due to atmospheric pressure, as well as referenced to the NGVD 1929 vertical datum. The elevation data were received in XYZ- format, with the horizontal datum relative to Massachusetts state plane 1927 and the vertical datum referenced to NGVD 1929. Figure 2 shows the tidal elevation for the period August 9 through September 10, 1992 at three locations: Cape Cod Bay (labeled as Location #1, offshore of the inlet), Mussel Point (Location #2), and western harbor near Calves Pasture Point (Location #3). The curves have a predominant 12.42-hour variation around the lunar semi-diurnal (twice-a-day), or M 2, tidal constituent. There was also a strong modulation of the lunar and solar tides, resulting in the familiar spring-neap fortnightly cycle. The spring (maximum) tide range was approximately 4 meters (13.1 feet), and occurred on August 29. The neap (or minimum) tide range was 2.6 meters (8.6 feet), occurring August 24th. Figure 3 shows the tidal elevation observations for locations within the harbor system: mouth of Scorton Creek (Location #4), upper Scorton Creek (Location #6), and upper Bridge Creek (Location #5). These tide signals show the effects of frictional damping through the estuary, specifically a reduction in tide range as one progresses into the system. At upper Bridge Creek, and potentially at upper Scorton Creek, it appears as if the tide gauge may have gone dry at each low tide, failing to measure the lowest water elevations. This is identified as an abrupt truncation of the ebb tide signal, and was likely due to the gauge being installed above the low water elevation. The data obtained from this previous study were of good quality overall; the exception may have been the Bridge Creek elevation time series. However, this specific data set still provides useful information for model calibration purposes. The bathymetric and topographic survey data provided outstanding horizontal coverage of both the harbor and salt marsh, and provided the basis for the numerical model grid generation. Vertical observations were stated to be within 0.1 feet (less than 3 cm). The contoured elevation data, overlaid with the shoreline is shown in Figure 4. 4

Figure 2. Tidal elevation observations for Cape Cod Bay (Location #1 of Figure 1), Mussel Point (Location #2), and western Harbor locations (location #3). Figure 3. Tidal elevation curves for mouth of Scorton Creek (Location #4 of Figure 1), upper Scorton Creek (Location #6), and upper Bridge Creek (Location #5). 5

2.2 Tidal Harmonic Analysis Analyses of the tide and bathymetric data provided insight into the hydrodynamic characteristics of each system. Harmonic analysis of the tidal time series produced tidal amplitude and phase of the major tidal constituents, and provided assessments of hydrodynamic efficiency of each system in terms of tidal attenuation. This analysis also yielded an assessment of the relative influence of non-tidal, or residual, processes (such as wind forcing) on the hydrodynamic characteristics of each system. Harmonic analyses were performed on the time series from each gauge location. Harmonic analysis is a mathematical procedure that fits sinusoidal functions of known frequency to the measured signal. The amplitudes and phase of 23 known tidal constituents result from this procedure. Table 1 presents the amplitudes of the eight largest tidal constituents (see note to define tides). The M 2, or the familiar twice-a-day lunar semi-diurnal, tide is the strongest contributor to the signal with an amplitude of 4.5 feet in Cape Cod Bay. The range of the M 2 tide is twice the amplitude, or 9 feet. The diurnal tides, K 1 and O 1, possess amplitudes of approximately 0.36 feet. Other semidiurnal tides, the S 2 (12.00 hour period) and N 2 (12.66-hour period) tides, have amplitudes of 0.75 feet and 1.25 feet, respectively. The M 4 tide, a higher frequency harmonic of the M 2 lunar tide (exactly half the period of the M 2, or 6.21 hours), results from frictional attenuation of the M 2 tide in shallow water. The M 4 is insignificant in Cape Cod Bay (about 0.03 feet), but is shown to grow progressively in amplitude with distance away from the inlet. At Bridge Creek, the M 4 constituent is the second largest tidal constituent (approximately 0.72 feet), signaling the effects of frictional mechanisms through the creeks. Shallow estuaries, such as Barnstable Harbor, typically exhibit significant growth of the M 2 harmonics (specifically M 4 and M 6 ) due to the frictional damping of the tide. Table 1 also shows the decay, or attenuation, of the M 2 tide as it propagates through the estuary. The M 2 tide is greatest in Cape Cod Bay, and becomes progressively smaller as the tidal wave moves west into the system. This decay of M 2 is consistent with the growth of the M 4 constituent, although the relationship between M 2 decay and M 4 growth is non-linear, with a complex dependence upon friction values (i.e. surface roughness) as well as system geometry (i.e. channel widths, depths, and sinuosity). Table 1. Tidal Constituents for Barnstable Harbor System computed using tide gauge data from August-September 1992 (Van der Molen, 1997). amplitude (feet) M 2 M 4 M 6 S 2 N 2 K 1 O 1 M sf Period (hours) 12.42 6.21 4.14 12.00 12.66 23.93 25.82 354.61 Offshore (Inlet) 4.49 0.03 0.13 0.75 1.25 0.36 0.36 0.10 Mussel Point 4.36 0.16 0.20 0.72 1.21 0.36 0.36 0.16 Harbor (west) 4.33 0.36 0.16 0.69 1.18 0.36 0.36 0.16 Scorton Creek (mouth) 4.17 0.59 0.03 0.66 1.12 0.36 0.36 0.23 Scorton Creek (upper) 3.90 0.82 0.16 0.56 0.98 0.33 0.36 0.33 Bridge Creek (upper) 2.46 0.72 0.16 0.36 0.62 0.30 0.36 0.49 Note: M 2 tide is the principal lunar semi-diurnal constituent; M 4 represents the quarter-diurnal overtide of the M 2 constituent; M 6 the sixth-diurnal overtide of the M 2 constituent; S 2 is the principal solar semi-diurnal constituent; N 2 is the larger lunar elliptic semi-diurnal constituent; K 1 is the lunisolar diurnal constituent; O 1 is the lunar diurnal constituent; and M sf is the lunisolar synodic fortnightly constituent. 6

N Scorton Creek Wells Creek Sandy Neck Mussel Point Beach Point Spring Creek Bridge Creek Millway Brickyard Creek Figure 4. Bathymetry data represented on 3-foot contours. Dark blue areas are deep water, green represents salt marsh, and aqua areas represent intertidal flats. Elevations are relative to NGVD 1929. The tides range from approximately +7 feet to approximately 4 feet, meaning at low tide areas above 4 feet are dry and at high tide areas below +7 feet are submerged. Blue areas are submerged a majority of the time. 7

Table 2 presents the phase delay of the M 2 tide at the same locations. Phase delay means the length of time the tide is delayed at inland locations, for example, the data shows it takes about 15 minutes longer for the tide to reach Mussel Point (location 2 of Figure #1, just inside the inlet) relative to Cape Cod Bay. The tide is delayed one hour in Bridge Creek (location #5) relative to Cape Cod Bay. Consistent with the amplitude decay of the M 2 tide (Table 1), the phase delays increase with distance into the system. Table 2. M 2 Phase Delays (principal lunar semi-diurnal tide) Barnstable Harbor System August-September 1992 (Delay in minutes relative to Cape Cod Bay). Mussel Point 15.21 Harbor (west) 26.31 Scorton Creek (mouth) 33.29 Scorton Creek (upper) 50.13 Bridge Creek (upper) 59.74 Analysis of the data show that the Barnstable Harbor system, with its shallow intertidal flats, expansive salt marsh regions, and winding channels and creeks, distorts the tide significantly relative to Cape Cod Bay. This distortion of the tide is evidenced as reduction in M 2 tide amplitude, M 2 phase delays, and growth of the M 4 harmonic with increasing distance into the system. The result of this distortion is a longer duration of the ebb tide (a slower, gradual draining of the estuary) and a swifter, but briefer flood tide (see Figure 5). Scaling of Figure 5 shows that the Cape Cod Bay tides (dashed line) have a flood duration of approximately 6.05 hours, and an ebb duration of approximately 6.37 hours. This nearly-equivalent duration of the flood versus ebb tide means the tide is minimally distorted prior to entering Barnstable Harbor. Similar scaling of the tide in upper Scorton Creek shows the ebb tide is approximately 8.72 hours in duration, with the flood phase about 3.72 hours in duration. The time asymmetry between the flood and ebb phases is another indication of tidal distortion through the estuary. Since the flood tide phase is brief, it also means corresponding flow is much stronger on the flood phase than on the ebb, since (conservation laws of physics demand) the same amount of water volume must enter the system on the flood as leaves on the ebb. This volume is transported in a shorter amount of time; hence, to conserve mass, the corresponding flow rates must be greater on the flood than during the ebb. These hydrodynamic characteristics must be accounted for when evaluating the system residence times, or flushing rates, to accurately predict how well an estuarine system can tolerate pollutant loadings. M 4 governs the shape of the tide, and relationships between M 2 and M 4 indicate whether an estuary is flood- or ebb-dominant (Friedrichs and Aubrey, 1988). M 4 emerges as a harmonic of M 2 as a result of non-linear friction effects. M 4 is the quarterdiurnal (occurring 4 times daily) overtide of M 2 with a period (6.21 hours) equal to half the period of M 2 (12.42 hours). A relation between the phases of M 2 and M 4, seasurface phase, can be used to classify an estuary as flood- or ebb-dominant based on the asymmetrical shape of the tide curve. Sea surface phases for the entire Barnstable Harbor estuary demonstrated flood-dominance: the tendency to trap sediment. 8

Figure 5. Example of tidal distortion in upper Scorton Creek. The solid line is the Scorton Creek tide (location #6 of Figure 1) ; the dashed line represents the tide in Cape Cod Bay (location #1). Tidal distortion within this estuary shows up as a reduction in the tidal range as well as a delay in the times of high and/or low water. In addition, the ebb tide has a longer duration, representative of the slow draining marsh and intertidal flats, and a more rapid flood tide phase. The brief flood tide means the tidal currents are is stronger (faster) on the flood phase than on the ebb phase. Flood-dominant systems trap sediment because current velocities are more swift when the tide is rising; therefore, more sediment is deposited within the system on the rising tide than can be transported out of the system on the falling tide. The relative height of M 4 and M 2 tidal constituents (M 4 /M 2 ), indicates the strength of the flood- or ebbdominance. M 4 /M 2 ranged from 0.007 to 0.29 for Barnstable Harbor, indicative of weak to very strong flood-dominance compared to numerous estuaries studied by Friedrichs and Aubrey (1988). In comparison, the studied estuaries along the U.S. Atlantic coast exhibited M 4 /M 2 ratios ranging from 0.003 (Townsend Inlet, NJ) to 0.26 (within North Channel in the Nauset, MA system). Although the eastern portion of Barnstable Harbor indicates relatively weak flood-dominance, the creeks within the western portion exhibit strong flood-dominance and high sediment trapping capabilities. In general, large salt marshes in Massachusetts, such as the western portion of Barnstable Harbor, are 9

accumulating sediment at a faster rate than the relative rise of sea-level; therefore, the marsh area has gradually expanded over the past 3,000 years (Oldale, 1992). In addition to the tidal analysis, the data were further evaluated to determine the importance of other physical processes, other than gravitational tidal forcing, to changes in water surface elevation. These other processes include wind forcing (set-up or setdown) within the estuary, as well as other non-tidal oscillations of the sea surface. Variations in water surface elevation can also be affected by freshwater discharge into the system, if these volumes are relatively large. This analysis calculated the energy (or variance) of the original water elevation time series, and compared these energy values to that of the purely tidal signal (recreated by summing the contributions from the 23 known harmonic constituents). Subtracting the tidal signal from the original elevation time series resulted with the non-tidal, or residual, portion of the water elevation changes. The energy of this non-tidal signal is compared to the tidal signal, and yields a quantitative measure of how important these non-tidal physical processes can be to hydrodynamic circulation within the estuary. The results of this analysis are posted in Table 3. Table 3. Percentages of Tidal versus Non-Tidal Energy Barnstable Harbor August- September 1992. Total Variance (ft 2 sec) Total(%) Tidal (%) Non-tidal (%) Cape Cod Bay 11.44 100 99.6 0.4 Beach Point 10.91 100 99.4 0.6 Barnstable Harbor (west) 10.72 100 99.4 0.6 Scorton Creek (mouth) 10.18 100 99.3 0.7 Scorton Creek (upper) 9.29 100 97.9 2.1 Bridge Creek (upper) 4.30 100 93.2 6.8 Table 3 shows that the energy of the signal in Cape Cod Bay was largest; as should be expected given the tidal attenuation through the system. Also, the energy of the signal decreases with distance from the inlet, with the lowest energy found in upper regions of the creeks. The analysis also shows that tides are responsible for over 99% of the water level changes in Barnstable Harbor; wind effects in this data set were negligible. In the creeks, tides are still responsible for over 93% of the elevation variation, with inputs from other sources accounting for the remaining energy. This relative increase in non-tidal energy within the creeks is likely due to the decrease in tidal energy within the creeks rather than a growth of residual forces. 3. Numerical Model Development The focus of this study was the development of a numerical model capable of accurately simulating hydrodynamic circulation within this estuary. Once calibrated, the model was used to calculate water volumes for selected sub-embayments (e.g., creek systems, and the Millway) as well as determine the volumes of water exchanged during each tidal cycle. These parameters are used to calculate system residence times, or 10

flushing rates. Use of a calibrated numerical model is the most accurate and reliable method to determine system flushing rates. The technical approach consisted of four essential tasks: Model Set-up. Use the field observations to develop the model grid domain, including all elevation data to represent the marshes, creeks, tidal flats, and channels in a realistic manner. The tidal elevation measurements obtained outside the inlet (in Cape Cod Bay) were used as the primary boundary condition, forcing the model with field observations which include all physical processes that affect variations in water level: tides (primarily), winds, and other non-tidal oscillations of the sea surface. Calibration. Once the model domain and boundary conditions were specified, model results were compared to water level measurements obtained inside the estuary during the same time period as the forcing (or boundary condition) observations. Water level variations simulated by the model were compared to actual observations; these comparisons allow tuning of the model parameters in an iterative attempt to minimize differences between model predictions and actual measured data. Verification. Once calibrated to a specific set of conditions, the model was then verified using a second, different set of conditions. This verification set of conditions represented periods of reduced (neap) tidal ranges as well as periods of larger (spring) tidal conditions. This verification run assured that the model correctly simulates estuary hydrodynamics for a variety of conditions. Determination of Flushing Rates. Once calibrated with minimal error, the model is configured to calculate system volumes, as well as volume flow through selected cross-sections (also called tidal prism). These two parameters allow for accurate determination of flushing rates. 3.1 Numerical Model Description This study of the Barnstable Harbor system utilized a state-of-the-art computer model to evaluate tidal circulation and flushing. The particular model employed was the RMA-2V model developed by Resource Management Associates (King, 1990). It is a two-dimensional, depth-averaged finite element model, capable of simulating transient hydrodynamics. The model is widely accepted and tested for analyses of estuaries or rivers. Applied Coastal staff members have utilized RMA-2V for numerous flushing studies on Cape Cod, including West Falmouth Harbor, Falmouth s finger ponds, Popponesset Bay, and the Pleasant Bay estuary. In its original form, RMA-2V was developed by William Norton and Ian King under contract with the U.S. Army Corps of Engineers (Norton et al., 1973). Further development included the introduction of one-dimensional elements, state-of-the-art preand post-processing data programs, and the use of elements with curved borders. Recently, the graphic pre- and post-processing routines were updated by Brigham Young University through a package called the Surfacewater Modeling System or SMS (BYU, 1998). SMS is a front- and back-end software package that allows the user to 11

easily modify model parameters (such as geometry, element coefficients, and boundary conditions), as well as view the model results and download specific data types. While the RMA model is essentially used without cost or constraint, the SMS software package requires site licensing for use. RMA-2V is a finite element model designed for simulating one- and twodimensional depth-averaged hydrodynamic systems. The dependent variables are velocity and water depth, and the equations solved are the depth-averaged Navier- Stokes equations. Reynolds assumptions are incorporated as an eddy viscosity effect to represent turbulent energy losses. Other terms in the governing equations permit friction losses (approximated either by a Chezy or Manning formulation), Coriolis effects, and surface wind stresses. All the coefficients associated with these terms may vary from element to element. The model utilizes quadrilaterals and triangles to represent the prototype system. Element boundaries may either be curved or straight. The time dependence of the governing equations is incorporated within the solution technique needed to solve the set of simultaneous equations. This technique is implicit; therefore, unconditionally stable. Once the equations are solved, corrections to the initial estimate of velocity and water elevation are employed, and the equations are re-solved until the convergence criteria is met. 3.2 Grid Generation and Boundary Conditions The grid generation process for the model was simplified by the use of the SMS package. The digital shoreline and bathymetry data were imported to SMS, and a finite element grid was generated to represent the estuary with 3584 elements and 10227 nodes (Figure 6(A)). All regions in the system were represented by two-dimensional (depth-averaged) elements. The finite element grid for the system provided the detail necessary to evaluate accurately the variation in hydrodynamic properties within the estuary. Fine resolution was required to simulate the numerous channel constrictions that significantly impact the estuarine hydrodynamics. The SMS grid generation program was used to develop quadrilateral and triangular two-dimensional elements throughout the estuary. Reference water depths at each node of the model were interpreted from bathymetry data obtained in the field surveys. The model computed water elevation and velocity at each node in the model domain. Grid resolution was governed by two factors: 1) expected flow patterns, and 2) the bathymetric variability in each region. Relatively fine grid resolution was employed where complex flow patterns were expected. For example, smaller node spacing in each creek and/or channel was designed to provide a more detailed analysis in these regions of rapidly varying flow. Also, elements through channels were designed to account for the rapid changes in bathymetry caused by shoaling and scour processes. Widely spaced nodes were defined for much of the marsh and intertidal flats, where flow patterns did not change dramatically. Appropriate implementation of wider node spacing and larger elements reduced computer run time with no sacrifice of accuracy. Three types of boundary conditions were employed for the RMA-2V model: 1) "slip" boundaries, 2) freshwater inflow, and 3) tidal elevation boundaries. All of the elements with land borders have "slip" boundary conditions, where the direction of flow was constrained shore-parallel. The model generated all internal boundary conditions from the governing conservation equations. Freshwater recharge was specified at the 12

upper end of each creek, although these values were quite small relative to the tidal prism. Freshwater runoff is negligible into this system (Ayers, 1959), approximately 3 10 5 ft 3 per tidal cycle, or less than 0.03% of the system tidal prism. The model was forced using water elevations measurements obtained just offshore of the inlet in Cape Cod Bay (see discussion in the previous section). This measured time series consists of all physical processes affecting variations of water level: tides, winds, and other non-tidal oscillations of the sea surface. The rise and fall of the tide in Cape Cod Bay is the primary driving force for estuarine circulation. Dynamic (time-varying) model simulations specified a new water surface elevation in Cape Cod Bay every 30 minutes. The model specifies the water elevation at the offshore boundary, and uses this value to calculate water elevations at every nodal point within the system, adjusting each value according to solutions of the model equations. Changing water levels in Cape Cod Bay produce variations in surface slopes within the estuary; these slopes drive water either into the system (if water is higher in the Bay) or out of the system (if water levels fall in the Bay). The model boundary condition changed every 30 minutes (the model time step), despite the measurements being obtained every 5 minutes, to allow the model to run more quickly. An example of model output is shown in Figure 7, which shows the distribution of velocities in the harbor during the ebb portion of a tide cycle. Due to the relatively large grid size and the wetting/drying of the marsh plain, the model time step was set at 30 minutes to allow for reasonable computer run time (under 24 hours). The RMA-2V model allows incorporation of wetting and drying to simulate natural marsh systems. Elements that have a bottom elevation higher than the local tide level are effectively removed from the hydrodynamic solution scheme. When the water level rises above the marsh plain or tidal flat, the elements are re-introduced to the model. This simulation of marsh plain wetting and drying requires substantially greater computational resources than a model simulation that does not require wetting/drying. For example, 300 time steps (a 150-hour simulation) required approximately 15 hours of computer time for the case with wetting and drying, where a grid of this size without wetting/drying would only require 3-to-4 hours of computer time. 3.3 Calibration Procedure After developing the finite element grid and specifying boundary conditions, the model was calibrated. Calibration ensured the model predicted accurately what was observed in nature during the field measurement program. Numerous model simulations were required (20+) to calibrate the model, with each run varying specific parameters such as friction coefficients, turbulent exchange coefficients, and subtle modifications to the system bathymetry (for example, small changes to channel cross sections, creek bank slopes, channel depths, etc), to achieve a best fit to the data. Calibration of the flushing model required a close match between the modeled and measured tides in each of the sub-embayments where tides were measured (e.g. upper Scorton Creek). Initially, a six-day period was calibrated to obtain visual agreement between modeled and measured tides. Once visual agreement was achieved, a longer period was modeled to calibrate the model based on dominant tidal constituents discussed in Section 2. The seven-day period was extracted from a longer simulation to avoid effects of model spin-up (i.e. the first few time steps, typically one 13

A. Computational mesh B. Mesh divisions for material properties 5 Scorton Creek 7 15 13 Bridge/Spring Creek 4 1 Wells Creek 16 8 10 2 11 3 6 Main Harbor Basin 9 14 Millway 17 Brickyard Creek Figure 6. Finite element grid of Barnstable Harbor and Great Marsh RMA2 model, showing (A) computational mesh, and (B) divisions of mesh material types used to compute flushing volumes and vary bottom friction factors. The numbers on (B) illustrate the various material types describes in Table 4. Thick dashed lines indicate areas used for flushing volume calculations. 14

tidal cycle, when the model adjusts to the boundary conditions), and to focus on average tidal conditions. The calibration was performed for a seven-day period beginning 0600 hours EST on August 9, 1992. This representative time period was selected because it included average tidal conditions typical in the estuary during the 30-day deployment period. The tide range during this time did not include the maximum spring nor minimum neap tides, rather tide ranges which were largely consistent throughout the calibration interval. The simulation of spring-neap tides was left for the verification stage (next section). Friction inhibits flow along the bottom of estuary channels or other flow regions where velocities are relatively high. Friction is a measure of the channel roughness, and can cause both significant amplitude attenuation and phase delay of the tidal signal. Friction is approximated in RMA-2V as a Manning coefficient. Initially, Manning's friction coefficient between 0.02 and 0.035 were specified for all elements. These values correspond to typical Manning's coefficients determined experimentally in smooth earthlined channels with no weeds (low friction) to winding channels with pools and shoals with higher friction (Henderson, 1966). To improve model accuracy, friction coefficients were varied throughout the model domain. First, the Manning s coefficients were matched to bottom type. For example, lower friction coefficients were specified for the smooth sandy channel in the entrance channel, versus the silty bottom of the shallow regions in the upper creeks, which provided greater flow resistance. Final model calibration runs incorporated various specific values for Manning's friction coefficients, depending upon flow damping characteristics of separate regions within each estuary. Manning's values for different bottom types were selected based on the Civil Engineering Reference Manual (Lindeburg, 1992) and values required to obtain a close match between measured and modeled tides. Upper Scorton Creek, for example, was found to calibrate better using a lower friction coefficient of 0.20. On the marsh plains, damping of flow velocities typically is controlled more by form drag associated with marsh plants than the bottom friction described above. However, simulation of this form drag is performed using Mannings coefficients as well, with values ranging from 2-to-10 times the friction coefficients used in channels. Final calibrated friction coefficients are summarized in Table 4 for the various areas shown in Figure 6(B). Turbulent exchange coefficients approximate energy losses due to internal friction between fluid particles. The significance of turbulent energy losses increases where flow is more swift, such as inlets and bridge constrictions. According to King (1990), these values are proportional to element dimensions (numerical effects) and flow velocities (physics). The Barnstable Harbor model was mildly sensitive to turbulent exchange coefficients, specifically in the entrance channel of strong turbulent flow. In other regions where the flow was generally weak, for example the intertidal flats, the model was insensitive to changes in turbulent exchange coefficients. The calibration procedure proved that, in addition to changes in friction and turbulence coefficients, the model was also mildly sensitive to changes in system geometry. This fact is not unexpected, and is the reason why accurate bathymetry and topography data are required for these models. While the bathymetry and topography data set obtained for this study was extensive: spatial coverage as well as vertical 15

Figure 7. Example output from RMA2 hydrodynamic model of Barnstable Harbor during ebb tide. Color contours are of velocity magnitude (red is greatest velocity). Vectors indicate flow direction and relative velocity magnitude (scaled by the arrow lengths). 16

resolution of some features were not well documented. For example, it was found that changes in the slopes of creek banks were important, and resulted in modification of the amplitude and phase of shallow-water overtide tidal constituents (M 4, M 6 ). These changes in creek geometry produced variations typically in the model calibration of order 0.1 feet. Thus, failure to resolve precisely creek geometry was considered the main source of calibration differences, and that better creek geometry information may have reduced these errors, especially in the overtide terms. These errors were of order tenths of feet (0.1-0.4 ft), or about 2-10% of the overall tide range. Table 4. Manning's roughness coefficients input to RMA-2 model of Barnstable Harbor. Material type divisions are shown in Figure 6(B). material type fiction factor Region type Bottom type 1 0.030 Inlet Sand 2 0.035 Harbor Sand 3 0.035 Harbor Sand 4 0.100 Marsh Peat 5 0.035 Creek Sand 6 0.030 Harbor Sand 7 0.020 Creek Sand 8 0.030 Flats Mud 9 0.030 Flats Mud 10 0.030 Inlet Sand 11 0.030 Flats Mud 12 0.035 Harbor Sand 13 0.035 Creek Sand 14 0.035 Creek Sand 15 0.100 Marsh Peat 16 0.100 Marsh Peat 17 0.100 Marsh Peat A best-fit of model predictions for the first tide gauge deployment was achieved using the aforementioned values for friction and turbulent exchange. Marsh porosity feature of the RMA-2V model was utilized to simulate the storage characteristics of the salt marsh. Wetting/Drying of system elements was enabled such that if the water level dropped close to an element elevation, the element was removed from the grid and did not affect subsequent flow calculations. The calibration process required determination of where the system geometry, as represented in the model, may have been inaccurate. Therfore, many experimental model runs were performed to determine how changes to creek bank slopes or channel widths and depths affected the model results. These trial runs achieved a good visual fit between the model simulations and the field data. Examples of the tide curves for each of the five inner-estuary locations are shown in Figure 8. 3.4 Model Verification The verification run was performed for an approximate seven-day period beginning 1800 hours EST on August 21, 1992. This representative time period was 17

selected because it included a wider variety of tidal conditions during the 30-day deployment period. Throughout the selected seven-day period, the tide range varied from approximately 8.6 ft (neap tides) to 13.1 feet (spring tides). Comparison of the model output and data observations for this simulation is shown as Figure 9. Visual agreement between the two curves is good, suggesting the model accurately predicts tidal hydrodynamics within the Barnstable harbor system. Although visual calibration revealed the modeled tidal hydrodynamics were reasonable, tidal constituent calibration was required to quantify the accuracy of the models. Calibration of M 2 was the highest priority since M 2 accounted for a majority of the forcing tide energy in the system. Due to the duration of the model runs, four dominant tidal constituents were selected for constituent comparison: K 1, M 2, M 4, and M 6. A constituent analysis was performed on the output data from each model run, and these results were compared to a constituent analysis of the field data over the same time period. Errors between the model run and data were evaluated for each case. Measured tidal constituent heights (H) and time lags (φlag) shown in Table 5 for the calibration period differ from those in Tables 1 and 2 because constituents were computed for only seven days, rather than the entire thirty-day period represented in Tables 1 and 2. Table 5. Comparison of Tidal Constituents from calibrated RMA2 model and measured tidal data during same time period (August to September 1992). Error between measured and computed tidal constituents is given also. Model Verification Run Location Constituent amplitude (ft) Phase (deg) M 2 M 4 M6 K1 φm2 φm4 Offshore 5.28 0.04 0.18 0.47 0.90 110.21 Mussel Point 5.08 0.18 0.19 0.47 8.49-50.90 Harbor (west) 4.86 0.41 0.15 0.47 15.30-33.63 Scorton Creek (mouth) 4.66 0.65 0.09 0.47 21.09-22.27 Scorton Creek (upper) 4.46 0.67 0.10 0.47 32.65-4.01 Bridge Creek (upper) 3.18 0.84 0.31 0.40 38.70 35.18 Measured tidal Data Location Constituent amplitude (ft) Phase (deg) M2 M4 M6 K1 φm2 φm4 Offshore 5.28 0.04 0.18 0.47 0.90 110.23 Mussel Point 5.12 0.27 0.23 0.46 8.64-55.86 Harbor (west) 5.02 0.52 0.19 0.46 14.50-42.08 Scorton Creek (mouth) 4.82 0.83 0.10 0.46 17.98-27.23 Scorton Creek (upper) 4.36 1.05 0.30 0.39 26.89-0.65 Bridge Creek (upper) 2.72 0.86 0.29 0.40 34.39 32.69 Error Location Error amplitude (ft) Phase error (min) M2 M4 M6 K1 φm2 φm4 Mussel Point 0.033 0.083 0.042 0.008 0.3 10.3 Harbor (west) 0.167 0.108 0.033 0.008 1.7 17.5 Scorton Creek (mouth) 0.167 0.183 0.008 0.008 6.4 10.3 Scorton Creek (upper) 0.100 0.383 0.200 0.075 11.9 7.0 Bridge Creek (upper) 0.458 0.017 0.017 0.003 8.9 5.15 18

The constituent calibration revealed excellent agreement between modeled and measured tides. Errors associated with tidal constituent height were on the order of centimeters, which was of the same order of magnitude as the accuracy of the tide gauge (0.03 ft). Time lag errors (between 0 and 12 minutes) were much less than the time increment resolved by the model (30 minutes), indicating good agreement between the model and data. Although agreement between modeled and measured tides indicated accurate simulation of tidal hydrodynamics, the amplitude and phase errors generally increased toward the western portion of the Barnstable Harbor system (Table 5). For most of the estuary, the error associated with the amplitude of the four major tidal constituents is less than 0.2 feet; however, the errors are slightly higher in Scorton Creek (upper) and Bridge Creek (upper), principally due to differences in the overtide constituents (M 4 and M 6 ). In Scorton Creek, the model under-predicts the amplitude of the M 4 constituent by 0.4 ft. Within Bridge Creek, the model over-predicts the amplitude of the M 2 constituent by 0.46 ft. Since tidal attenuation through the western portion of Barnstable Harbor (the marsh and creeks area) is highly dependent on channel configuration and subtle variations in marsh topography, it is not surprising that the largest errors in the model are observed in this region. As shown in Figures 8 and 9, the modeled water elevation fluctuations within the western portion of the Barnstable Harbor system closely match the measurements. 3.5 Wetting/Drying Processes The model verification procedure simulated correctly tidal hydrodynamics throughout the system. The hydrodynamics were complicated by wetting/drying cycles on the marsh plain as well as in intertidal regions. These wet/dry areas will tend to store waters on the ebb tide, slowing releasing as the water level drops within the creeks and channels. This store-and-release characteristic of these regions was partially responsible for the distortion of the tidal signal, and the elongation of the ebb phase of the tide. On the flood phase, water rise within the channels and creeks initially until water surface elevation reaches the marsh plain, at this point the water level rise becomes nearly constant as water fans out over the marsh surface. The rapid flooding of the marsh surface corresponds to a flattening out of the tide curve approaching high water. Figure 10 shows water depths in the harbor and marsh system when the tide is highest in Cape Cod Bay (upper plot) and during low water in Cape Cod Bay (lower plot). The blue areas on the map represent areas where the water depth exceeds 10 feet; orange areas represent marsh or intertidal regions where the water depth is zero (or dry). Figure 10 shows that much of the harbor and creeks contain deep water (greater than 10 feet) at high tide; the extreme western areas of the marsh are still dry. Because the upper figure represents a snapshot during high water in the Bay, this graphic illustrates the phase delay of the M 2 tide as these western marsh regions are not yet inundated (upper plot). Flooding of the western marsh regions takes place approximately one hour after high water in the bay. The intertidal flats along the southern edge of the harbor, as well as the marsh plain, are dry during low water (lower plot). During low tide, the only areas containing much water are the harbor channels and creeks. 19

Figure 8. Comparison of the model output to the observed field data for the model calibration runs. Errors are greatest in the creek regions, where significant tidal distortion was observed. 20

Figure 9. Verification model run compared to measured data. Error analysis is presented in Table 5. 21

Water depths during high tide Low Tide Figure 10: Map of water depths through Barnstable Harbor and Great Marsh during high tide conditions in Cape Cod Bay (upper plot, water surface elevation is 7.75 ft NGVD) and low tide conditions (lower plot, water surface elevation is -5.0 feet NGVD). Dark blue defines areas where the water depth exceeds 10 feet. Orange defines areas that are dry. 22